How the Model Works
Both models have the same shape. Each takes a base failure rate for the belt or chain and adjusts it for how hard and how hot it works. Each then adds a fixed failure rate for the pulleys or sprockets.
The factors multiply the belt or chain rate only. The pulley or sprocket rate is added afterward.
1. Belt drive
\[ \lambda_{BD} = \lambda_{BD,B}\cdot C_{BL}\cdot C_t\cdot C_{PD}\cdot C_{BT}\cdot C_{BV}\cdot C_{SV} + \lambda_P \qquad\text{(Eq. 21-7)} \]
| Symbol | Meaning |
|---|
| λBD,B | Base failure rate of the belt, 40 failures per million hours |
| CBL | Belt loading, the ratio of actual to rated horsepower (Figure 21.6) |
| Ct | Belt operating temperature (Figure 21.7) |
| CPD | Driven pulley diameter (Figure 21.8) |
| CBT | Belt type (Table 21-2) |
| CBV | Operating service (Table 21-3) |
| CSV | Shock environment (Table 21-4) |
| λP | Pulleys: 0.8 per million hours for flat pulleys, 1.5 for grooved |
2. Chain drive
\[ \lambda_{CD} = \lambda_{CD,B}\cdot C_{CV}\cdot C_{CS}\cdot C_{CT}\cdot C_{CI}\cdot C_{ST} + \lambda_S \qquad\text{(Eq. 21-11)} \]
| Symbol | Meaning |
|---|
| λCD,B | Base failure rate of the chain, 15 failures per million hours |
| CCV | Operating service (Table 21-7) |
| CCS | Chain speed (Table 21-8) |
| CCT | Chain operating temperature (Table 21-9) |
| CCI | Lubrication method (Table 21-10) |
| CST | Sprocket design, 19 / ST (Figure 21.16) |
| λS | Driver and driven sprockets, 0.8 failures per million hours |
3. Tension and speed (information)
The handbook relates belt and chain life to tension, but its failure-rate equations use the ratios above, not the tensions themselves. The page shows the speeds and tensions for reference.
Belt speed is V = πDN/12 (Eq. 21-1) and working tension is TW = 33,000 hp/V (Eq. 21-3). Chain speed is S = PNn/12 (Eq. 21-8) and chain tension is T = 33,000 hp/S.
A belt also carries bending tension TB = CB/d (Eq. 21-4) and centrifugal tension TC = MV2 (Eq. 21-5). Its peak tension is TPEAK = TT + TB + TC (Eq. 21-6). The peak is what ties to belt life.
Those need belt-specific constants (CB and M) that the handbook does not tabulate, so they are not computed here.
Which belts the model covers
The belt model is for power transmission V-belts. Table 21-2 gives a belt type factor only for the classical sections Y, Z, A, B, C and D and the narrow wedge sections SPZ, SPA, SPB and SPC. All of these run on grooved pulleys, so the calculator sets the pulley type for you.
The handbook describes flat belts and timing belts, but it gives no belt type factor for them. You can still pick them and enter your own CBT. A flat belt uses the flat pulley rate, and a timing belt uses the grooved rate. Treat those results as rough.
Small timing belts such as MXL, XL and L are outside the model. They are chosen for positioning, not power, and they run on pulleys smaller than the 2.5 to 8.5 in range of the pulley size factor. For those, use the belt maker’s life rating.
4. Step by step
- Pick belt or chain.
- Enter the load, speed, temperature and sizes. Pick the service and shock (or lubrication) conditions from the handbook tables.
- The calculator multiplies the base rate by each factor, then adds the pulley or sprocket rate.
- Convert to FIT and MTBF, and, with a mission time, to expected failures and survival probability.
Read the result with care. Belt life depends heavily on installation tension and alignment. Chain life depends on lubrication and wear elongation. A handful of factors cannot fully capture any of these.
The handbook quotes about 20,000 to 25,000 h for a well-applied V-drive and at least 12,000 h for a timing belt. Use those lives as a sanity check on the MTBF the calculator gives.