The indexing table ran at 60 cycles a minute, driving a six-station rotary table through a cam. It had run fine for a year, then the follower roller cracked. Not wore out — cracked, right through the bearing race. The replacement roller lasted four months. The cam was a standard cycloid curve, which is what the indexer manufacturer supplied as the default. The default was the problem.
Cycloid motion is the textbook favorite because its acceleration is perfectly sinusoidal, meaning zero jerk at the start and end of the index. Zero jerk sounds ideal. It is not, at high speed, and here is why.
What the curves actually do
A cam indexer moves the table from stop to stop. The motion curve defines position, velocity, acceleration, and jerk through the index. Three curves dominate the catalogs:
- Cycloid (sinusoidal acceleration). Peak acceleration is moderate, but it’s reached early and the jerk, while zero at the endpoints, spikes to a sharp maximum in the middle of the rise.
- Modified trapezoid. Acceleration rises quickly, holds constant, then drops. Lower peak jerk than cycloid, slightly higher peak acceleration.
- Modified sine. A compromise, smooth and forgiving, popular for general use.
The trouble with cycloid at speed is the jerk spike. Jerk is the rate of change of acceleration, and it’s what shakes a machine. A high jerk spike at mid-index excites the vibration modes of the table and the structure. The follower feels it as an impact load. Run it fast enough, and the impact load exceeds the roller rating.
The numbers, for a 60-degree index in 0.5 seconds (that’s the motion time at 60 cycles/min with a 50% dwell):
The peak acceleration for a cycloid is 2π times the average acceleration. For modified trapezoid it’s about 2.0 times average, but peak jerk is roughly half of cycloid’s. In practice, at this speed, the cycloid’s peak jerk was the dominant term in the roller load.
Why the manufacturer’s default is cycloid
Cycloid is the default in a lot of indexer software because it’s the mathematically cleanest curve and it produces zero jerk at the stops, which makes the machine quiet at low speed. At 60 cycles a minute with a rotary table carrying tooling, the machine was never quiet. The default was fine for the indexing market’s common speeds. This application outran the default.
The customer’s reaction was to blame the indexer, then the roller supplier, then the lubricant. All wrong. The roller was rated for a load at a given speed, and the curve choice had pushed the dynamic load past that rating. A bigger roller would have lasted longer, but the right fix was the curve.
The change that worked
We switched the cam profile to a modified trapezoid. The indexer manufacturer re-ground the cam (the unit was designed for interchangeable cams, which is worth paying for if you run fast indexing). Peak jerk dropped to about half, the impact loading on the roller dropped correspondingly, and the table stopped shaking at the end of the index. The new roller has run three years. The table also got quieter, which nobody expected but everybody noticed.
The general guidance that came out of this job:
- Below 30 cycles a minute, cycloid is fine and smooth. Use it.
- Between 30 and 60, use modified sine or modified trapezoid. The jerk starts to matter.
- Above 60, or with heavy tables, do a dynamic load check on the follower roller instead of trusting the catalog’s static rating.
And one more thing we learned the hard way: when a follower roller cracks at the race, do the motion analysis before buying a bigger roller. A bigger roller treats the symptom. The curve is the disease. The difference in cost between a re-ground cam and a series of cracked rollers is not close.
Cycloid gives you textbook acceleration and a jerk spike that breaks followers at speed. Modified trapezoid trades a little acceleration for half the jerk, and the machine lives. When an indexer cracks rollers, look at the motion curve first. The roller was doing exactly what the cam asked it to do. The cam asked too much.
