Reduction of shaking forces in a slider crank mechanism
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The object of this study was to determine the periodic angular speed of the crankshaft of a slider crank mechanism which will minimize the shaking forces and torque of the mechanism on the block. Both the inertial shaking force and torque cannot be equal to zero for any position of the mechanism. Therefore, the term FS, the sum of the square of the magnitude of the inertial shaking force and the force acting at a moment arm of unity needed to produce the inertial shaking torque, was minimized with respect to the angular acceleration of the crankshaft. This produced a differential equation of the form 02 = X02^2 . When integrated, this equation produces a periodic angular crankshaft speed, 02, which will minimize FS. Depending upon the mechanism parameters, the angular speed obtained from 02 = X 02^2 may or may not produce significant reductions in the inertial shaking forces and torque as compared to the case of a constant crankshaft speed. For one physical example an 82% maximum reduction in FS with a 0.3% speed variation was obtained.
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