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Chapter 9

Q. 9.10

Design a pair of plastic gears for a paper shredder to transmit 0.25 horsepower at a pinion speed of 1160 rpm. The pinion will be mounted on the shaft of an electric motor that has a diameter of 0.625 in with a keyway for a 3/16 × 3/16 in key. The gear is to rotate approximately 300 rpm.

Given Data:

P = 0.25 hp, n_P = 1160 rpm,
Shaft diameter = D_s = 0.625 in, Keyway for a 3/16 × 3/16 in key.
Approximate gear speed = n_G = 300 rpm

Step-by-Step

Verified Solution

Use the design procedure outlined in this section.
Step 1. Consider the given data.
Step 2. Specify N_P = 18 and P_d = 16 (Design decisions)
Step 3. D_P = N_P/P_d = 18/16 = 1.125 in. This seems reasonable for mounting on the 0.625 in motor shaft.
Step 4. Compute the transmitted load,
W_t = (126 000)(P)/(n_PD_P) = (126 000)(0.25)/[(1160)(1.125)] = 24.1 lb

Step 5. Specify 20° full-depth teeth. Then Y = 0.521 for 18 teeth from Table 9–15.
Step 6. Specify a safety factor, SF. The shredder will likely experience light shock; the preference is to operate the gears without lubrication. Specify SF = 1.50 from Table 9–1.
Step 7. Specify unfilled nylon. From Table 9–14, s_{at} = 6000 psi.
Step 8. Compute the required face width using Equation (9–42).

F=\frac{W_tP_d(SF)}{S_{at}Y}=\frac{(24.1)(16)(1.50)}{(6000)(0.521)}=0.185 in

Step 9. The dimensions seem reasonable.
Step 10.Appendix 2 lists a preferred size for the face width of 0.200 in.

Comment:

In summary, the proposed pinion has the following features:
P_d = 16, N_P = 18 teeth, D_P = 1.125 in, F = 0.200 in, Bore = 0.625 in,
Keyway for a 3/16 × 3/16 in key. Unfilled nylon material.

Step 11. Gear design: Specify F = 0.200 in, P_d = 16. Compute the number of teeth in the gear.
N_G = N_P(n_P/n_G) = 18(1160/300) = 69.6 teeth
Specify N_G = 70 teeth
Pitch diameter of gear = D_G = N_G/P_d = 70/16 = 4.375 in
From Table 9–15, Y_G = 0.728 by interpolation.
Stress in gear teeth using Equation (9–41):

σ_t=\frac{W_tP_d(SF)}{FY}=\frac{(24.1)(16)(1.50)}{(0.200)(0.728)}=3973 psi

Comment:

This stress level is safe for nylon. The gear could also be made from acetal to achieve better wear performance.

 

TABLE 9–1 Suggested Overload Factors, K_o
Driven Machine
Power source Uniform Light shock Moderate shock Heavy shock
Uniform 1.00 1.25 1.50 1.75
Light shock 1.20 1.40 1.75 2.25
Moderate shock 1.30 1.70 2.00 2.75
TABLE 9–14 Approximate Allowable Tooth
Bending Stress, s_{at}, in Plastic
Gears
Approximate allowable
bending stress, s_{at}, psi (MPa)
Material Unfilled Glass-filled
ABS 3000 (21) 6000 (41)
Acetal 5000 (34) 7000 (48)
Nylon 6000 (41) 12 000 (83)
Polycarbonate 6000 (41) 9000 (62)
Polyester 3500 (24) 8000 (55)
Polyurethane 2500 (17)
Table 9–15 Lewis Tooth Form Factor, Y, for
Load Near the Pitch Point
Tooth form
Number
teeth
14 1/2° Full depth 20° Full depth 20° Stub
14 0.54
15 0.566
16 0.578
17 0.512 0.587
18 0.521 0.603
19 0.534 0.616
20 0.544 0.628
22 0.559 0.648
24 0.509 0.572 0.664
26 0.522 0.588 0.678
28 0.535 0.597 0.688
30 0.54 0.606 0.698
34 0.553 0.628 0.714
38 0.566 0.651 0.729
43 0.575 0.672 0.739
50 0.588 0.694 0.758
60 0.604 0.713 0.774
75 0.613 0.735 0.792
100 0.622 0.757 0.808
TABLE A2–1 Preferred Basic Sizes
Fractional (in) Decimal (in) SI metric (mm)
\begin{array}{ll}1 / 64 & 0.015625 \\1 / 32 & 0.03125 \\1 / 16 & 0.0625 \\3 / 32 & 0.09375\\1 / 8 & 0.1250\end{array} \begin{array}{ll}5 & 5.000 \\5 \frac{1}{4} & 5.250 \\5 \frac{1}{2} & 5.500 \\5 \frac{3}{4}& 5.750 \\6 & 6.000\end{array} \begin{array}{rrr}0.010 & 2.00 & 8.50 \\0.012 & 2.20 & 9.00 \\0.016 & 2.40 & 9.50 \\0.020&2.60 & 10.00 \\0.025 & 2.80 & 10.50\end{array} \begin{array}{ll}1.0 & 40 \\1.1 & 45 \\1.2 & 50 \\1.4 & 55 \\1.6 & 60\end{array}
\begin{array}{cc}5 / 32 & 0.15625 \\3 / 16 & 0.1875 \\1 / 4 & 0.2500 \\5 / 16 & 0.3125 \\3/ 8 & 0.3750\end{array} \begin{array}{ll}6 \frac{1}{2} & 6.500 \\7 & 7.000 \\7 \frac{1}{2} & 7.500 \\8 & 8.000 \\8\frac{1}{2} & 8.500\end{array} \begin{array}{lll}0.032 & 3.00 & 11.00 \\0.040 & 3.20 & 11.50 \\0.05 & 3.40 & 12.00 \\0.06& 3.60 & 12.50 \\0.08 & 3.80 & 13.00\end{array} \begin{array}{ll}1.8 & 70 \\2.0 & 80 \\2.2 & 90 \\2.5 & 100 \\2.8 & 110\end{array}
\begin{array}{cc}7 / 16 & 0.4375 \\1 / 2 & 0.5000 \\9 / 16 & 0.5625 \\5 / 8 & 0.6250\end{array} \begin{array}{cc}9 & 9.000 \\9 \frac{1}{2} & 9.500 \\10 & 10.000 \\10 \frac{1}{2}&10.500\end{array} \begin{array}{lll}0.10 & 4.00 & 13.50 \\0.12 & 4.20 & 14.00 \\0.16 & 4.40 & 14.50 \\0.20 &4.60 & 15.00\end{array} \begin{array}{ll}3.0 & 120 \\3.5 & 140 \\4.0 & 160 \\4.5 & 180\end{array}
\begin{array}{cc}11 / 16 & 0.6875 \\3 / 4 & 0.7500 \\7 / 8 & 0.8750\end{array} \begin{array}{ll}11 & 11.000 \\11 \frac{1}{2} & 11.500 \\12 & 12.000\end{array} \begin{array}{lll}0.24 & 4.80 & 15.50 \\0.30 & 5.00 & 16.00 \\0.40 & 5.20 & 16.50\end{array} \begin{array}{ll}5.0 & 200 \\5.5 & 220 \\6 & 250\end{array}
\begin{array}{cc}1 & 1.000 \\1 \frac{1}{4} & 1.250 \\1 \frac{1}{2} & 1.500 \\1 \frac{3}{4}& 1.750\end{array} \begin{array}{ll}12 \frac{1}{2} & 12.500 \\13 & 13.000 \\13 \frac{1}{2} & 13.500 \\14 &14.000\end{array} \begin{array}{lll}0.50 & 5.40 & 17.00 \\0.60 & 5.60 & 17.50 \\0.80 & 5.80 & 18.00 \\1.00 &6.00 & 18.50\end{array} \begin{array}{rr}7 & 280 \\8 & 300 \\9 & 350 \\10 & 400\end{array}
\begin{array}{cc}2 & 2.000 \\2 \frac{1}{4} & 2.250 \\2 \frac{1}{2} & 2.500 \\2 \frac{3}{4}& 2.750\end{array} \begin{array}{ll}14 \frac{1}{2} & 14.500 \\15 & 15.000 \\15 \frac{1}{2} & 15.500 \\16 &16.000\end{array} \begin{array}{lll}1.20 & 6.50 & 19.00 \\1.40 & 7.00 & 19.50 \\1.60 & 7.50 & 20.00 \\1.80 &8.00 &\end{array} \begin{array}{ll}11 & 450 \\12 & 500 \\14 & 550 \\16 & 600\end{array}
\begin{array}{ll}3 & 3.000 \\3 \frac{1}{4} & 3.250 \\3 \frac{1}{2} & 3.500 \\3 \frac{3}{4}& 3.750\end{array} \begin{array}{ll}16 \frac{1}{2} & 16.500 \\17 & 17.000 \\17 \frac{1}{2} & 17.500 \\18 &18.000\end{array} \begin{array}{cc}18 & 700 \\20 & 800 \\22 & 900 \\25 & 1000\end{array}
\begin{array}{cc}4 & 4.000 \\4 \frac{1}{4} & 4.250 \\4 \frac{1}{2} & 4.500 \\4 \frac{3}{4}& 4.750\end{array} \begin{array}{ll}18 \frac{1}{2} & 18.500 \\19 & 19.000 \\19 \frac{1}{2} & 19.500 \\20 &20.000\end{array} \begin{aligned}&28 \\&30 \\&35\end{aligned}