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The Multibody Dynamics Module User's Guide

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The Multibody Dynamics Module User's Guide Multibody Dynamics Module User’s Guide Multibody Dynamics Module User’s Guide © 1998–2018 COMSOL Protected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474; 7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patents pending. This Documentation and the Programs described herein are furnished under the COMSOL Software License Agreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the terms of the license agreement. COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trademarks. Version: COMSOL 5.4 Contact Information Visit the Contact COMSOL page at www.comsol.com/contact to submit general inquiries, contact Technical Support, or search for an address and phone number. You can also visit the Worldwide Sales Offices page at www.comsol.com/contact/offices for address and contact information. If you need to contact Support, an online request form is located at the COMSOL Access page at www.comsol.com/support/case. Other useful links include: • Support Center: www.comsol.com/support • Product Download: www.comsol.com/product-download • Product Updates: www.comsol.com/support/updates • COMSOL Blog: www.comsol.com/blogs • Discussion Forum: www.comsol.com/community • Events: www.comsol.com/events • COMSOL Video Gallery: www.comsol.com/video • Support Knowledge Base: www.comsol.com/support/knowledgebase Part number: CM023801 Contents Chapter 1: Introduction About the Multibody Dynamics Module 10 What Can the Multibody Dynamics Module Do? . 10 Where Do I Access the Documentation and Application Libraries? . 11 Overview of the User’s Guide 15 Chapter 2: Multibody Dynamics Modeling The Multibody Dynamics Model 18 Rigid and Flexible Parts . 18 Meshing . 18 Connecting Parts . 19 Gears . 19 Connecting to Other Physics Interfaces . 20 Joints 21 About Joints . 21 Prismatic Joint . 30 Hinge Joint . 31 Cylindrical Joint . 31 Screw Joint . 33 Planar Joint . 34 Ball Joint . 35 Slot Joint . 35 Reduced Slot Joint . 36 Fixed Joint . 37 Distance Joint . 37 Universal Joint . 37 CONTENTS | 3 Attachments 39 Cam-Follower 42 Springs and Dampers 43 Gears 44 About Gears . 44 About Gear Pairs. 46 Gear Geometries 50 Gear Tooth Geometry (External: 2D) . 51 Gear Tooth Geometry (Internal: 2D) . 51 Rack Tooth Geometry (2D) . 52 Spur Gear Geometry (External: 2D) . 53 Spur Gear Geometry (Internal: 2D). 53 Spur Rack Geometry (2D) . 54 Spur Gear Geometry (External: 3D) . 55 Spur Gear Geometry (Internal: 3D). 55 Helical Gear Geometry (External: 3D). 56 Helical Gear Geometry (Internal: 3D) . 57 Bevel Gear Geometry (3D) . 58 Worm Gear Geometry (3D) . 59 Spur Rack Geometry (3D) . 60 Helical Rack Geometry (3D) . 61 Bearings 63 Bearing Modeling . 63 Initialization in Time-Dependent Studies 65 Geometric Nonlinearity 66 Multiphysics Couplings 67 The Fluid-Multibody Interaction Interface . 68 The Fluid-Multibody Interaction, Assembly Interface . 71 4 | CONTENTS Chapter 3: Multibody Dynamics Theory Joint Theory 76 Representation of Rotations . 76 Prismatic Joint Theory . 78 Hinge Joint Theory . 82 Cylindrical Joint Theory . 84 Screw Joint Theory . 86 Planar Joint Theory . 87 Ball Joint Theory . 88 Slot Joint Theory . 89 Reduced Slot Joint Theory . 91 Fixed Joint Theory . 93 Distance Joint Theory . 93 Universal Joint Theory. 94 Theory for Joint Constraints . 97 Theory for Joint Locking . 103 Theory for Springs and Dampers on Joints . 106 Theory for Prescribed Motion on Joints . 108 Theory for Applied Forces and Moments on Joints . 110 Theory for Friction in Joints. 111 Theory for Joint Forces and Moments Computation . 118 Cam-Follower Theory 121 Cam . 121 Follower . 121 Closest Point Determination . 121 Cam with Boundary Selection . 122 Cam with Edge Selection . 123 Cam-Follower Connection Force Computation . 124 Spring-Damper Theory 126 Connection Points and Spring Length . 126 Deactivation . 127 Spring and Damping Forces . 127 Spring and Damping Energies . 128 CONTENTS | 5 Gear Theory 130 Spur Gear Theory . 130 Helical Gear Theory . 132 Bevel Gear Theory . 134 Worm Gear Theory . 135 Spur Rack Theory . 136 Helical Rack Theory. 138 Gear Pair Theory 139 Theory for Gear Pairs . 139 Theory for Worm and Wheel . 147 Theory for Rack and Pinion . 149 Theory for Gear Elasticity . 152 Theory for Transmission Error . 159 Theory for Backlash. 160 Theory for Gear Friction . 162 Chapter 4: Multibody Dynamics The Multibody Dynamics Interface 166 Domain, Boundary, Edge, Point, and Pair Nodes for the Multibody Dynamics Interface. 171 Initial Values . 175 Initially Rigid . 176 Attachment . 177 Rigid Domain . 179 Center of Rotation Nodes . 181 Initial Values (Rigid Domain) . 182 Prismatic Joint . 183 Hinge Joint . 185 Cylindrical Joint . 186 Screw Joint . 187 Planar Joint . 188 Ball Joint . 188 Slot Joint . 189 Reduced Slot Joint . 190 6 | CONTENTS Fixed Joint . 191 Distance Joint . 192 Universal Joint . 193 Joint Elasticity . 195 Constraints . 197 Locking . 199 Spring and Damper . 202 Prescribed Motion . 204 Applied Force and Moment . 206 Friction . 207 Contact Area . 210 Joint Axis. 210 Input Shaft Orientation . 210 Output Shaft Orientation. 211 Center of Joint Nodes . 211 Source Point Nodes. 212 Destination Point Nodes . 212 Source Filter . 213 Destination Filter. 213 Spring-Damper . 214 Source Point (for Spring-Damper) . 215 Destination Point (for Spring-Damper) . 216 Base Motion . 216 Cam-Follower . 217 Spur Gear . 220 Helical Gear. 223 Bevel Gear . 224 Worm Gear . 225 Spur Rack . 226 Helical Rack. 227 Gear Axis . 228 Rack Axis. 228 Gear Pair . 229 Worm and Wheel . 231 Rack and Pinion . 232 Gear Elasticity . 233 Transmission Error . 235 Backlash . 237 CONTENTS | 7 Friction (Gear). ..
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