Cylinder and Valve Sizing
Cylinder and Valve Sizing
Cylinder sizing is the most important step when designing a new hydraulic servo system. The stroke of the cylinder is usually dictated by the application, and many different combinations of cylinder bore and supply pressure can work. It’s just that some combinations work better than others.
There are five design criteria for choosing the cylinder bore:
- Stall force requirements must be met or exceeded, which applies to presses and similar machines.
- The rod diameter must be large enough to avoid buckling based on the rod length and the load.
- The natural frequency must be 2 to 100 times higher than the frequency of acceleration, depending on required following error, the damping factor, and control algorithm used.
- Enough force must be available to accelerate the load in both the extend and retract directions.
- Cavitation (formation of air bubbles in the fluid) must be prevented while decelerating. Usually, this only happens when extending a heavy load, then trying to decelerate quickly, known as an over-running load.
The first two criteria are pretty straightforward. Criteria One is easy to calculate, and Criteria Two requires looking up specifications from the cylinder manufacturer to check if the rod diameter is large enough. Criteria Three, however, depends on the control algorithm used by the electronic control. This is where a hydraulic motion controller can pay for itself. Simple PLC-type control may use only a proportional gain. The physical system’s natural frequency will need to be very high to obtain a suitable response. Unfortunately, increasing the natural frequency by a factor of two requires increasing the cylinder bore by about the same amount but increases the flow requirement by a factor of four. This can be expensive. Hydraulic motion controllers with a PID and velocity plus acceleration feed forwards (FFs), require a natural frequency of about four times the frequency of acceleration. The best hydraulic servo controllers may allow the natural frequency to be reduced to about two times the frequency of acceleration. Being able to use smaller-diameter cylinders for the same application saves a lot of money, as long as the other criteria above are met.
This graph shows where in the motion profile the key velocities and forces occur. These four values are needed for the two VCCM equations to calculate the area of the powered end of the cylinder, Ape.
Criteria Four is difficult to calculate. Typically, maximum force is required when accelerating the load. Assuming the motion controller uses S-curves while ramping, the peak acceleration occurs at half the maximum steady-state velocity. This means that multiplying the supply pressure by the area of the piston, then dividing by the mass, will not provide a valid answer. The reason is that pressure losses occur as the oil flows through the valve to the pushing side of the piston. Also, backpressure acts on the exhaust side of the piston to push oil out of the cylinder. This means the pressure on the pushing side and exhausting side of the piston are unknown without doing some math. The differential force can be calculated and used to calculate the potential acceleration at half of the required steady-state velocity.
Criteria Five must be met to avoid cavitation while decelerating. Cavitation from an over-running load is common when attempting to decelerate loads where the rod is pointing down, or must be decelerated quickly. Cavitation usually is only a problem on the cap end of the cylinder. Calculating this requires knowing the braking force required to decelerate from the maximum steady-state velocity without causing pressure in the cap end of the cylinder to go to zero.
Calculating the Natural Frequency
A couple different formulas are used for calculating the natural frequency. The one I prefer is:
The hard part is keeping the units correct. The natural frequency has units of radians per second. To convert from radians per second to Hertz, divide by 2π.
The natural frequency, in Hz, must be compared to the frequency of acceleration. The cylinder bore must be increased until the natural frequency is four times the frequency of acceleration. This is based on the assumption that a PID algorithm will be used with feed forwards. I use a computer program that will index through a table of cylinder sizes from smallest to largest until the natural frequency requirement is met.