Results of a motor simulation

Figure 1. Motor speed at no load shows minor variation due to mechanical design. Variations become more pronounced as load increases, and, ultimately result in a stall condition that can be overcome only by increasing inlet flow or reducing load torque.

Figure 2. Even though performance of a tighter motor differs from that shown in Figure 1, the range of leakage variation still occurs over a range of 8 to 1.

A program to simulate hydraulic motor performance at low speed was developed over the last several editions of "Motion Control." The actual program was entered into an Interdata timeshared mini-computer and allowed to run until a simulated time of 2.8 sec was reached. For the particular motor, this allowed the shaft to reach steady-state speed. The simulated shaft speed is graphed against time in Figures 1 and 2.

The results clearly show how the amount of speed fluctuation increases with load torque. With light load, the speed rises, overshoots slightly, then settles to a relatively stable steady-state level of about 5 radians/sec (roughly 50 rpm). That small a speed ripple most likely could not even be detected without sensitive instruments in an actual experiment.

Sources of speed variation
With a load of 1500 or 3000 Ncm, an expected drop occurs in average steady-state speed — even though the injected flow remains constant. The amount of speed fluctuation also increases. These both result directly from the variations in leakage resistance.

Imagine the motor to be in a shaft position where little leakage occurs — a "tight" motor. The inlet flow causes pressure to rise, which results in acceleration. An instant later, however, the shaft has moved to a position of higher leakage. With constant inlet flow, pressure drops, and the motor decelerates. Thus, the speed fluctuates with shaft position.

As the load increases, two phenomena contribute to the fluctuations. First, the increased load necessarily raises the inlet pressure under constant inlet flow. The amount of flow leaking around the motor's displacement members is affected by the fluid pressure. That is, under light load, the varying leakage resistance is inconsequential because the pressure is low.

However, as load increases, the leakage resistance becomes the predominant factor contributing to instability. Thus, variation in leakage resistance will predict the increased instability with increased loading; displacement variations alone will not.

The second phenomenon is strictly mechanical. The increased load causes the average speed to drop. This also reduces the frequency with which the variations excite the inertia and other dynamic elements in the system. At some load, speed and frequency are so low that the inertia and hydraulic capacitance can no longer "carry the motor over the humps." The inevitable result brings the motor to a jerky halt. This was the case for the 3500 N-cm trace in Figure 1. The motor shaft first jumped off to a flying start, fluttered for a while, then ground to a halt. Speed was captured by static friction, and even though the simulation showed that pressure was building, it never rose high enough to break the rotating elements away. In later simulations, conditions actually caused the motor to start and stop.

Additional conclusions
The results also show that the total variation in leakage resistance is the predominanant factor affecting low-speed stability, which is evident in comparing Figure 1 to Figure 2. The only difference is that leakage flow ranged from a 1 to 8 gpm in Figure 1, whereas in Figure 2, the leakage ranged from 0.5 to 4. gpm. This makes the motor of Figure 2 "tighter," but it still has an 8to-1 leakage variation.

Note that instability still increases with load, and in both cases a stall can be achieved. The significant difference is that is takes approximately twice the load to produce the same degree of instability in the tighter motor. Only 3500 N-cm were needed to stall the leaky motor, but the tighter motor required 6000 Ncm. Note also that the motor of Figure 2 restarted after stalling.

Conclusions
Based on 1-rpm tests on an actual 10 in.³ motor, leakage variations may be as high as 8 to 1 in a "bad" motor. Simulation using actual test data on leakage variations shows that they are the predominant factor affecting low-speed stability. Leakage variation explains why certain motors experience smoothness under light loading and jerkiness under heavy load. Although the amount of leakage affects the load at which a certain degree of instability occurs, a tight motor under heavier loading will be as jerky as a leaky motor when the percent change in resistance is the same. It must be concluded, however, that a tight motor performs better than a leaky one.

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