Comparison of Cam and Servomotor Solutions to a Motion Problem A Major Qualifying Project Report: Submitted to the Faculty of the WORCESTER POLYTECHNIC INSTITUTE In partial fulfillment of the requirements for the Degree of Bachelor of Science By Toby Callahan Patrick Hunter Raymond Ranellone Matthew Rhodes Date: Approved: Professor Eben C. Cobb Professor Robert L. Norton 1) Cam 2) Servo This report represents the work of one or more WPI undergraduate students submitted to the faculty as evidence of completion of a degree requirement.WPI routinely publishes these reports on its web site without editorial or peer review. i 1 Abstract The manufacturing lines of the sponsoring company utilize cam‐follower systems where complex motion is required, as they are the traditional means of obtaining such motion. Some equipment utilizing servomechanism actuation has been introduced by the sponsoring company as a potential avenue for the improvement of manufacturing systems. Further insight into the suitability of such mechanisms as replacements for cam‐follower systems was desired. To that end, design and manufacture of a Cam‐Servo Test Machine actuated by either cam‐ follower or servomechanism was undertaken by the project’s participants. The resulting Cam‐ Servo Test Machine was intended to output 200 cycles per minute of a complex reciprocating motion in either mode of actuation. The machine design employed a timing belt speed reduction in its drive train, which had an unintended deleterious impact on system stiffness. A revised design employing a larger servomotor without a speed reduction was developed and analyzed in its stead. The project team concluded that a larger servomotor, directly mounted, can be a suitable replacement for a cam‐follower system at a cost that is several orders of magnitude greater. ii Table of Contents 1 Abstract..........................................................................................................................ii 2 Introduction .................................................................................................................. 1 3 Background ................................................................................................................... 3 3.1 Core Components .................................................................................................. 3 3.1.1 Cam Driven Linkages ....................................................................................... 3 3.1.2 Servomotor Driven Linkages ........................................................................... 4 3.1.3 Cam‐Driven Versus Servomotor‐Driven Mechanisms .................................... 5 3.2 Software Tools ....................................................................................................... 9 3.2.1 Pro/ENGINEER ................................................................................................. 9 3.2.2 Mathcad ........................................................................................................ 10 3.2.3 DYNACAM\LINKAGES .................................................................................... 12 4 Goal Statement ........................................................................................................... 14 5 Task Specifications ...................................................................................................... 15 6 Design ......................................................................................................................... 16 6.1 Linkage Solution .................................................................................................. 16 6.2 Application of Slider Linkage to Design Problem ................................................ 22 6.3 Cam Geometry .................................................................................................... 26 6.4 Linkage Geometry ............................................................................................... 27 6.5 Drive‐Train Selection ........................................................................................... 32 6.5.1 On‐Hand Motors and Speed Reduction ........................................................ 32 6.5.2 Permanent Magnet DC Motor ...................................................................... 33 6.5.4 Kollmorgen AC Servomotor ........................................................................... 36 6.5.5 Timing Belts ................................................................................................... 39 6.5.6 Potential Single‐Motor Drive Trains .............................................................. 40 6.5.7 Potential Two Motor Drive Train .................................................................. 45 6.6 Drive Train Decision ............................................................................................ 45 6.7 Servomotor Analysis ............................................................................................ 46 6.7.1 Inertial Mass Reduction ................................................................................ 51 6.7.2 Transmission Shaft Mass Reduction ............................................................. 53 6.7.3 Theoretical Servomotor Accuracy ................................................................. 53 6.8 Packaging ............................................................................................................. 56 6.8.1 Driving Subassembly ..................................................................................... 57 6.8.1.1 Transmission Shaft ................................................................................. 57 6.8.1.2 Linkage Members ................................................................................... 58 6.8.1.3 Cam and Crank Shafts ............................................................................ 59 6.8.1.4 Slider ....................................................................................................... 60 6.9 Method of Changing Drive Mode ........................................................................ 61 7 Stress Analysis ............................................................................................................ 62 7.1 Tension of Belt on Camshaft Pulley: ................................................................... 64 7.2 Shaft Loading and Stress and Moment Analysis ................................................. 68 7.3 Reaction Forces Exerted by Bearing onto Camshaft ........................................... 71 iii 7.3.1 Shear and Moment Diagrams: ...................................................................... 72 7.3.2 Points of Interest and Stress Cubes: ............................................................. 73 7.4 Shaft Failure Modes and Safety Factors: ............................................................ 77 8 Vibration Analysis (Single‐Motor CSTM) .................................................................... 78 8.1 Vibration Model .................................................................................................. 78 8.2 Mass Model ......................................................................................................... 79 8.3 Spring Model ....................................................................................................... 80 8.4 Damper Model .................................................................................................... 89 8.5 Cam Mode ........................................................................................................... 89 8.6 Results ................................................................................................................. 91 8.6.1 Implications of the Servomotor Driven System on Position Error of the Slider 94 9 Conclusion .................................................................................................................. 96 10 Recommendations .................................................................................................. 97 10.1 Anti‐Backlash Gearbox .................................................................................... 97 10.2 Motor Re‐Selection ........................................................................................ 100 10.3 CSTM Design Changes ................................................................................... 102 10.4 Shaft Coupling and Phase Preservation......................................................... 104 10.5 Additional Considerations ............................................................................. 106 10.6 Vibration Analysis .......................................................................................... 106 10.7 Re‐Design Overview ....................................................................................... 109 11 References ............................................................................................................ 112 12 Bibliography .......................................................................................................... 113 13 Appendix A: Vector Loop Analysis for Fourbar Linkage with zero offset ............. 115 13.1 Position Analysis ............................................................................................ 115 13.2 Velocity Analysis ............................................................................................ 117 13.3 Acceleration Analysis ....................................................................................