Harmonic Motion
Using the representative range of sliding friction losses, these curves include double the torque required for acceleration (to compensate for leaving the inlet pressure system on and continuing to power the rotary actuator during deceleration with a throttle discharge) plus the coefficient of friction values indicated. The maximum torque required from the rotary actuator, for moving a weight, is given approximately by the following equation:
Where R is the torque arm length (feet), t is the time for a rotation of 1800 (seconds) C& and CfA are the coefficents of friction of the moving weight (horizontally) and the torque arm slide (vertically). Although T= lb - ft, we have converted the values shown graphically on these curves to lb in of torque per lb of weight moved for the two frictional condition.
To select the torques required to transfer a 100 lb load a distance of 6 ft in 3 seconds, assuming a coefficient of friction of 0.05, refer to the HARMONIC MOTION TORQUE CURVE for low friction. Reading up from 3 sec to the R = 3 ft (6 ft diameter = 3 ft radius) curve, you then read to the left column to 5.7 lb-in of torque per pound to be moved. Multiply 5.7 x 100 lb = 570 lb-in torque for acceleration, deceleration, and friction. That's very little torque for that much work!
Likewise, moving the same load in one second would require 35 lb-in per lb of load, or 3,500 lb-in of torque.
Now let us examine the same load, but assuming a coefficent of friction of 0.25 using the HARMONIC TORQUE CURVE for high friction. Following the same procedure, a speed of 3 seconds requires 13 lb-in per lb of load, or a total of 1,300 lb-in of torque, and 1 second requires 40 lb-in per lb of load, or a total of 4,000 lb-in of torque.
Note: The foregoing curves were developed from theoretical considerations to illustrate the selection of rotary actuators for a specific application. Flo-Tork does not intend, nor do we imply, that these same performance characteristics will prevail in your application, and the curves are to be used as guides only.
Caution: See Circuit Considerations for hydraulic circuit considerations. A typical hydraulic system for a harmonic motion application suggests the use of cross-over relief valves to eliminate excess pressure build-up in the Flo-Tork actuator should the operator try to stop the load at the midpoint by closing the discharge valve completely. An alternate method would be to install accumulators on each side of the rotary actuator to absorb the hydraulic shock. See Rotary Motion and Rotary Formulas for applicable formulas, and Technical Data for technical data.