USFDC Home  USF Electronic Theses and Dissertations   RSS 
Material Information
Subjects
Notes
Record Information

Full Text 
xml version 1.0 encoding UTF8 standalone no
record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam Ka controlfield tag 001 001935139 003 fts 005 20080421143737.0 006 med 007 cr mnuuuuuu 008 080421s2007 flua sbm 000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0002279 040 FHM c FHM 035 (OCoLC)225865583 049 FHMM 090 TJ145 (ONLINE) 1 100 Acosta, Carlos Felipe. 0 245 Dependency of loosening parameters on secondary locking features of threaded inserts h [electronic resource] / by Carlos Felipe Acosta 260 [Tampa, Fla.] : b University of South Florida, 2007. 3 520 ABSTRACT: This thesis presents a study of the dependency of loosening parameters on secondary locking features of threaded inserts subjected to dynamic shear loads. Secondary locking is used to assist and/or provide redundancy to the primary locking feature (threads) in preventing preload loss in almost any mechanical applications. Two different secondary locking features are studied: the Locking HeliCoil insert and the Loctite Threadlocker (R) applied before assembly to a Standard HeliCoil insert. Five parameters are studied in this thesis: percentage loss of initial preload, initial rate of preload loss, secondary rate of preload loss, steadystate value, and the final preload value. Statistical analysis was used to quantify the dependencies between locking levels. Results show that the loss of initial preload is dependent on secondary locking features, the initial and secondary rate of preload loss are dependent on secondary locking features, the steadystate value and the final preload value are dependent on secondary locking features. Also, due to secondary locking features, 83% of the "Locking HeliCoil with Braycote" tests reached steadystate while only 16% of the "Standard HeliCoil with Loctite" tests reached steadystate even though the final preload value were higher for "Standard HeliCoil with Loctite." 502 Thesis (M.S.)University of South Florida, 2007. 504 Includes bibliographical references. 516 Text (Electronic thesis) in PDF format. 538 System requirements: World Wide Web browser and PDF reader. Mode of access: World Wide Web. 500 Title from PDF of title page. Document formatted into pages; contains 163 pages. 590 Advisor: Daniel P. Hess, Ph.D. 653 HeliCoil. Bolt. Transverse vibration. Prevailing torque. Loctite. 690 Dissertations, Academic z USF x Mechanical Engineering Masters. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.2279 PAGE 1 Dependency of Loosening Parameters on Secondary Locking F eatures of Threaded Inserts by Carlos Felipe Acosta A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Depart ment of Mechanical Engineering College of Engineering University of South Florida Major Professor: Daniel P. Hess, Ph.D. Craig Lusk, Ph.D. Nathan Crane, Ph.D. Date of Approval: October 31 2007 Keywords: Heli Coil bolt transverse vibration, p revailing torque, Loctite Copyright 2007, Carlos Felipe Acosta PAGE 2 Dedication To my mother who taught me the fundamentals of ethics, morals and love helping me to grow professionally and spiritually. She has been a supportive mother, a best f riend, and a great life mentor. To my late father who evoked in me the principles of honor, loyalty and discipline. Your love accompanies me in every phase of my life. PAGE 3 Acknowledgments I would like to express my deepe st gratitud e to my maj or professor Dr. Daniel Hess for his expert guidance in this journey. His undeniable patience and extensive knowledge were critical factors in the completion of this work. I would like to extend this gratitude to Dr. Craig Lusk and Dr. Nathan C rane for taking the time to be in my committee as well as sharing their knowledge of engineering. PAGE 4 i Table of Content s List of Tables ................................ ................................ ................................ ..................... iv List of Figures ................................ ................................ ................................ .................... vi A bstract ................................ ................................ ................................ ............................ xix C hapter 1 Introduction ................................ ................................ ................................ .. 1 1.1 Introduction ................................ ................................ ................................ ........ 1 1.2 Background ................................ ................................ ................................ ........ 3 1 .3 Overview ................................ ................................ ................................ ............ 8 C hapter 2 Raw Data ................................ ................................ ................................ ...... 9 2.1 Introduction ................................ ................................ ................................ ........ 9 2.2 Apparatus ................................ ................................ ................................ ........... 9 2. 3 Test s pecimens ................................ ................................ ................................ 10 2. 4 Installation ................................ ................................ ................................ ........ 1 1 2. 5 Test s pecifications ................................ ................................ ............................ 1 2 2. 6 Test d ata ................................ ................................ ................................ ........... 1 2 Chapter 3 E xtraction of L oosening P arameters ................................ .......................... 33 3.1 Introduction ................................ ................................ ................................ ...... 33 3.2 Percentage l oss of i nitial preload parameter ................................ ........ 3 4 3.2.1 Data e xtraction ................................ ................................ ...... 3 4 PAGE 5 ii 3.2.2 Statistical a nalysis ................................ ................................ 38 3.3 Initial r ate of preload l oss parameter ................................ ................... 4 4 3.3.1 Data e xtraction ................................ ................................ ...... 4 4 3.3.2 Statistical a nalysis ................................ ................................ 48 3.4 Secondary r ate of preload l oss parameter ................................ ............ 5 5 3.4. 1 Data e xtraction ................................ ................................ ...... 5 5 3.4.2 Statistical a nalysis ................................ ................................ 59 3.5 Steady s tate value parameter ................................ ............................... 64 3.5.1 Data e xtraction ................................ ................................ ...... 6 4 3.5.2 Statistical a nalysis ................................ ................................ 68 3.6 Final p reload v alue parameter ................................ .............................. 68 3.6.1 Data e xtraction ................................ ................................ ...... 68 3.6.2 Statistical a nalysis ................................ ................................ 7 1 Cha pter 4 I nterpretation of R esults ................................ ................................ ............. 78 4.1 Introduction ................................ ................................ ................................ ...... 78 4.2 Percentage l oss of i nitial preload parameter ................................ .................... 8 0 4.3 Initial r ate of preload l oss parameter ................................ ............................... 8 3 4.4 Secondary r ate of preload l oss parameter ................................ ........................ 8 4 4.5 Steady state / final preload value parameter ................................ .................... 8 5 C hapter 5 Conclusions ................................ ................................ ................................ 8 7 R eferences ................................ ................................ ................................ .......................... 9 1 A ppendices ................................ ................................ ................................ ......................... 9 3 Appendix A: Data e xtracted for all locking levels ................................ ................. 9 4 PAGE 6 iii Appendix B: Zoomed data plots fo r the percentage loss of initial preload parameter ................................ ................................ ................................ .............. 10 1 Appendix C : Zoomed data plots for the initial rate of preload loss parameter ................................ ................................ ................................ .............. 12 0 Appendix D : Zoomed data plots for the secondary rate of preload loss parameter ................................ ................................ ................................ .............. 1 39 Appendix E : Zoomed data plots for the steady state and the final p reload v alue parameter ................................ ................................ ....................... 15 2 PAGE 7 iv List of Tables Table 2.1 Torque te st data ................................ ................................ .......................... 32 Table 3.1 Data extracted for all locking levels ................................ .......................... 3 6 Table 3 .2 Percent age loss of initial preload ................................ ............................... 37 Table 3.3 ANOVA table for the percentage loss of initial preload ............................ 40 Table 3.4 LSD method table for the percentage loss of initial preload ..................... 43 Table 3.5 95 percent confidence intervals for the percentage loss of initial preload ................................ ................................ ......................... 43 Table 3.6 I nitial rate of preload loss for all locking levels (lb/cycle) ........................ 4 6 Table 3.7 ANOVA table for the initial rate of preload loss ................................ ....... 5 1 Table 3.8 LSD method table for th e initial rate of preload loss ................................ 5 4 Table 3.9 95 percent confidence intervals for the initial rate of preload loss ................................ ................................ ............................ 5 4 Table 3.10 Secondary rate of preload loss for all locking levels (lb/cycle) ................. 5 8 Table 3.11 ANOVA table for the secondary rate of preload lo ss ................................ 6 1 Table 3.12 95 percent confidence interval s for the secondary rate of preload loss ................................ ................................ ............................ 6 3 Table 3.13 Steady state value s for all locking levels (lb), (nr: never reached) ............ 6 6 Table 3.14 Final preload values for all locking levels (lb), (**bolt broke) ................. 7 0 Table 3.15 t test statistic table for the final preload value ................................ ........... 7 4 PAGE 8 v Table 3.16 95 percent confidence interval s for the final preload value ....................... 7 6 Table 4.1 Minimum, mean and maximum angle of twist ................................ .......... 8 1 Table 4.2 Preload due to angle of twist ................................ ................................ ...... 8 3 Table 5.1 Depende ncy of loosening parameters on secondary locking features ................................ ................................ ................................ ....... 89 Table A.1 tandard Heli Coil with Braycote ......................... 9 4 Table A.2 Extracted data Locking Heli Coil with Braycote .......................... 9 5 Table A.3 E xtracted Heli Coil with Loc ............................ 9 6 Table A.4 Heli Coil ................. 9 7 Table A.5 Heli Coil .................. 98 Table A.6 Heli Coil .................... 99 Table A.7 Extracted data from Standard Heli Coil and Locking Heli Coil with B raycote ................................ .................. 10 0 PAGE 9 vi List of Figures Figure 1.1 Block on incline plane ................................ ................................ ................. 4 Figure 1.2 Effect of prevailing torque in reducing loosening [11] ................................ 6 Figure 1.3 Locking Heli Coil [14] ................................ ............................... 6 Fi gure 2.1 Schematic of test machine ................................ ................................ ......... 10 Figure 2.2 Preload Heli Coil run number 1 ................................ ................................ .............................. 13 Figure 2.3 Preload Heli Coil run number 2 ................................ ................................ .............................. 13 Figure 2.4 Preload d Heli Coil run number 3 ................................ ................................ .............................. 14 Figure 2.5 Preload Heli Coil run number 4 ................................ ................................ .............................. 14 Figure 2.6 Preload Heli Coil run number 5 ................................ ................................ .............................. 15 Figure 2.7 Preload tandard Heli Coil run number 6 ................................ ................................ .............................. 15 Figure 2.8 Preload Heli Coil run number 7 ................................ ................................ .............................. 16 Figure 2.9 Preload Heli Coil run number 8 ................................ ................................ .............................. 16 Figure 2.10 Preload vs. cycles Heli Coil run number 9 ................................ ................................ .............................. 17 PAGE 10 vii Figure 2.11 Preload Heli Coil run number 10 ................................ ................................ ............................ 17 Figure 2.12 Preload Heli Coil run number 11 ................................ ................................ ............................ 18 Figure 2.13 Preload Heli Coil run number 12 ................................ ................................ ............................ 18 Figure 2.14 Preload Heli Coil run number 13 ................................ ................................ ............................ 19 Figure 2.15 Preload Heli Coil run number 14 ................................ ................................ ............................ 19 Figure 2.16 Preload Heli Coil run number 15 ................................ ................................ ............................ 20 Figure 2.17 Preload Heli Coil run number 16 ................................ ................................ ............................ 20 Figure 2.18 Preload Heli Coil run number 17 ................................ ................................ ............................ 21 Fig ure 2.19 Preload Heli Coil run number 18 ................................ ................................ ............................ 21 Figure 2.20 Preload Heli Coil run number 19 ................................ ................................ ............................ 22 Figure 2.21 Preload Heli Coil run number 20 ................................ ................................ ............................ 22 Figure 2.22 Preload Heli Coil run number 21 ................................ ................................ ............................ 23 Figure 2.23 Preload Heli Coil run number 22 ................................ ................................ ............................ 23 Figur e 2.24 Preload Heli Coil run n umber 23 ................................ ................................ ............................ 24 Figure 2.25 Preload Heli Coil run number 24 ................................ ................................ ............................ 24 PAGE 11 viii Figure 2.26 Preload Heli Coil run number 25 ................................ ................................ ............................ 25 Figure 2.27 Preload Heli Coil with Loctite run number 26 ................................ ................................ ............................ 25 Figure 2.28 Preload Heli Coil run number 27 ................................ ................................ ............................ 26 Figure 2.29 Preload Heli Coil run number 28 ................................ ................................ ............................ 26 Figure 2.30 Preload Heli Coil with run number 29 ................................ ................................ ............................ 27 Figure 2.31 Preload Heli Coil run number 30 ................................ ................................ ............................ 27 Figure 2.32 Preload Heli Coil run numb er 31 ................................ ................................ ............................ 28 Figure 2.33 Preload Heli C oil run number 32 ................................ ................................ ............................ 28 Figure 2.34 Preload Heli Coil run number 33 ................................ ................................ ............................ 29 Figure 2.35 Preload Heli Coil run number 34 ................................ ................................ ............................ 29 Figure 2.36 Preload d Heli Coil run number 35 ................................ ................................ ............................ 30 Figure 2.37 Preload Heli Coil run number 36 ................................ ................................ ............................ 30 Figure 3.1 Representation of looseni ng parameters (run number 18) ......................... 33 Figure 3.2 Loosening curve Heli Coil wit run number 18 ................................ ................................ ............................ 3 5 Figure 3.3 Zoomed loosening curve for Heli Coil with run number 18 ................................ ................................ ........... 3 5 Figure 3.4 Box plot for the percentage loss of initial preload ................................ ..... 3 8 PAGE 12 ix Figure 3.5 Normal probability plot of residuals for the percentage loss of initial preload ................................ ................................ ............................. 4 0 Figure 3.6 Multiple comparison s of means for the percentage loss of initial preload ................................ ................................ ................................ ........ 42 Figure 3. 7 Loosening curve Heli Coil run number 11 ................................ ................................ ............................ 4 5 Figure 3.8 Zoomed loosening curve for Heli Coil with B run number 11 ................................ ................................ ........... 46 Figure 3.9 Composite tangent lines for Heli Coil ............. 47 Figure 3.10 Composite tangent lines for Heli Coil .............. 47 Figure 3.11 Composite tangent lines for Heli Coil ................ 4 8 Figure 3.12 Box plot for the initial rate of preload loss ................................ ................ 49 Figure 3.13 Normal probability plot of residuals for the initial rate of preload loss ................................ ................................ ................................ 51 Figure 3.14 Multiple comparison s of means for the initial rate of preload loss ............ 5 3 Fi gure 3.15 Loosening curve Heli Coil run number 3 ................................ ................................ .............................. 5 7 Figure 3.16 Zoomed loosening curve for Heli Coil with run number 3 ................................ ................................ ............. 5 7 Figure 3.17 Box plot for the secondary rate of preload loss ................................ ......... 59 Figure 3.18 Normal probability plot for the secondary rate of preload loss ................. 61 Figure 3.19 Multiple comparison s of means for the secondary rate of preload loss ................................ ................................ ................................ 6 3 Figure 3.20 Loosening curve for Heli Coil run number 22 ................................ ................................ ............................ 6 5 Figure 3.21 Zoomed loose ning curve Heli Coil run number 22 ................................ ................................ ............................ 6 6 PAGE 13 x Figure 3. 22 All steady state value plot s Heli Coil with ................................ ................................ ................................ ... 6 7 Figure 3.23 All steady state value plots Heli Coil ........... 6 7 Figure 3.24 Loosenin g curve for Standard Heli Coil run number 33 ................................ ................................ ............................ 69 Figure 3.25 Zoomed loosening curve Standard Heli Coil run number 33 ................................ ................................ ............................ 7 0 Figure 3.26 Box plot for the final preload value ................................ ........................... 7 2 Figure 3.27 Normal probability plot of residua ls for the final preload value ............... 7 4 Figure 3.28 Multiple comparisons of means for the final preload value ...................... 7 6 Figure 4.1 Reaction forces on bolts ................................ ................................ ............. 79 Figure B.1 Loss of initial preload for andard Heli Coil with run number 1 ................................ ................................ ........... 10 1 Figure B.2 Lo ss of initial preload andard Heli Coil with run number 2 ................................ ................................ ........... 102 Figure B.3 Loss of initial preload Heli Coil with run number 3 ................................ ................................ ........... 102 Figure B.4 Loss of initial preload Heli Coil with run n umber 4 ................................ ................................ ........... 103 Figure B.5 Loss of initial preload Heli Coil with run number 5 ................................ ................................ ........... 103 Figure B.6 Loss of initial preload Heli Coil with Braycote run number 6 ................................ ................................ ........... 104 Figure B.7 Loss of initial preload Heli C oil with run nu mber 7 ................................ ................................ ........... 104 Figure B.8 Loss of initial preload Heli Coil with run number 8 ................................ ................................ ........... 105 Figure B.9 Loss of initial preload Heli Coil with run number 9 ................................ ................................ ........... 105 PAGE 14 xi Figure B.10 Loss of initial pre load Heli Coil with run number 10 ................................ ................................ ......... 106 Figure B.11 Loss of initial preload Heli Coil with B run number 1 1 ................................ ................................ ......... 106 Figure B.12 Loss of initial preload Heli Coil with run number 12 ................................ ................................ ......... 107 Figure B.13 Loss of initial preload Locking Heli Coil with run number 13 ................................ ................................ ......... 107 Figure B.14 Loss of initial preload Locking Heli Coil with run number 14 ................................ ................................ ......... 108 Figure B.15 Loss of initial preload Locking Heli Coil with run number 15 ................................ ................................ ......... 108 Figure B.16 Loss of initial preload Locking Heli Coil with run number 16 ................................ ................................ ......... 109 Figure B.17 Loss of initial preload Locking Heli Coil with Br run number 17 ................................ ................................ ......... 109 Figure B.18 Loss of initial preload Heli Coil with run number 18 ................................ ................................ ......... 110 Figure B.19 Loss of initial preload Locking Heli Coil with run number 19 ................................ ................................ ......... 110 Figure B.20 Loss of initial preload Locking Heli Coil with run number 20 ................................ ................................ ......... 111 Figure B.21 Loss of initial preload Locking Heli Coil with run number 21 ................................ ................................ ......... 111 Figure B.22 Loss of initial preload Locking Heli Coil with run number 22 ................................ ................................ ......... 112 Figure B.23 Loss of initial preload Locking Heli Coil with Brayco run number 23 ................................ ................................ ......... 112 Figure B.24 Loss of initial preload Locking Heli Coil with run number 24 ................................ ................................ ......... 113 PAGE 15 xii Figure B.25 Loss of initial preload Heli Coil with Loctite run num ber 25 ................................ ................................ .......................... 113 Figure B.26 Loss of initial preload ndard Heli Coil run number 26 ................................ ................................ .......................... 114 Figure B.27 Loss of initial preload Heli Coil run number 27 ................................ ................................ .......................... 114 Figure B.28 Loss of initial preload Heli Coil run number 28 ................................ ................................ .......................... 115 Figure B.29 Loss o f initial preload Heli Coil run number 29 ................................ ................................ .......................... 115 Figure B.30 Loss of initial preload Heli Coil run number 30 ................................ ................................ .......................... 116 Figure B.31 Loss of initial preload Heli Coil run number 31 ................................ ................................ .......................... 116 Figure B.32 Loss of initial preload Heli Coil run number 32 ................................ ................................ .......................... 117 Figure B.33 Loss of initial preload Heli Coil run number 33 ................................ ................................ .......................... 117 Figure B.34 Loss of initial preload Heli Coil run number 3 4 ................................ ................................ .......................... 118 Figure B.35 Loss of initial preload Heli Coil run number 35 ................................ ................................ .......................... 118 Figure B.36 Loss of initial preload Heli Coil with run number 36 ................................ ................................ .......................... 119 Figure C. 1 Initial rate of preload loss Heli Coil with run number 1 ................................ ................................ ........... 1 2 0 Figure C. 2 Initial rate of preload loss Heli Coil with run number 2 ................................ ................................ ........... 12 1 Figure C.3 Initial rate of preload loss Heli Coil with run number 3 ................................ ................................ ........... 121 PAGE 16 xiii Figure C.4 Initial rate of preload loss Heli Coil with run number 4 ................................ ................................ ........... 122 Figure C.5 Initial rate of preload loss Heli Coil with run number 5 ................................ ................................ ........... 122 Figure C.6 Initial rate of preload loss rd Heli Coil with run number 6 ................................ ................................ ........... 123 Figure C.7 Initial rate of preload loss Heli Coil with run number 7 ................................ ................................ ........... 123 Figure C.8 Initial rate of preload loss Heli Coil with run number 8 ................................ ................................ ........... 124 Figure C .9 Initial rate of preload loss Heli Coil with run number 9 ................................ ................................ ........... 124 Figure C.10 Initial rate of preload loss Heli Coil with run number 10 ................................ ................................ ......... 125 Figure C.11 Initial rate of preload loss Heli Coi l with run numb er 11 ................................ ................................ ......... 125 Figure C.12 Initial rate of preload loss Heli Coil with run number 12 ................................ ................................ ......... 126 Figure C.13 Initial rate of preload loss Heli Coil with run number 13 ................................ ................................ ......... 126 Figure C.14 Initi al rate of preload loss Heli Coil with run number 14 ................................ ................................ ......... 127 Figure C.15 Initial rate of preload loss Heli Coil with run number 15 ................................ ................................ ......... 127 Figure C.16 Initial rate of preload loss Heli Coil with Br run number 16 ................................ ................................ ......... 128 Figure C.17 Initial rate of preload loss Heli Coil with run number 17 ................................ ................................ ......... 128 Figure C.18 Initial rate of preload loss Heli Coil with run number 18 ................................ ................................ ......... 129 PAGE 17 xiv Figure C.19 Initial rate of preload loss Heli Coil with run number 19 ................................ ................................ ......... 129 Figure C.20 Initial rate of preload loss Heli Coil with run number 20 ................................ ................................ ......... 130 Figure C.21 Initial rate of preload loss Heli Coil with run number 21 ................................ ................................ ......... 130 Figure C.22 Initial rate of preload loss Heli Coil with run number 22 ................................ ................................ ......... 131 Figure C.23 Initial rate of preload loss Heli Coil with run number 23 ................................ ................................ ......... 131 Figure C.24 Initial rate of preload loss Heli Coil with run number 24 ................................ ................................ ......... 132 Figure C.25 Initial rate of preload loss Heli Coil run number 25 ................................ ................................ .......................... 132 Figure C.26 Initial rate of preload loss Heli Coil run number 26 ................................ ................................ .......................... 133 Figure C.27 Initial rate of preload loss Heli Coil run number 27 ................................ ................................ .......................... 133 Figure C.28 Initial rate of preload loss Heli Coil run nu mber 28 ................................ ................................ .......................... 134 Figure C.29 Initial rate of preload loss H eli Coil run nu mber 29 ................................ ................................ .......................... 134 Figure C.30 Initial rate of preload loss Heli Coil run number 30 ................................ ................................ .......................... 135 Figure C.31 Initial rate of preload loss Heli Coil run number 31 ................................ ................................ .......................... 135 Figure C.32 Ini tial rate of preload loss Heli Coil run number 32 ................................ ................................ .......................... 136 Figure C.33 Initial rate of preload loss Heli Coil run number 33 ................................ ................................ .......................... 136 PAGE 18 xv Figure C.34 Initial rate of preload loss Heli Coil with Loc run number 34 ................................ ................................ .......................... 137 Figure C.35 Initial rate of preload loss Heli Coil run number 35 ................................ ................................ .......................... 137 Figure C.36 Initial rate of preload loss Heli Coil run nu mber 36 ................................ ................................ .......................... 138 Figure D.1 Secondary rate of pre load loss Heli Coil with run number 1 ................................ ................................ ........... 139 Figure D.2 Secondary rate of preload loss Heli Coil with run number 2 ................................ ................................ ........... 140 Figure D.3 Secondary rate of preload loss Heli Coil with B run number 3 ................................ ................................ ........... 140 Figure D.4 Secondary rate of preload loss Heli Coil with run number 4 ................................ ................................ ........... 141 Figure D.5 Secondary rate of preload loss Heli Coil with r un number 5 ................................ ................................ ........... 141 Figure D.6 Secondary rate of preload lo ss Heli Coil with run number 6 ................................ ................................ ........... 142 Figure D.7 Secondary rate of preload loss Heli Coil with run number 7 ................................ ................................ ........... 142 Figure D.8 Secondary rate of preload loss Heli Coil with run number 8 ................................ ................................ ........... 143 Figure D.9 Secondary rate of preload loss Heli Coil with run number 9 ................................ ................................ ........... 143 Figure D.10 Secondary rate of preload loss Heli Coil with run number 10 ................................ ................................ ......... 144 Figure D.11 Secondary rate of preload loss Heli Coil with run number 11 ................................ ................................ ......... 144 Figure D.12 Secondary rate of preload loss Heli Coil with Braycote run number 12 ................................ ................................ ......... 145 PAGE 19 xvi Figure D.13 Secondary rate of preload loss Heli Coil with run numbe r 13 ................................ ................................ ......... 145 Figure D.14 Secondary rate of preload loss Heli Coil with run n umber 14 ................................ ................................ ......... 146 Figure D.15 Secondary rate of preload loss Heli Coil with run number 15 ................................ ................................ ......... 146 Figure D.16 Secondary rate of preload loss Heli Coil with run number 16 ................................ ................................ ......... 147 Figure D.17 Secondary rate of preload loss Heli Coil with run number 17 ................................ ................................ ......... 147 Figure D.18 Secondary rate of preload loss Locking Heli Coil with run number 18 ................................ ................................ ......... 148 Figure D.19 Secondary rate of preload loss Heli Coil with run number 19 ................................ ................................ ......... 148 Figure D.20 Secondary rate of preload loss Heli Coil with run number 20 ................................ ................................ ......... 149 Figure D.21 Secondary rate of preload loss f Heli Coil with run number 21 ................................ ................................ ......... 149 Figure D.22 Secondary rate of preload loss Heli Coil with run number 2 2 ................................ ................................ ......... 150 Figure D.23 Secondary rate of preload loss Heli Coil with B run number 23 ................................ ................................ ......... 150 Figure D.24 Secondary rate of preload loss Heli Coil with run number 24 ................................ ................................ ......... 151 Figure E.1 Steady state value Heli Coil with run number 13 ................................ ................................ ......... 1 52 Figure E.2 Steady state value Heli Coil with ................................ ................................ ......... 1 53 Figure E.3 Steady state value Heli Coil with run number 15 ................................ ................................ ......... 15 3 PAGE 20 xvii Figure E.4 Steady state value Heli Coil with run number 16 ................................ ................................ ......... 154 Figure E.5 Final preload value Heli Coil with run n umber 17 ................................ ................................ ......... 154 Figure E.6 Steady state value Locking Heli Coil with run number 18 ................................ ................................ ......... 155 Figure E.7 Steady state value Heli Coil with run number 19 ................................ ................................ ......... 155 Figure E.8 Final preload value Locking Heli Coil with run number 20 ................................ ................................ ......... 156 Figure E.9 Steady state value Heli Coil with B run number 21 ................................ ................................ ......... 156 Figure E.10 Steady state value Heli Coil with run number 22 ................................ ................................ ......... 157 Figure E.11 Steady stat e value Heli Coil with run number 23 ................................ ................................ ......... 157 Figure E.12 Steady state value Heli Coil with run number 24 ................................ ................................ ......... 158 Figure E.13 Final preload value Heli Coil run number 25 ................................ ................................ .......................... 158 Figure E. 14 Steady state value Heli Coil run number 26 ................................ ................................ .......................... 159 Figure E.15 Final preload value Heli Coil run number 27 ................................ ................................ .......................... 159 Figure E .16 Final preload value Heli Coil run number 28 ................................ ................................ .......................... 1 60 Figure E.17 Final preload value Heli Coil with Loctite run number 30 ................................ ................................ .......................... 160 Figure E.18 Final preload value Heli Coil run number 31 ................................ ................................ .......................... 161 PAGE 21 xviii Figure E.19 Steady state value Heli Coil ru n number 32 ................................ ................................ .......................... 161 Figure E.20 Final preload value Heli Coil run number 33 ................................ ................................ .......................... 162 Figure E.21 Final preload value Heli Coil run number 34 ................................ ................................ .......................... 162 Figure E.22 Final preload value Heli Coil wit run number 35 ................................ ................................ .......................... 1 63 Figure E.23 Final preload value Heli Coil run number 36 ................................ ................................ .......................... 163 PAGE 22 xix Dependency of Loosening Parameters on Secondary Locking Features of Threaded Inserts Carlos Felipe Acosta ABSTRACT This thesis presents a study of the dependency o f loosening parameters on secondary locking feature s of threaded inserts subjected to dynamic shear loads Secondary locking is used to assist and/or provide redundancy to the primary locking feature (threads) in preven ting preload loss in almost any mechanical applications. Two different secondary locking features are studied : t he Locking Heli Coil insert and the Loctite Threadlocker applied before assembly to a S tandard Heli Coil insert. Five parameters are studied in this thesis: p ercentage loss of initial preload initial rate of preload loss, s econdary rate of preload loss, steady state value and the final preload value. Statistical analysis was used to quantify the dependen cies between locking levels. R esults show that the loss of initial preload is dependent on secondary locking features, the initial and secondary rate of preload loss are dependent on secondary locking features the steady state value and the final preload value are dependent on secondary locking features. Also, due to secondary locking features, 83% of the Locking Heli Coil with tests reached steady state while only 16 % of the Standard Heli Coil with PAGE 23 xx Loctite tests reached steady state even though the final preload value were higher fo r Standard Heli Coil with Loctite PAGE 24 1 C hapter 1 I ntroduction 1.1 Introduction Threaded fasteners are a very important element in nonpermanent joints. They are widely used because of their many benefits. One of the main advantages of threaded fastene rs is that they allow the maintenance (inspection, cleaning and repair) of components in machines. Another main advantage is the ability to develop a clamping force in which the threads of the bolt or the primary locking mechanism are engaged against the c lamped elements by the threads of either nuts, ta p p ed holes or thread ed inserts c ausing elongation of the bolts. Loosening of threaded fasteners due to dynamic shear loading is an ongoing problem that not only threatens the lifespan of the machine but can also threaten the life of human beings in catastrophic failures Thus, the use of secondary locking mechanisms is often used to increase the resistance against loosening and provide redundancy Nonetheless, there are still catastrophic failures such as th e bolt related failure that took the life of Milena Del Valle, a facility maintenance worker at a restaurant in Boston. She was driving with her husband to pick up her brother in law from the Logan International Airport when a faulty bolt fixture that supp orted a concrete panel from the I 90 tunnel ceiling fell on top of her car. Investigators found that bolt loosened completely PAGE 25 2 even though high strength epoxy was utilized They concluded that the epoxy failed to bond properly. Furthermore, studies on secon dary locking features are needed to better understand their looseni ng resistance in order to prevent accident s such as the ceiling failure on I nterstate 90. Specifically, this thesis will focus on identify ing the dependency of loosening parameters on seco ndary locking features of thread inserts that are subjected to dynamic shear loads. This informati on can then be used to provide better insight for engineers in understanding, selecting or designing secondary locking mechanism s In this thesis the looseni ng parameters studied in clude: the percentage loss of initial preload the initial rate of preload loss, the secondary rate of preload loss, the steady state and the final preload value. The dependencies of the loosening parameters for each secondary locki ng feature are determined statistically. PAGE 26 3 1.2 Background In a bolt, the threads are considered one of the most important elements because of their helical nature which not only leads to the ability to be assembl ed and disassembl ed, but also they are respo nsible for the performance of the bolt. The l oosening of threaded fasteners due to transverse vibration ha s been a subject of study since the mid are several references about loosening that were reviewed and that are cited in this thesis. Early research on loosening due to transverse vibration was performed by Junker. He explains how, under transverse vibration (shear loading), the incline plane and friction forces in the bolt play a major role in the loosening process. Junker [1] explains his theory of loosening by the analogy of a block on top of an incline plane, as shown in Figure 1.1 where part a shows the friction forces between the block and the incline in equilibrium (no motion). However, when subjected to a transverse vibration str ong enough to overcome the frictional force between the block and the incline, the bolt would slip in the direction of the transverse vibration as well as down the incline shown in part b of Figure 1.1 Junker showed that loosening due to severe shear loa dings results from a slippage of the head and the threads when bending forces overcome frictional forces between the engaged threads as well as the head of the bolt [1]. Hess [2] has analyzed the problem of s elf loosening for several years and explains tha t the main mechanism of self loosening is relative thread s lip and component slip, caused by static and dynamic forces, moments, and/or reduced friction, manifesting themselves in joints through bending, pressure fluctuations, shocks, impacts, thermal expa nsion, and axial force fluctuations. PAGE 27 4 Figure 1 .1 Block on incline plane. Pai a nd Hess [3, 4] developed Junker s theory further by showing that in addition to complete slip, loosening can also result from the accumulation of localized slip. Bolt Science [5] lists that the common causes of the relative motion in bolted joints threads are ; 1. Component bending that results in forces being induced at the friction surface. If slip occurs, the head and threads will slip, which can cause loosening. 2. Different ial thermal effect caused by either differences in temperature or differences in clamped materials. 3. Applied forces on the joint that lead to shifting of the joint surface s can induce bolt loosening. Sanclemente and Hess [6] focused on the parameters in fluencing loosening in which it was shown that preload and fastener material are the most significant. These studies have been excellent sources in providing a clearer understanding of loosening in bolts. However, these studies are only focused on loosenin g of bolted joints without any secondary locking feature. Bickford [7] documents other sources of preload loss such as bolt relaxation. He c ites a report by Fisher and Struik [8] that tested bolt tension and found a preload loss of 2% to 11% immediately after tightening and 3.6% after the next 21 days and concludes that the bolt does undergo relaxation. Bickford [7] also comments on an experiment he PAGE 28 5 performed on bolts and found that a torsional relaxation of 50% occurred when the wrench was removed. He co ncluded that embedment (plastic deformation that occurs in the area of clamped component and the fastener [7]) allows the relaxation, not only axially but also torsional ly to occur. Nonetheless, it is unclear whether in these experiments secondary locking features were used. According to Ibrahim [9], r elaxation effects cause time dependent boundary conditions and depend on the level of structural vibration. During operation, the non linear random response can usually change the joint mechanical properties which creates new self induced uncertainties. Bickford [7] refers to the Motosh [10] equation where the input torque is resisted by three reaction forces produced by the stretch of the bolt, the friction between the engaged threads and the friction betwe en the face of the nut and the washer or joint (prevailing torque is added when present). In addition, he comments on the effect of prevailing torque on preload loss under vibratory motion as a mean s to prevent loosening of the bolt. He also list s and desc ribes on a variety of secondary locking mechanism s that help to reduce loosening. Hess [2] comments on ways to improve loosening resistance by the increase of preload finer thread pitch, higher thread and head friction, tighter tolerances, higher excitati on frequency, and lower excitation amplitude. Finkelston [11] s hows that the prevailing torque (the distor tion or modification of metal threads, bolts or nuts to provide some inference with the matting part that is not dependant entirely on friction force s [7]) reduces the rate of preload loss when the effective prevailing torque counteract s the loosen ing torque as shown in Figure 1.2 H e claim s that the prevailing torque could stop the rate of preload loss. However, Figure 1.2 PAGE 29 6 1 2 5 10 20 50 100 200 500 1000 2000 Average vibration life (cycles) 6 5 4 3 2 1 0 is only for one test sample which prevents him from draw ing any meaningful statistical conclusions. F igure 1.2 Effect of prevaili ng torque in reducing loosening [11] Figure 1.3 Locking Heli Coil rip coil [14]. Generally, in order to prevent loosening, safety wire, coa tings and inserts, thread locking adhesives and spring washers are use d [12]. However, these secondary locking mechanisms have their limitations and do not necessarily prevent relaxation. Wolfe [13] focus es on the advantages of thread inserts over conventi onal methods (i.e. nuts). Hillclif tools [14] provides an overview of the free running thread insert as well as an explanation Preload (1000lb) PAGE 30 7 on the Locking Heli Coil system as a alternat ive secondary locking mechanism consisting of a grip coil, shown in Figure (1.3), th at when bent outward creates high pressure on the bolt which secures it against loosening. Henkel Corp [15] explains that Loctite Threadlocker fills microscopic gaps between the interfacing threads and when it come s in contact with metal, in the absence of air, it polymerize to a tough solid. Bardon [16] documents on thread lockers as an effective and inexpensive way to ensure reliable performance in machinery. Liquid anaerobic adhesiv es such as Loctite Threadlocker help against vibrations as well as leak age and corrosion. In short, there is a lack of literature where the dependency of loosening parameters on secondary locking features is statistically analyzed. The literature does show the overall advantage of secondary locking features. However, it is i mportant to quantify, statistically, the dependencies of the loosening parameters on secondary locking features in order to better understand their behavior since it would help engineers to better design and maintain equipment or even improve secondary loc king mechanism technology. PAGE 31 8 1.3 Overview This thesis focuses on the dependency of loosening parameters on secondary locking mechanism s Chapter 2 describes the test data and apparatus, test specimens and experimental procedure s It also provides plots of the raw data ( loosening plots ) which are used in this study. Chapter 3 focuses on the extrac t ion of the loosening parameter s used in this thesis. A lso, in this chapter statistical analysis is performed on the extracted data in order to quantify the result s Chapter 4 gives meaning to the statistical results obtained in C hapter 3. Finally Chapter 5 stat es the conclusions PAGE 32 9 C hapter 2 Raw Data 2.1 Introduction This chapter presents the preload versus cycle data used in this thesis. The data is from an experiment performed on testing the loosening of threaded fasteners subjected to dynamic shear with different locking levels. The data was obtained using a DIN 65151 or Junker type [1] test machine which provides transverse vibration. 2.2 Apparatus The test apparatus used to obtain the data is shown in Figure 2.1. It consists of a top plate clamped to a rigid fixed base through a threaded insert using a test screw. In order to minimize sliding friction and galling, roller bearings are used between the to p plate and the fixed base. Cyclic shear loads are applied to the top plate by an arm linked to an adjustable eccentric. The apparatus is driven by a 5 HP AC motor through an adjustable pulley arrangement while load cells measure screw preload and the shea r force acting on the top plate. An LVDT transducer (linear variable differential transformer) located at the end of the plate, was used to measure the transverse displacement of the plate. PAGE 33 10 Figure 2.1 Schematic of test machine. 2.3 Test s pecimens The test specimens were NAS 1004 1/4 28 UNJF 3A hex head screws [17] with: 1. Standard free running Heli Coil inserts with Braycote 601 EF high vacuum grease. 2. Locking Heli Coil with Braycote 601 EF high vacuum grease 3. Standard free running Heli Coil insert s with Loctite 242 Threadlocker. Twelve tests were run for each configuration or locking level for a total of thirty six runs. The specifications for the screws, washers and Heli Coil s inserts used in these test are the following: 1. Thirty six NAS1004 29A, 28 U NJF 3A, 2.356 inch long, hex head screws, made of A286 stainless steel [17] 2. Thirty six NAS 1149 C0463R washers for inch screw made of corrosion resistant steel with passivated finish [18] PAGE 34 11 3. Twenty four MS124696, 0.375 inch long, standard, free running He li Coil inserts, made of 304 stainless steel [19] 4. Twelve MS21209 F4 15, 0.375 inch long, Heli Coil inserts, made of 304 stainless steel [19] New screws, washers and Heli Coil s were used for each test. In the test machine, a test screw secured the top pl ate to the fixed base by a cone and load fixture as shown in Figure 2.1 A test Heli Coil insert is installed into the load cell fixture. The cone was placed in the top plate and the load fixture sets in the preload load cell. The cone and load fixtures ar e made of 15 5 stainless steel and heat treated to RC35 and the surfaces grounded to 32in. The load cell fixture has tapped holes ready for Heli Coil installation and the cone has thru holes. 2.4 Installation All test specimens parts (screws, washers, cones and load fixtures with installed Heli Coil ) were pre cleaned in ultrasonic bath cleaner with MEK as the solvent for 3 minutes. The S tandard free running and L ocking Heli Coil inserts were installed in the nstructions [19]. Braycote 601 EF grease was applied under screw head and washer to all thirty six test specimens. Also, Braycote 601 EF grease was applied to cover screw threads and Heli Coil threads to twenty four test runs. The remaining twelve test spe cimens were sprayed with Loctite 7471 activator (primer T) five minutes prior to the application (two to three dro ps) of Loctite 242 Threadlocker the bolts were tightened to specified preload and allowed to cure for 24 hours. PAGE 35 12 2.5 Test s pecifications The experiment was conducted with Braycote lubricant applied under the screw head and washer, the Junker test machine is set at 15Hz with a 0.12 inch (3mm) eccentric, the preload at 2,400 lbs or 66% yield, and a record length of 160 seconds or 2,400 cycles. T he data was collected at 51.2 samples/second for a total of 8,192 data points for each measured variable for each test. The preload of 2,400 lbs was calculated by multiplying the 0.2% yield strength (100,000 psi ) by the 66% of the thread stress area which is 0.0364 in^2. 2.6 Test d ata All preload versus cycles plots are shown below for all three locking levels These Heli Coil with Braycote Heli Coil Heli Coil wi PAGE 36 13 Figure 2.2 Preload v s Heli Coil run number 1. Figure 2.3 Preload v s Heli Coil run number 2. PAGE 37 14 Figure 2.4 Preload v s Heli Coil with Braycot run number 3. Figure 2.5 Preload v s Heli Coil run number 4. PAGE 38 15 Figure 2.6 Preload v s Heli Coil run number 5. Figure 2.7 Preload v s Heli Coil with run number 6. PAGE 39 16 Figure 2.8 Preload v s Heli Coil run number 7. Figure 2.9 Preload v s Heli Coil run number 8. PAGE 40 17 Figure 2.10 Preload v s Heli Coil w run number 9. Figure 2.11 Preload v s Heli Coil run number 10. PAGE 41 18 Figure 2.12 Preload v s Heli Coil run number 11. Figure 2.13 Preload v s Heli Coil run number 12. PAGE 42 19 Figu re 2.14 Preload v s Heli Coil run number 13. Figure 2.15 Preload v s Heli Coil run number 14. PAGE 43 20 Figure 2.16 Preload v s cking Heli Coil run number 15. Figure 2.17 Preload v s Heli Coil run number 16. PAGE 44 21 Figure 2.18 Preload v s Heli Coil run number 17. Figure 2.19 Preload v s cycles Heli Coil run number 18. PAGE 45 22 Figure 2.20 Preload v s Heli Coil run number 19. Figure 2.21 Preload v s Heli Coil run number 20. PAGE 46 23 Figure 2.22 Preload v s cy Heli Coil run number 21. Figure 2.23 Preload v s Heli Coil run number 22. PAGE 47 24 Figure 2.24 Preload v s Heli Coil run number 23. Figure 2.25 Preload v s Heli Coil run number 24. PAGE 48 25 Figure 2.26 Preload v s Heli Coil run number 25. Figure 2.27 Preload v s Heli Coil run number 26. PAGE 49 26 Figure 2.28 P reload v s Heli Coil run number 27. Figure 2.29 Preload v s Heli Coil run number 28. PAGE 50 27 Figure 2.30 Preload v s Heli Coil run number 29. Figure 2.31 Preload v s Heli Coil run number 30. PAGE 51 28 Figure 2.32 Preload v s Heli Coil run number 31. Figure 2.33 Preload v s Heli Coil run number 32. PAGE 52 29 Figure 2.34 Preload v s Heli Coil run number 33. Figure 2.35 Preload v s Heli Coil run number 34. PAGE 53 30 Figure 2.36 Preload v s Heli Coil run number 3 5. Figure 2.37 Preload v s Heli Coil run number 36. PAGE 54 31 Note that for run number 29 ( Standard Heli Coil with Loctite ), the screw broke at 2,324 cycles. The corresponding preload versus cycle plot, F igure 2.30, reveals this rapid failure suggesting that the tests operate close to the lower bound of the screw fatigue life when the majority of the preload is maintained for close to the duration of the test. The initial and residual preload values were recorded, documented and provided from the preload measurements fo r a ll thirty six runs in Table 2.1 which shows the initial preload and torque; breakaway or removal torques; the assembly as well as the removal prevailing torques are also included in this table. The initial p reload varies from 2,315 to 2,385 lbs caused by joint embedment and assembly variation. B hour cure time period from tightening to testing, data runs from 25 to 36 ( S tandard Heli Coil with Loctite ), have lower initial preload th an the other levels of locking. Thus, some preload loss may be expected due to asperity relaxation (the deformation on the surface protuberances). Whereas the time period between tightening and testing for the other runs are about one minute where little t o no asperity relaxation occurs. The tightening torq ue for the data shown in Table 2.1 required to achieve the desired 2,400 lbs of preload Heli Coil from 100 ocking Heli Coil hows to be higher because of the assembly prevailing torque of 20 lbs. The higher required tightening torque values for Heli Coil Threadlocker compared with Braycote grease. The remo Heli Coil Heli Coil were found to be similar. In addition, The PAGE 55 32 discrepancies between the assembly prevailing torque and the removal prevailing torque Heli Co il Table 2.1 Torque test data PAGE 56 33 C hapter 3 E xtraction of L oosening P arameters 3.1 Introduction In order to asses the dependency of loosening parameters on secondary locking features, it is necessary to split each preload vs. cycles plot mentioned in Chapter 2 by stages These sections represent different loosening parameters experienced by the bolt; thus, facilitating the study of the effect of the secondary locking features during dynam ic shear loadings. Figure 3.1 is a representation of the states aforementioned illustrating the purpose of this chapter. Note that any transition area will not be studied in this thesis. Figure 3.1 Representation of loosening parameters (run number 18) PAGE 57 34 The focus of this chapter is to extract the following parameters from the preload versus cycle data presented in C hapter 2 : 1. Percentage loss of initial preload 2. Initial rate of preload loss 3. Secondary rate of preload loss 4. Steady state value 5. Final preload va lue Since there is variation in these parameters, statistical analysis is used to quantify them. 3.2 Percentage l oss of i nitial preload p arameter 3.2.1 Data e xtraction An initial loss of preload occurred almost immediately after the shear loading was app lied. To assess this preload loss, data n eeded to be extracted. Matlab v 7.3 plotting tool was us ed to display the data. Figure 3.2 clearly shows an initial preload loss starting almost immediately after zero cycles. In order to quantify the percentage los s, we zoomed on th e graph as shown in Figure 3.3 where two data points were extracted as displayed with black squares on the plot The first data point was located at zero cycles before the shear load was applied and the second data point was taken at the first minimum value. All data poi nts are presented in Table 3.1 Note that all zoomed plots for this section are shown in the a ppendix B. PAGE 58 35 Figure 3.2 Loosening curve Heli Coil Figure 3.3 Zoomed loosening cur ve Heli Coil number 18 PAGE 59 36 Table 3.1 Data extracted for all locking levels PAGE 60 37 To extract the percentage loss of initial preload the following equation (3.1) was used: Percentage loss = (3.1) where is the initial preload at zero cycles and is the preload after the initial drop. Table 3.2 presents the percentage loss of initial preload for all locking levels along with the statistical mean, median, varianc e and range. Table 3.2 Percentage loss of initial preload PAGE 61 38 3.2.2 Statistical a nalysis The resulting response data (percentage loss of initial preload ) from the 36 t est are presented in Table 3.2 There are twelve observations for each locking leve l. The basic statistic mean, median, variance and range for each sample were included. It can be noted Heli Coil Heli Coil Heli Coil wit different. Figure 3.4 Box plot for the p ercentage loss of initial preload Figure 3.4 shows a box plot for the three levels of locking. The sample median, for each treatment, is represented by the center line of the rectangular box. Th e ends of the rectangles represent the upper and lower quartile of each sample and the black PAGE 62 39 whiskers extend to indicate their extent. This graphical analysis, suggests that the initial preload loss is dependent on secondary locking features. Furthermore, a statistical analysis is performed to be more objective in this result. The analysis of variance (ANOVA) will compare the means of these levels by measuring the overall variability in the data [20]. However, in order to use ANOVA, the sample population sh ould be normally distributed, and the population sample should have equal variance. However, modest violations of these assumptions can be allowed without affecting the results [20]. In order to asses the dependency of the secondary locking features on th e initial preload loss, two hypothe ses are developed: 1. All population means are equal ( : = = ), or 2. At least one mean is different. Where Heli Coil Heli Coil Heli Coil Before any analysis could be performed, the assumption of normality needs to be tested [20] Plotting the residuals (observation values minus sample mean) on a normal probability plot helps check normality between the sample population s. This is shown in Figure 3.5 where the data points show the empirical probability versus the value for each r esidual sample for both levels. The solid linear fit shows that the distribution is approximately normal. Note that for this data set, modest variations from normality and equal sample variances are found, yet this is acceptable since the analysis of varia nce allow minor violations of these assumptions. PAGE 63 40 Fi gure 3.5 Normal probability plot of residuals for the percentage loss of initial preload. Table 3.3 ANOVA table for the percentage loss of initial preload Table (3.3) summarized the ANOVA calcula tions. Note that the mean square value is larger than the value of the error which suggests that the treatments means may be different. The ratio of the mean square and the error is referred as the testing value or ( = 30.3). This value is compared to an appropriate upper tail percentage point of the F distribution with an alpha error of 0.05. Moreover, the critical value is PAGE 64 41 = 3.3. Since the critical value is less than testing value ( > ), is rejected. Therefore, there is dependency of initial preload loss due to a secondary locking feature. Figure 3.6 shows a graphical interpretation of these results where the multcompare function of Matlab v 7.3 was used. The multcompare function displays a graph with each group mean represented by a symbol and an interval around the symbol [ 21 ] The interval is approximated by following formula: (3.2) Where is the mean of each locking level, is the t critical value, is the mean square of the error and is the number of samples. Tw o means are significantly different if th eir intervals are disjoint, and are not significantly different if their intervals overlap [21] This figure suggests that the mean for the S tandard Heli Coil with Loctite is significantly different when compared with the other two locking levels. Also, the comparison intervals of the Standard Heli Coil with Braycote and the Locking Heli Coil with Braycote overlap which suggests that these means may be statistically similar. To quantify these findings the Fisher Method of least significant difference (LSD) is be used. PAGE 65 42 Figure 3.6 Multiple comparisons of means for the percentage loss of initial preload The Fisher Method of least significant difference (LSD) is used for comparing all pairs of means where the t test statistic distribution is used fo r testing a hypothesis [20]. In order to use this method, a new hypothesis is created: the population means for pairs are equal ( = = ). Where and are the population means for each locking level. The pairs of means are considered s ignificantly different if the following condition is met: (3. 3 ) where and are the sample means of the locking levels to be compared. is the t value of the Student's t distribution as a function of the probability and the degrees PAGE 66 43 of freedom of the error. is the mean square of the error. n is th e number of samples. Table 3.4 summarizes the results of this analysis. Table 3.4 LSD method table for the percentage loss of initial preload. Table 3.4 agrees with the ANOVA analysis aforementioned. This time, however, it can be said that the initial drop o f preload loss for Standard Heli Coil with Braycote and Locking Heli Coil with Braycote are not significantly different Finally, a 95 percent confidence interval s on each locking level mean is computed. Thus, showing that the population mean of each treatment (percent loss of initial preload ) will lie between these interva ls. This is shown in Table 3.5 Table 3.5 95 percent confidence intervals for the percentage loss of initial preload. PAGE 67 44 In this section the dependency of initial preload loss par ameter on secondary locking features are studied On this basis, the results in this section reveal the following: 1. Loss of initial preload is dependent on secondary locking features. 2. The mean loss of initial preload Heli Coil d the mean loss of initial preload Heli Coil not significantly different 3. The mean loss of initial preload Heli Coil mean loss of initial preload Heli Coil s ignificantly different 4. The mean loss of initial preload Heli Coil mean loss of initial preload Heli Coil significantly different 3.3 Initial r ate of preload l oss p arameter 3.3.1 Data e xtr action After the initial drop of preload occurs, the bolt begins to loosen following the criteria described by Pai and Hess [3, 4] where the loosening in the fastener is due to the accumulation of localized slip at the contact surfaces denoted, in this th esis, as the initial rate of preload loss. To quantify the initial rate of preload loss, each preload versus cycles plot was zo omed in as shown in Figure 3.8 (all zoomed plots for this section are shown in appendix C). Then, two data points were extracte d, shown with a square, along a tangent line that was manually fitted at the lower bound of the envelope graph (this location was PAGE 68 45 chosen to provide a worse case scenario of loosening). The data extracted is documented in tables (A.1), (A.2) and (A.3) in ap pendix A. With the set of two data point the initial rate of preload loss was calculated using the following formula [22] : (3. 4 ) Where is the initial rate of preload loss, is the ch ange in the y coordinate or preload and is the change in the x coordinate or cycles These valu es are documented in T able 3.6 Note that the equation above will result in a negative number which implies a loss. Figure 3.7 Loosening curve andar d Heli Coil PAGE 69 46 Figure 3.8 Zoomed loosening curve Heli Coil with number 11 Table 3.6 Initial rate of preload loss for all locking levels (lb/cycle) PAGE 70 47 The tangent lines are t hen calculated using the point slope formula [22] shown as : (3. 5 ) Where is the unknown preload is the unknown cycles, is the initial rate of preload loss and ( ) are coordinates of a point of the line (data points). The tangent l ines are plotted in Figure 3.9 3.10 and 3.11 for tandard Heli Coil with Braycote Locking Heli Coil with Braycote and Standard Heli Coil with Loctite respectively. Figure 3.9 tandard Heli Coil Figure 3.10 Composite tangent lines Heli Coil PAGE 71 48 Figure 3.11 Composite tangent lines Heli Coil It can be noted that the lines in Figure 3.9 and 3.10 appear similar whereas the lines in Figure 3.11 looked different which lead us to suspect dependencies of secondary locking features in the initi al rate of prel oad loss. Thus, statistical tools are used to quantify any dependency. 3.3.2 Statistical a nalysis The initial rates of preload loss from the 36 runs are presented in Table 3.6 There are twelve observations for each locking levels. The statistical sample mean, median, variance and range are included for the sample. There are similarities in the means of Heli Coil Heli Coil Heli Coil PAGE 72 49 Figure 3 .12 Box plot for the initial rate of preload loss. Figure 3.12 shows a box plot for the three levels of locking. The sample median is represented by the center line of the rectangular box for each locking level. The ends of the rectangles represent the u pper and lower quartile and the black whiskers extend to indicate the extent of the sample. This graphical analysis suggests, as expected, that the initial mean rate of preload loss decreases with the use of a secondary locking feature. An additional stati stical analysis is performed on the groups to better quantify any difference in means. Principally, since there is variation in the observations for these two levels samples, the analys is of variance (ANOVA) compare s the means of these levels by measuring the overall variability in the data [20]. In order to use ANOVA, the sample population should be normally distributed and the population sample should have equal variance, yet modest departures from these assumptions will not significantly alter the result s [20]. PAGE 73 50 In order to determine the dependency of the secondary locking feature on the initial rate of preload loss, two hypotheses ar e created: 1. All population means are equal ( : = = ), 2. At least one mean is different, w here Heli Coil Heli Coil Heli Coil Befor e any analysis could be performed, the assumption of normality needed to be ensured. Plotting the residuals (observation values minus sample mean) on a normal probability plot helps check normality between the sample popula tions. This is shown in Figure 3.13 where the data points show the empirical probability versus the value for each residual sample for both levels. The solid linear fit shows that the distribution is approximately normal. Note that for this data set, modest variations from normality and equal sample variances are found, yet this is acceptable since the analysis of variance allow minor violations of these assumptions [20]. PAGE 74 51 Figure 3.13 Normal probability plot of residuals for the initial rate of preload loss. Table 3.7 ANOVA table for the initial rate of preload loss. Table 3.7 summarized the ANOVA calculations. Note that the mean square value is larger than the value of the error which suggests that the treatments means may be different. The ratio of the mean square and the error i s referred as the testing value or ( = 44.4). This value is compared to an appropriate upper tail percentage point of the F distribution with an alpha error of 0.05 Moreover, the critical value is = 3.3. PAGE 75 52 Since the critical value is less than testing value ( > ) is rejected. Therefore, at least one mean is different which implies that there is a dependency on the initial pr eload loss due to a secondary locking feature. Figure 3.14 shows a graphical interpretation of these results where the multcompare function of Matlab v 7.3 was used. The multcompare function displays a graph with each group mean represented by a symbol a nd an interval around the symbol [21]. The interval is approximated by the following formula: (3.6) Where is the mean of each locking level, is the t critical value, is the mean square of the error and is the number of samples. Tw o means are significantly different if their intervals are disjoint, and are not significantly different if their intervals overlap [21] This figure suggests t hat the mean for the tandard Heli Coil with Loctite is significantly different when compared with the other two locking levels. Also, the comparison intervals of the Standard Heli Coil with Braycote and the Locking Heli Coil with Braycote overlap wh ich suggests that these means may be statistically similar. To quantify these findings, the Fisher Method of least significant difference (LSD) is used. PAGE 76 53 Figu re 3.14 Multiple comparisons of means for the initial rate of preload loss. The Fisher Method of least significant difference (LSD) is used for comparing all a hypothesis [20]. Therefore, in order to use this method, a new hypothesis is created: the population means for pairs are equal ( = = ). Where and are the population means for each locking level. The pairs of means will be considered significantly different if the following condition [20] is met: (3. 7 ) Where and are the sample means of the treatments to be compared. is the t value of the Student's t distribution as a fu nction of the probability and the degrees of PAGE 77 54 freedom of the error. is the mean square value of the error and n is the number of samples. Table 3. 8 summarizes the results of this analysis. Table 3.8 LSD method table for the initia l rate of preload loss. Table 3.8 agrees with the analysis of variance where there is a dependency of secondary locking feature on the initial rate of preload loss. However, statistically, it can be said that the initial drop of preload loss for Stan dard Heli Coil with Braycote and Locking Heli Coil with Braycote are not significantly different Lastly, a 95 percent confidence interval on each locking level mean is computed. Thus, showing that the population mean of each treatment (initial rate of preload loss) will lie between these int ervals. This is shown in Table 3.9 Table 3.9 95 perce nt confidence intervals for the initial rate of preload loss. PAGE 78 55 In this section the parameter of the initial rate of preload loss with secondary lock ing fe atures was analyzed. The l ow rate values mean less loosening. On this basis, the results in this section reveal the following: 1. Initial rate of preload loss is dependent o n secondary locking features. 2. The initial mean rate of preload Heli Coil the initial mean rate of preload Heli Coil not significantly different 3. The initial mean rate of preload Heli Coil the initial mean rate of preload Standard Heli Coil significantly different 4. The initial mean rate of preload Heli Coil initial mean rate of preload Heli Coil significantly different 3.4 Secon dary r ate of preload l oss p arameter 3.4.1 Data e xtraction After the initial rate of preload loss, the bolt undergoes the loosening criteria described by Junker Pai and Hess [1 3, 4 ] where the loosening in the fastener is due to complete slip at the cont act surfaces. In this thesis, this is referred to as the secondary rate of preload loss. This parameter was only extracted to Standard Heli Coil with Braycote and Locking Heli Coil with Braycote as a mean to quantify any difference between PAGE 79 56 them. Note t hat Standard Heli Coil with Loctite did not exhibit this loosening parameter and is therefore not included in this section. To quantify the secondary rate of preload loss, each preload versus cycles plot wa s zoomed in as shown in Figure 3.16 (all zoomed plots are shown in appendix D). Then, two data points were extracted, shown with a square, along a tangent line that was manually fitted at the lower bound of the envelope graph (this location was chosen to provide a worse case scenario of loosening). The data ex tracted is documented in Table A.7 in appendix A. With the set of two data point s the secondary rate of preload loss was calculated using the following formula [22] (3. 8 ) Where is the secondary ra te of preload loss, is the change in the y coordinate or preload and is the change in the x coordinate or cycles These values are documented in table 3.10 T he equation above will result in a negative number which implies a loss. PAGE 80 57 Figure 3.15 Loosening curve Heli Coil run number 3 Figure 3.16 Zoomed loosening curve for Heli Coil with run number 3 PAGE 81 58 Table 3.10 Secondary rate of preload loss for all locking levels (lb/cycle) The tangent lines are then calculated using the point slope formula [22] shown as (3. 9 ) Where is the unknown preload is the unknown cycles, is the secondary rate of preload loss and ( ) are coordinates of a point of the line (data points). Table 3.10 shows a difference in the mean rate for each locking level. Thus, as it was expected, the St andard Heli Coil with Braycote loosens more rapidly than the Locking Heli Coil with Braycote A statistical analysis will determine any dependencies of the se condary ocking Heli Coil with Braycote PAGE 82 59 3.4.2 Statistical a nalysis The Secondary rates of preload loss from the 24 runs are presented in Table 3.10 There are twelve observations for each locking levels. The statistical sample mean, median, variance and range are included for the sample. Ther e are differences in the Heli Coil Heli Coil with Braycote Figure 3 .17 Box plot for the secondary rate of preload loss Figure 3.17 shows a box plot for the three levels of locking. The sample median is represented by the center line of the rectangular box for each locking level. The ends of the rectangles represent the upper and lower quartile and the black whiskers extend to indicate the extent of the sample. This graphical analysis suggests, as expect ed, that the secondary mean rate of preload loss decreases with the use of a secondary locking feature. PAGE 83 60 An additional statistical analysis is performed on the groups to better quantify any difference in means. Principally, since there is variation in the observations for these two levels samples, the analysis of variance (ANOVA) will compare the means of these levels by measuring the overall variability in the data [20]. In order to use ANOVA, the sample population should be normally distributed and the po pulation sample should have equal variance, yet modest departures from these assumptions will not significantly alter the results [20] In order to determine the dependency of the secondary locking feature on the secondary rate of preload loss two hypoth eses are created: 1. All population means are equal ( : = ), 2. The means are different ( : ), w here is Heli Coil Heli Coil Before any analysis could be performed, the assumption of normality needed to be ensured. Plotting the residuals (observation va lues minus sample mean) on a normal probability plot helps check normality between the sample populations. This is shown i n Figure 3.18 where the data points show the empirical probability versus the value for each residual sample for both levels. The soli d linear fit shows that the distribution is approximately normal. Note that for this data set, modest variations from normality and equal sample variances are found, yet this is acceptable since the analysis of variance allow minor violations of these assu mptions [20] PAGE 84 61 Figure 3.18 Normal probability plot for the secondary rate of preload loss. Table 3.11 ANOVA table for the secondary rate of preload loss. Table 3.11 summarized the ANOVA calculations. Note that the mean square value is larger than the value of the error which suggests that the treatments means may be different. The ratio of the mean square and the error is referred as the testing value or ( = 40.6). This value is compared to an appropriate u pper tail percentage point of the F distribut ion with an alpha error of 0.05 Moreover, the critical value is = 4.3. Since the critical value is less than testing value ( > ) PAGE 85 62 is rejected. Therefore, the means are different which implies that there is a dependency on the initial preload loss due to a secondary locking feature. Figure 3.19 shows a graphical interpretation of these results where the multcompare functio n of Matlab v 7.3 was used. The multcompare function displays a graph with each group mean represented by a symbol and an interval around the symbol [21]. The interval is approximated by following formula: (3.10) Where is the mean of each locking level, is the t critical value, is the mean square of the error and is the number of samples. Tw o means are significantly different if their in tervals are disjoint, and are not significantly different if their intervals overlap [21] This figure suggests that the mean tandard Heli Coil with Braycote is significantly different when compared with the Locking Heli Coil with Braycote PAGE 86 63 Figure 3.19 Multiple comparisons of means for the secondary rate of preload loss Lastly, a 95 percent confidence interval on each locking level mean is computed. Thus, showing that the population mean of each treatment ( secondary rate of preload loss) will lie between these int ervals. This is shown in Table 3.12 Table 3.12 95 percent confidence intervals for the secondary rate of preload loss. In this section the dependency of secondary rate of preload loss parameter on secondary locking feature s was analyzed. Standard Heli Coil with Loctite did not exhibit this parameter and therefore is not included in this analysis. The Low rate values PAGE 87 64 mean more resistance to loosening. On this basis, the results in this section reveal the following: 1. Seconda ry rate of preload loss is dependent on secondary locking features. 2. The secondary mean rate of preload Heli Coil and the secondary mean rate of preload Heli Coil are significantly different 3.5 Steady s tate v alue p arameter 3.5.1 Data e xtraction The effect of prevailing torque on preload loss is to self lock the fastener by generating frictional resistance to rotation between engaged treads [11] the Screwlock feature found in the Locking He li Coil consists o f a grip coil that when it is bent outwards creates high pressures on the bolt [14]. Therefore, the prevailing torque counteracts the loosening torque reducing and can even stopping preload loss [11]. A naerobic thread lockers are design to reduce loosening due to vibration by filling the gaps between the engaged threads. When the thread locker dries, i t becomes a hard polymer [15]. T herefore, it increases the friction forces that opposes to the loosening moments. The purpose of this secti on is to quantify the steady state value, which consists of a value such that preload is constant because loosening due to transverse vibration has stop ped resulting the use of the secondary locking feature found in the Locking Heli Coil as well as the se condary locking feature created by the Loctite Threadlocker . To quantify a steady state condition, data needed to be extracted. Figure 3.20 is a representative example of a steady state condition reached after 1000 cycles. In order to PAGE 88 65 extract the data, w e zoomed into the graph as shown in Figure 3.21 where two data points, shown with the squares, were extracted along a horizontal line fitted into the lower bound of the e nvelope graph where signs of a s teady state characteristic were present. Note that all the zoomed graphs are presented in the appendix E. The dat a was documented in table 3.13 Figure 3.20 Loosening curve Heli Coil w ith run number 22. PAGE 89 66 Figure 3.21 Zoomed loosening curve for ocking Heli Coil run number 22 Table 3.13 Steady state values for all locking levels (lb), (nr: never reached) PAGE 90 67 Table 3.13 L ocking Heli Coil teady state Heli Coil Heli Coil represented by a zero. Figures 3.22 and 3.23 portray all the steady state values for all locking levels. Figure 3.22 All steady state value plots ocking Heli Coil with Bray Figure 3.23 All steady state value plots Heli Coil PAGE 91 68 3.5.2 Statistical a nalysis Note that a statistical comparative analysis can not be performed on the s teady state parameter consistent between any locking levels and the variance between the groups a significantly different. However s ince Standard Heli Coil with Braycote always lost its entire preload it is strongly suspected that the steady state parameter is dependent on secondary locking feature s Based on the data and the figures a forementioned in this section, it can be conclude d that : 1. Standard Heli Coil with Braycote loosened completely. 2. 83.3% of Locking Heli Coil with Braycote reached steady state 3. 16.7% o f Sta ndard Heli Coil with Loctite reached steady state. 4. The steady state condition is dependent on the secondary locking feature. 5. There is not enough data to perform a statistical analysis comparing all locking levels 3 .6 Final preload v alue p arameter 3.6.1 Data e xtraction Since a comparative statistical analysis was not performed on the steady state value, the final preload value was extracted in order to asses not only any loosening dependency due to secondary locking features, but also to quantify the sec ondary locking feature with the best locking performance. Note that the comparative assessment is only on the final preload value of the Standard Heli Coil with Loctite against the final preload values reached by the Locking Heli Coil with Braycote PAGE 92 69 Standard Heli Coil with Braycote will not be considered in this assessment since it has already been determined that there was complete loosening and it was denoted by the number zero. Hence, the only meaningful statistical representation Standard Heli C oil with Braycote has for this section is to state that there exists a dependency on secondary locking features in resisting preload loss. To quantify the final preload value, data needed to be extracted. The data was extracted by zooming into the figure and the final recorded value was extracted shown with the square. Figure 3.25 shows a representative example of a final preload value extracted for Standard Heli Coil with Braycote Note that all the zoomed graphs are presented in the appendix E. Th e da ta was documented in T able 3.14 Figure 3.24 Loosening curve for Standard Heli Coil with Loctite run number 33. PAGE 93 70 Figure 3.25 Zoomed Standard Heli Coil with Loctite run number 33. Table 3.14 Final preload values for all lockin g levels (lb) (** bolt broke) PAGE 94 71 Table 3.14 shows a mean of Standard Heli Coil with Loctite to be higher than the Locking Heli Coil with Braycote ; suggestin g that Loctite Threadlocker is a better secondary locking feature in resisting bolt loosening Note that run number 29 broke and there is not a final preload value recorded for this plot. Note that for Standard Heli Coil with Braycote complete loosening of the bolt occurred at this stage represented in the table with a zero. 3.6.2 Statistical a nalysis The final preload values from the 36 runs are presented in Table 3.14 There are twelve observations for each locking levels. The statistical sample mean, median, variance and range are included for the sample. Note that since Standard Heli Coil with Braycote loosened completely, it will not be considered for this statistical ana lysis. However, base d on Table 3 .14, it can be concluded that there is a significant dependency of secondary locking feature in resisting loosening since neither Locking Heli Coil with Braycote or Standard Heli Coil with Loctite lost its entire preload at this stage. Nonetheless, there is one question that prevails. Which of the secondary locking features is best? To answer this question a statistical analysis will be perform on the final preload values. PAGE 95 72 F igure 3.26 Box plot for the final preload value. Figure 3.26 shows a box plot for Locking Heli Coil with Braycote and Standard Heli Coil with Loctite The sample median is represented by the center line of the rectangular box for each locking level. The ends of the rectangles represent the upper and lower quartile and the black whiskers extend to indicate the extent of the sample. This graphical analysis suggests that with the use of Loctite preload is maintain ed at higher values. However, the variability of these values is quite high. An additional statistical analysis is performed on the groups to better qu antify any difference in means. The t test statistic will compare the means of these levels even though the variances and the sample size are not equal. In order to use t test statistic, the sample population should be normally distributed, yet modest departures from these assumptions will not significantly alter the results [20] PAGE 96 73 In order to determine the best locking performance of the secondary locking feature on the final preload v alue, two hypotheses are created: 1. All population means are equal ( : = ). 2. The means are different ( : ), w here is Locking Heli Coil with Braycote Standard Heli Coil Before any analysis could be perf ormed, the assumption of normality needed to be ensured. Plotting the residuals (observation values minus sample mean) on a normal probability plot helps check normality between the sample popula tions. This is shown in Figure 3.27 where the data points sh ow the empirical probability versus the value for each residual sample for both levels. The solid linear fit shows that the distribution is approximately normal. Note that for this data set, variations from normality are found, but they are at the end poin ts. Nonetheless, this is acceptable since the t test statistic allows minor violations of these assumptions [20] PAGE 97 74 Figure 3.27 Normal probability plot of residuals for the final preload value Table 3.15 t test statistic table for the final preload v alue. Table 3.15 shows a summary of the result of t test mean comparison of the Locking Heli Coil with Braycote and Standard Heli Coil with Loctite To test the hypothesis is calculated by the following equation [20] : ( 3.11 ) Where is the mean of each locking levels, i s the sample variance of each group PAGE 98 75 and is the sample size of each locking levels. Thus, is c ompared to an appropriate one tail percentage point of which is an approximation of the t distribution where is calculated by [20] : ( 3.12 ) Since is less t han ( 4.8 < 2.6 ), is rejected. Thus, concluding that not only the means of the groups are significantly different, but also that the means of Standard Heli Coil with Loctite is higher than Locking Heli Coi l with Braycote Figure 3.28 shows a graphical interpretation of these results where the multcompare function of Matlab v 7.3 was used. The multcompare function displays a graph with each group mean represented by a symbol and an interval around the symb ol [21]. The interval is approximated by following formula: (3.1 3 ) Where is the mean of each locking level, is the t critical value, is the mean square of the error and is the number of samples. Tw o means are significantly different if their intervals are disjoint, and are not significantly different if their intervals overlap [21] This figure suggests that the mean for the Locking Hel i Coil with Braycote is significantly different when compared with the Standard Heli Coil with Loctite PAGE 99 76 Figure 3.28 Multiple comparisons of means for the final preload value. Lastly, a 95 percent confidence interval on each locking level mean is c omputed. Thus, showing that the population mean of each treatment (final preload value) will lie between these int ervals. This is shown in Table 3.16. Table 3.16 95 percent confidence intervals for the final preload value. This section focused on qua ntifying the dependency of the final preload value parameter on secondary locking features. Based on th e calculations and the figures aforementioned in this section we can conclude the following: PAGE 100 77 1. Standard Heli Coil with Braycote loosened completely. 2. Fina l preload value parameter is dependent on secondary locking features 3. Standard Heli Coil with Loctite has, statistically, the best locking performance of the group. 4. Locking Heli Coil with Braycote reaches steady state more often than any other group. PAGE 101 78 C hapter 4 I nterpretation of R esults 4.1 Introduction This thesis has quantified the dependencies of loosening parameters on s econdary locking features. To better understand the loosening process, it is important to understand, first, the forces that act on the bolt at the moment of assembly are not only friction forces at the head and threads that act against the input torque, but also elastic components and even prevailing torque will contribute against it [7]. Figure 4.1 shows the reacti on forces on a bolt. Figure 4.1 a represents a bolt at the moment of assembly where is the input torque, is the reaction moment created by the friction between the head of the bolt and the washer or joint, is the reaction moment created by the threads of the nut and the Heli Coil threads, is the a reaction moment due to the torsional stress stored in the bolt, is the reaction moment created due to th e stretch of the bolt by the interaction of the incline plane of the threads of the bolt and the Heli Coil threads, is the prevailing torque due to secondary locking features. PAGE 102 79 Figure 4.1 Reaction forces on bolts Figure 4.1 a shows the reaction moments as the torque is applied. The bolt is being stretched and some of the applied torque is stored as torsion due to the difference of the frictional moments of the head and threads [3, 4]. Once the desired torque is achieved, the wrench is t aken off the bolt. Figure 4.1b shows the bolt after assembly; here the bolt has stretched; also, axial and torsional relaxation takes place [7]. Note that friction and the prevailing torque are responsible to maintain the preload The instan t transverse vibration is induced to the joint, the friction forces might be overcome and the loosening process starts [1, 2]. The following is the analysis of the results at every parameter studied in this thesis. The Motosh [10] equation was modified an d it is used in this section to explain the behavior of the secondary locking features. The modified torque equation proposed by Bickford [7] is: (4.1) (a) (b) PAGE 103 80 Where is the b reakaway torque or torque require for r emoval, is the Preload created in the fastener, is the pitch of the threads is the c oefficient of friction between Heli Coil and bolt threads, is the effective contact radius of the threads, is the joint, is the surface, is the half angle of the threads, is the Prevailing torque (if applicable). In order to represent a condition for maintaining preload if no external moments are present, the torque preload equation w as modified as follow: (4.2) The term at the left side of the equation is the reaction created by the elongation of the bolt and the incline plane of the threads, the term at the right hand side are the reactions created by the fri ction of the thread and head respectively and the reaction created by the prevailing torque. Note that this equation does not include dynamic effects from external sources. 4.2 Percentage l oss of i nitial preload p arameter Initial preload loss is observed almost immediately after the tests begins, which suggest that the two requirements for loosening explained by Pai and Hess [3, 4] are satisfied. The first requirement would be the torsional moments at the head at the onset of loosening, the second require ment, including its factors, is achieved the moment the shear loading begins [3, 4]. Thus, the friction is reduced enough to allow the moment due to the PAGE 104 81 stored torsion to be released. This explains the initial drop of preload experienced by the three diffe rent locking levels. Also, the bolt was tightened through the head of the bolt which increases torsion in the bolt. It was noted that the percentage loss of preload for Standard Heli Coil with Loctite was statistically higher that any of the two other l ocking levels (2% higher). This is expected since, only Loctite was applied at the thread inste ad of Braycote for the other two cases. This increases the friction coefficient in the engaged threads, creating a greater moment at the head. Hence, more preloa d was store d in torsional deformation. The average angle of twist along with the minimum, maximum angle of twist was calculated. Assuming that the bolt is a simple circular bar and the bar is in pure torsion, the angle of twist ( ) c an be calculated by the following equation [23] : (4.3) Where is the t orque applied to the bolt is the effective length of the bolt; is the shear modulus of ela sticity and moment of inertia Thus, the angle of twist is are shown in table 4.1 Table 4.1 Minimum, mean and maximum angle of twist PAGE 105 82 In order to correlate the angle of twist to a preload value, the following expression was u sed [ 7 ] : (4.4) where is the stiffness of the bolt and is the bolt stretch. In order to find the stiffness of the bolt the following equation was used [ 7 ] : (4. 5) where is the modulus of elasticity ( ); is the tensile stress area ( ) and is effective length of the bolt ( ). The refore The tensile stress area is calculated using the following expression [ 7 ] : (4.6) where is the diameter of the bolt ( ) and is the number of threads per inch ( ). To calculate the bolt stretch, 7 ] was used : (4.7) In which is the nut rotation in degrees and is the pitch in inches. Thus, a nut rotation of would be the angle of twist (in degrees ) in order to simulate the stretch of the bolt i f the bolt twist ed From using all of the above informat ion the minimum mean and maximum preload is docum ented in table 4.2. PAGE 106 83 Table 4.2 Preload due to angle of twist Moreover, Table 4.2 summarizes the preload calculation if the bolt in th is study experienced the aforementioned angles of twists. In terms of preload loss, this preload calculation would repr esent a range of 6.1% to 7.6% of preload loss The data, in chapter 2, gave a range of percentage of preload loss of 4.9% to 14.4%. Note that the calculated angle of twist is only for a bar in pure torsion whereas a bolt would not only experience torsional stress but also longitudinal stress. Thus, the angle of twist is a n approximate calculation. However, it still falls within the range of the values obtained by the data. 4.3 Initial r ate of preload l oss p arameter The initial rate of preload loss occurs after the release of torsional energy and only localized slips occurs at the contact surfaces that accumulates over the loading cycles and causes loosening slips over the entire contact. [3, 4] Chapter 3 shows that there was a loosening dependency on the secondary locking feature. However, the difference was only for the Standard Heli Coil with Loctite while the other two cases remained statistically similar. This suggests that the Loctite actually reduced the rate of loosening significantly. However, th e Screwlock found at the Locking Heli Coil with Braycote seemed to be almost ineffective in this period since the rate of loosening was not significantly different to the Standard Heli Coil with PAGE 107 84 Braycote This situation can be explained using the modif ied torque preload equation [7] : (4.8) ocking Heli Coil with Braycote it can be noticed that a third term on the righ t hand side, which is the term related to the prevailing torque caused by the Locking Heli C oil with Braycote depends on the amount of preload Thus, when the preload is high, the prevailing torque is not dominant and almost ineffective The prevailing to rque would only become dominant when the amount of preload decreases. By doing so, the amou nt of prevailing torque would be divided by a smaller value of preload and therefore resulting in a more dominant term. For the case of Standard Heli Coil with Loctite the equation is as follow (4.9) Loctite fills the gap betwe en the engaged thread. Hence, increasing the friction coefficient in the first component at the right hand side ( ). 4.4 Secondary r ate of preload l oss p arameter The secondary rate of preload loss occurs when complete head and threa d slip occurs at the contact surfaces previously explained by Junker [1]. Chapter 3 quantified this loss only for the Standard Heli Coil with Braycote and the Locking Heli Coil with Braycote since Standard Heli Coil with Loctite shows a different loo sening process quantified in the Initial rate of preload loss section. PAGE 108 85 Chapter 3 shows a significant dependency of the secondary locking featured in the loosening process. It shows that the two locking levels are significantly different where Locking Hel i Coil with Braycote resisted loosening better than the tandard Heli Coil with Braycote suggesting that the Screwlock shows a good performance because the preload has decreased enough to counteract with the prevailing torque making this term significan t Equation (4.10) shows again that as the preload decreases the prevailing torque becomes more significant. (4.10) 4.5 Steady s tate / f inal preload v alue p arameter The effect of prevailing torque on preload loss is to sel f lock the fastener by generating frictional resistance to rotation between engaged treads [11] the Locking Heli Coil insert consists of a grip coil that when it is bent outwards creates high pressures on the bolt [14]. Therefore, the prevailing torque cou nteracts the loosening torque that can reduce and can even stop preload loss [11]. A naerobic thread lockers are design to reduce loosening due to vibration by filling the gaps between the engaged threads. When the thread locker dries, it becomes a hard po lymer [15]; therefore increasing the friction force that opposes the loosening moments. Chapter 3 quantified the dependencies and found a steady state that is dependent on secondary locking feature for the Locking Heli Coil with Braycote suggesting tha t the Screwlock is dominant when in average 80% of the initial preload is lost. Equation (4.10) will demonstrate that as the preload decreases to about 80% of initial preload the PAGE 109 86 prevailing torque is dominant. Thus, the preload loss is contained. Standar d Heli Coil with Loctite did not reach steady state as frequent ly as the Locking Heli Coil with However, the final preload value s w ere statistically analyzed and showed that state, Standard Heli Coil with Loctite had a better locking performance because the Threadlocker filled the gap and increased the friction coefficient PAGE 110 87 C hapter 5 Conclusions In order to study the dependency of the loosening parameter on secondary locking features of threaded fa steners the loosening pr ocess was divided in five parameters: Initial preload loss, initial rate of preload loss, secondary rate of preload loss, steady state value and final preload value. Statistical analysis was used to quantify the dependencies conclu ding the following: For the dependency of the initial preload loss parameter on secondary locking features it can be concluded that: 1. Loss of initial preload is dependent on secondary locking features. 2. The mean loss of initial preload Heli Coi l mean loss of initial preload Heli Coil not significantly different 3. The mean loss of initial preload Heli Coil mean loss of initial preload Heli Coil w significantly different 4. The mean loss of initial preload Heli Coil mean loss of initial preload Heli Coil significantly different PAGE 111 88 For the parameter of the initial rate of preload loss with secondary locking features the following can be concluded: 1. Initial rate of preload loss is dependent on secondary locking features. 2. The initial mean rate of preload Heli Coil the initial mean rate of preload Heli Coil not significantly different 3. The initial mean rate of preload Heli Coil the initial mean rate of preload Heli Coil significantly different 4. T he initial mean rate of preload Heli Coil initial mean rate of preload Heli Coil significantly different For t he dependency of secondary rate of preload loss paramete r on secondary locking features the following can be concluded: 1. Standard Heli Coil with Loctite did not exhibit this parameter and therefore is not included in this analysis 2. Secondary rate of preload loss is dependent o n secondary locking features. 3. The secondary mean rate of preload Heli Coil and the secondary mean rate of preload Heli Coil are significantly different For the dependency of the steady state value parameter on secondary loc king features it can be concluded that: 1. Standard Heli Coil with Braycote loosened completely. PAGE 112 89 2. 83.3% of Locking Heli Coil with Braycote reached steady state. 3. 16.7% o f Standard Heli Coil with Loctite reached steady state. 4. The steady state condition is dependent on the secondary locking feature. 5. There is not enough data to perform a statistical analysis comparing all locking levels. For the dependency of the final preload value parameter on secondary locking features it can be concluded that: 1. Standard Heli Coil with Braycote loosened completely. 2. Final preload value parameter is dependent on secondary locking features. 3. Standard Heli Coil with Loctite has, statistically, the best locking performance of the group. 4. Locking Heli Coil with Braycote reach es steady state more often than any other group. Table 5.1 Dependency of loosening parameters on secondary locking features PAGE 113 90 In short, there is a clear dependency on the loosening parameter on secondary locking features. Table 5.1 summarizes the depen dencies of loosening parameters on the individual secondary locking features provided by the prevailing torque and Loctite. Note that two loosening parameters (Percentage loss of initial preload and initial rate of preload loss) were independent on the sec ondary locking feature in the Locking Heli Coil with Braycote but were dependent on the Standard Heli Coil with Loctite PAGE 114 91 References 1. Junker, G. H. (1969). New Criteria for Self Loosening of Fasteners Under Vibration, Society of Automotive Eng ineers Transactions Vol. 78, pp. 314 335. 2. Hess, D. P. (1998). Vibration and Shock Induced Loosening, Chapter 40 in Handbook of Bolts and Bolted Joints New York: Marcel Dekker Inc., pp. 757 824. 3. Pai, N.P. and Hess, D.P. (1997). Experimental Study of L oosening of Threaded Fasteners Due to Dynamic Shear Load, Journal of Sound and Vibration Vol. 253, pp. 585 692 4. Pai, N.P. and Hess, D.P. (2002). Three Dimensional Finite Element analysis of threaded fastener loosening due to dynamic shear load, Engineeri ng Failure Analysis Vol. 9, pp. 383 402. 5. Bolt Science, (1999 02). Vibration Loosening of Bolts and Threaded F asteners, www.boltscience.com/pages/vibloose 6. Sanclemente, J.A. and Hess, D.P. (2006) Parametric Study of Threaded Fastener Loosening Due to Cyclic Transverse Load, Engineering Failure Analysis Vol. 14, pp. 239 249, 2006 7. Bickford, J .H. (1995). An Introduction to the Design and Behavior of Bolted Joints 3 rd ed., Marcel Dekker Inc. 8. Fi sher, J. W., and Str uik, J. H. A. (1974), Guide to D esign Criteria for Bolted and Riveted Joints, Wiley, New York, pp. 57 58 9. Ibrahim R. A ., and Pettit, C. L. (2003). Uncertainties and D ynamic P roblems of B olted J oints and O ther F asteners Journal of s ound and vibration pp. 872 873 10. Motosh, N. (1976). Development of D esign C harts for B olts P reload ed up to the P lastic R ange Eng. Ind. 11. F inkelston, R. F. (1972). How Much Shake Can Bolted Joints Take Machine Design pp. 122 125. PAGE 115 92 12. Eccles, W. (1984). Bo lted J oint D esign, Engineering Design Vol. 10, pp. 10 14. 13. Wolfe, P E Functions P erformed by T hread I nserts 120 122. 14. http://www.hillcliff tools.com/helicoil.html 15. Henkel Technologies. (2007) The Adhesive Sourcebook Vol. 7, http://www.henkelna.com 16. Bardon A. (2004). Thread L ocking T echnolog ies, Plant Engineering Vol. 58 Barrington, Iss. 8; pp. 56 59. 17. NAS 1003 thru 1020, (1991). National Aerospace Standard, pp. 1 3. 18. NAS 1149, (1994). National Aerospace Standard, pp. 1 6. 19. Emhart Teknologies, 2003. Heli Coil Bulletin, www.emhart.com 20. Montgomery, D. C., Design and Analysis of Experiments 6 th ed., New Jersey: John Wiley & Sons, Inc., 2005. 21. The Mathworks Inc. (2007) Matlab v 7.3 Technical Support, http://www.mathworks.com 22. Smith, R. T and Minton, R. B (2002). Calculus 2 nd ed. New York: McGraw Hill, Inc., pp 13 14. 23. Gere, J. M. (2004 ). Mechanics of Materials, 6 th ed., California : Thomson Learning, Inc., pp 185 219. PAGE 116 93 A ppendices PAGE 117 94 Appendix A: Data extracted for all locking levels This appendix depicts the points obtained during the ex traction of data for the initial rate of preload loss, secondary rate of preload loss and for the s teady state value of all locking levels. Also, the points extracted for secondary rate of preload loss and final preload value. Table A.1 Extracted data f r o m Standard Heli Coil with Braycote PAGE 118 95 Appendix A (continued) Table A.2 Extracted data f r om Locking Heli Coil with Braycote PAGE 119 96 Appendix A (continued) Table A.3 Extracted data f rom Standard Heli Coil with Loctite PAGE 120 97 Appendix A (continued) The following tables were calculated using the slope point equation used in chapter 3. These data points are used for the plotting of the rates of preload loss and the s teady state values. Table A.4 Refined data points from Standard Heli Coil with Brayc ote PAGE 121 98 Appendix A (continued) Table A.5 Refined data points from Locking Heli Coil with Braycote PAGE 122 99 Appendix A (continued) Table A.6 Refined data points from Standard Heli Coil with Loctite PAGE 123 100 Appendix A (continued) The following dat a points were extracted to quantify the secondary rate of preload loss. Table A.7 E xtracted data from Standard Heli Coil and Locking Heli Coil with Braycote PAGE 124 101 Appendix B: Z oomed data plots for the percentage loss of initial preload p arameter These plots were used in order to extract the values used in C hapter 3 under the percentage loss of preload loss section Figure B.1 Loss of initial preload Heli Coil run number 1 PAGE 125 102 Appendix B (continued) Figure B.2 Loss of initial preload Heli Coil run number 2 Figure B .3 Loss of initial preload Heli Coil run number 3 PAGE 126 103 Appendix B (continued) Figure B.4 Loss of initial preload Heli Coil run number 4 Figure B.5 Loss of initial preload Heli Coil run number 5 PAGE 127 104 Appendix B (continued) Figure B.6 Loss of initial preload Heli Coil run number 6 Figure B. 7 Loss of initial preload Heli Coil run number 7 PAGE 128 105 Appendix B (continued) Figure B.8 Loss of initial preload Heli Coil run number 8 Figure B.9 Loss of initial preload Heli Coil w run number 9 PAGE 129 106 Appendix B (continued) Figure B.10 Loss of initial preload Heli Coil run number 10 Figure B.11 Loss of initial preload Heli Coil run number 11 PAGE 130 107 Appendix B (continu ed) Figure B.12 Loss of initial preload Heli Coil run number 12 Figure B.13 Loss of initial preload Heli Coil run number 13 PAGE 131 108 Appendix B (continued) Figure B.14 Loss of initial preload Locking Heli Coil run number 14 Fi gure B.15 Loss of initial preload Heli Coil run number 15 PAGE 132 109 Appendix B (continued) Figure B.16 Loss of initial preload Heli Coil run number 16 Figure B.17 Loss of initial preload Heli Coil run number 17 PAGE 133 110 Appendix B (continued) Figure B.18 Loss of initial preload Heli Coil run number 18 Figure B.19 Loss of initial preload g Heli Coil run number 19 PAGE 134 111 Appendix B (continued) Figure B.20 Loss of initial preload Heli Coil run number 20 Figure B.21 Loss of initial preload Heli Coil run number 21 PAGE 135 112 Appendi x B (continued) Figure B.22 Loss of initial preload Heli Coil run number 22 Figure B.23 Loss of initial preload Heli Coil run number 23 PAGE 136 113 Appendix B (continued) Figure B.24 Loss of initial pr eload Heli Coil run number 24 Figure B.25 Loss of initial preload Heli Coil run number 25 PAGE 137 114 Appendix B (continued) Figure B.26 Loss of initial preload Heli Coil run n umber 26 Figur e B.27 Loss of initial preload Heli Coil run number 27 PAGE 138 115 Appendix B (continued) Figure B.28 Loss of initial preload Heli Coil run number 28 Figure B.29 Loss of initial preload Heli Coil run number 29 PAGE 139 116 Appendix B (continued) Figure B.30 Loss of initial preload Heli Coil run number 30 Figure B.31 Loss of initial preload Heli Coil run number 31 PAGE 140 117 Appendix B (continued) Figure B.32 Loss of initial preload Heli Coil run number 32 Figure B.33 Loss of initial preload Heli Coil run number 33 PAGE 141 118 Appendix B (continued) Figure B.34 Loss of initial preload Heli Coil run number 34 Figure B.35 Loss of initial preload Heli Coil run number 35 PAGE 142 119 Appendix B (continued) Figure B.36 Loss of initial preload Heli Coil with Loc run number 36 PAGE 143 120 Appendix C: Zoomed data plots for the initial rate of preload loss parameter These plots were used in order to obtain the initial rate of preload loss used in C hapter 3. Figure C.1 Initial rate of preload loss Heli Coi l run number 1 PAGE 144 121 Appendix C (continued) Figure C.2 Initial rate of preload loss Heli Coil run number 2 Figure C.3 Initial rate of preload loss Heli Coil number 3 PAGE 145 122 Appendix C (continued) Figu re C.4 Initial rate of preload loss Heli Coil run number 4 Figure C.5 Initial rate of preload loss Heli Coil run number 5 PAGE 146 123 Appendix C (continued) Figure C.6 Initial rate of preload loss Heli Coil run number 6 Figure C.7 Initial rate of preload loss Heli Coil run number 7 PAGE 147 124 Appendix C (continued) Figure C.8 Initial rate of preload loss Heli Coil run number 8 Figure C.9 Initial rate of preload loss Heli Coil run number 9 PAGE 148 125 Appendix C (continued) Figure C.10 Initial rate of preload loss Heli Coil run number 10 Figure C.11 Initial rate of preload loss Heli Coil run number 11 PAGE 149 126 Appendix C (continued) Figure C.12 Initial rate of preload loss Heli Coil run number 12 Figure C.13 Initial rate of preload loss for Heli Coil run number 13 PAGE 150 127 Appendix C (continued) Figure C.14 Initial rate of preload loss Heli Coil run number 14 Figure C.15 Initial rate of preload loss Heli Coil run number 15 PAGE 151 128 Appendix C (continued) Figure C .16 Initial rate of preload loss Heli Coil run number 16 Figure C.17 Initial rate of preload loss Heli Coil run number 17 PAGE 152 129 Appendix C (continued) Fi gure C.18 Initial rate of preload loss Heli Coil run number 18 Figure C.19 Initial rate of preload loss Heli Coil run number 19 PAGE 153 130 Appendix C (continued) Figure C.20 Initial rate of preload loss Heli Coil run number 20 Figure C.21 Initial rate of preload loss Heli Coil run number 21 PAGE 154 131 Appendix C (continued) Figure C.22 Initial rate of preload loss Heli Coil r un number 22 Figure C.23 Initial rate of preload loss Heli Coil run number 23 PAGE 155 132 Appendix C (continued) Figure C.24 Initial rate of preload loss Heli Coil run number 24 Figure C.25 Initial ra te of preload loss Heli Coil run number 25 PAGE 156 133 Appendix C (continued) Figure C.26 Initial rate of preload loss Heli Coil run number 26 Figure C.27 Initial rate of preload loss Heli C oil run number 27 PAGE 157 134 Appendix C (continued) Figure C.2 8 Initial rate of preload loss Heli Coil run number 28 Figure C.29 Initial rate of preload loss Heli Coil run number 29 PAGE 158 135 Append ix C (continued) Figure C.30 Initial rate of preload loss Heli Coil run number 30 Figure C.31 Initial rate of preload loss Heli Coil run number 31 PAGE 159 136 Appendix C (continued) Figure C.32 Initial rate of preload loss Heli Coil number 32 Fi gure C.33 Initial rate of preload loss Heli Coil number 33 PAGE 160 137 Appendix C (continued) Figure C.34 Initial rate of preload loss Hel i Coil number 34 Figure C.35 Initial rate of preload loss Heli Coil number 35 PAGE 161 138 Appendix C (continued) Figure C.36 Initial rate of preload loss Heli Coil number 36 PAGE 162 139 Ap pendix D: Zoomed data plots for the secondary rate of preload loss parameter These plots were used in order to obtain the secondary rate of preload loss in C hapter 3. Figure D.1 Secondary rate of preload loss for Heli Coil with Braycote nu mber 1 PAGE 163 140 Appendix D (continued) Figure D.2 Secondary rate of preload loss Heli Coil with Braycote number 2 Figure D.3 Secondary rate of preload loss Heli Coil with Braycote number 3 PAGE 164 141 Appendix D (continued) Figure D.4 Secondary rate of preload loss Heli Coil with Braycote number 4 Figure D.5 Secondary rate of preload loss Heli Coil with Braycote number 5 PAGE 165 142 Appendix D (continued) Figure D.6 Secondary r ate of preload loss Heli Coil with Braycote number 6 Figure D.7 Secondary rate of preload loss Heli Coil with Braycote number 7 PAGE 166 143 Appendix D (continued) Figure D.8 Secondary rate of preload loss Hel i Coil with Braycote number 8 Figure D.9 Secondary rate of preload loss Heli Coil with Braycote number 9 PAGE 167 144 Appendix D (continued) Figure D.10 Secondary rate of preload loss Heli Coil with Braycote number 10 Figure D.11 Secondary rate of preload loss Heli Coil with Braycote number 11 PAGE 168 145 Appendix D (continued) Figure D.12 Secondary rate of preload loss Heli Coil with Braycote number 12 Figure D.13 Secondary rate of preload loss Locking Heli Coil with Braycote number 13 PAGE 169 146 Appendix D (continued) Figure D.14 Secondary rate of preload loss Locking Heli Coil with Braycote number 14 Figure D.15 Secondary rate of preload loss Locking Heli Coi l with Braycote number 15 PAGE 170 147 Appendix D (continued) Figure D.16 Secondary rate of preload loss Locking Heli Coil with Braycote number 16 Figu re D.17 Secondary rate of preload loss Locking Heli Coil with Braycote number 17 PAGE 171 148 App endix D (continued) Figure D.18 Secondary rate of preload loss Locking Heli Coil with Braycote number 18 Figure D.19 Locking Heli run number 19 PAGE 172 149 Appendix D (continued) Figure D.20 S econdary rate of preload loss Locking Heli Coil with Braycote number 20 Figure D.21 Secondary rate of preload loss Locking Heli Coil with Braycote number 21 PAGE 173 150 Appendix D (continued) Figure D.22 Secondary rate of preload loss Locking Heli Coil with Braycote number 22 Figure D.23 Secondary rate of preload loss Locking Heli Coil with Braycote number 23 PAGE 174 151 Appendix D (continued) Figure D.24 Secondary rate of preload loss Locking Heli Coil with Braycote n number 24 PAGE 175 152 Appendix E: Zoomed data plots for the steady stat e and the final preload value parameter These plots were used in order to obtain the steady state value (if applicable) and also the finale preload value used in C hapter 3. Figure E.1 St eady state value ocking Heli Coil run number 13 PAGE 176 153 Appendix E (continued) Figure E.2 Steady state value ocking Heli Coil run number 14 Figu re E.3 Steady state value ocking Heli Coil with Bray run number 15 PAGE 177 154 Appendix E (continued) Figure E.4 Steady state value ocking Heli Coil run number 16 Figure E.5 Final preload value Heli Coil run number 17 PAGE 178 155 Appendix E (continued) Figure E.6 S teady state value Heli Coil run number 18 Figure E.7 Steady state value Heli Coil run number 19 PAGE 179 156 Appendix E (continued) Figure E.8 Final preload value ocking Heli Coil run number 20 Figure E.9 Steady state value ocking Heli Coil run number 21 PAGE 180 157 Appendix E (continued) Figure E .10 Steady state value ocking Heli Coil run number 22 Figure E.11 Steady state value ocking He li Coil run number 23 PAGE 181 158 Appendix E (continued) Figure E.12 Steady state value Heli Coil with run number 24 Figure E.13 Final preload value Heli Coil run number 25 PAGE 182 159 Appendix E (continue d) Figure E.14 Steady state value tandard Heli Coil run number 26 Figure E.15 Final preload value tandard Heli Coil run number 27 PAGE 183 160 Appendix E (continued) Figure E.16 Final preload value tandard Heli C oil run number 28 Figure E.17 Final preload value Heli Coil with run number 30 PAGE 184 161 Appendix E (continued) Figure E.18 Final preload value tandard Heli Coil run number 31 Figure E.19 Steady st ate value tandard Heli Coil run number 32 PAGE 185 162 Appendix E (continued) Figure E.20 Final preload value tandard Heli Coil run number 33 Figure E.21 Final preload value tandard Heli Coil run numbe r 34 PAGE 186 163 Appendix E (continued) Figure E.22 Final preload value andard Heli Coil run number 35 Figure E.23 Final preload value tandard Heli Coil run number 36 