How to Work with Mechanical Resonance in Motion Control Systems

Mechanical resonance can be a problem for almost any motion control system, from nimble machines that wrap food or assemble electronics to large, lumbering lines that coat film, to high-precision metal-cutting mills and lathes. Problems with resonance usually occur during installation, as servo-loop gains are adjusted to coax the machine to meet specifications.

By George Ellis, Kollmorgen April 1, 2000


Motion control

Servo motors and drives

Simulation software

Motion system tuning

Sidebars: Useful terms in mechanical resonance

Mechanical resonance can be a problem for almost any motion control system, from nimble machines that wrap food or assemble electronics to large, lumbering lines that coat film, to high-precision metal-cutting mills and lathes. Problems with resonance usually occur during installation, as servo-loop gains are adjusted to coax the machine to meet specifications.

Raising loop gains makes the machine perform better move faster, settle quicker between moves, and better resist outside disturbances. But when the gains go too high, resonance causes instability. The first sign of resonance might be a faint, pure ringing, which sounds like a tuning fork. More often, it’s an irregular grinding noise, something like a foghorn. Sometimes the oscillations increase gradually and other times they appear so suddenly and with such vigor as to send a startled engineer lurching for the off switch.

In a simple rigid-body model (left), motor and load positions (P M and P L ) and velocities (V M and V L ) have identical values. A more realistic model (right) includes the effect of a compliant coupling.

Resonance sources

‘Springiness’ or compliance in the coupling between components of a machine causes resonance. A very common example is the compliance of a shaft coupling between the motor and load. Resonance can also come from compliance between the motor and feedback device or from a compliant motor mount that allows the motor frame to resonate within the machine frame.

Mechanical resonance occurs readily in motion systems; all that’s needed is two inertias coupled by compliant transmission components (inertias J M and J L , respectively, see Motor and Load Models diagram). Engineers often ignore this coupling and assume that the load and motor are rigidly coupled as shown in the first model on the left.

In reality, the motor and load inertias are two separate bodies with independent positions and velocities, as the right side of the Motor and Load Coupling Models shows. The bodies are linked by a spring, K S , which is a combination of all the compliant couplings that connect the motor to the load, including shaft couplings, gearboxes, leadscrews, and belts. K S (also called the spring constant) defines how easily the coupling deflects and is often measured in Newton-meter per radians (Nm/rad); a larger K S value indicates a stiffer coupling.

In addition to spring forces, compliant couplings also provide viscous damping forces. Damping forces are produced in proportion to the velocity difference between the motor and load, rather than position difference, as is the case with spring forces. Usually, damping forces are intrinsic properties of the materials used to form couplings; although in rare cases, separate damping devices are added. Mechanical damping helps stabilize the system considerably. Unfortunately, materials commonly used for transmission parts, such as steel, provide very little mechanical damping.

Frequency Effects

These ModelQ software screens compare typical step velocity response of a system with high-frequency resonance (left) and low-frequency resonance (right). Vertical velocity scale is 5 rpm/div; horizontal time scale is 20 msec/div.

High- and low-frequency effects

Mechanical resonance in servo systems takes two forms: high- and low-frequency. High frequency becomes the problem where resonant frequency of the driven load is very high compared to the servo-system response rate. It is more common on mechanically stiff machines such as machine tools. A simulated step response of a machine with high-frequency resonance is shown under Frequency Effects (left screen shot). A small magnitude oscillation rides on the step response. High frequency resonance often produces a pure sound similar to a tuning fork.

Low-frequency resonance is the problem where the resonant frequency is nearer to (but still significantly above) the servo-system response rate. Low-frequency resonance is more common in industrial applications. Unless a machine is built to be especially stiff, as is the case with machine tools, it will be more susceptible to low-frequency resonance. The right screen capture shows the step response of a typical low-frequency resonance problem. Low-frequency resonance produces a rough, unpleasant sound, something like a foghorn or a garbage disposal.

Stiffening Effects

Stiffening the coupling between the motor and driven load decreases resonance.This step response for 8,000 Nm/rad coupling stiffness is much improved overthat of the 1st ModelQ screen (left side in the previous illustration), which had2,000 Nm/rad stiffness. Scaling is 5 rpm/div vertical; 20 msec/div horizontal.

Cure by stiffening

Mechanical improvements should be considered first among a number of ways to improve resonance. Stiffening the transmission usually improves resonance problems. For example, comparing the left- side screen shot (Frequency Effects) to the last screen shows the improvement obtained when mechanical stiffness is increased from 2,000 to 8,000 Nm/rad.

Common ways to stiffen the machine include:

Shorten shafts, use larger diameter shafts;

Use stiffer gearboxes;

On belt-driven machines, use shorter, wider, reinforced, or multiple belts;

Use idlers in machines with belts that run long distances;

Use larger leadscrews and stiffer ball nuts;

Reinforce the machine frame; and

Oversize coupling components.

Spring constants of the system elements add, according to the following equation, so that one ‘loose’ component can single-handedly reduce the overall spring constant, K S , significantly.

When stiffening a machine, start with the loosest components. Stiffness values of most transmission components are available from vendors, usually as catalog data.

Cure by extra damping

Another mechanical cure is to add viscous damping. However, this can be difficult in practice because materials with large inherent viscous damping do not normally make good transmission components. In fact, sometimes the steps used to stiffen the machine will lower the damping. And this can actually reduce machine performance.

Sometimes, the unexpected loss of viscous damping can cause resonance problems in the field. When a machine is assembled at the factory, it can have its greatest viscous damping. Mechanical linkages are tight because the machine has not been in operation. If the machine is tuned with aggressive gains, problems in the field are likely to occur. After the machine has operated for a few weeks, the seals and joints will loosen, resulting in a net loss of damping. This can create new resonance problems, and the machine may need to be retuned. Since this usually occurs after the machine is delivered, a service trip may be required.

Cure by inertia changes

Reducing the ratio of load-to-motor inertia will improve resonance problems; reducing load inertia is the best way to improve this ratio. Load inertia can be reduced directly by decreasing the mass of the driven load or by changing its dimensions. In geared or belted systems, the load inertia felt by the motor (called the reflected inertia ) can also be reduced indirectly by increasing the gear ratio. The inertia reflected from the load to the motor is reduced by N 2, where N is the gear ratio. ( N>1 indicates speed reduction from motor to load.) Because of the square relationship, even small increases in the gear ratio will significantly reduce the reflected inertia. Similar effects are realized by changing lead-screw pitch or pulley diameter ratios.

Any steps to reduce load inertia will usually help the resonance problem. However, most machine designers work hard to minimize load inertia for nonservo reasons such as cost, peak acceleration, weight, or structural stress so that it’s uncommon to be able to reduce load inertia after the machine has been designed.

The next alternative for reducing the load/motor inertia ratio is to raise the motor inertia by choosing a different motor. For the example, raising motor inertia from 0.0002 kg-m2(1stscreen shot, Frequency Effects) to a value of 0.0042 kg-m2makes a significant improvement in resonance typical of that shown in the last screen shot (under Stiffness Effect).

Unfortunately, raising motor inertia increases the total (motor and load) inertia. This means more torque is required from the motor/drive set to maintain the original acceleration; this can increase the cost of the motor and the drive. Still, this solution is commonly used because it so effectively improves resonance problems.

One common misconception about the load/motor inertia ratio is that it is optimal when the inertias are equal or matched . Experience shows that more responsive control systems require smaller load-to-motor inertia ratios. Load/motor ratios of three to five are common in typical servo applications, while less demanding applications will work even with larger ratios. Nimble machines often require the load to be nearly matched. The most responsive applications require the load inertia to be no larger than about 70% of the motor inertia. Maximum load/motor inertia ratio also depends on machine compliance: stiffer machines will forgive larger ratios. In fact, direct-drive systems ( CE , March 2000, p. 152), which remove the transmission and its associated compliance, allow load/motor inertia ratios of hundreds or even thousands while still maintaining high servo response rates.

The most common position for anti-resonant filters in the servo loop is just ahead of the current controller.

Electrical cures

After exhausting mechanical cures, engineers are left with electrical cures. These methods are functions of the drive or motion controller, which is designed to reduce resonance problems. The primary electrical cures for resonance are low-pass and notch filters (see filter location diagram).

Low-pass filters work well for high-frequency resonance and can easily lower the filter bandwidth from 1,000 Hz (as in Frequency Effects, left screen shot) to 200 Hz, which nearly eliminates resonance. Low-pass filters usually do not work well with low-frequency resonance. In fact, attempting to use low-pass filters to cure low-frequency resonance will usually increase instability. For the example of the right screen shot, which has a low-pass filter of 1,000 Hz, reducing the filter bandwidth to 200 Hz would cause considerable instability.

The main problem of low-pass filters is that they degrade the servo performance of a loop, especially when the filter bandwidth must be reduced to levels near the servo response rate.

Notch filters

Notch filters offer an alternative. They can often remove resonance without compromising performance. Like low-pass filters, they work well for high-frequency resonance. As the name implies, notch filters’ key limitation is that they work only for a narrow frequency range. Parameters of the notch filter must be set precisely. If the resonant frequency changes significantly, the notch filter will not be effective.

Unfortunately, resonant frequencies commonly change on practical machines. Load inertia can vary during machine operation. Also, the spring ‘constant’ may change; for example, compliance of a leadscrew will vary when the load is located in different positions.

Because of these and other manufacturing tolerances, different copies of the same machine will often have significant variation of resonant frequency. Notch filters work best when the machine construction and operation allow little variation of the resonant frequency, and when the notch can be individually tuned for each machine. Notch filters do not work well on low-frequency resonance.

Try it yourself

Simulations used to create the screen captures shown in this article were generated with ModelQ simulation software for Microsoft Windows. This easy to use program was developed by the author. You can visit and download ModelQ free of charge. Install the program, launch it, and press ‘Run’ to see the 1stscreen. Click on the About the Model… button to display an explanation of the model and instructions on how to reproduce the other screens and more examples. You can continue to experiment by further modifying simulation parameters.

For more information, visit info .

Author Information

George Ellis is senior scientist at Kollmorgen (Radford, Va.), where he does research and design in motion control. His other recent activities include a seminar, ‘How to Improve Servo Systems,’ offered at various North American sites, and a new book, Control System Design Guide, (2nd Edition), to be published by Academic Press this spring. Contact George at

Useful terms in mechanical resonance

Bandwidth A measure of responsiveness for a filter or a servo system. Assume a system, when subjected to a low-amplitude, low-frequency sinusoidal command, produces an output Y. Bandwidth of that system is the frequency of command high enough to reduce the output to 0.707 x Y.

Damping forces Rotary or linear forces that are approximately proportional to the difference in velocity of two objects.

Inertia The opposition a mass provides to accelerating a force or torque. It’s often called moment of inertia and measured in kg-m

Low-pass A filter that attenuates high-frequency signals while passing low-frequency signals. Low-pass filters are commonly used to reduce noise and resonance problems.

Notch filter A filter that attenuates a narrow band of frequencies while passing signals with frequencies above or below that band (or notch). Notch filters are commonly used to reduce resonance problems.

Reflected inertia The mass the motor senses from the load. When the transmission includes a gear or pulley ratio, the reflected inertia is equal to the actual load inertia divided by N N is the gear or pulley ratio.

Resonant frequency The frequency at which a closed-loop servo controller oscillates. This is usually equal to or near the natural frequency of the compliantly coupled motor and load inertias,

where K S is the total spring constant (Nm/rad) and J M and J L are motor and load inertias (kg-m

Servo gains Tuning settings, such as proportional-integral (PI) gains, which are adjusted to achieve servo performance in a motion control loop.

Servo loops Velocity and position loops of a servo motion system.

Servo response rate The rate at which a servo controller provides response to commands. See also bandwidth .

Spring forces Rotary or linear forces that are approximately proportional to the difference in positions of two objects.

P M and P L Motor and load position values. In a compliantly coupled system, the motor and load have different positions.

T E Electromagnetic torque or the torque produced by the motor.

V M and V L Motor and load velocity values. In a compliantly coupled system, the motor and load have different velocities.