Companion to Gear Lapping: More Than Noise
Every tooth engagement pushes a gear set a little off its ideal motion. That transmission error repeats at the gear-mesh frequency and becomes the whine you hear. Pick a gear type, change tooth counts, speed and tooth errors, then switch between unlapped and lapped to see, and hear, what changes.
Gold is marking compound; bare steel shows where the teeth have touched, which is the contact pattern. Unlapped: a small patch at the toe and tip edge. Lapped: a larger patch centred on the tooth. Illustrative, not measured. Teeth use spherical involute profiles and circular-arc (face-milled) tooth traces; the hypoid pinion position comes from tangent pitch cones with a Gleason-style offset correction.
Shown slowed down, with the error motion exaggerated so you can see it. Gold dots and lines mark tooth 1.
Tooth errors · Unlapped
Plays the simulated mesh at its real frequencies. Switch the finish or the gear type while it plays to hear the change.
Teeth engage at teeth × shaft speed. Errors that repeat on every tooth show up as tall lines at 1×, 2× and 3× this frequency. These lines are the whine, and lapping lowers them most.
Helical, spiral bevel, hypoid and worm teeth overlap across the face, so several teeth share the load and each engagement is softer. The mesh lines drop as the overlap ratio rises, and drop furthest near whole-number values.
Runout makes the mesh force rise and fall once per revolution, which puts sidebands around the mesh lines at the shaft frequencies. In a planetary set, each planet passing the sensor does the same at the carrier frequency.
Simplified model for teaching, not design. Transmission error is the sum of the mesh harmonics, scaled by the face overlap of each gear type; a fixed pattern of tooth spacing errors on each gear; runout that modulates the mesh once per revolution; and a sliding-friction floor that is highest for hypoid and worm sets. The planetary model sums each planet's mesh, weighted by its distance from a sensor on the fixed ring. The spectrum is a 65,536-point FFT with a Hann window, in dB re 1 µm. The 3D bevel and hypoid teeth use spherical involute profiles (base cone from sin δb = sin δ · cos α) along circular-arc, face-milled tooth traces, which is close to real geometry but not a full machine-setting simulation. Error values and efficiency ranges are illustrative, not measurements. Read the article: Gear Lapping: More Than Noise.