Modeling and robust control of worm-gear driven systems

Abstract

This paper investigates modeling and control issues associated with worm-gear driven systems. In the modeling part, both static and dynamic analyses are conducted to investigate the characteristics of the worm-gear. The static analysis reveals not only the non-backdrivability but also the dependency of break-in torques ou the loading torque, direction of motion as well as crucial system parameters. The dynamic analysis generates four linear equations of motion, of which , at any particular instant, only one applies. The applicable equation at any given instant depends on the direction of motion and the relative magnitude between the input torque and the loading torque. In the control part, a sliding controner is designed based on the modeling results.The controner can provide robustness against variations of system parameters caused by the speed-dependent nature of the coefficient of friction. Because the dependency of the dynamic equation on the operating condition may render the controller ill-defined in some scenarios, a lemma is proved and can be used to select proper control parameters to guarantee the well-definedness of the controller.. The proposed control scheme is applied to a worm-gear driven positioning platform.Experimental results indicate the proposed control system achieves 20% of the tracking error of a conventional PID control.

Dynamics Modeling of Gear Transmissions with Asymmetric Load-Dependent Friction

“…The expression (12) states that the tangential component λ t is within the interval [−µ|λ n |, µ|λ n |] in the static friction and is on the boundary of the interval in the kinetic friction. Solving (11) with respect to λ t and λ n considering the constraint (10) yields the following expression: By setting m κ 2 m, f u κ fu , γ u µ/ tan θ v , γ v µ/ tan θ u , and λ µλ n sin(θ u + θ v )/sin θ u and considering (12), one can rewrite (13) as follows:…”

“…In many of these previous approaches, different expressions must be switched between the forward-driving and backdriving cases, which are defined by the direction of the power flow. Some researchers [2], [6], [10], [11], [14] use different inertia values between the forwarddriving and backdriving cases. Most previous methods cannot handle the static friction state, where the direction of the power flow cannot be defined.…”

Worm gear mechanism with switchable backdrivability

“…However, mechanisms that use a worm gear do not have compliance, because a worm gear does not have backdrivability. Moreover, because of the non-backdrivability of the worm gear, it requires complicated control methods [7,8]. If a worm gear that can switch its backdrivability is developed, it can be used for a robot that requires compliance.…”

Dynamics study and diagnostics with vibration analysis from worm gear manufactured by reverse engineering techniques

“…However, the relative motion between worm and gear teeth is pure sliding, and so it should be expected that friction plays a dominant role in the performance of worm-gear driven systems. Frictions induce nonlinearities to the system dynamics and are usually the major source of motion disturbances and instability in feedback control [4].…”