Dynamic behaviour of a vibratory linkage mechanism with bearing clearance
The work presented involves the theoretical and experimental studies of the kinematic and dynamic effects of bearing clearance in linkage mechanisms. In the test mechanism developed a six-bar linkage, having a test plain bearing, is oscillated at amplitude of 17.5 mm within the frequency range 4-7 Hz. A transducer assembly is used to measure the impact accelerations which are related to clearance size, mass distribution, spring load and excitation configuration, ( the vibrators are independently phased ). The motion-analysis of the test mechanism including clearance at a bearing is described using Lagrangian mechanics. The behaviour of the system is obtained by solving the coupled time-dependent equations using Kutta-Merson integration procedure. The method proves to be lengthy in computation time and not easily applied in design. Further, it is shown that there is little difference, in a gross sense, between the results so found and results obtained assuming no bearing clearance. An empirical formula relating the three parameters, clearance size, the rate of change of contact position and the corresponding minimum reaction force is derived from the no-clearance analysis. The. variation of this empirical relationship with excitation frequency is found to be similar to that obtained for the experimental impact levels. Thus it may be used to describe the impact accelerations and its numerical significance as a design criterion is suggested. The experimental work also demonstrates that the pattern of the impact levels remains unchanged when the bearing is oil film lubricated. Some simple design guides using the empirical relationship on a four-bar chain are suggested and general application from a practical point of view is discussed.