Vibration and resonance testing for robot joints

By Tolerance Labs engineering team · Updated 18 October 2026

A joint that is stable on the bench can buzz, ring or shake once a link and payload are attached. The cause is almost always a resonance, and simple tests find it before it limits the robot.

Estimate first: stiffness and inertia

A rough estimate tells you which frequency range to test. Treat the joint and its link as a torsional spring of stiffness k carrying an inertia J. The natural frequency is f = (1/2π) × √(k ÷ J).

• Joint torsional stiffness from the datasheet: 4,000 N·m/rad. Link and payload inertia about the axis: 0.08 kg·m².
• √(4,000 ÷ 0.08) = √50,000 ≈ 224 rad/s, and f ≈ 224 ÷ 6.28 ≈ 35.6 Hz.
• The link also twists. If its torsional stiffness at the joint is 12,000 N·m/rad, the two in series give k = 1 ÷ (1/4,000 + 1/12,000) = 3,000 N·m/rad.
• √(3,000 ÷ 0.08) = √37,500 ≈ 194 rad/s, and f ≈ 194 ÷ 6.28 ≈ 30.8 Hz.

Real robots have several modes: link bending, flex in the base and mounting, and parts such as covers and cable bundles. The estimate gives you the first mode to look for. Tests find the rest, and they find the real damping, which no estimate gives.

Tap test with an accelerometer

A tap test, or impact test, needs a small hammer, an accelerometer and a recorder that can compute a spectrum. Fix the accelerometer near the end of the link, tap the structure, and record the decaying vibration. Peaks in the spectrum are natural frequencies.

• Mount the accelerometer with a stud or adhesive for the widest frequency range. Wax and magnets are quicker but lower the upper frequency limit.
• Keep the accelerometer light compared with the part it sits on. A common rule of thumb is less than a tenth of the local mass, or the sensor lowers the frequency it measures.
• Sample at 2.56 times the highest frequency of interest or more, a common analyzer convention, with an anti-alias filter.
• Tap several times and average. A soft hammer tip puts energy into low frequencies, a hard tip into high ones.
• Test in the states the robot works in: brake engaged, servo holding, and at more than one pose and payload.

With an instrumented hammer that measures the impact force, you also get a frequency response function and damping. Without one, you still get the frequencies. Then add a known mass at the end of the link and tap again. Peaks that move down belong to the joint and link; peaks that stay put belong to the base or the fixture.

Sine sweep through the driver's torque command

The joint can excite itself. Add a small sinusoidal torque to the driver’s torque command, step or sweep its frequency, and record the motor encoder and, if fitted, the output encoder. Many drivers have a built-in frequency response tool. If yours does not, log the torque command and the encoders at 1 kHz or more.

• Keep the amplitude small, typically a few percent of rated torque, but large enough to overcome friction so that the joint moves.
• Hold a small bias torque so that the gear teeth stay in contact, or backlash dominates the result.
• Keep only a low-gain position loop to hold the pose, so that the controller does not hide the response.
• Sweep from well below to well above the estimate, for example 1 to 200 Hz, with more points near the peaks.
• Repeat at two or three amplitudes. If the peak moves with amplitude, friction or backlash is part of what you measure.

Reading a Bode plot

A Bode plot shows the response in two graphs against frequency on a log scale: magnitude in dB and phase in degrees. From torque command to motor velocity, a rigid joint looks like a pure inertia: magnitude falls at 20 dB per decade with a steady phase. A flexible link adds a dip, the antiresonance, followed by a peak, the resonance, with a phase swing between them. From torque to the output encoder, only the peak appears, followed by a steeper fall. If the tool reports coherence, trust only frequencies where it is close to 1.

Damping comes from the width of the peak. With half-power points, 3 dB below the peak, at f₁ and f₂, the damping ratio is about ζ ≈ (f₂ − f₁) ÷ (2 × f_n). Example: a peak at 31 Hz with half-power points at 29.5 Hz and 32.5 Hz gives ζ ≈ (32.5 − 29.5) ÷ (2 × 31) = 3.0 ÷ 62 ≈ 0.048, about 5% of critical damping. That is a lightly damped structure, and its peak is sharp.

How resonance limits bandwidth

The first resonance sets an upper limit on how fast the position and velocity loops can be tuned. Backlash and torsional stiffness explains the rule of thumb and how backlash adds to the problem, so it is not repeated here. What the test adds is the real frequency at each pose and payload, instead of an estimate. Use the lowest value you measure across the working range. Tuning robot joint control loops covers how to tune once you know it.

Notch filters and structural fixes

A notch filter in the driver removes a narrow band of the torque command around the resonance, so the controller does not excite it. Set the center frequency from the measured peak, the width from how far the peak moves with pose and payload, and the depth to remove enough gain. A notch adds phase lag below its center, so a wide or deep notch close to the loop bandwidth costs stability. When the resonance moves a lot, a wider notch, a low-pass filter or gains that change with pose can work better than one narrow notch.

Filters treat the symptom. Structural fixes raise the resonance or add damping:

• Stiffen the link and the mounting. A flexible base, or a bolted joint with too few bolts, often sets the first mode.
• Reduce inertia at the end of the link: a lighter gripper, motors moved closer to the axis.
• Choose a stiffer joint. Frequency rises with √k, so doubling stiffness raises it by about 41%.
• Add damping material or a tuned mass damper where a mode cannot be moved.
• Keep resonances away from known excitation frequencies, such as gait frequency, gear mesh and torque ripple; see cogging torque and torque ripple.

Equipment

For torque, speed and efficiency tests on the same bench, see dynamometer testing a robot joint.

Checklist

• Estimate the first mode from stiffness and inertia, with the link in series.
• Tap test with a light, rigidly mounted accelerometer, at more than one pose and payload.
• Sweep the torque command with a bias torque and a low-gain position loop.
• Read resonance, antiresonance and damping from the Bode plot, where coherence is good.
• Use the lowest measured resonance to set the loop bandwidth.
• Tune notch filters to the measured peak and its spread across poses.
• Fix the structure where filters cost too much phase.

Compare stiffness across harmonic joint modules and QDD joint modules, and check filter options in motor drivers.