Abstract
In this paper, a constant speed control of slider-crank mechanisms for machine tools is proposed. A joint-task space hybrid controller based on a second-order sliding mode control and time-base generator was used to guarantee a constant speed trajectory tracking and a complete turn of the mechanism crank. A switching criterion was implemented in order to avoid the singularities located at the two extreme positions of the slider stroke. A trapezoidal speed profile with parabolic blends was designed directly over task space slider trajectory considering a constant cutting speed, the workpiece dimensions and the slider stroke length. Stability of the second-order sliding mode control was validated with the Lyapunov stability theory. Simulations were carried out to verify this approach.
Highlights
The slider-crank mechanism is known as quick-return mechanism
The outline of the paper is as follows: Section II is related with the statement of the problem, Section III shows the switching criterion for the singularity points avoidance; the speed profile design is proposed in Section IV and the controller design is shown in Section V; the simulation studies are discussed in Section VI, and Section VII concludes the paper
The results show that the reciprocating method needs an optimization procedure, that is, a mechanism synthesis to guarantee a constant cutting speed profile
Summary
The slider-crank mechanism is known as quick-return mechanism. It is a closed-chain mechanism and is widely used in machines and cutting tools. The approach fails to consider singularities of slider stroke, contact force and the mechanical advantage in the analysis [28] The solution of this method has a fixed mechanism configuration and an approximate constant velocity profile is obtained by the control of both, the cutting and return stroke. A constant speed control of slider-crank mechanism which addresses the above areas of opportunity is obtained, in order to generate uniform cuts throughout the workpiece by means of an hybrid joint-task space controller. In order to avoid the singularity points and ensure a complete turn of the input crank, a switching criterion is proposed which switches the task space controller into the open loop. The outline of the paper is as follows: Section II is related with the statement of the problem, Section III shows the switching criterion for the singularity points avoidance; the speed profile design is proposed in Section IV and the controller design is shown in Section V; the simulation studies are discussed in Section VI, and Section VII concludes the paper
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