Influences of System Imperfections on the Performance of Cam-Follower Systems - Kim, Ho-Ryong (My University, 1982)
The cam-follower mechanism is a most important machine element used to control the complicated motion of machine parts, and the accuracy of the motions and subsequent machine performance depends on the cam-follower output. Imperfections in the system affect this output, and an investigation of all possible effects is carried out here through the analytical and simulation means developed.
The imperfections considered here include all factors that cause a design to deviate from the theoretical model. These factors have generally been neglected in the past because of their complexity. They are classified in the following three categories:
1. Geometrical Imperfections
a) Machining or manufacturing errors: Tolerances
b) Backlashes or clearances
2. Kinematic Imperfections
a) Non-constant angular velocity of cam
b) Impossibility of a perfectly manufactured cam profile
c) Asymmetry between rise and return period
3. Dynamic Imperfections
a) Inertial mass
b) Flexibility of system elements
c) Energy dissipation
The performance of the system is indicated by its responses, such as time responses (displacements, velocities and accelerations) and inertial responses (contact forces or stresses, torques and inertia forces).
To investigate the effects of the imperfections, the mechanism of a translating roller follower-cam system driven by a motor through a rigid coupling is simulated on a digital computer dynamically and stochastically. The dynamic simulation, which will produce the effects of the kinematic and dynamic imperfections, is accomplished on the basis of an eleven degree of freedom model which was carefully devised to include all possible properties or factors concerning the real system behaviour, such as flexibility of cam shaft, non-constant angular velocity of the cam due to torsional vibration, jump phenomenon caused by inertia force, preloading of the retaining spring, cantilever effects of follower due to pressure angle, nonlinear damping, and the exact contact condition between cam and roller follower. In the model, an analytical method to calculate the spring constant of the interface between cam and follower is introduced by using Hertzian deflection characteristics. To analyse the effects of geometric imperfections which involve random characteristics, the ground and finished cam profile is modelled stochastically by generating normally distributed random numbers and applying a cubic polynomial spline function to obtain the cam profile.
Thus, the compounded effects of tolerances and flexibility in the system can be investigated.
The motion equations derived from the dynamic model and stochastic model consist of simultaneous nonlinear differential equations in which the factors having a random nature are implicitly included. To solve the motion equations the refined Runge-Kutta algorithm is utilized so that the computing accuracy can be controlled.
The PDP-11/34 minicomputer and its graphic peripheral devices are exploited by the overlay technique. Intermediate results are transferred to subsidiary memory while renewing the previously executed memory, so as to diminish the processing cost of the dynamic and stochastic simulation program as well as to compensate for the insufficient main memory.
Finally, the results of the simulation are analyzed and compared with the work of other researchers, in which the effect of an imperfect profile has usually been neglected.
Keywords: Mechanical Engineering; Mechanical Engineering