The nominal velocity ratio is
VR = 575/275 = 2.09
Specify an overload factor of K_o = 1.50 from Table 9–1 for a uniform power source and moderate shock for the meat grinder. Then compute design power,

P_{des} = K_{o}P = (1.50)(15 kW) = 22.5 kW
From Figure 9–11, m = 5 is a reasonable trial module. Then
N_P = 18 (design decision)
D_P = N_Pm = (18)(5) = 90 mm
N_G = N_P(VR) = (18)(2.09) = 37.6 (Use 38)
D_G = N_Gm = (38)(5) = 190 mm
Final output speed = n_G = n_P(N_P/N_G)
n_G = 575 rpm × (18/38) = 272 rpm (OK)

Center distance = C = (N_P + N_G)m/2[Table 8–1]
C = (18 + 38)(5)/2 = 140 mm (OK)
In SI units, the pitch line speed in meters per second (m/s) is
v_t = πD_Pn_P/(60 000) = [(π)(90)(575)]/(60 000) = 2.71 m/s
In SI units, the transmitted load, W_t, is in newtons (N). If the power, P, is in kW, and v_t is in m/s,
W_t = 1000(P)/v_t = (1000)(15)/(2.71) = 5536 N
Face width, F: Let’s specify the nominal F = 12m = 12(5) = 60 mm

Factors in stress analysis:

K_o = 1.50 (found earlier)
K_s = 1.00 (Table 9–2; m = 5)              K_B = 1.00 (Use solid gear blanks)
K_R = 1.00 (Table 9–11; 0.99 reliability)                  S_F = 1.00 (No unusual conditions)
K_v = 1.31 (Figure 9–16;      A_v = 11)
K_m = 1.21 (Figures 9–12 and 9–13;  F = 60 mm;  F/D_P = 60/90 = 0.67)
J_P = 0.315; J_G = 0.380 (Figure 9–10; N_P = 18, N_G = 38)
C_p = 191 (Table 9–7)      I = 0.092 (Figure 9–17)

Pinion contact stress:
(Equation 9–23)

S_{c}=C_{P} \sqrt{\frac{W_{t} K_{o} K_{s} K_{m} K_{v}}{F D_{P} l}}=191 \sqrt{\frac{(5536)(1.50)(1.0)(1.21)(1.31)}{(60)(90)(0.092)}}=983 \mathrm{MPa}
Adjustments for number of cycles, from Figures 9-21 and 9-22:
Y_{N p}=0.94 \quad Z_{N P}=0.91 \quad Y_{N G}=0.96 \quad Z_{N G}=0.92
Required s_{a C P}=s_{C}(S F)\left(K_{R}\right) / Z_{N P}=983 \mathrm{MPa}(1.0)(1.0) / 0.91=1080 \mathrm{MPa}
Using S_{a c P}=1080 \mathrm{MPa}, Figure 9-19 shows the required hardness =\mathrm{HB} 396 for through-hardened Grade 1 steel. This is acceptable but near the upper end of recommended range.

Material specification:

From Figure A4–5 (other possibilities exist),
SAE 4340 OQT 800; HB 415; s_y = 1324 MPa; s_u = 1448 MPa; 12% elongation.

Check other stresses:

The contact stress for the gear and the bending stress for the pinion and the gear are expected to require less material hardness and strength.
Required s_{acG} = s_c(SF)(K_R)/Z_{NG} = 983 MPa(1.0)(1.0)/0.92 = 1068 MPa
This is slightly lower than for the pinion (OK)

\begin{aligned}S_{t P} &=\frac{W_{t} K_{0} K_{S} K_{B} K_{m} K_{v}}{F m J_{P}}=\frac{(5536)(1.50)(1)(1)(1.21)(1.31)}{(60)(5)(0.315)}=139 \mathrm{MPa} \\\text { Required } S_{a t P} &=S_{t P}(S F)\left(K_{R}\right) / Y_{N P}=139 \mathrm{MPa}(1.0)(1.0) / 0.94=148 \mathrm{MPa}\end{aligned}
Referring to Figure 9-18, it is obvious that bending stress requires far lower hardness for the gear teeth, less than HB 180. The stress in the gear is always less than that in the pinion so it will obviously be safe as well.

Summary of the Design:
P=15.0 \mathrm{~kW} from an electric motor to a large meat grinder
Pinion speed: n_{P}=575 \mathrm{rpm}
Gear speed: n_{G}=272 \mathrm{rpm}
Number of teeth: N_{P}=18 ; N_{G}=38 Center distance: C=140.00 \mathrm{~mm}
Module: m=5 \mathrm{~mm}
Diameters: D_{P}=90 \mathrm{~mm} ; D_{G}=190 \mathrm{~mm}
Material: Steel-SAE 4340 OQT 800

Comment:

A redesign may be considered with several possible approaches:
1. Increase the face width, F, to lower the stresses and permit the choice of a material with more moderate required hardness and better ductility. The recommended upper limit of face width is 16m = 16(5) = 80 mm.
2. Increase the size of pinion and its number of teeth (same module) to lower stresses.
Possible trial: Module: m = 5 mm Number of teeth: N_P = 22; N_G = 46
Center distance: C = 170.00 mm Diameters: D_P = 110[latex] mm; [latex]D_G = 230 mm
3. Consider case-hardened steel for the initial design, rather than through-hardened steel. A smaller design is possible.