Light Truck Frame Joint Stiffness Study

Light Truck Frame Light Truck Frame Light Truck Frame Light Truck Frame

Joint Stiffness Study Joint Stiffness Study Joint Stiffness Study Joint Stiffness Study

Phase 2 Final ReportPhase 2 Final ReportPhase 2 Final ReportPhase 2 Final Report

A study of light

truck frame joint

stiffness.

Auto/Steel Partnership MembersAuto/Steel Partnership MembersAuto/Steel Partnership MembersAuto/Steel Partnership Members

DaimlerChrysler Corporation

Dofasco Inc.

Ford Motor Company

General Motors Corporation

Ispat Inland Inc.

Nucor Corporation

Severstal North America Inc.

United States Steel Corporation

This report is for general information only. The material contained herein should not be used without first securing competent advice with respect to its suitability for any given application. This report is not intended as a representation or warranty on the part of Auto/Steel Partnership – or any other person named herein – that the information is suitable for any general or particular use, or free from infringement of any patent or patents. Anyone making use of the information assumes all liability arising from such use. This report is intended for use by Auto/Steel Partnership members only. For more information, please contact the Auto/Steel Partnership, 2000 Town Center, Suite 320, Southfield, MI 48075-1123 or phone: 248.945.4777, fax: 248.356.8511, website: www.a-sp.org.

Light Truck Frame Joint Stiffness Study

October 1, 2003

Altair Report No.: A/SP-005-2

Prepared For:

Auto/Steel Partnership

Prepared By: Arun Kumar, Senior Project Engineer Jeff Hopkins, Project Engineer Michael White, Engineering Manager

Report: A/SP-005-2 Light Truck Frame Joint Study i

PREFACE EXECUTIVE SUMMARY

The Light Truck Frame Project Group entrusted Altair Engineering Inc. to conduct the Light Truck Frame Joint Stiffness Study. This report is a continuation of the Phase 1 Study [1, 2]. It comprises the results of Phase 2 – the study of ten additional joints typically used in light truck frames. The Phase 2 results are presented in two documents. This document describes the study and its results. The second document, an Excel Spreadsheet, is an interactive tool that frame designers may use to determine the stiffness for variations of the five joints in Phase 1 and the ten joints in Phase 2. This tool will help designers reduce the weight of light truck frames.

Report: A/SP-005-2 Light Truck Frame Joint Study ii

EXECUTIVE SUMMARY EXECUTIVE SUMMARY

Background

Designing a light truck frame joint with the correct stiffness is always a challenging proposition for frame designers. A survey of current production frames found that most frames used joint styles from a group of approximately fifteen joints. Frame designers see some merit in using these same joint styles, but the information regarding these joint styles is either not well documented or is not available to others in a useful format. The ASP Lightweight SUV Frames Project Team felt that a study to determine the relative stiffness of the joints, along with a tool to communicate the results of the study to frame designers, would allow for better decision-making in the concept phase and would facilitate lighter weight frame designs.

This study is divided into two phases, Phase 1 and Phase 2. The Phase 1 study, which has already been completed, is comprised of five joints. A project report for the Phase 1 study has been published [1] and is available on the ASP website [5]. An Excel Spreadsheet Toolbox [2] was also developed in Phase 1 and it too is available on the A/SP website. The Phase 2 study is a continuation of the Phase 1 study, and it is comprised of ten additional joints. This report presents information developed in the Phase 2 study.

Project Goals

The goal of the Phase 2 study was to provide frame designers with the same objective data and tools used in Phase 1 to facilitate early concept choices for ten additional frame joints.

In order to achieve the goals, the scope of the project involves the following steps:

• Perform physical testing on multiple (three) samples of two riveted joints.

• Correlate the physical testing and finite element analysis for the two riveted joints.

• Evaluate the sensitivity of the joint stiffness to the various joint design parameters for the two riveted and eight welded joints.

• Create the Joint Stiffness Toolbox that incorporates Design Rules and sensitivity analysis for the five joints of Phase 1 and the ten additional joints of Phase 2.

Project Results

The testing and finite element analysis processes followed to evaluate the stiffness of the ten joints was similar to the Phase 1 study. An interactive Joint Stiffness Toolbox was developed to document the study results, and to provide a mechanism for frame designers to use the data in the design process. The Toolbox is based on an interactive worksheet. The spreadsheet allows the designer or engineer to modify the geometric and gage properties of the joint members and calculates the joint stiffness and relative mass based on the new properties.

Report: A/SP-005-2 Light Truck Frame Joint Study iii

TABLE OF CONTENTS

Preface ....................................................................................................................................... i Executive Summary................................................................................................................. ii Table of Contents.................................................................................................................... iii List of Tables........................................................................................................................... iv List of Figures .......................................................................................................................... v Acknowledgments ................................................................................................................... x Phase 2 Joints Summary ........................................................................................................ 1 Riveted Joint Testing............................................................................................................... 5 Introduction .................................................................................................................... 5 Test Specimen (Joint) Description ................................................................................. 5 Test Specimen (Joint) Preparation............................................................................... 11 Test Joint Fixturing....................................................................................................... 12 Test Joint Deflection Measurement.............................................................................. 15 Test Joint Force Application......................................................................................... 15 Joint 6 Testing.............................................................................................................. 16 Joint 7 Testing.............................................................................................................. 19 Repeatability of Riveted Joints..................................................................................... 21 Rivet Diagnostic Testing .............................................................................................. 21 Riveted Joint Correlation ...................................................................................................... 31 Introduction .................................................................................................................. 31 Initial FEA Models ........................................................................................................ 31 Model Changes to Improve Correlation ....................................................................... 33 Final FEA Models......................................................................................................... 34 Final Correlation between FEA and Test Data............................................................. 36 Joint Stiffness Summary....................................................................................................... 38 Sensitivity Study .................................................................................................................... 41 Introduction .................................................................................................................. 41 Study Models ............................................................................................................... 41 Joint Parameters .......................................................................................................... 41 Toolbox ................................................................................................................................... 75 Introduction .................................................................................................................. 75 Bi-linear Stiffness for Riveted Joints 6 and 7 ............................................................... 75 References.............................................................................................................................. 97 Appendix A: Test Data Plots................................................................................................. 98 Appendix B: Design Variables............................................................................................ 104 Appendix C: Screening DOE Study.................................................................................... 114 Appendix D: Phase 1 Joint 2A DOE ................................................................................... 120 Appendix E: Material Test Results ..................................................................................... 129 Appendix F: Phase 2 Joints Description ........................................................................... 134

Report: A/SP-005-2 Light Truck Frame Joint Study iv

LIST OF TABLES

Table 1: Test Joint Stiffnesses for Joints 6 and 7 .................................................................................................................................30 Table 2: Joint 6 Stiffness Comparison between Initial FEA and Test Data ..........................................................................................33 Table 3: Joint 7 Stiffness Comparison between Initial FEA and Test Data ..........................................................................................33 Table 4: Rivet and Rivet Hole Dimensions for Joints 6 and 7...............................................................................................................34 Table 5: Joint 6 Stiffness Comparison between Final FEA and Test Data ...........................................................................................36 Table 6: Joint 7 Stiffness Comparison between Final FEA and Test Data ...........................................................................................37 Table 7: Stiffness Summary for all Joints..............................................................................................................................................38 Table 8: Design Variables Eliminated / Added from Screening DOE .................................................................................................119

Report: A/SP-005-2 Light Truck Frame Joint Study v

LIST OF FIGURES EXECUTIVE SUMMARY

Figure 1: Joint 6: Hat Section to Channel Section ..................................................................................................................................1 Figure 2: Joint 7: Hat Section (with Bracket) to Twin Channel Sections.................................................................................................1 Figure 3: Joint 8: Rectangular Tube Section to Rectangular Tube Section............................................................................................2 Figure 4: Joint 9: Circular Tube Section through Channel Section .........................................................................................................2 Figure 5: Joint 10: Rectangular Tube Section through Rectangular Tube Section.................................................................................2 Figure 6: Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section ...........................................................................3 Figure 7: Joint 12: Deep Hat Section to Rectangular Tube Section .......................................................................................................3 Figure 8: Joint 13: Full Height Channel Section to Rectangular Tube Section.......................................................................................3 Figure 9: Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section........................................................................4 Figure 10: Joint 15: Full Height Channel Section to Channel Section ....................................................................................................4 Figure 11: Joint 6: Hat Section to Channel Section (finite element representation) ...............................................................................5 Figure 12: Joint 7: Hat Section (with Bracket) to Twin Channel Sections (finite element representation)..............................................5 Figure 13: Joint 6: Hat Section to Channel Section Physical Representation (isometric view) ..............................................................6 Figure 14: Joint 6: Hat Section to Channel Section Physical Representation (rear view) ......................................................................7 Figure 15: Joint 6: Hat Section to Channel Section Rivet Attachments ..................................................................................................8 Figure 16: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Physical Representation (front view) ....................................9 Figure 17: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Physical Representation (rear view)...................................10 Figure 18: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Rivet Attachments ..............................................................11 Figure 19: Joint 6: Hat Section to Channel Section Specimen Preparation .........................................................................................12 Figure 20: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Fore-Aft Loading Setup ......................................................13 Figure 21: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Torsional Loading Setup.....................................................14 Figure 22: Measurement Fixture used for Joint Testing .......................................................................................................................15 Figure 23: Joint 6 Fore-Aft Loadcase Test Data ...................................................................................................................................16 Figure 24: Joint 6 Fore-Aft Loadcase Analysis and Test Data Comparison .........................................................................................17 Figure 25: Joint 6 Vertical Loadcase Analysis and Test Data Comparison ..........................................................................................18 Figure 26: Joint 7 Vertical Loadcase Test Data ....................................................................................................................................19 Figure 27: Joint 7 Vertical Loadcase Analysis and Test Data Comparison ..........................................................................................20 Figure 28: Joint 7 Vertical Loadcase Analysis and Test Data Comparison ..........................................................................................21 Figure 29: Joint 6 Fore-Aft Loadcase Test Data Repeatability .............................................................................................................22 Figure 30: Joint 7 Fore-Aft Loadcase Test Set up to study Rivets........................................................................................................23 Figure 31: Joint 7 Area-V Rivet X-direction Displacement....................................................................................................................24 Figure 32: Joint 7 Area-V Rivet Y-direction Displacement....................................................................................................................25 Figure 33: Joint 7 Area-V Rivet Z-direction Displacement ....................................................................................................................26 Figure 34: Variations in Rivet Expansion inside Rivet Holes ................................................................................................................27 Figure 35: Joint 7 Area-U Rivet X-direction Displacement....................................................................................................................27 Figure 36: Joint 7 Area-U Rivet Y-direction Displacement....................................................................................................................28 Figure 37: Joint 7 Area-U Rivet Z-direction Displacement....................................................................................................................29

Report: A/SP-005-2 Light Truck Frame Joint Study vi


Figure 38: Joint 6 Initial Finite Element Model ......................................................................................................................................31 Figure 39: Joint 7 Initial Finite Element Model ......................................................................................................................................32 Figure 40: Example Rivet Representation in the Initial FEA model ......................................................................................................32 Figure 41: Example Rivet Representation in the Final FEA model.......................................................................................................34 Figure 42: Rivet 3D-Solid Elements used in the Final FEA model........................................................................................................35 Figure 43: Rivet 3D Graphical Illustration .............................................................................................................................................36 Figure 44: Example of Original Joint 6 Geometry (left) vs. Modified Joint 6 Geometry for Study (right) ..............................................41 Figure 45: Main Effect Plot for Joint 6: Hat Section to Channel Section Stiffness Kθθθθz .........................................................................42 Figure 46: Main Effect Plot for Joint 6: Hat Section to Channel Section Stiffness Kθθθθx .........................................................................43 Figure 47: Main Effect Plot for Joint 6: Hat Section to Channel Section Stiffness Kθθθθy .........................................................................44 Figure 48: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθθθθz (Design Variables from 1

through 7)....................................................................................................................................................................................45 Figure 49: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθθθθx (Design Variables from 1

through 7)....................................................................................................................................................................................46 Figure 50: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθθθθy (Design Variables from 1

through 7)....................................................................................................................................................................................47 Figure 51: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθθθθz (Design Variables from 8

through 15)..................................................................................................................................................................................48 Figure 52: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθθθθx (Design Variables from 8

through 15)..................................................................................................................................................................................49 Figure 53: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθθθθy (Design Variables from 8

through 15)..................................................................................................................................................................................50 Figure 54: Main Effect Plot for Joint 8: Rectangular Tube Section to Rectangular Tube Section Stiffness Kθθθθz ...................................51 Figure 55: Main Effect Plot for Joint 8: Rectangular Tube Section to Rectangular Tube Section Stiffness Kθθθθx ...................................52 Figure 56: Main Effect Plot for Joint 8: Rectangular Tube Section to Rectangular Tube Section Stiffness Kθθθθy ...................................53 Figure 57: Main Effect Plot for Joint 9: Circular Tube Section through Channel Section Stiffness Kθθθθz ................................................54 Figure 58: Main Effect Plot for Joint 9: Circular Tube Section through Channel Section Stiffness Kθθθθx ................................................55 Figure 59: Main Effect Plot for Joint 9: Circular Tube Section through Channel Section Stiffness Kθθθθy ................................................56 Figure 60: Main Effect Plot for Joint 10: Rectangular Tube Section Through Rectangular Tube Section Stiffness Kθθθθz.......................57 Figure 61: Main Effect Plot for Joint 10: Rectangular Tube Section Through Rectangular Tube Section Stiffness Kθθθθx.......................58 Figure 62: Main Effect Plot for Joint 10: Rectangular Tube Section Through Rectangular Tube Section Stiffness Kθθθθy.......................59 Figure 63: Main Effect Plot for Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section Stiffness Kθθθθz...................60 Figure 64: Main Effect Plot for Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section Stiffness Kθθθθx...................61 Figure 65: Main Effect Plot for Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section Stiffness Kθθθθy...................62 Figure 66: Main Effect Plot for Joint 12: Deep Hat Section to Rectangular Tube Section Stiffness Kθθθθz...............................................63 Figure 67: Main Effect Plot for Joint 12: Deep Hat Section to Rectangular Tube Section Stiffness Kθθθθx...............................................64 Figure 68: Main Effect Plot for Joint 12: Deep Hat Section to Rectangular Tube Section Stiffness Kθθθθy...............................................65 Figure 69: Main Effect Plot for Joint 13: Full Height Channel Section to Rectangular Tube Section Stiffness Kθθθθz ..............................66 Figure 70: Main Effect Plot for Joint 13: Full Height Channel Section to Rectangular Tube Section Stiffness Kθθθθx ..............................67 Figure 71: Main Effect Plot for Joint 13: Full Height Channel Section to Rectangular Tube Section Stiffness Kθθθθy ..............................68

Report: A/SP-005-2 Light Truck Frame Joint Study vii


Figure 72: Main Effect Plot for Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section Stiffness Kθθθθz ...............69 Figure 73: Main Effect Plot for Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section Stiffness Kθθθθx ...............70 Figure 74: Main Effect Plot for Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section Stiffness Kθθθθy ...............71 Figure 75: Main Effect Plot for Joint 15: Full Height Channel Section to Channel Section Stiffness Kθθθθz .............................................72 Figure 76: Main Effect Plot for Joint 15: Full Height Channel Section to Channel Section Stiffness Kθθθθx .............................................73 Figure 77: Main Effect Plot for Joint 15: Full Height Channel Section to Channel Section Stiffness Kθθθθy .............................................74 Figure 78: Bi-Linear Joint Stiffness for Rivet Joints 6 and 7 .................................................................................................................76 Figure 79: Joint 6 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ........................................................................77 Figure 80: Joint 6 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules ...........................................................78 Figure 81: Joint 7 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ........................................................................79 Figure 82: Joint 7 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules ...........................................................80 Figure 83: Joint 8 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ........................................................................81 Figure 84: Joint 8 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules ...........................................................82 Figure 85: Joint 9 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ........................................................................83 Figure 86: Joint 9 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules ...........................................................84 Figure 87: Joint 10 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ......................................................................85 Figure 88: Joint 10 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules .........................................................86 Figure 89: Joint 11 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ......................................................................87 Figure 90: Joint 11 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules .........................................................88 Figure 91: Joint 12 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ......................................................................89 Figure 92: Joint 12 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules .........................................................90 Figure 93: Joint 13 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ......................................................................91 Figure 94: Joint 13 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules .........................................................92 Figure 95: Joint 14 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ......................................................................93 Figure 96: Joint 14 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules .........................................................94 Figure 97: Joint 15 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results ......................................................................95 Figure 98: Joint 15 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules .........................................................96 Figure 99: Joint 6 Fore-Aft Loadcase Displacement-1..........................................................................................................................98 Figure 100: Joint 6 Fore-Aft Loadcase Displacement-2........................................................................................................................98 Figure 101: Joint 6 Vertical Loadcase Displacement-1.........................................................................................................................99 Figure 102: Joint 6 Vertical Loadcase Displacement-2.........................................................................................................................99 Figure 103: Joint 6 Torsional Loadcase Displacement-1....................................................................................................................100 Figure 104: Joint 6 Torsional Loadcase Displacement-2....................................................................................................................100 Figure 105: Joint 7 Fore-Aft Loadcase Displacement-1......................................................................................................................101 Figure 106: Joint 7 Fore-Aft Loadcase Displacement-2......................................................................................................................101 Figure 107: Joint 7 Vertical Loadcase Displacement-1.......................................................................................................................102 Figure 108: Joint 7 Vertical Loadcase Displacement-2.......................................................................................................................102 Figure 109: Joint 7 Torsional Loadcase Displacement-1....................................................................................................................103 Figure 110: Joint 7 Vertical Loadcase Displacement-2.......................................................................................................................103

Report: A/SP-005-2 Light Truck Frame Joint Study viii


Figure 111: Joint 6 Final DOE Design Variables ................................................................................................................................104 Figure 112: Joint 7 Final DOE Design Variables ................................................................................................................................105 Figure 113: Joint 8 Final DOE Design Variables ................................................................................................................................106 Figure 114: Joint 9 Final DOE Design Variables ................................................................................................................................107 Figure 115: Joint 10 Final DOE Design Variables ..............................................................................................................................108 Figure 116: Joint 11 Final DOE Design Variables ..............................................................................................................................109 Figure 117: Joint 12 Final DOE Design Variables ..............................................................................................................................110 Figure 118: Joint 13 Final DOE Design Variables ..............................................................................................................................111 Figure 119: Joint 14 Final DOE Design Variables ..............................................................................................................................112 Figure 120: Joint 15 Final DOE Design Variables ..............................................................................................................................113 Figure 121: Joint 6 Screening DOE Sensitivity Plots ..........................................................................................................................114 Figure 122: Joint 7 Screening DOE Sensitivity Plots ..........................................................................................................................114 Figure 123: Joint 8 Screening DOE Sensitivity Plots ..........................................................................................................................115 Figure 124: Joint 9 Screening DOE Sensitivity Plots ..........................................................................................................................115 Figure 125: Joint 10 Screening DOE Sensitivity Plots ........................................................................................................................116 Figure 126: Joint 11 Screening DOE Sensitivity Plots ........................................................................................................................116 Figure 127: Joint 12 Screening DOE Sensitivity Plots ........................................................................................................................117 Figure 128: Joint 13 Screening DOE Sensitivity Plots ........................................................................................................................117 Figure 129: Joint 14 Screening DOE Sensitivity Plots ........................................................................................................................118 Figure 130: Joint 15 Screening DOE Sensitivity Plots ........................................................................................................................118 Figure 131: Phase 1 Joint 2 Boxed to Lipped Channel.......................................................................................................................120 Figure 132: Phase 1 Joint 2A Full Boxed to Lipped Channel .............................................................................................................121 Figure 133: Phase 1 Joint 2A Full Boxed to Lipped Channel (view 1)................................................................................................122 Figure 134: Phase 1 Joint 2A Full Boxed to Lipped Channel (view 2)................................................................................................122 Figure 135: Phase 1 Joint 2A Full Boxed to Lipped Channel (view 3)................................................................................................123 Figure 136: Main Effect Plot for Phase 1 Joint 2A Full Boxed to Lipped Channel Stiffness Kθz.........................................................124 Figure 137: Main Effect Plot for Phase 1 Joint 2A Full Boxed to Lipped Channel Stiffness Kθx.........................................................125 Figure 138: Main Effect Plot for Phase 1 Joint 2A Full Boxed to Lipped Channel Stiffness Kθy.........................................................126 Figure 139: Phase 1 Joint 2A Joint Stiffness Toolbox Spreadsheet Input and Calculated Results....................................................127 Figure 140: Phase 1 Joint 2A Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules.......................................128 Figure 141: Stress versus Strain Curve for Joint 6 Crossmember......................................................................................................129 Figure 142: Stress versus Strain Curve for Joint 6 Siderail ................................................................................................................130 Figure 143: Stress versus Strain Curve for Joint 7 Crossmember......................................................................................................131 Figure 144: Stress versus Strain Curve for Joint 7 Inner Siderail .......................................................................................................132 Figure 145: Stress versus Strain Curve for Joint 7 Outer Siderail ......................................................................................................133 Figure 146: Joint 6: Hat Section to Channel Section (view 1).............................................................................................................134 Figure 147: Joint 6: Hat Section to Channel Section (view 2).............................................................................................................135 Figure 148: Joint 7: Hat Section (with Bracket) to Twin Channel Sections (view 1) ...........................................................................136 Figure 149: Joint 7: Hat Section (with Bracket) to Twin Channel Sections (view 2) ...........................................................................137

Report: A/SP-005-2 Light Truck Frame Joint Study ix


Figure 150: Joint 7: Hat Section (with Bracket) to Twin Channel Sections (view 3) ...........................................................................138 Figure 151: Joint 8: Rectangular Tube Section to Rectangular Tube Section (view 1) ......................................................................139 Figure 152: Joint 8: Rectangular Tube Section to Rectangular Tube Section (view 2) ......................................................................140 Figure 153: Joint 9: Circular Tube Section through Channel Section (view 1) ...................................................................................141 Figure 154: Joint 9: Circular Tube Section through Channel Section (view 2) ...................................................................................142 Figure 155: Joint 10: Rectangular Tube Section Through Rectangular Tube Section (view 1) ..........................................................143 Figure 156: Joint 10: Rectangular Tube Section Through Rectangular Tube Section (view 2) ..........................................................144 Figure 157: Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section (view 1)......................................................145 Figure 158: Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section (view 2)......................................................146 Figure 159: Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section (view 3)......................................................147 Figure 160: Joint 12: Deep Hat Section to Rectangular Tube Section (view 1)..................................................................................148 Figure 161: Joint 12: Deep Hat Section to Rectangular Tube Section (view 2)..................................................................................149 Figure 162: Joint 13: Full Height Channel Section to Rectangular Tube Section (view 1) .................................................................150 Figure 163: Joint 13: Full Height Channel Section to Rectangular Tube Section (view 2) .................................................................151 Figure 164: Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section (view 1) ..................................................152 Figure 165: Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section (view 2) ..................................................153 Figure 166: Joint 15: Full Height Channel Section to Channel Section (view 1).................................................................................154 Figure 167: Joint 15: Full Height Channel Section to Channel Section (view 2).................................................................................155

Report: A/SP-005-2 Light Truck Frame Joint Study x

ACKNOWLEDGMENTS EXECUTIVE SUMMARY

Altair would like to acknowledge the following members of the A/SP Lightweight SUV Frames Project Team for their valuable assistance in establishing Phase 2 of study, and guiding it to a successful conclusion.

Gary Banasiak General Motors Corporation

Ravir Bhatnagar Ispat Inland Inc.

John Caito The Budd Company

Jim Cran Cran Associates Inc.

Ted Diewald Auto/Steel Partnership

Mike Gulas Dofasco Inc.

Tom Hedderly Ford Motor Company

Ed Law DaimlerChrysler Corporation

Marek Marchwica Stelco Inc.

Jim O’Connor Vehma International of America

David Ruhno United States Steel Corporation

Michael Shih United States Steel Corporation

Altair would like to make special mention of the following who provided the test joints and CAD data used in Phase 2:

Gary Banasiak General Motors Corporation

Report: A/SP-005-2 Light Truck Frame Joint Study 1

PHASE 2 JOINTS SUMMARY CUTIVE SUMMARY

Two riveted joints (Figure 1and Figure 2) and eight welded joints (Figure 3 through Figure 10) were considered in the Phase 2 Study. The following figures are pictorial illustrations of those joints. Descriptions of the Joints are given in Appendix F.

Figure 1: Joint 6: Hat Section to Channel Section

Figure 2: Joint 7: Hat Section (with Bracket) to Twin Channel Sections



Figure 3: Joint 8: Rectangular Tube Section to Rectangular Tube Section

Figure 4: Joint 9: Circular Tube Section through Channel Section

Figure 5: Joint 10: Rectangular Tube Section through Rectangular Tube Section



Figure 6: Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section

Figure 7: Joint 12: Deep Hat Section to Rectangular Tube Section

Figure 8: Joint 13: Full Height Channel Section to Rectangular Tube Section



Figure 9: Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section

Figure 10: Joint 15: Full Height Channel Section to Channel Section


RIVETED JOINT TESTING CUTIVE SUMMARY

Introduction

Two riveted joints (displayed in Figure 11 and Figure 12) were chosen for testing in Phase 2. The Team was confident that welded joints would correlate well based on its experience in Phase 1, but wanted correlation for the two riveted joints. Three samples of each of the two riveted joints were tested to determine the load versus deflection curve using the procedure developed in Phase 1 and documented in SAE Paper 2003-01-0241 [3]. The test results are summarized in stiffness Table 1 (see page number 30).

Figure 11: Joint 6: Hat Section to Channel Section (finite element representation)

Figure 12: Joint 7: Hat Section (with Bracket) to Twin Channel Sections (finite element representation)

Test Specimen (Joint) Description

The physical representation of the two riveted joints considered for testing are displayed in Figure 13, Figure 14, Figure 16 and Figure 17. Rivet attachments for the two riveted joints are displayed in Figure 15 and Figure 18.



Figure 13: Joint 6: Hat Section to Channel Section Physical Representation (isometric view)

Figure 13 displays the sub-components of the riveted Joint 6. The main sub-components are the side rail and crossmember. These two sub-components are joined together using four rivets. The End Plates displayed are part of the test set-up and are used to hold the joint in place when applying the loads. Figure 15 displays a close-up view of the rivet attachments between the side rail and crossmember.

Side Rail

Crossmember

End Plates (part of test set up)

Brackets



Figure 14: Joint 6: Hat Section to Channel Section Physical Representation (rear view)

Side Rail

End Plates (part of test set up)

Brackets



Figure 15: Joint 6: Hat Section to Channel Section Rivet Attachments

Rivets (attachment between crossmember and side rail)

Side Rail

Crossmember



Figure 16: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Physical Representation (front view)

Figure 16 displays the sub-components of the riveted Joint 7. The main sub-components are the following: inner side rail, outer side rail, upper crossmember and outer crossmember. The inner and outer side rails are welded together, as displayed in the figure. This figure also displays the upper welds, but similar welds are in the bottom too (not seen in the picture). The upper and lower crossmembers are welded together, as displayed in the figure. The side rails and crossmembers are attached together with six rivets. Figure 18 displays the rivet attachment scheme employed in attaching the side rails and the crossmembers. The End Plates displayed are part of the test set-up and are used to hold the joint in place when applying the loads.

Upper Crossmember

Lower Crossmember

Inner Side Rail

Outer Side Rail

Welding between Inner and Outer Side Rails

Welding between upper and lower crossmember



Figure 17: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Physical Representation (rear view)

Outer Side Rail

End Plates (part of the test set up)

Inner Side Rail



Figure 18: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Rivet Attachments

Test Specimen (Joint) Preparation

The test joints and the surrounding frame material were removed with a plasma cutter from the frames containing the test joints. Figure 19 displays an area in the frame from which Joint 6 was cut out off. Rough cuts (shown by dotted white line in the figure) were made at a distance far enough from the joint area to avoid changing the material properties of the steel from the high heat. Final cuts at the required distance were performed on a band saw.

Rivets (between side rails and crossmember

Inner Side Rail

Upper Crossmember

Outer Side Rail

Lower Crossmember



Figure 19: Joint 6: Hat Section to Channel Section Specimen Preparation

Test Joint Fixturing

Both the joints were equipped with thick steel plates (3/4-inch thickness) on each end of the side rail and on the end of the crossmember. These plates were welded to the member ends. During test setup, each joint was oriented with the side rail positioned parallel to the ground and the crossmember perpendicular. Longitudinal end plates were bolted to angle brackets that were in turn bolted to a bedplate. This proved to be a sufficiently stiff fixturing method verified by a dial indicator during testing. A steel tube sandwiched between two steel plates was bolted to the crossmember end plate. This allowed force application at a distance away from the joint, increasing deflection to a measurable level while keeping the applied loads to a reasonable level.

Figure 20 and Figure 21 display the complete test set up for the fore-aft and torsional loadcases. The test set up for the vertical loadcase was identical to the fore-aft loadcase, except that the load was applied in a different direction.

Crossmember

Rough-cut mark

Side Rail



Figure 20: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Fore-Aft Loading Setup

Figure 20 displays the typical test set up employed for the Fore-Aft loadcase. Also displayed in the picture is the ‘measurement fixture’ used for measuring the displacement corresponding to the loadcase. Linear Variable Displacement Transducers (LVDTs) were used to measure the displacement. The test set up for the Vertical loadcase is identical to the Fore-Aft loadcase. In the vertical loadcase, however, the load is applied at a different point in the test fixture as displayed in the above figure. Also, the LVDTs are located such that vertical displacements are measured.

Joint

Fore-Aft load application point for that loadcase

Measurement fixture

LVDTs to measure displacements

Vertical load application point in that loadcase



Figure 21: Joint 7: Hat Section (with Bracket) to Twin Channel Sections Torsional Loading Setup

Figure 21 displays the typical test set up employed for the Torsional loadcase. Also displayed in the picture is the ‘measurement fixture’ used for measuring the displacement corresponding to the loadcase. Linear Variable Displacement Transducers (LVDTs) were used to measure the displacement.

Joint

Torsional load (using two pneumatic cylinders)

Measurement fixture



Figure 22: Measurement Fixture used for Joint Testing

Figure 22 displays a close up of the measurement fixture used for the joint testing. This measurement fixture is bolted to the joints along with the load application set up. LVDTs are fastened to this fixture to measure displacement.

Test Joint Deflection Measurement

Deflections were measured using five Linear Variable Displacement Transducers (LVDTs). The Fore-Aft and Vertical loadcases used three transducers to measure deflection. The three transducers were placed parallel to the side rail and were in line with the line of action of the force being applied. The Torsional loadcase used two transducers to measure deflection. Contact points for all the transducers were on additional surfaces that were not receiving any of the applied loads. Figure 22 displays the measurement fixture employed during the testing phase.

Test Joint Force Application

For each load case (Fore-Aft, Vertical and Torsion), the loads were increased to the desired value, reduced back to zero load, and then repeated in the opposite direction. This process was repeated three times for each of the three samples. Air cylinders were used to apply the force on all the joints. Measurements were taken as force was increased to maximum, decreased back to zero, increased to maximum in the opposite direction and then decreased back to zero to provide a continuous hyterisis loop. Figure 20 and Figure 21 displays the typical test set up employed during the testing phase.

Bar for measuring torsional deflections

Bar for measuring fore-aft and vertical

deflections

Fore-Aft load application point

Vertical load application point

Torsional load application

Plate bolted to the joint



Joint 6 Testing

The displacement for each test was measured at increments as the joint was cyclically loaded and unloaded (see Appendix A for all test data plots). The average slope of the measured displacement was fit and used to calculate the joint’s stiffness. An explanation and example of this process is described below.

The test results were evaluated for repeatability. Figure 23 displays the test data for Joint 6 in the Fore-Aft loadcase. Three samples of Joint 6 were tested and three tests were conducted on each sample.

Figure 23: Joint 6 Fore-Aft Loadcase Test Data

Test Data (3 samples and 3 tests for each sample)



The test data was averaged over the 9 curves (3 samples and 3 tests for each sample). Figure 24 displays the comparison between the average linear fit test data and final FEA model results (see Rivet Joint Correlation section) for the Fore-Aft loadcase for Joint 6.

Figure 24: Joint 6 Fore-Aft Loadcase Analysis and Test Data Comparison

Test Data - Average Linear Fit

Analysis Data

Average Linear Fit Test Data



The Vertical and Torsional loadcases were evaluated in the same way as the Fore-Aft loadcase. The vertical loadcase plots are displayed in Figure 25.

Figure 25: Joint 6 Vertical Loadcase Analysis and Test Data Comparison

Analysis Data





Joint 7 Testing

The method used to evaluate the stiffness of Joint 6 was also used to evaluate the stiffness of Joint 7 (see Figure 26, Figure 27 and Figure 28). See Appendix A for all test data plots.

Figure 26: Joint 7 Vertical Loadcase Test Data





Figure 27 displays the comparison between analysis data and average linear fit test data for Joint 7 in the Vertical loadcase.

Analysis Data





Figure 28 displays the test data, average linear fit test data and analysis data of the Vertical loadcase for Joint 7.

Repeatability of Riveted Joints

Each joint sample was tested three times in each of the loading directions. Good repeatability across the 3 tests for each sample was achieved, which indicates that testing was performed in a consistent manner.

Rivet Diagnostic Testing

Though test repetability was achieved across the 3 tests for a given sample, there were differences in the test data among the 3 samples for a given joint.

Analysis Data

Test Data




For instance, Figure 29 shows there was significant difference in the test data between the three samples for the Joint 6 Fore-Aft loadcase.

Figure 29: Joint 6 Fore-Aft Loadcase Test Data Repeatability

In total, there are nine curves (three samples and three tests per sample) displayed in Figure 29. Although test-to-test variation (per sample) is insignificant, sample-to-sample variation is significant. The curves in Figure 29 are delineated into three sections, A, B and C. Section A and C correspond to the extremeties of loading and Section B corresponds to the on-center loading. Moreoever, Section A relates to the negative loading direction and Section C relates to the positive loading direction.

The following points are noted based on the observation of the test data displayed in Figure 29.

• Section A indicates that sample-to-sample variation is significant.

• Section B indicates that the slope in the +/- 1000N load range is not consistent with the slopes beyond that range. The higher slope indicates that the samples are more compliant. Compliant is defined as the ratio of resultant displacement to the applied force, i.e., high compliance implies that the joint displaces more for a given amount of force than a less compliant joint. In other words, compliance is the inverse of stiffness.

Section - B

Section - A

Section - C



• Sections A and C indicate similar and consistent slopes beyond the +/- 1000N load range.

This behavior was identified more in the Fore-Aft loadcase than in the other two loadcases for both joints.

With significant differences as illustrated in Figure 29, it was evident that further diagnostic testing was requried to better characterize the joint behavior. To understand the underlying phenomenon, one joint sample was chosen and tested. The joint sample chosen was Sample-3 of Joint 7 and the loadcase chosen was Fore-Aft.

Five of the six rivets in Joint 7 (sample 3) were instrumented to track the deflection of the rivets in each of the three directions (X, Y and Z) during the test. Figure 30 shows the five rivets that were tracked during the test. The test setup used was identical to the previous testing and the Fore-Aft loadcase was selected because of the significant variations observed in that loadcase. The sixth rivet could not be observed because of physical constraints.

Figure 30: Joint 7 Fore-Aft Loadcase Test Set up to study Rivets

Test results were plotted for displacements of the rivet, crossmember and side rail inner at two areas, U and V, illustrated in Figure 30. Figure 31, Figure 32 and Figure 33, respectively, show the X, Y and Z direction displacement of the rivets, the crossmember and the side rail inner at area-V. In Figure 33,



Figure 34, and Figure 35, the abcissa corresponds to the load applied to the joint (in lbs.) and the ordinate corresponds to the measured displacement (in mm) of the rivet.

Figure 31: Joint 7 Area-V Rivet X-direction Displacement

X

C1C2

C3

RIVET CROSSMEMBER SIDE RAIL



Figure 32: Joint 7 Area-V Rivet Y-direction Displacement

Y

C1

C2

C3




Figure 33: Joint 7 Area-V Rivet Z-direction Displacement

In Figure 31 throught Figure 33, the curve "C3" (red-colored) represents the displacement of rivet; the curve "C2" (green-colored) represents the displacement of the crossmember; and, the curve "C1" (blue-colored) represents the displacement of side rail inner.

Observing the X-direction displacement data, it is clear that the rivet and side rails do not displace as much as the crossmember. The crossmember not only moves independent of the other two but also has significantly more displacement than the others. Observing the same behavior in Y-direction displacement data, it is also clear that the rivet and crossmember move significantly more than the side rail inner does. It is noted here that the X and Y direction displacements are a direct result of the compliance that exists between the rivet, crossmember and side rail inner. However, the Z-direction displacement of all the three components are consistent with each other. Since the Fore-Aft load is applied via the crossmember, this additional compliance in the crossmember translates into additional deflection of the joint, resulting in lower joint stiffness values in that direction.

Similar behavior is observed at Area U (see Figure 30) of Joint 7 in the Fore-Aft loadcase. Figure 37 displays the X, Y and Z direction displacement test data of the rivet, crossmember and side rail inner at area U of the joint. The other rivet areas did not show significant differences in displacement.

The results were shown to an experienced frame engineer, who looked at the test results and explained that the rivet typically does not expand into the entire hole in all of the riveted joints, due to normal manufacturing variations. Figure 34 illustrates the variations seen in the rivet expansion inside the rivet hole in typical riveted joints.

Z

C1

C2C3




Figure 34: Variations in Rivet Expansion inside Rivet Holes

Figure 35: Joint 7 Area-U Rivet X-direction Displacement

Two thickness rivet

Three thickness rivet

X

C1

C2

C3




Figure 36: Joint 7 Area-U Rivet Y-direction Displacement

Y

C1

C2

C3




Figure 37: Joint 7 Area-U Rivet Z-direction Displacement

Though a real world joint will exhibit this slip behavior, the finite element analysis does not capture this slip mechanism. The test joint stiffness is lower than the finite element data because of the additional compliance in the test joints in the +/- 1000N load range. The test data in the area "off-center" does agree with the finite element data. This behavior was expected by the Team when the riveted joints were added to the matrix. This test work is the first public riveted joint stiffness test data that the team is aware of.

Based on this information, the stiffness for some of the loadcases of the two joints were recalculated. As noted, the slopes of the negative and positive load directions beyond the +/- 1000N range are consistent with each other. Therefore, this slope was used to compute the stiffness and was compared to the stiffness from the finite element analysis (see section on Riveted Joint Correlation). The resultant comparison produced better correlation between the test data and finite element analysis. See A/SP Phase 1 [1] report to understand the formulae employed to compute the stiffness. Table 1 presents the initial and final stiffnesses of Joints 6 and 7.

Z

C1

C2

C3




Table 1: Test Joint Stiffnesses for Joints 6 and 7

Kθθθθx

(kN-m/deg)

Kθθθθz

(kN-m/deg)

Kθθθθy

(kN-m/deg) JOINT DESCRIPTION Initial Final Initial Final Initial Final

Joint 6: Hat Section to Channel Section

14.36 22.06 3.20 3.20 2.85 2.85

Joint 7: Hat Section (with Bracket) to Twin Channel Sections

13.81 26.71 3.07 3.96 2.38 2.38


RIVETED JOINT CORRELATION

Introduction

Finite element analysis (FEA) techniques were used to demonstrate the correlation of each joint. Correlation was attemped for Joints 6 and 7 between the finite element models and test data. The finite element model was created using the CAD data that was supplied. The CAD data was checked against the actual dimensions of the test sample joints to establish dimensional validity of the CAD data. An initial finite element model was created using 2D shell elements (quad and tria types) and 1D rigid elements. The 1D rigid elements were used to establish the riveted connection between the crossmember, siderail and other components. This type of representaion assumes that no relative motion can occur between the components in the riveted joints. Later, for a more accurate representation of the rivets themselves, 3D solid elements were used in the finite element models.

Initial FEA Models

The initial finite element (FEA) models were created for Joints 6 and 7. These are called "initial" because these finite element models used 1D rigid elements to establish riveted connections, i.e., the connections were considered perfect. Figure 38 and Figure 39 show the initial finite element models for Joints 6 and 7.

Figure 38: Joint 6 Initial Finite Element Model

Side Rail

Crossmember

Bracket

Bracket

Bracket



Figure 39: Joint 7 Initial Finite Element Model

The initial finite element models developed for the two joints (6 and 7) were in close agreement with the joint samples established for testing. The rivets were modeled using 1D rigid elements. Figure 40 shows a close-up view of the rivet modeling technique employed in the initial finite element model for both the joints.

Figure 40: Example Rivet Representation in the Initial FEA model

In this figure, components A and B are attached together using a rivet. The circular rivet hole is approximated as a hexagon, which is valid for finite element analysis. Each perpendicular node on component-A (shown in green color) is directly connected to the corresponding node on component-B

Outer Side Rail

Inner Side Rail

Upper Crossmember

Lower Crossmember

Component - A

Component - B (Transparent color)

Rivet attachments using 1D rigid

elements



(shown in transparent color) using 1D rigid elements. This type of modeling technique does not allow for any slippage to occur between the various components or for slippage to occur between the rivets and the components. Table 2 and Table 3 display the stiffness results for the finite element analysis and test samples. The nine curves (three tests for each sample and three samples for each joint) were averaged, and the slope of this averaged curve was reported as stiffness for each of the joint test samples.

Table 2: Joint 6 Stiffness Comparison between Initial FEA and Test Data

LOADCASE ANALYSIS TEST DEVIATION

Fore-Aft (Kθz stiffness, kN-m/deg) 24.18 14.36 41%

Vertical (Kθx stiffness, kN-m/deg) 3.53 3.20 9%

Torsion (Kθy stiffness, kN-m/deg) 3.53 2.85 19%

Table 3: Joint 7 Stiffness Comparison between Initial FEA and Test Data





Model Changes to Improve Correlation

It is evident from Table 2 and Table 3 that the correlation is good in some loadcases but poor in a majority of the other loadcases for the two joints. Reviewing the FEA animation results indicated that there were three possible areas of improvement, which are listed below.

• Effect of end boundary conditions.

• Effect of applying loads at the shear center.

• Rivet and its hole modeling accuracy.

Further analysis was performed on both the joints to demonstrate the effects from the boundary conditions variation or effects from not applying loads at the shear center. All analyses for both the joints pointed to the fact that there was no significant improvement in correlation between the analysis and test data. The only possible area remaining for improvement was the rivets themselves, since the rivets were idealized in the initial FEA model. Therefore, more information was requested on the rivets in order to improve modeling accuracy and to increase correlation. The rivet and its hole dimensions were obtained from the rivet manufacturer and the rivet processing techniques were understood. The relevant rivet dimensions for the Joints 6 and 7 are displayed in Table 4.



Table 4: Rivet and Rivet Hole Dimensions for Joints 6 and 7

Rivet Diameter 9.6 mm

Rivet Hole Diameter 10.8 mm

Final FEA Models

Changes from the Initial FEA model were incorporated into the Final FEA model. Notably, the rivets were more accurately modeled using the available rivet information (see Table 4). 3D solid elements were used to model the rivet of diameter 9.6mm while the rivet hole was maintained at the prescribed test joint sample diameter of 10.8mm. Apart from the rivet modeling technique, there was no difference between the Initial and Final FEA models. Figure 41 displays the close-up view of the modified rivet modeling technique used for the Final FEA model for both the joints.

Figure 41: Example Rivet Representation in the Final FEA model

Component - A

Component - B

Rivet (modeled using 3D solid elements)

1D rigid element for attachment



Figure 43, below, displays the 3D solid model of the rivet used in the analyses to improve correlation. This figure shows only the rivet and the rivet holes are in the individual components that make up the joint. The 3D rivet model fits inside the rivet holes with attachments to the individual components at those points shown by RBE2 elements. These RBE2 elements establish rigid connection between the 3D rivet and the individual components of the joint.

Figure 42: Rivet 3D-Solid Elements used in the Final FEA model

Figure 43 displays the 3D graphical illustration of the rivet.

3D solid element model of the Rivet

1D rigid elements to connect rivet to other Components

Rivet Diameter

Rivet Height



Figure 43: Rivet 3D Graphical Illustration

Final Correlation between FEA and Test Data

The FEA analyses were performed and the analyses results were once again correlated to the test data as shown in Table 5 and Table 6.

Table 5: Joint 6 Stiffness Comparison between Final FEA and Test Data


Fore-Aft (Kθz stiffness, kN-m/deg) 22.09 22.06 0.12%



Rivet Diameter

Rivet Height



Table 6: Joint 7 Stiffness Comparison between Final FEA and Test Data





The correlation was good between the final FEA models and the test data. As indicated in the Phase 1 report, deviations of up to thirty percent are acceptable. In the two joints considered here, the percentage deviation between analysis and test data is well under thirty percent.

It is noted here that the stiffnesses from testing for Joints 6 and 7 were recomputed. The information presented in the Rivet Diagnostic Testing sub-section (see Riveted Joint Testing section) explains why the stiffnesses for the test data were recomputed. Referring to Table 2, Table 3, Table 5 and Table 6 (all four stiffness tables), the Fore-Aft loadcase test stiffnesses were recomputed for both the joints and the Vertical loadcase test stiffness was recomputed for Joint 7 only. The Torsional loadcase stiffnesses correlated well with the finite element data, and therefore it was not recomputed for both the joints.


JOINT STIFFNESS SUMMARY

The following section presents the joint stiffness results for all the eleven joints considered in this study. The three stiffness values correspond to the fore-aft (Kθθθθz), vertical (Kθθθθx) and torsional (Kθθθθy) loadcases.

Table 7: Stiffness Summary for all Joints

JOINT DESCRIPTION Vertical Load

Kθθθθx

(kN-m/deg)

Fore-Aft Load Kθθθθz

(kN-m/deg)

Torsion Load Kθθθθy

(kN-m/deg) Analysis:

K2 = 22.09 K2 = 3.24 K2 = 3.01

K1 = 7.34 K1 = 1.08 K1 = 1.03

Test:


22.06 3.20 2.85

Analysis:

K2 = 30.64 K2 = 4.44 K2 = 2.14

K1 = 10.22 K1 = 1.48 K1 = 0.72

Test:


26.71 3.96 2.38

Joint 8: Rectangular Tube Section to Rectangular Tube Section

0.31 1.40 4.66

Joint 9: Circular Tube Section through Channel Section

0.32 0.69 13.40



Joint 10: Rectangular Tube Section Through Rectangular Tube Section

11.20 1.86 6.69

Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section

7.41 0.95 12.15

Joint 12: Deep Hat Section to Rectangular Tube Section

2.31 2.65 0.69

Joint 13: Full Height Channel Section to Rectangular Tube Section

0.72 9.36 1.00

Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section

1.57 8.22 7.27



Joint 15: Full Height Channel Section to Channel Section

0.70 4.98 0.98

Joint 2A: Full Box to Lipped Channel

3.26 4.38 39.46


SENSITIVITY STUDY

Introduction

An important requirement of the study was to establish a set of frame joint Design Rules. By using FEA, we were able to establish guidelines for the ten joint types included in Phase 2 of the study. The designer will be able to use the Design Rules to predict the stiffness of a joint that is similar to one of the ten types in the study.

Study Models

To normalize the joints for the sensitivity study, the joint models needed to be modified. Geometric factors of the joint’s surrounding structure were removed to eliminate its influence on the joint stiffness. These changes included straightening out the crossmember and side rail. Figure 44 shows the modified joint geometry compared to the original for Joint 6.

Figure 44: Example of Original Joint 6 Geometry (left) vs. Modified Joint 6 Geometry for Study (right)

The study models for the ten joints in Phase 2 are shown in Appendix B. Joint 2, included in Phase 1 of the study, was slightly simplified as explained in Appendix D. A study model was prepared for the simplified joint (Joint 2A). The study model for Joint 2A is shown in Appendix D.

Joint Parameters

The joint parameter variables are component thickness and shape. The thickness of each of the joint components is allowed to vary within a certain range for each joint. The shape variables include:

• Side rail height

• Side rail width

• Crossmember height

• Crossmember width


SENSITIVITY STUDY

• Flange width

• Crossmember placement height on side rail

An initial screening study was conducted to determine the key parameters. That is, the ones having the greatest effect on stiffness (Appendix C). The influence of the key parameters on the stiffness of each joint for each load case is shown in Figure 45 through Figure 77. For each plot, the Y-axis shows the relative stiffness. The X-axis, for each component listed, shows how the stiffness varied over the range of values allowed for each parameter. For example, the point furthest left of a parameter’s plotted line would be the minimal allowed value for that parameter, and the point furthest right of the line would be the stiffness at the upper value for the specified parameter. For the crossmember thickness in Figure 45, the stiffness is 39 when the crossmember thickness is lowest at 2mm and the stiffness of the joint is 60 when the crossmember thickness is 5 mm.

Figure 45: Main Effect Plot for Joint 6: Hat Section to Channel Section Stiffness Kθz

Large Influence on Stiffness

Small Influence on Stiffness

Main Effects: Joint 6

Stiffness Kθθθθz


SENSITIVITY STUDY

Figure 46: Main Effect Plot for Joint 6: Hat Section to Channel Section Stiffness Kθx


Stiffness Kθθθθx


SENSITIVITY STUDY

Figure 47: Main Effect Plot for Joint 6: Hat Section to Channel Section Stiffness Kθy


Stiffness Kθθθθy


SENSITIVITY STUDY

Figure 48: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθz (Design Variables from 1 through 7)




SENSITIVITY STUDY

Figure 49: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθx (Design Variables from 1 through 7)




SENSITIVITY STUDY

Figure 50: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθy (Design Variables from 1 through 7)




SENSITIVITY STUDY

Figure 51: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθz (Design Variables from 8 through 15)




SENSITIVITY STUDY

Figure 52: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθx (Design Variables from 8 through 15)




SENSITIVITY STUDY

Figure 53: Main Effect Plot for Joint 7: Hat Section (with Bracket) to Twin Channel Sections Stiffness Kθy (Design Variables from 8 through 15)




SENSITIVITY STUDY

Figure 54: Main Effect Plot for Joint 8: Rectangular Tube Section to Rectangular Tube Section Stiffness Kθz




SENSITIVITY STUDY

Figure 55: Main Effect Plot for Joint 8: Rectangular Tube Section to Rectangular Tube Section Stiffness Kθx




SENSITIVITY STUDY

Figure 56: Main Effect Plot for Joint 8: Rectangular Tube Section to Rectangular Tube Section Stiffness Kθy




SENSITIVITY STUDY

Figure 57: Main Effect Plot for Joint 9: Circular Tube Section through Channel Section Stiffness Kθz




SENSITIVITY STUDY

Figure 58: Main Effect Plot for Joint 9: Circular Tube Section through Channel Section Stiffness Kθx




SENSITIVITY STUDY

Figure 59: Main Effect Plot for Joint 9: Circular Tube Section through Channel Section Stiffness Kθy




SENSITIVITY STUDY

Figure 60: Main Effect Plot for Joint 10: Rectangular Tube Section Through Rectangular Tube Section Stiffness Kθz




SENSITIVITY STUDY

Figure 61: Main Effect Plot for Joint 10: Rectangular Tube Section Through Rectangular Tube Section Stiffness Kθx




SENSITIVITY STUDY

Figure 62: Main Effect Plot for Joint 10: Rectangular Tube Section Through Rectangular Tube Section Stiffness Kθy




SENSITIVITY STUDY

Figure 63: Main Effect Plot for Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section Stiffness Kθz




SENSITIVITY STUDY

Figure 64: Main Effect Plot for Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section Stiffness Kθx




SENSITIVITY STUDY

Figure 65: Main Effect Plot for Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section Stiffness Kθy




SENSITIVITY STUDY

Figure 66: Main Effect Plot for Joint 12: Deep Hat Section to Rectangular Tube Section Stiffness Kθz




SENSITIVITY STUDY

Figure 67: Main Effect Plot for Joint 12: Deep Hat Section to Rectangular Tube Section Stiffness Kθx




SENSITIVITY STUDY

Figure 68: Main Effect Plot for Joint 12: Deep Hat Section to Rectangular Tube Section Stiffness Kθy




SENSITIVITY STUDY

Figure 69: Main Effect Plot for Joint 13: Full Height Channel Section to Rectangular Tube Section Stiffness Kθz




SENSITIVITY STUDY

Figure 70: Main Effect Plot for Joint 13: Full Height Channel Section to Rectangular Tube Section Stiffness Kθx




SENSITIVITY STUDY

Figure 71: Main Effect Plot for Joint 13: Full Height Channel Section to Rectangular Tube Section Stiffness Kθy




SENSITIVITY STUDY

Figure 72: Main Effect Plot for Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section Stiffness Kθz




SENSITIVITY STUDY

Figure 73: Main Effect Plot for Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section Stiffness Kθx




SENSITIVITY STUDY

Figure 74: Main Effect Plot for Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section Stiffness Kθy




SENSITIVITY STUDY

Figure 75: Main Effect Plot for Joint 15: Full Height Channel Section to Channel Section Stiffness Kθz




SENSITIVITY STUDY

Figure 76: Main Effect Plot for Joint 15: Full Height Channel Section to Channel Section Stiffness Kθx




SENSITIVITY STUDY

Figure 77: Main Effect Plot for Joint 15: Full Height Channel Section to Channel Section Stiffness Kθy




TOOLBOX

Introduction

A design experiment was run using Altair HyperStudy [4]. The experiment considered the linearity of the joint parameters and the interactions between them on the joint stiffness. The mathematical response of each joint was programmed into an Excel spreadsheet. Designers and engineers will be able to enter joint dimensions, thickness, and any discrete variables simulated in the DOE, and obtain calculated joint stiffnesses. The Excel spreadsheet allows the user to input any joint definition that is within the DOE experiment range.

The spreadsheets also contain Design Rules and Observations to be considered when making design decisions. The Design Rules were created from finite element and sensitivity analysis data to help make stiffer joints. The Joint Observations contained information regarding joint deflection and welding information stemming from the analytical results.

The spreadsheet for each of the ten joints in Phase 2 of the study is shown in Figure 79 through Figure 98. The spreadsheet for Joint 2A is shown in Appendix D. There are two figures for each joint. The first figure shows the input and calculated results for the joint stiffness, and the second figure shows the Joint Observations, Notes and Design Rules.

Bi-linear Stiffness for Riveted Joints 6 and 7

In Appendix A, it may be observed that the riveted Joints 6 and 7 exhibit different stiffness at different load ranges. The stiffness between the +/- 1000N load range is consistenly less than that in the load range beyond +/- 1000N load. It was imperative to capture this behavior in the toolbox since a physical joint is expected to behave in just the same manner. To account for this bi-linear stiffness in the toolbox, it was decided to provide two stiffness values. The first stiffness value corresponds to the operation of the joint in the +/- 1000N load range and the second stiffness value corresponds to the load range beyond +/- 1000N. The actual stiffness of the joint should fall within the two stiffness values.

Figure 78 displays the general bi-linear nature of the stiffness for the two riveted joints. In the figure, it is shown that the stiffnesses K1 and K2 represent the stiffness of the joint. K1 is the stiffness of the joint when it is operated beyond the +/- 1000N load and K2 is the stiffness when it is operated within the +/-1000N load. It is clear from the figure that stiffness K1 will always be greater than K2. We determined from joint test data that the ratio of the two stiffness was constant:

In the above equation, the "constant" is derived from the test data and it is specific to each joint. In the toolbox, the stiffness K1 is calculated using the DOE results. To determine stiffness K2, the following equation is used.

constant2

1 =K

K

constant1

2

KK =


TOOLBOX

Figure 78: Bi-Linear Joint Stiffness for Rivet Joints 6 and 7


TOOLBOX

Figure 79: Joint 6 Joint Stiffness Toolbox Spreadsheet Input and Calculated Results



TOOLBOX

Figure 80: Joint 6 Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules

Side Rail thickness

beyond +/- 1000

.

actual stiffness

The calculated stiffnesses will be


TOOLBOX




TOOLBOX


which to input

stiffnesses will be displayed in red.

beyond 1000

.

actual stiffness of the


TOOLBOX


Joint 8


TOOLBOX


in which to input calculated stiffnesses


TOOLBOX


Joint 9: Circular Tube Section through Channel Section


TOOLBOX


in which

stiffnesses will be

a tubular section.


TOOLBOX


Joint 10:


TOOLBOX


in which stiffnesses will be

because the crossmember is welded to siderail on both front and back vertical walls.

back) deflect a lot.

* Taller Siderail will worsen the stiffness because the vertical walls do not get support from the top and bottom horizontal walls.


TOOLBOX


Joint 11:


TOOLBOX


in which to input and evaluate data, case 1 and case 2. The calculated stiffnesses will be displayed in red.

Lower side Rail deflects moderately.

Side Rail front vertical wall deflects a lot.

Not much side rail or cap deflection is observed

cap as thick as possible.


TOOLBOX


Joint 12:


TOOLBOX



a lot.

of the joint.


TOOLBOX


Joint 13: Full Height Channel Section to Rectangular Tube Section


TOOLBOX




TOOLBOX


Joint 14:


TOOLBOX




TOOLBOX


Joint 15: Full Height Channel Section to Channel Section


TOOLBOX



* There is a lot of flange deflection.


REFERENCES

1. Lewis, Katy; Spencer, Christian; White, Michael: “Light Truck Frame Stiffness Study”, Auto/Steel Partnership, Report No. A/SP-005-1, July 25, 2001.

2. Altair Engineering, Inc.: “Joint Stiffness Toolbox”, Excel Spreadsheet, Auto/Steel Partnership, July 2001.

3. Spencer, Christian; Vartanian, Katy; White, Michael; Law, S.Edward: “Light Truck Frame Joint Stiffness Study”, Society of Automotive Engineers Paper 2002-01-0241.

4. Altair Engineering, Inc.: Hyperstudy, 2002.

5. A/SP Website http://www.a-sp.org.


APPENDIX A: TEST DATA PLOTS

The following figures are the plots of all the test data for the two joints (Joint 6 and 7).

Figure 99: Joint 6 Fore-Aft Loadcase Displacement-1




Figure 101: Joint 6 Vertical Loadcase Displacement-1




Figure 103: Joint 6 Torsional Loadcase Displacement-1















APPENDIX B: DESIGN VARIABLES

The figures in this appendix illustrate the joint design variables that were considered for the final DOE study. These are the same design variables (shape and thickness) that are included in the joint stiffness toolbox.

(All dimensions are measured from midplane to midplane.)

Figure 111: Joint 6 Final DOE Design Variables









(Measured to the bottom of the Rectangular Tube Section.)





(Measured to the bottom of the Circular Tube Section.)





(Measured to the bottom of the Rectangular Tube Section.)






















APPENDIX C: SCREENING DOE STUDY

Screening DOE Study

Before performing the final design of experiments (DOE) study, an initial screening DOE study was performed to study the influence of design parameters on joint stiffness. Screening the design parameters helped to eliminate those that did not contribute much to the stiffness of the joints. This section of the report presents the results of the screening DOE and lists those parameters that were eliminated from or added to the final DOE study.

Figure 121: Joint 6 Screening DOE Sensitivity Plots




















Based on the sensitivity information from this screening DOE study, the following parameters were either eliminated from the screening DOE study or added to the final DOE study.

Table 8: Design Variables Eliminated / Added from Screening DOE

JOINT DESIGN PARAMETER ELIMINATED / ADDED

Joint 6 Bottom Rear Patch Gage (eliminated).

Joint 7 None eliminated.

Joint 8 Crossmember Top/Bottom Flange Width (added).



Joint 11 Cap Width on Side Rail (eliminated).

Cap Flange Width in Contact with Side Rail (eliminated).

Crossmember Flange Contact Length (eliminated).

Diameter of Hole in the Crossmember (eliminated).

Joint 12 Dimple Height (eliminated).

Dimple Length (eliminated).

Crossmember Lower Flange Width on Side Rail (eliminated).

Crossmember Upper Flange Width on Side Rail (eliminated).

Joint 13 Crossmember Horizontal Weld Flange Width Top/Bottom (added).




APPENDIX D: PHASE 1 JOINT 2A DOE

Joint 2 from Phase 1 was modified and a new version, hereafter referred to as Joint 2A, was developed. The same DOE analysis was performed on this joint and this appendix documents the results from that study. Figure 131 displays the original Joint 2 from the Phase 1 study. Figure 132 displays the new Joint 2A.

Figure 131: Phase 1 Joint 2 Boxed to Lipped Channel



Figure 132: Phase 1 Joint 2A Full Boxed to Lipped Channel

Observe from Figure 132 and Figure 136 that the only modification to the new joint consists of the Side Rail being closed off by Plate B, thereby creating a box section.



Figure 133: Phase 1 Joint 2A Full Boxed to Lipped Channel (view 1)


Side Rail End Square (A)

Side Rail Plate

Side Rail C Channel

Crossmember

Indicates Weld

Indicates Weld




Figure 136 through Figure 138 display the main effects on stiffness of the various parameters for Joint 2A.

Figure 139 and Figure 140 display the Toolbox and Design Rules respectively for Joint 2A.

Indicates Weld



Figure 136: Main Effect Plot for Phase 1 Joint 2A Full Boxed to Lipped Channel Stiffness Kθz

Main Effects: Joint 2A




Figure 137: Main Effect Plot for Phase 1 Joint 2A Full Boxed to Lipped Channel Stiffness Kθx





Figure 138: Main Effect Plot for Phase 1 Joint 2A Full Boxed to Lipped Channel Stiffness Kθy





Figure 139: Phase 1 Joint 2A Joint Stiffness Toolbox Spreadsheet Input and Calculated Results

Joint 2A:



Figure 140: Phase 1 Joint 2A Joint Stiffness Toolbox Spreadsheet Joint Observations and Design Rules

The calculated stiffnesses


APPENDIX E: MATERIAL TEST RESULTS

Tension testing was performed on the coupons cut from the joint materials. The tension testing was done as per the ASTM E8 standard. The results of this testing are presented in the form of Stress versus Strain curve. Figure 141, Figure 142, Figure 143, Figure 144 and Figure 145 display the Stress versus Strain data for the coupons cut from Joint 6 crossmember, Joint 6 siderail, Joint 7 crossmember, Joint 7 inner siderail and Joint 7 outer siderail respectively.

Figure 141: Stress versus Strain Curve for Joint 6 Crossmember



Figure 142: Stress versus Strain Curve for Joint 6 Siderail



Figure 143: Stress versus Strain Curve for Joint 7 Crossmember



Figure 144: Stress versus Strain Curve for Joint 7 Inner Siderail



Figure 145: Stress versus Strain Curve for Joint 7 Outer Siderail


APPENDIX F: PHASE 2 JOINTS DESCRIPTION

This appendix describes the 10 joints in greater detail.

Figure 146: Joint 6: Hat Section to Channel Section (view 1)

Crossmember

Side Rail



Figure 147: Joint 6: Hat Section to Channel Section (view 2)

Rivet

Rivet

Rivet

Rivet

Crossmember

Side Rail



Figure 148: Joint 7: Hat Section (with Bracket) to Twin Channel Sections (view 1)

Inner Side Rail

Outer Side Rail

Upper Crossmember

Lower Crossmember




Rivet

Rivet

Rivet

Rivet

Rivet Rivet

Welding between Lower and Upper Crossmembers

Inner Side Rail

Outer Side Rail

Upper Crossmember

Lower Crossmember




Welding between Outer and Inner

Side Rails

Welding between Outer and Inner Side Rails



Figure 151: Joint 8: Rectangular Tube Section to Rectangular Tube Section (view 1)

Welding between Side Rail and Crossmember

Rectangular Tube Section




Figure 152: Joint 8: Rectangular Tube Section to Rectangular Tube Section (view 2)

Welding between Side Rail and Crossmember





Figure 153: Joint 9: Circular Tube Section through Channel Section (view 1)

Circular Tube Channel Section

Welding between Circular Tube and Channel Sections



Figure 154: Joint 9: Circular Tube Section through Channel Section (view 2)

Welding between Circular Tube and Channel Sections

Tube Section

Channel Section



Figure 155: Joint 10: Rectangular Tube Section Through Rectangular Tube Section (view 1)

Rectangular Tube Section Rectangular

Tube Section

Welding between the two rectangular sections



Figure 156: Joint 10: Rectangular Tube Section Through Rectangular Tube Section (view 2)

Welding between the two rectangular sections





Figure 157: Joint 11: Rectangular Tube Section (Angled) to Rectangular Tube Section (view 1)



(Angled)

Welding between the two

rectangular sections






(Angled)

Cap

Welding between Cap and Tube

Section




Welding between the two Sections


(Angled)




Figure 160: Joint 12: Deep Hat Section to Rectangular Tube Section (view 1)


Deep Hat Section




Figure 161: Joint 12: Deep Hat Section to Rectangular Tube Section (view 2)



Deep Hat Section



Figure 162: Joint 13: Full Height Channel Section to Rectangular Tube Section (view 1)


Full Height Channel Section

Welding between two

sections



Figure 163: Joint 13: Full Height Channel Section to Rectangular Tube Section (view 2)



Welding between two sections



Figure 164: Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section (view 1)


Full Height Rectangular Tube Section




Figure 165: Joint 14: Full Height Rectangular Tube Section to Rectangular Tube Section (view 2)


Full Height Rectangular Tube Section




Figure 166: Joint 15: Full Height Channel Section to Channel Section (view 1)

Channel Section





Figure 167: Joint 15: Full Height Channel Section to Channel Section (view 2)

Channel Section



Documents

Light Truck Frame Joint Stiffness Study