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## Q. 7.3

For the belt drive layout shown in Figure 7–28 perform the following calculations for the kinematics of the drive:

a. Specify the number of teeth and the pitch diameter of each sheave.
b. Calculate the velocity ratio of the belt drive and the angular velocity of the driven sheave.
c. Calculate the belt linear velocity.
d. Determine the center distance using a 1200-8MGT-30 belt.

## Verified Solution

Given: Data in Figure 7–28. Input sprocket speed = 1400 rpm
a. Pitch diameters: From Table 7–4,
P32-8MGT-30 sprocket: 32 teeth; Pitch diameter = 3.208 in
P80-8MGT-30 sprocket: 80 teeth; Pitch diameter = 8.020 in
b. Velocity ratio: Using Equation (7–4)  in Section 7–2,

$V R=\frac{n_{\text {driving }}}{n_{\text {driven }}}=\frac{N_{\text {driven }}}{N_{\text {driving }}}=\frac{80}{32}=2.50$
Driven speed of the driven sprocket:
$n_{\text {driven }}=\frac{n_{\text {driving }}}{V R}=\frac{1400 \mathrm{rpm}}{2.5}=560 \mathrm{rpm}$
c. Belt speed: Using Equation (7-3) in Section 7-2,
$v_{\text {bell }}=\frac{P D_{\text {driving }}}{2} n_{\text {driving }}=\frac{3.208 \mathrm{in}}{2} \cdot 1400 \frac{\mathrm{rev}}{\mathrm{min}} \cdot \frac{2 \pi \mathrm{rad}}{\mathrm{rev}} \cdot \frac{1.0 \mathrm{ft}}{12 \mathrm{in}}=1175.8 \mathrm{ft} / \mathrm{min}$
d. Center distance: From Table 7-7, using 32 and 80 teeth and $1200-8 \mathrm{MGT}-30$ belt,
$C D=14.61 \mathrm{in}$

 TABLE 7–4 Sprockets with 8 mm Belt Pitch Dim’s all widths 20-mm Wide belt 30-mm Wide belt 50-mm Wide belt 85-mm Wide belt No. of teeth Pitch dia. Flange dia. Sprocket number Bushing size Sprocket number Bushing size Sprocket number Bushing size Sprocket number Bushing size 22 2.206 2.559 P22-8MGT-20 1108 P22-8MGT-30 1180 N/A N/A N/A N/A 24 2.406 2.756 P24-8MGT-20 1108 P24-8MGT-30 1180 N/A N/A N/A N/A 26 2.607 2.953 P26-8MGT-20 1108 P26-8MGT-30 1180 N/A N/A N/A N/A 28 2.807 3.15 P28-8MGT-20 1108 P28-8MGT-30 1180 P28-8MGT-50 MPB N/A N/A 30 3.008 3.346 P30-8MGT-20 1210 P30-8MGT-30 1210 P30-8MGT-50 1210 N/A N/A 32 3.208 3.543 P32-8MGT-20 1210 P32-8MGT-30 1210 P32-8MGT-50 1210 N/A N/A 34 3.409 3.819 P34-8MGT-20 1610 P34-8MGT-30 1610 P34-8MGT-50 1610 P34-8MGT-85 1615 36 3.609 3.937 P36-8MGT-20 1610 P36-8MGT-30 1610 P36-8MGT-50 1610 P36-8MGT-86 1615 38 3.81 4.134 P38-8MGT-20 1610 P38-8MGT-30 1610 P38-8MGT-50 1610 P38-8MGT-87 1610 40 4.01 4.331 P40-8MGT-20 1610 P40-8MGT-30 2012 P40-8MGT-50 2012 P40-8MGT-88 2012 44 4.411 4.764 P44-8MGT-20 2012 P44-8MGT-30 2012 P44-8MGT-50 2012 P44-8MGT-89 2012 48 4.812 5.157 P48-8MGT-20 2012 P48-8MGT-30 2012 P48-8MGT-50 2012 P48-8MGT-90 2012 56 5.614 5.945 P56-8MGT-20 2012 P56-8MGT-30 2012 P56-8MGT-50 2517 P56-8MGT-91 2517 64 6.416 6.772 P64-8MGT-20 2012 P64-8MGT-30 2517 P64-8MGT-50 2517 P64-8MGT-92 2517 72 7.218 7.598 P72-8MGT-20 2012 P72-8MGT-30 2517 P72-8MGT-50 2517 P72-8MGT-93 3020 80 8.02 8.386 P80-8MGT-20 2517 P80-8MGT-30 2517 P80-8MGT-50 2517 P80-8MGT-94 3020 90 9.023 N/A P90-8MGT-20 2517 P90-8MGT-30 2517 P90-8MGT-50 3020 P90-8MGT-95 3020 112 11.229 N/A N/A N/A P112-8MGT-30 2517 P112-8MGT-50 3020 P112-8MGT-96 3020 144 14.437 N/A N/A N/A P144-8MGT-30 2517 P144-8MGT-50 3020 P144-8MGT-97 3535 192 19.249 N/A N/A N/A N/A N/A P192-8MGT-50 3020 P192-8MGT-98 3535
 TABLE 7–7 8-mm Pitch GT Drive Selection Table Sprocket combinations Center distance (inches) Driver Driven Velocity ratio 920-8MGT P.L. 36.220 115 teeth 960-8MGT P.L. 37.795 120 teeth 1040-8MGT P.L. 40.945 130 teeth 1064-8MGT P.L. 41.890 133 teeth 1120-8MGT P.L. 44.094 140 teeth 1160-8MGT P.L. 45.669 145 teeth 1200-8MGT P.L. 47.244 150 teeth 1224-8MGT P.L. 48.189 153 teeth 1280-8MGT P.L. 50.394 160 teeth 1440-8MGT P.L. 56.693 180 teeth 1512-8MGT P.L. 59.528 189 teeth 1584-8MGT P.L. 62.362 198 teeth 1600-8MGT P.L. 62.992 200 teeth 1760-8MGT P.L. 69.291 220 teeth 1800-8MGT P.L. 70.866 225 teeth 2000-8MGT P.L. 78.740 250 teeth 22 22 1.000 14.65 15.43 17.01 17.48 18.58 19.37 20.16 20.63 21.73 24.88 26.3 27.72 28.03 31.18 31.97 35.9 24 24 1.000 14.33 15.12 16.69 17.17 18.27 19.06 19.84 20.32 21.42 24.57 25.98 27.4 27.72 30.87 31.65 35.59 26 26 1.000 14.02 14.8 16.38 16.85 17.95 18.74 19.53 20 21.1 24.25 25.67 27.09 27.4 30.55 31.34 35.28 28 28 1.000 13.7 14.49 16.06 16.54 17.64 18.43 19.21 19.69 20.79 23.94 25.35 26.77 27.09 30.24 31.02 34.96 30 30 1.000 13.39 14.17 15.75 16.22 17.32 18.11 18.9 19.37 20.47 23.62 25.04 26.46 26.77 29.92 30.71 34.65 32 32 1.000 13.07 13.86 15.43 15.91 17.01 17.8 18.58 1906 20.16 23.31 24.72 26.14 26.46 29.61 30.39 34.33 34 34 1.000 12.76 13.54 15.12 15.59 16.69 17.48 18.27 18.74 19.84 22.99 24.41 25.83 26.14 29.29 30.08 34.02 36 36 1.000 12.44 13.23 14.8 15.28 16.38 17.17 17.95 18.43 19.53 22.68 24.09 25.51 25.83 28.98 29.76 33.7 38 38 1.000 12.13 12.91 14.49 14.96 16.06 16.85 17.64 18.11 19.21 22.36 23.78 25.2 25.51 28.66 29.45 33.39 40 40 1.000 11.67 12.46 14.03 14.5 15.61 16.39 17.18 17.65 18.76 21.91 23.32 24.74 25.06 28.21 28.99 32.93 44 44 1.000 11.18 11.97 13.54 14.02 15.12 15.91 16.69 17.17 18.27 21.42 22.83 24.25 24.57 27.72 28.5 32.44 48 48 1.000 10.55 11.34 12.91 13.39 14.49 15.28 16.06 16.54 17.64 20.79 22.21 23.62 23.94 27.09 27.87 31.81 56 56 1.000 9.29 10.08 11.65 12.13 13.23 14.02 14.8 15.28 16.38 19.53 20.95 22.36 22.68 25.83 26.61 30.55 64 64 1.000 8.03 8.82 10.39 10.87 11.97 12.76 13.54 14.02 15.12 18.27 19.69 21.1 21.42 24.57 25.35 29.29 72 72 1.000 9.13 9.61 10.71 11.5 12.28 12.76 13.86 17.01 18.43 19.84 20.16 23.31 24.1 28.03 80 80 1.000 9.45 10.24 11.02 11.5 12.6 15.75 17.17 18.58 18.9 22.05 22.84 26.77 24 30 1.250 13.85 14.64 16.22 16.69 17.79 18.58 19.37 19.84 20.94 24.09 25.51 26.93 27.24 30.39 31.18 35.12 32 40 1.250 12.43 13.22 14.8 15.27 16.37 17.16 17.95 18.42 19.52 22.67 24.09 25.51 25.82 28.97 29.76 33.7 64 80 1.250 9.1 9.57 10.68 11.47 12.26 12.73 13.84 16.99 18.41 19.83 20.14 23.29 24.08 28.02 72 90 1.250 9.25 10.04 10.83 11.3 12.41 15.56 16.98 18.4 18.72 21.87 22.66 26.6 24 32 1.333 13.7 14.48 16.06 16.53 17.63 18.42 19.21 19.68 20.78 23.93 25.35 26.77 27.08 30.23 31.02 34.96 30 40 1.333 12.59 13.38 14.95 15.42 16.53 17.32 18.1 18.58 19.68 22.83 24.25 25.66 25.98 29.13 29.92 33.85 36 48 1.333 11.48 12.27 13.85 14.32 15.42 16.21 17 17.47 18.57 21.72 23.14 24.56 24.87 28.03 28.81 32.75 48 64 1.333 9.26 10.05 11.63 12.1 13.2 13.99 14.78 15.25 16.36 19.51 20.93 22.35 22.66 25.81 26.6 30.54 24 36 1.500 13.36 14.15 15.73 16.2 17.3 18.09 18.88 19.35 20.46 23.61 25.02 26.44 26.76 29.91 30.7 34.63 32 48 1.500 11.78 12.57 14.15 14.62 15.73 16.52 17.3 17.78 18.88 22.03 23.45 24.87 25.18 28.34 29.12 33.06 48 72 1.500 8.58 9.37 10.96 11.43 12.54 13.33 14.12 14.6 15.7 18.86 20.28 21.7 22.01 25.17 25.96 29.9 22 44 2.000 12.87 13.66 15.24 15.71 16.81 17.6 18.39 18.87 19.97 23.12 24.54 25.96 26.28 29.43 30.22 34.16 24 48 2.000 12.38 13.17 14.75 15.23 16.33 17.12 17.91 18.39 19.49 22.65 24.06 25.48 25.8 28.95 29.74 33.68 28 56 2.000 11.41 12.2 13.79 14.26 15.37 16.16 16.95 17.42 18.53 21.69 23.11 24.53 24.84 28 28.79 32.73 32 64 2.000 10.43 11.22 12.81 13.29 14.4 15.19 15.98 16.46 17.56 20.73 22.15 23.57 23.88 27.04 27.83 31.77 36 72 2.000 9.43 10.24 11.83 12.31 13.42 14.22 15.01 15.49 16.6 19.76 21.18 22.61 22.92 26.08 26.87 30.81 40 80 2.000 8.42 9.23 10.84 11.32 12.44 13.23 14.03 14.51 15.62 18.79 20.22 21.64 21.96 25.12 25.91 29.85 56 112 2.000 9.18 10 10.94 11.63 14.85 16.29 17.73 18.05 21.23 22.03 25.99 72 144 2.000 12.22 13.7 14.02 17.26 18.06 22.07 32 80 2.500 8.97 9.78 11.4 11.88 13.01 13.81 13.81 15.08 16.2 19.38 20.81 22.23 22.55 25.71 26.51 30.46 36 90 2.500 7.71 8.55 10.19 10.68 11.82 1.62 12.62 13.91 15.03 18.22 19.66 21.09 21.4 24.58 25.37 29.32 24 72 3.000 10.27 11.08 12.69 13.17 14.29 15.08 15.08 16.36 17.47 20.65 22.07 23.5 23.82 26.98 27.77 31.72 30 90 3.000 8.1 8.94 10.6 11.09 12.23 13.04 13.85 14.33 15.46 18.65 20.09 21.52 21.84 25.02 25.81 29.77 48 144 3.000 12.29 13.81 15.31 15.64 18.92 19.73 23.76