An Advanced Numerical Model of Gear Tooth Loading from Backlash and Profile Errors

This study demonstrates the early transient dynamic loading on teeth within a fixed-axis gear transmission arising from backlash and geometric manufacturing errors by utilizing a non-linear multi-body dynamics software model. Selection of the non-linear contact parameters such as the stiffness, force exponent, damping, and friction coefficients are presented for a practical transmission. Backlash between gear teeth which is essential to provide better lubrication on tooth surfaces and to eliminate interference is included as a defect and a necessary part of transmission design. Torsional vibration is shown to cause teeth separation and double-sided impacts in unloaded and lightly loaded gearing drives. Vibration and impact force distinctions between backlash and combinations of transmission errors are demonstrated under different initial velocities and load conditions. Additionally, the loading dynamics of a crank-slider mechanism with two-stage gear driving train is analyzed. The backlash and manufacturing errors in the first stage of the gear train are distinct from those of the second stage. By analyzing the signal at a location between the two stages, the mutually affected impact forces are observed from different gear pairs, a phenomenon not observed from single pair of gears

Domains Of Operation And Interference For Bodies In Mechanisms And Manipulators

. Domains associated with one or more working bodies of a mechanism or manipulator are defined that characterize the range of operation of the bodies and interference that may occur between the bodies. The equations defining domains are derived in terms of equations defining the kinematics of the mechanism and the geometry of the working bodies. Analytical criteria defining the boundaries of such domains are derived and numerical methods for computing families of generators on boundaries are outlined. The criteria and numerical methods presented are applied to planar mechanism and manipulator examples. 1. Introduction Criteria for boundaries of workspaces of mechanisms and manipulators, using conditions associated with singularity of constraint Jacobian or velocity transformation matrices, have been developed by a number of authors in the recent past. Litvin [6] used the implicit function theorem to define singular configurations of mechanisms as criteria for boundaries of workspaces...