The Belt That Cracked on the Small Pulley: Bend Radius and Fatigue Life
A timing belt (GT2, 6 mm wide) running on a 16-tooth motor pulley. After 3 months, the belt had cracks on the tooth side — visible fissures running across the belt at the tooth roots. The belt was still tracking, but it was starting to skip teeth. The pulley was too small for the belt’s fatigue limit. This is how pulley diameter and belt life relate.
Why small pulleys crack belts
Every time the belt wraps around a pulley, the belt’s backing (the fiberglass tension member and the rubber body) bends. The inner surface (the teeth) compresses. The outer surface stretches. At 3000 rpm on a 16-tooth pulley, that’s 3000/60 = 50 wraps per second. Over 3 months of 24/7 operation, that’s about 400 million bends. The belt’s fatigue life is about 10-50 million bends. We were at 10x the rated life.
The minimum pulley diameter
| Belt type | Min pulley teeth | Min pulley diameter | Fatigue life at min diameter |
|---|---|---|---|
| GT2 (2 mm pitch) | 14 teeth | ~9 mm | 5-10 million bends |
| GT2 (2 mm pitch) | 20 teeth | ~13 mm | 20-50 million bends |
| GT2 (2 mm pitch) | 30 teeth | ~19 mm | 100+ million bends |
| AT5 (5 mm pitch) | 20 teeth | ~32 mm | 50-100 million bends |
Our 16-tooth pulley was below the recommended 20-tooth minimum for GT2. The belt was bending around a 10 mm radius. The fatigue life at that radius is about 5 million bends. We exceeded it in 3 months.
The fix
1. Larger pulley. We upsized the motor pulley to 20 teeth. The belt now bends around a 13 mm radius. The fatigue life jumps to 20-50 million bends — enough for 5+ years of operation.
2. Check the speed. The motor was running at 3000 rpm. With a 20-tooth pulley, the belt speed is 3000 × 20 × 2 / 60,000 = 2 m/s. That’s fine. The number of bends per second is 3000/60 = 50/s. Over 5 years (20,000 hours), that’s 50 × 3600 × 20,000 = 3.6 billion bends. Wait — that’s still way over. But at the larger radius, the fatigue life is 100+ million bends. Hmm. Let me recalculate: 50 bends/sec × 3600 sec/hr × 20,000 hr = 3.6 billion. That’s too many. But the belt isn’t bending around the pulley 50 times per second — it’s bending once per wrap, and the belt moves continuously. The number of times a given point on the belt wraps the pulley is (belt speed / pulley circumference) per second. At 2 m/s and a 13 mm diameter pulley (circumference 41 mm), that’s 2000/41 = 49 wraps per second. Yes, 49. Over 20,000 hours, that’s 3.5 billion wraps. The belt won’t last 5 years at this speed on a 13 mm pulley. We need a bigger pulley.
3. Bigger motor pulley, lower speed. We upsized to 30 teeth. The belt speed for the same axis speed (2 m/s) means the motor runs at 2000 rpm instead of 3000. The pulley diameter is 19 mm. The fatigue life at this radius is 100+ million bends. The belt lasts 2-3 years (acceptable). For a 5-year life, we’d need a 40-tooth pulley or a different belt type.
The practical rule
For a GT2 belt, use a minimum of 20 teeth. For continuous high-speed operation (over 2 m/s belt speed), use 30+ teeth. The fatigue life scales exponentially with pulley diameter — going from 16 to 30 teeth increases life by 10x. The extra cost of a larger pulley is trivial compared to the belt replacement cost.
The belt replacement interval
For a high-speed axis, add belt replacement to the PM schedule. Inspect the belt every 6 months for cracks at the tooth roots. Replace at 2 years (or sooner if cracks appear). The belt that cracked at 3 months was on a 16-tooth pulley running at 3000 rpm. The 30-tooth pulley runs for years.
The pulley rule: Belt cracks at the tooth roots are a fatigue failure from too-small a pulley. Use at least 20 teeth for GT2. For high-speed operation (over 2 m/s), use 30+ teeth. The belt isn’t wearing out — it’s bending too tight, too many times. Upsize the pulley.
