Question 13.4: Analysis of a Roller-Chain Drive A three-strand ANSI No. 60,...
Analysis of a Roller-Chain Drive
A three-strand ANSI No. 60, ¾ in. pitch roller chain transmits power from a N_{1}-tooth driver sprocket operating at n_{1} rpm. Determine
a. The design power capacity
b. The tension in the chain
c. The factor of safety n of the chain on the basis of ultimate strength
Given: N_1=19, p=3 / 4 \text { in., } n_1=1000 rpm
Assumptions: The input power type is an internal combustion (IC) engine, mechanical drive. The type of driven load is moderate shock. With the exception of the tensile force, all forces are taken to be negligible.
See Tables 13.7 through 13.10.
a. For driver sprocket H_r = 20.6 hp, type B lubrication is required (Table 13.8). Service factor K_{1} = 1.4 (Table 13.9). From Table 13.10 for three strands, K_{2} = 2.5. Applying Equation 13.26, we have
H_d=H_r K_1 K_2 (13.26)
H_d=20.6(1.4)(2.5)=72.1 hp
b. The average chain velocity, by Equation 13.24, is
V=\frac{N p n}{12} (13.24)
V_1=\frac{19(0.75)(1000)}{12}=1187.5 fpm
Equation 13.25 results in
F_1=\frac{33,000 hp }{V}=\frac{396,000 hp }{p N n} (13.25)
F_1=\frac{33,000(72.1)}{1187.5}=2.0 kips
c. The ultimate strength, for a single-strand chain, is 7.03 kips (Table 13.7). The allowable load for a three-strand chain is then F_{all} = 7.03(3) = 21.09 kips. Hence, the factor of safety is
n=\frac{F_{\text {all }}}{F_1}=\frac{21.09}{2.0}=10.5
Comment: The analysis is based on 15 khr of chain life, since other estimates are not available.
| Table 13.7 Sizes and Strengths of Standard Roller Chains |
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| Roller | ||||||
| Chain No. | Pitch, p (in.) | Diameter, d (in.) | Width, b (in.) | Pin Diameter, d_{p} (in.) | Link Plate Thickness, t (in.) | Minimum Ultimate Strength (lb) |
| 25 | \frac{1}{4} | 0.130 | \frac{1}{8} | 0.0905 | 0.030 | 780 |
| 35 | \frac{3}{8} | 0.200 | \frac{3}{16} | 0.141 | 0.050 | 1760 |
| 41 | \frac{1}{2} | 0.306 | \frac{1}{4} | 0.141 | 0.050 | 1500 |
| 40 | \frac{1}{2} | \frac{5}{16} | \frac{5}{16} | 0.156 | 0.060 | 3125 |
| 50 | \frac{5}{8} | 0.400 | \frac{3}{8} | 0.200 | 0.080 | 4480 |
| 60 | \frac{3}{4} | \frac{15}{32} | \frac{1}{2} | 0.234 | 0.094 | 7030 |
| 80 | 1 | \frac{5}{8} | \frac{5}{8} | 0.312 | 0.125 | 12.500 |
| 100 | 1 \frac{1}{4} | \frac{3}{4} | \frac{3}{4} | 0.375 | 0.156 | 19.530 |
| 120 | 1 \frac{1}{2} | \frac{7}{8} | 1 | 0.437 | 0.187 | 28.125 |
| 140 | 1 \frac{3}{4} | 1 | 1 | 0.500 | 0.219 | 38.280 |
| 160 | 2 | 1 \frac{1}{8} | 1 \frac{1}{4} | 0.562 | 0.250 | 50.000 |
| 180 | 2 \frac{1}{4} | 1 \frac{13}{32} | 1 \frac{13}{32} | 0.687 | 0.2811 | 63.280 |
| 200 | 2 \frac{1}{2} | 2 \frac{9}{16} | 1 \frac{1}{2} | 0.781 | 0.312 | 78.125 |
| 240 | 3 | 1 \frac{7}{8} | 1 \frac{7}{8} | 0.937 | 0.375 | 112.500 |
| Source: ANSI/ASME Standard B29.1M-1993. | ||||||
| Table 13.9 Service Factors (K_{1}) for Single-Strand Roller Chains |
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| Type of Input Power | |||
| Type of Driven Load | IC Engine Hydraulic Drive |
Electric Motor or Turbine |
IC Engine Mechanical Drive |
| Smooth | 1.0 | 1.0 | 1.2 |
| Moderate shock | 1.2 | 1.3 | 1.4 |
| Heavy shock | 1.4 | 1.5 | 1.7 |
| Source: ANSI/ASME Standard B29.1M-1993 | |||
| Table 13.10 Multiple-Strand Factors (K_{2}) for Roller Chains |
|
| Number of Strands | Multiple-Strand Factor |
| 2 | 1.7 |
| 3 | 2.5 |
| 4 | 3.3 |
| Source: ANSI/ASME Standard B29.1M-1993. | |
