Before digital servocontrol, the general rule in positioning applications was to shoot for a 1:1 ratio between motor and load inertia. Today, thanks to speedy chips that can adjust for load disturbances in real time, mismatches as high as 100:1, even 1,000:1, are feasible.
Whether the mismatch is too large depends on the mechanical design of the system. Because the motor will have only a small amount of kinetic energy compared to the load, the servo amplifier must inject high current (energy) quickly into the coils to compensate for sudden load changes. This requires a very high mechanical load servo gain. If there’s too much backlash or compliance in the system, it may be prone to stability problems and other inaccuracies. Fortunately, there are simple ways to detect and minimize backlash as well as compliance.
Lost motion and the load
Backlash, or lost motion, is a mechanical effect that lets the motor shaft be turned back and forth over a limited range without moving the load. When released, the shaft remains in its last position.
Backlash, in effect, temporarily uncouples and re-couples the load from the motor as it changes speed and direction. This can lead to control problems, however. If the servo is tuned to work under no-load conditions, it may perform poorly when the load is re-connected. On the other hand, if the servo is tuned for the load, it may be unstable when the load disconnects.
The most noticeable symptom of backlash is an audible energy loss in the form of a loud buzz that occurs usually when the motor is stopped. One way to eliminate this is to apply a pre-load torque to the load so that backlash is taken up. Another way is to lower servo gain, but this usually makes system response “soft.” Sometimes the gain is set so low that the servo cannot stabilize the position loop, resulting in uncontrollable oscillations from 1 to 5 Hz.
The only way to really solve the problem is to eliminate the mechanical sources of backlash. Otherwise, this energy may overheat the motor or ruin the mechanical components of the system.
One of the more common mechanical sources is keyways or set screws that couple the load to the motor shaft. Keyways are fine for many mechanical systems, but they are inadequate for digital-based servo systems. A better coupler is a clamp style coupling, such as a taper lock bushing.
Other sources of backlash include mis-adjusted spur gears and generalpurpose gear reducers. A better choice is a precision planetary gearhead.
The wind up
Compliance also rotates the input shaft without moving the load. However, it doesn’t uncouple motor and load. In essence, it “winds up” the mechanical system like a spring. When released, the input shaft snaps back close to its original position.
Compliance effects show up as a torsional resonant frequency that may cause the servo to oscillate between 100 to 500 Hz. Unlike the buzz caused by backlash, you’ll often hear a pure tone. Tuning the servo won’t change the frequency, but it may lower the amplitude. Another way to lower the amplitude is to apply a friction load, which dampens the oscillation.
As with backlash buzz, uncorrected compliance will overheat the motor and possibly damage the mechanism.
The source of compliance? One of the most common is a long drive shaft with the bulk of the load inertia far from the motor. It is often surprising how much windup can exist in what appears to be a substantial shaft. Take, for example, a 1 in. diameter stainless steel shaft about 18 in. long. Applying a 500 lb-in. load, the shaft will wind up almost 0.5 degrees.
If you attach a motor with a moment of inertia of 0.0476 lb-in.-s2 on one end and a load inertia 100 times larger on the other end, the natural frequency of the system will be about 184 Hz.
Because you may encounter resonance problems if the natural frequency of a system is less than 500 Hz, play it safe and raise the frequency. For this type of system, natural frequency is proportional to the square of the shaft diameter and inversely proportional to the square root of shaft length. Therefore, in the above example, increasing the shaft diameter to about 1.7 in., or decreasing shaft length to 2.5 in., achieves a natural frequency of about 500 Hz.
Solving resonance problems
Usually, the least stiff portion of the drive train, normally the shaft coupling, determines the natural frequency. Selecting the right mechanical coupling is always important, but when there is a large inertia mismatch it is doubly so, as a poor choice can result in a low resonant frequency. Helical style couplings are almost never stiff enough to avoid problems unless the load inertia is insignificant.
A typical inexpensive helical coupling rated for 500 lb-in. of torque has a stiffness of approximately 72 x 103 lb-in./rad. If used on the load system described earlier, it will limit the system’s natural frequency to less than 197 Hz and the system will likely experience resonance problems.
Instead, a good choice is a bellows style coupling with taper lock bushings. Such a coupling, rated similarly to the helical coupling with a stiffness of 433 x 103 lb-in./rad, will have a natural frequency of 480 Hz, which is less likely to affect operation. Stiffness specifications are available from the manufacturer.
Therefore, in servo applications it is usually best to avoid helical, disc, oldham, split beam, and jaw-type couplers. Metal bellows provide the best results.
In addition, be sure to properly attach the coupler to the shaft. A clamping or taper lock is the best way to go.
If there is more than one un-stiff component in the drive train, the effects are additive. And if the moments of inertia of components located between these couplings are significant compared to the overall load inertia, the calculations become more complex and usually result in multiple resonant frequencies.
Speed reducers handle instability
One way to reduce system instability is to add a speed reducer. It cuts the reflected inertia by the square of the reduction ratio. It also increases resolution at the motor, improves performance at low load speeds, and lets the motor run at a higher speed, which provides more kinetic energy to overcome load disturbances. This reduces the gain and bandwidth requirements for the servo. However, a speed reducer adds its efficiency losses, inaccuracies and compliance effects to the system.
Timing belts are an economical and accurate way to attain modest speed reductions. For servo applications, choose one with a high tensile stiffness and low backlash, such as those that use aramid tensile members and a modified curvilinear tooth profile. The tensile member uses fibers that result in a stiffness better than a solid steel shaft. Their efficiency is 95% or better.
The pulley mechanisms, though, add inertia to the system. Designers can minimize this inertia by choosing low mass or custom pulleys. These are available from most belt manufacturers.
The calculations for windup and resonant frequency of a timing belt can get tricky because you must take belt tension and load forces into account when deciding what spring rate of the belt, or EA value, to use. Unless you are already familiar with the techniques, seek the assistance of your belt supplier.
It is not difficult to design a timing belt drive that is as stiff or stiffer than a typical direct-coupled load. This solution not only significantly increases the natural frequency, it can also change the amplitude of the resonance. It considerably dampens the system, and, for a given natural frequency, allows higher gain settings before resonance becomes a problem. Another advantage is that it lets the motor run at a higher speed which, if the motor inertia is small compared to the load, provides better operation.
Resonances can be more of a problem when the system is stopped than when it is moving under load. Slightly reducing belt tension will decouple the motor and load somewhat, which when combined with the damping from the belt, can reduce resonance problems. Do not reduce tension too much, though, or accuracy will suffer. The slack side of the belt should always be under some tension.
If belt tension must be high, always use a jack shaft with its own bearings to isolate the motor shaft from the load. Otherwise, high tension can generate a radial load on the shaft that can drastically reduce bearing life.
As a last resort, notch filtering
Ideally, a notch filter added to the servodrive exactly counters any mechanical resonance and eliminates the effects of low natural frequencies. Used correctly, it can eliminate the need to redesign the mechanical portion of a servo system.
However, the filter only works if the servo components do not undergo significant change over time. As mechanisms wear or heat up, their natural frequencies can change. The natural frequency of the system also changes as the load inertia changes. A once stable system can lose its stability if the natural frequency shifts enough. When this happens, the notch filter may no longer be able to cancel out resonance.
Another disadvantage involves multiple resonant loads with their multiple natural frequencies. If you design a notch filter wide enough to cover all of them, you may end up with a low pass filter that reduces servo response considerably.
While many mechanical problems can be resolved using notch filters, they don’t address the root cause of the problem and therefore are not a universal cure.
Michael Oakley is vice president of customer support engineering at Ormec Systems Corp., Rochester, N.Y.