Constant state restriction of gear meshing gap

The influence of static difference on the system is uncertain: on the one hand, there are many factors affecting the backlash, and some factors have uncertainties, such as changes in ambient temperature, stiffness changes in tooth surface meshing, etc., when these factors are combined It will be more complicated. On the other hand, when a pair of gears meshes and rotates, the two teeth that are engaged each time are varied.
For example, when the number of teeth is Z1 and the two gears of Z2 are engaged, the least common multiple meshing of Z1Z2 occurs. This poses a challenge to the final control of motion accuracy, especially if the end motion is not certain (for example, the robot randomly grabs an object). To simplify the problem, ignore this uncertainty, assuming that each pair of gear meshes with the same backlash.
Return idling and load change are the typical manifestations of the influence of the system static difference on the system. Return idling and return idling is a problem often considered in the side gap. It occurs when the gear rotates in one direction and then reverses. The driving wheel has an angular idling before the driving of the driven wheel (equivalent to the fixed output end, the input end is free to rotate) angle). This cycle. This idling will cause the phase lag of the system (eg) [5].
The backlash idling feature shows the gearbox as a subsystem under which the output is defined as oθ, the input is iθ, and the linear ratio is k=1/i (123...niiiii=, ni means deceleration per stage Ratio, n=1, 2, 3...).
The gear box system block 2 shows that the backlash causes a linear relationship of the output phase displacement and is /2k. Equation (3) also shows that the backlash causes the output phase displacement and is /2k. This has no additive effect on the backlash during the drive. If it is rotated an odd number of times, the output phase shift is /2k. If rotated a few times, the output phase shift is /2k. This shows that the gear backlash is one of the system static differences. This can be concluded by considering the gearbox as a pair of gear drives. A more rigorous proof can be proved by mathematical induction. (2) Load change direction In addition to the return idling, it can reflect the influence of the backlash on the system. When the load changes direction, it also has a close relationship with the backlash.
The emergence of these situations directly leads to the output phase lag that is often mentioned in dynamic error, and the amplitude becomes smaller [6]. However, from the viewpoint of static error, the phase lag means that the position of the output drifts and the accuracy is lowered. The input signal is taken as: 46.3sinxt=, and the output comparison diagram with no backlash and backlash is simulated by matlab as shown.
The output comparison chart with no backlash and backlash can be seen from the figure as the amplitude becomes smaller and the phase angle lags. It can also be observed that at the signal peak position, the output is constant. This is a good example of the fact that when the black box is input, the backlash will be characterized by a smaller amplitude, a phase lag and a dead zone. It should be noted that the phase lag is a fixed value, which also indicates that the backlash has no cumulative effect on the position error of the system.
Conclusion The influence of gear backlash on the system is mainly static and dynamic. This paper focuses on the static impact. The backlash is manifested when a drive or load change occurs. The positional accuracy decreases and the motion amplitude becomes smaller. However, the backlash has no cumulative effect on the error of the moving position.

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