VIBRATIONS OF CAM MECHANISMS AND THEIR
VIBRATIONS OF CAMMECHANISMS AND THEIRCONSEQUENCES ON THE DESIGN *)BYM. P. KOSTER*) Thesis, Technical University Eindhoven, October 1973.Promotors: Prof. Dr Ir J. D. Janssen and Prof. Ir W. van der Hoek.Philips Res. Repts Suppl. 1973, No. 6.
CONTENTSSYMBOLS1. INTRODUCTION1.1. Mechanisms1.2. Why the interest in the dynamics of cam mechanisms1.3. State of the art1.4. The aim of the present investigation1.5. Survey of the present investigation11239102. MODELLING2.1. Introduction2.2. Degrees of freedom2.2.1. Continuous systems2.2.2. Discrete systems2.2.2.1. Static and dynamic coupling2.2.2.2. Static coupling only2.3. Dynamic model2.3.1. Transmission ratio2.3.2. Addition of motions2.3.3. Dynamic models of machine components2.3.4. Example2.4. Reduction2.4.1. Reduction of linear dimensions2.4.2. Reduction of mass2.4.3. Reduction of stiffness2.4.4. Reduction of a linear, viscous damper2.4.5. Reduction of viscosity2.4.6. Example2.5. Details of the dynamic model2.5.1. Variable transmission ratio tan a2.5.2. Variable magnitudes of m / and c /131313131515252929323333353535363737383840403. SINGLE-DEGREE-OF-FREEDOM MODEL WITH CONSTANTFICTITIOUS ANGULAR VELOCITY3.1. Introduction3.2. Assumptions3.2.1. Constant fictitious angular velocity3.2.1.1. Infinitely rigid camshaft3.2.1.2. Backlash-free transmission3.2.1.3. Constant input angular velocity42424242424343
3.3.3.4.3.5.3.6.3.7.3.8.3.2.2. Lumped mass3.2.3. Decay of residual vibration3.2.4. No damping during cam riseDynamic responseDampingMaximum and zero pointsBacklashMany degrees of freedom3.7.1. Transfer function3.7.2. Natural frequencies3.7.3. ResponseConclusions4. SINGLE-DEGREE-OF-FREEDOM MODEL WITH VARIABLEFICTITIOUS ANGULAR VELOCITY, "CAMSHAFT-1" . . . .4.1. Introduction4.2. Assumptions4.2.1. Constant input angular velocity4.2.2. Constant mass4.2.3. Variable stiffness4.2.4. No damping during cam rise4.2.5. Constant pitch radius4.3. Description of the model4.3.1. Equations4.3.2. Dimensionless numbers4.3.2.1. Introduction4.3.2.2. Definitions4.3.2.3. Dimensionless parameters4.3.2.4. Dimensionless equations4.4. Methods of solution4.4.1. Approximative method4.4.2. Numerical method4.5. Results of the CAMSHAFT-1 program4.5.1. Acceleration phase4.5.2. Deceleration phase4.5.3. Natural frequency4.5.4. Residual vibration4.5.5. Response graphs4.6. Simple method for calculating the lowest natural frequency . .4.7. 061626264646465656666687070717173747477
TWO-DEGREES-OF-FREEDOM MODEL, "CAMSHAFT-2" . .5.1. Introduction". . .5.2. Assumptions5.2.1. Two degrees of freedom5.2.2. Constant input angular velocity5.3. Description of the model5.3.1. Equations5.3.2. Dimensionless numbers5.3.2.1. Definitions5.3.2.2. Dimensionless parameters5.3.2.3. Dimensionless equations5.4. Method of solution5.5. Results of the CAMSHAFT-2 program5.5.1. Shaftflexibility5.5.2. Acceleration phase of the cam rise5.5.3. Deceleration phase of the cam rise5.5.4. Residual vibration5.5.5. Dynamic behaviour of the shaft5.5.6. Response graphs5.5.7. Natural frequencies5.5.7.1. Highest natural frequency5.5.7.2. Lowest natural frequency5.6. Extension to more degrees of freedom5.7. 093949498FOUR-DEGREES-OF-FREEDOM MODEL, "DYNACAM" . .6.1. Introduction6.2. Assumptions6.2.1. Four degrees of freedom6.2.2. Damping6.2.3. Backlash and squeeze6.2.4. Follower jumping6.2.5. Nonconstant angular velocity of the driving machine . .6.3. Numerical calculations6.4. The purpose of the DYNACAM model6.5. Equations of the cam mechanism6.5.1. Input motion6.5.2. Backlash in reduction gear6.5.3. Torsion of the camshaft6.5.4. Deflection of the camshaft parallel to the direction ofmotion of the follower 6
6.5.5.Deflection of the camshaft perpendicular to the directionof motion of the follower roller1066.5.6. Frictional forces acting on the rotating system1066.5.7. Rotation of the cam1076.5.8. Displacement of the cam parallel to the direction of motion of the follower roller1076.5.9. Displacement of the cam perpendicular to the direction ofmotion of the follower roller1076.5.10. Cam curve1076.5.11. Instantaneous slope of the cam curve, instantaneous pitchradius, instantaneous roller displacement, and instantaneous roller velocity1076.5.12. Backlash of the roller in its groove1096.5.13. Deformation of the follower linkageIll6.5.14. External friction of the follower linkage1126.5.15. Motion of the follower output member1136.5.16. Follower spring1136.5.17. External forces1136.5.18. Damping1136.5.19. Integrals1136.5.20. Initial conditions1146.6. Block diagram1176.7. Equations of the asynchronous motor and the reduction gear 1177. ANALYSIS OF MACHINE DYNAMICS7.1. Introduction7.2. Particulars of the test mechanism7.3. Measuring equipment7.4. Follower-response measurements explained by means of simulation7.4.1. Static characteristics7.4.1.1. Backlash7.4.1.2. Stiffness7.4.1.3. Hysteresis7.4.2. Measured dynamic characteristics7.4.3. Simulation with the DYNACAM program7.4.4. Traversing of backlash7.4.5. Damping7.4.6. Squeeze7.4.7. Conclusions7.5. Follower jumping. . . .7.6. Flexible 147147v
8. COMPARISON OF THE RESPONSES OF THE VARIOUSDYNAMIC MODELS WITH THOSE OF REAL MECHANISMS,AND RULES OF DESIGN1518.1. Introduction1518.2. Comparison of the responses of the various dynamic models ofcam mechanisms with those of real mechanisms1518.2.1. Four-degrees-of-freedom model1518.2.2. Damping1568.2.3. Follower spring1568.2.4. Two-degrees-of-freedom model1568.2.5. Single-degree-of-freedom model with variable fictitiousangular velocity1578.2.6. The envelope curve U0{r, Fa)1578.2.7. Constant pitch radius1578.2.8. Conclusions1618.3. Selection of the asynchronous motor1628.4. Alternative cam curves1638.5. Rules of design1688.6. Conclusions1719. CONCLUSIONS AND RECOMMENDED FURTHER INVESTIGATIONS9.1. Conclusions9.2. Recommended further investigations9.2.1. Roller vibration9.2.2. Basic cam curve9.2.3. Damping9.2.4. Dynamic behaviour of the frame9.2.5. Considerations of practical design9.2.6. Dynamic behaviour of multibar linkages172172172172173173174174174APPENDIX 1. Dynamic models of machine components175APPENDIX 2. Nominal characteristics of the cycloidal and the modifiedsine cam curveA.2.1. IntroductionA.2.2. GeneralA.2.3. Cycloidal cam curveA.2.4. Modified sine cam curve179179179180182
APPENDIX 3. Rayleigh's method for the calculation of the lowestnatural frequency184;A.3.1. Introduction184A.3.2. Rayleigh's method184A.3.3. Exact method for lumped masses184A.3.4. Approximative single-degree-of-freedom system185A.3.5. The accuracy of Rayleigh's method in the two-degrees-of-freedom system185A.3.6. Measure of the accuracy of Rayleigh's method186A.3.6.1. Multi-degree-of-freedom systems186A.3.6.2. Intermediate masses exceed the output member mass 188A.3.6.3. Directive for calculation of the lowest natural frequency191APPENDIX 4. SqueezeA.4.1. Two-dimensional, steady-state viscous flowA.4.2. Squeeze192192193APPENDIX 5. Asynchronous motorA.5.1. IntroductionA.5.2. Electromagnetic torqueA.5.3. Equations of the motorA.5.4. Methods of solutionA.5.4.1. Motor considered as a second-order system . . . .A.5.4.1.1. Numerical solutionA.5.4.1.2. Analytical solutionA.5.4.2. Motor considered as a first-order systemA.5.4.3. Comparison of the actual response characteristics ofthe asynchronous motor with those of the variousdynamic modelsA.5.4.3.1. Second-order dynamic modelA.5.4.3.2. Efficiency of the reduction gearA.5.4.3.3. Spring loadA.5.4.3.4. DampingA.5.4.3.5. Analytical calculation, second-order systemA.5.4.3.6. Analytical calculation, first-order system .A.5.4.3.7. Motor-speed variations affecting the camfollower responseA.5.4.3.8. Conclusions195195195197198198198198203APPENDIX 6. Program "DYNACAM"211205205207207207208209209210
APPENDIX 7. Calculations of dynamic modelsA.7.1. IntroductionA.7.2. Indexing mechanismA.7.3. Cam follower mechanismA.7.3.1. Four-degrees-of-freedom modelA.7.3.2. Two-degrees-of-freedom model215215215218218221REFERENCES223
DYNAMIC MODELS WITH THOSE OF REAL MECHANISMS, AND RULES OF DESIGN 151 8.1. Introduction 151 8.2. Comparison of the responses of the various dynamic models of cam mechanisms with those of real mechanisms 151 8.2.1. Four-degrees-of-freedom model 151 8.2.2. Damping 156 8.2.3. Follower
41 Crane Cam 51 Beauty City View 49 Helicopter Cam 37 EFP on Tripod Lift Cam Lift Cam 36 35 47 EFP on Tripod 50 48 40 42 Hard Cam EFP on Tripod 43 EFP on Tripod EFP on Tripod 44 39 45 EFP on Tripod 2 EFP on Tripod 1 4 3 38 EFP on Tripod 41 49 Helicopter Cam 46 Scooter Cam 51 Beauty City View 37 3 KM MASS START M 36 35. 66 50 48 EFP on Tripod 40
AA242B: MECHANICAL VIBRATIONS 1/50 AA242B: MECHANICAL VIBRATIONS Undamped Vibrations of n-DOF Systems These slides are based on the recommended textbook: M. G eradin and D. Rixen, \Mechanical Vibrations: Theory and Applications to Structural Dynamics," Second Edition, Wiley, John & Sons, Incorporated, ISBN-13:9780471975465 1/50
separation of industrial cam-follower systems. Typical industrial cam-follower systems include a force closed cam joint and a follower train containing both substantial mass and stiffness. Providing the cam and follower remain in contact, this is a one degree-of-freedom (DOF) system. It becomes a two-DOF system once the cam and follower
Integrated CAD/CAE/CAM SystemsIntegrated CAD/CAE/CAM Systems Professional CAD/CAE/CAM ToolsProfessional CAD/CAE/CAM Tools - Unigraphics NX (Electronic Data Systems Corp - EDS)-CATIA (Dassault Systems-IBM)- Pro/ENGINEER (PTC) - I-DEAS (EDS) Other CAD and Graphics Packages - AutoCAD Mechanical Desktop / Inventor
Cam follower – standard 16 10.92 Large hydraulic cam follower – 32mm 16 14.95 Cam pulley – standard 2 21.50 RACELINE adjustable vernier pulley kit – pair 1 140.00 Cam pulley bolt 2 1.19 Cam belt 1 25.36 Cam belt tensioner pulley 1 25.2
cam/cran b (figure 2 ls ignition controller harnesses, pn 19355863 ignition (30a fused) h g f e coils 1-3-5-7 coils 2-4-6-8 k cam/crank crank cam/crank cam note: cam plugs directly into sensor, not oem pigtail. 24x crank 1x cam (rear) - included black crank sensor connecto
stud. When mounting the Cam Follower, it is easy to fix its location by tightening a set screw to the stepped por-tion. Thus, this type is suitable when a large number of Cam Followers are used in a machine such as a pallet changer. Cam Follower G Taking over the basic performance of Standard Type Cam Follower, this cam follower realizes a .
Lung anatomy Breathing Breathing is an automatic and usually subconscious process which is controlled by the brain. The brain will determine how much oxygen we require and how fast we need to breathe in order to supply our vital organs (brain, heart, kidneys, liver, stomach and bowel), as well as our muscles and joints, with enough oxygen to carry out our normal daily activities. In order for .
