As the arm approaches vertical the required torque becomes less because the
arm length (r) becomes shorter as a function of the sine of the angle.
The torque required at any position can be determined by:The torque required to put a load into motion by a rotary actuator is the sum of the static torque, the dynamic torque and the gravitational torque. Static torque is the torque of friction, dynamic torque is the torque required to accelerate to desired speed and gravitational torque is the torque necessary to lift a weight against gravity. It is suggested that an actuator with reserve capacity of at least 20 percent be selected to accommodate variations within the system.
The maximum torque required to rotate the weight (W) thru an angle Ø in a vertical plane will occur when the arm is horizontal. This torque is determined by the equation: T=Wr. If the arm mass is significant its effect on the torque required must be calculated.
As the arm approaches vertical the required torque becomes less because the
arm length (r) becomes shorter as a function of the sine of the angle.
The torque required at any position can be determined by:
T = Wr sin(theta)
The previous example does not include any considerations for friction. Friction Torque (Tf) can be determined by the product of the weight (W), the coefficient of friction (Cf) and the bearing radius (rb).
Tf = W Cf rb
Note: (W) should include the weight of the turntable as well as the load.
Torque (Tf) required to overcome friction must be added to the acceleration torque (Ta) prior to selecting the proper rotary actuator model. The friction torque can be subtracted from the deceleration torque if desired.
The torque (Ta) required to accelerate (rotate) unsupported weight in a horizontal plane can be determined by:
| Ta = Jalpha Where J = Wr2/g |
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Angular acceleration (alpha) is usually uniform and can be determined by:
alpha = (sigma2 - sigma1)/(t2 - t1)
Where sigma = (theta2 - theta1)/(t2 - t1)
Caution: See Caution note on Page 31.
Deceleration torque is often the least understood and in many cases the most important requirement to be considered.
The time required to decelerate the load within a given angle of rotation should usually be longer than the time required to accelerate the same load to a required speed. This is important because energy built up during uniform acceleration must be absorbed during deceleration by a build up of back pressure in the actuator cylinder.
Since energy in must equal the energy out, if the rotary actuator is used to decelerate the load, any reduction in deceleration time will result in increased back pressure which may be damaging to the rotary actuator and other system components. In all circuits this back pressure must be absorbed into the existing system.
Consider that acceleration energy equals torque times the angle of acceleration (Ta0a). In terms of kinetic energy it is:
Ek = (J sigma2)/2
The deceleration torque required to stop the load is the kinetic energy divided by the angle of deceleration:
Since deceleration energy must equal acceleration energy (TdOd=TaOa) and actuator pressure is proportional to torque, we can set up a simple example of angular travel and pressure. Example:
If a load is uniformily accelerated thru 100° rotation at 1,000 psi., you can determine the deceleration pressure to stop the load in 80° by the following:
Another example:
Uniformly accelerate a load thru 165° rotation at 500 psi.,
then stop the motion within the last 15° of rotation:
Deceleration pressure of 5,500 psi to dissipate the kinetic energy during the last 15° of rotation may prove to be destructive to the system.
Another example illustrates the use of flow control valves to control output flow. A mass accelerated through 40° at 2,000 psi, then moving at constant speed for 1250, will generate a destructive deceleration pressure of 5,333 psi to dissipate the kinetic energy within the last 15° of rotation
In addition, since it is difficult and in many cases impractical to remove system pressure during deceleration, one must consider the torque developed by the system pressure while driving the load through the deceleration distance (rotation) in addition to the kinetic energy already existing.
The optional FLO-TORK built in cushions are designed to help decelerate the load during the last 15° of rotation. The deceleration pressure should not exceed the rated pressure of the rotary actuator model selected.