Flexible Follower Response of a Translating Cam with Four Different Profiles for Rise-Dwell-Fall-Dwell motion

Authors: Jer-Rong Chang

Abstract:

The flexible follower response of a translating cam with four different profiles for rise-dwell-fall-dwell (RDFD) motion is investigated. The cycloidal displacement motion, the modified sinusoidal acceleration motion, the modified trapezoidal acceleration motion, and the 3-4-5 polynomial motion are employed to describe the rise and the fall motions of the follower and the associated four kinds of cam profiles are studied. Since the follower flexibility is considered, the contact point of the roller and the cam is an unknown. Two geometric constraints formulated to restrain the unknown position are substituted into Hamilton-s principle with Lagrange multipliers. Applying the assumed mode method, one can obtain the governing equations of motion as non-linear differential-algebraic equations. The equations are solved using Runge-Kutta method. Then, the responses of the flexible follower undergoing the four different motions are investigated in time domain and in frequency domain.

Keywords: translating cam, flexible follower, rise-dwell-falldwell, response

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081467

References:

[1]. Pasin, F., On dynamic stability of followers in cam mechanisms, Mechanism and Machine Theory, 18(2), 1983, 151-155.
[2]. Yilmaz, Y., and Kocabas, H., The vibration of disc cam mechanism, Mechanism and Machine Theory, 30(5), 1995, 695-703.
[3]. Felszeghy, S. F., Steady-state residual vibrations in highspeed, dewll-type, rotating disk cam-follower systems, Transactions of the ASME, Journal of Vibration and Acoustics, 127, 2005, 12-17.
[4]. Teodorescu, M. and Rahnejat, H., Mathematical modelling of layered contact mechanics of cam-tappet conjunction, Applied MathematicallyModelling, 31, 2007, 2610-2627.
[5]. Wu, L. I., Chang, W. T., and Liu, C. H., The design of varying-velocity translating cam mechanisms, Mechanism and Machine Theory, 42, 2007, 352-364.
[6]. Cveticanin, L., Stability of motion of the cam-follower system, Mechanism and Machine Theory, 42, 2007, 1238- 1250.
[7]. Wu, L. I., Liu, C. H., Shu, K. L., and Chou, S. L., Disk cam mechanisms with a translating follower having symmetrical double rollers, Mechanism and Machine Theory, 44, 2009, 2085-2097.
[8]. Naskar, T.K., and Acharyya, S., Measuring cam-follower performance, Mechanism and Machine Theory, 45, 2010, 678-691.
[9]. Chen, F. Y., Mechanics and Design of Cam Mechanisms, Pergamon Press, New York, 1982.