This equation expresses the relationships between supply pressure, valve coefficient, motor displacement, plus the two load variables, load torque, and load speed. At design time, we must have a knowledge of the load torque and shaft speed requirements. With the VCMM Equation, we solve for the motor displacement and at the same time impose the condition for optimality; that is, the stall torque.

Stall torque must be 1½ times the running torque at the design point. Of course, at stall, flow through the motor is only leakage.

Motor displacement can be calculated. However, there is a dilemma that often exists in hydraulic circuit design. Specifically, we need to know the mechanical efficiency of a motor as well as its leakage flow even before we know anything about the motor! Fortunately, if we have some experience with hydraulic motors, we can guess at reasonable values for the motor's mechanical efficiency and flow leakage, both under stall conditions.

A reasonable approximation is that the expected torque (mechanical) efficiency at stall will be 75 to 95% for most motors.

Determining flow leakage is more complicated. It is the leakage flow through the motor when full supply pressure is applied to the valve inlet port and the motor has so much load on the shaft that it cannot turn. Clearly, the only flow will be that which leaks through the motor's internal clearances. The value will be small compared to the flow at full speed.

Referring to Figure 1, imagine we apply so large a load to the shaft that it is brought to a halt, even though full pressure is applied and the valve is fully open. Motor flow would consist only of that which can squeeze by the small, stationary internal clearances. Now consider the amount of pressure drop across the fully opened valve with such a small flow. It will be especially small, if the motor has a reasonably high volumetric efficiency. When the maximum volumetric efficiency is between 80 and 95%, the valve pressure drop at stall will be about 3 to 10% of the applied supply pressure.

With these approximations, plus some engineering sense, we can calculate a fairly good estimate of the required motor displacement. Most likely, the exact calculated displacement will not be commercially available. Therefore, we will have to select the nearest displacement, along with the pressure, speed, and torque requirements, and assess the motor's suitability for the application.

The VCMM equation can be evaluated at the worst-case design point, then used to solve for the required valve coefficient. Clearly, the speed and torque values must reflect the worst-case design point, but so too, do the volumetric and mechanical efficiencies of the motor.

Note that the efficiencies at the full load operating point may be quite different from the efficiencies at stall. Inexperienced designers may estimate volumetric and mechanical efficiencies to fall between 75 and 95% for most motors. However, experienced designers should use values that they feel comfortable with.

There are many other observations, but their assessments will be left to the interested reader. An example problem will be introduced next month to help reveal other meaningful observations.