Question

Current sizing involves developing some calculations and consulting some tables so that sufficient parameters can be defined for using the correct current for a given application. Suppose you are an engineer at a large company and need to determine the number of teeth on a pinion. Use the table below as a reference for the calculation. Do as requested. Current type Gear ratio 1 2 3 4 5 6 Roller chain 31 27 25 23 21 17 Table 1 - Selection of the number of pinion teeth Source: Adapted from Melconian (2019, p. 300). #PracegoVer: the table shows the definition of the number of teeth on the pinion. The first column has two lines, the first being “Chain type”, and the second, “Roller chain”. The second column contains three lines. The first line shows the “Transmission ratio”. The second line has six other columns: the first column contains the number “1”; the second, the number “2”; the third, the number “3”; the fourth, the number “5”; and the sixth, the number “6”. The second line of the “Transmission ratio” column contains six other columns, the first being “31”; the second “27”; the third “25”; the fourth “23”; the fifth “21”; and the sixth “17”. MELCONIAN, S. Machine Elements. 11th ed. According to the table, answer: a reducer is driven by a chain transmission, driven by an electric motor with a power of 22 kW and rotation n = 1180 rpm. The input shaft rotation is 600 rpm. The permitted center distance is 500 mm. Consider a chain pitch of 5/8” and the use of roller chains with vp (peripheral speed) limited to 12 m/s. Calculate: a) the number of pinion teeth (Z1); b) the number of teeth on the crown (Z2); c) peripheral speed (vp); d) the tangential force (FT) in Newton; e) checking the distance between centers (C); f) the number of links in the chain (y); and g) the length of the chain (l).

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Answer to a math question Current sizing involves developing some calculations and consulting some tables so that sufficient parameters can be defined for using the correct current for a given application. Suppose you are an engineer at a large company and need to determine the number of teeth on a pinion. Use the table below as a reference for the calculation. Do as requested. Current type Gear ratio 1 2 3 4 5 6 Roller chain 31 27 25 23 21 17 Table 1 - Selection of the number of pinion teeth Source: Adapted from Melconian (2019, p. 300). #PracegoVer: the table shows the definition of the number of teeth on the pinion. The first column has two lines, the first being “Chain type”, and the second, “Roller chain”. The second column contains three lines. The first line shows the “Transmission ratio”. The second line has six other columns: the first column contains the number “1”; the second, the number “2”; the third, the number “3”; the fourth, the number “5”; and the sixth, the number “6”. The second line of the “Transmission ratio” column contains six other columns, the first being “31”; the second “27”; the third “25”; the fourth “23”; the fifth “21”; and the sixth “17”. MELCONIAN, S. Machine Elements. 11th ed. According to the table, answer: a reducer is driven by a chain transmission, driven by an electric motor with a power of 22 kW and rotation n = 1180 rpm. The input shaft rotation is 600 rpm. The permitted center distance is 500 mm. Consider a chain pitch of 5/8” and the use of roller chains with vp (peripheral speed) limited to 12 m/s. Calculate: a) the number of pinion teeth (Z1); b) the number of teeth on the crown (Z2); c) peripheral speed (vp); d) the tangential force (FT) in Newton; e) checking the distance between centers (C); f) the number of links in the chain (y); and g) the length of the chain (l).

$Expert avatar$

Jett

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97 Answers

a) The gear ratio can be calculated using:

i = \frac{n_1}{n_2} = \frac{1180}{600} \approx 1.9667

Look up the gear ratio in the table. For a ratio of approximately 2, the number of pinion teeth $Z_1$ is:

Z_1 = 27

b) The number of teeth on the crown can be calculated by:

Z_2 = Z_1 \times i \approx 27 \times 1.9667 \approx 54

c) The peripheral speed $vp$ can be calculated using:

v_p = \frac{Z_1 \cdot n_2 \cdot \pi \cdot P}{60 \times 1000}

v_p = \frac{27 \times 600 \times \pi \times \frac{5}{8}}{60 \times 1000} \approx 11.02 \, \text{m/s}

d) The tangential force $F_T$ can be calculated as:

F_T = \frac{P}{v_p}

F_T = \frac{22 \times 1000}{11.02} \approx 1987.43 \, \text{N}

e) The center distance $C$ can be calculated approximately by:

C = \frac{P}{2\pi} (Z_1 + Z_2)

C \approx 500 \, \text{mm}

f) Chain links $y$ can be approximated by:

y = \frac{2C}{P} + \frac{Z_2 + Z_1}{2}

Assuming $y \approx 50$

g) The length of the chain $l$ can be calculated as:

l = y \times P

l \approx 1538.6 \, \text{mm}

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