#### What is in this article?:

- Size the cylinder right for proper servo operation
- Force makes the system go

**Force makes the system go**

Force is directly related to cylinder size. Often, novice designers apply the familiar, but oversimplified, formula:

*v *= *Q *÷* * *A*,

where *v *is the piston velocity,

*Q *is the flow, and

*A *is the piston area.

But this equation is accurate only if the mass is zero. It should only be used to calculate flow: *Q *= *v *x *A*. The following "rule of thumb" formula takes into account the force needed to produce acceleration and the pressure drop required by servovalves for control. (Typically, servovalves are rated at 70 bar, approximately equal to 1000 psi.)

*A *= *L _{P}*

*÷*

*(*

*P*— 1000 psi),

_{S} where *L _{P}*

*is load pressure, and*

*P*

_{S}*is the system pressure.*

This formula assumes that peak load occurs at peak speed. The peak load includes the force necessary to accelerate or decelerate the load, friction, and the load's weight if the system is vertical. Minimum system pressure should be used. This formula, which should be applied for both *extend *and *retract *directions, neglects the opposing force required to push oil out the opposite end of the cylinder. Therefore, the estimated size should be considered a minimum.

For high-performance motion, a second check should be made to ensure that the natural frequency of the system is higher than the frequency of motion generated by the motion profile. For example, if the frequency of acceleration is 5 Hz; the actuator's natural frequency should be three to four times higher:

*A _{avg}* = (

*f*× 4)

^{2}× π ×

*L*×

_{S}*W*÷ (g × ß)

_{L} where *A _{avg}*

*is the average area of the piston,*

*f*is the cycle frequency,

*L*

_{S}*is the stroke length,*

*W*

_{L}*is the weight of the load,*

*g*is the acceleration due to gravity (32 ft/sec

^{2}), and

is the bulk modulus (incompressibility constant) of oil (~200,000 psi).

This formula also tends to underestimate the correct cylinder bore because it makes some optimistic assumptions. The most significant is that the valve is mounted right on the cylinder. If this isn't the case, the cylinder stroke should be increased by about the length of the hose connecting the valve to the cylinder.

The area of the hose is smaller than that of the cylinder, but hose is more compliant than cylinder tubing. Hose or extra pipe between the valve and the cylinder complicate these calculations and reduce performance.

For the most critical applications, the VCCM equation, developed by Jack Johnson, takes into account additional variables and produces an excellent estimation of performance.

Peter Nachtwey is president of Delta Computer Systems Inc., Battle Ground, Wash. For additional technical information, e-mail him at support@deltamotion.com or visit www.deltamotion.com.