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Mathematics for Machine Technology

John C. Peterson, Robert D. Smith

Chapter 48

Applications of Formulas to Spur Gears - all with Video Answers

Educators

Chapter Questions

03:03

Problem 1

Use the formula $N=\frac{1}{2} \sqrt{2 D P_n}$ with $D=5$ and $N=12$ to determine $P_n$. Round your answer to 3 decimal places.

AG
Ankit Gupta
Numerade Educator
00:28

Problem 3

The pitch $(P)$ of a spur gear equals the number $(N)$ of gear teeth divided by the pitch diameter $(D): P=\frac{N}{D}$. Determine $N$ when $P=5$ and $D=5.6000$ inches.

Sanchit Gogia
Sanchit Gogia
Numerade Educator
00:32

Problem 4

Solve $1.95 x-0.75 x=\frac{27-15}{5}$

James Kiss
James Kiss
Numerade Educator
01:14

Problem 5

If $p=5, q=3.4$, and $r=9$, what is the value of $\frac{p^2-q r}{4(p-q)}$ ?

James Kiss
James Kiss
Numerade Educator

Problem 6

Read the setting on the following 0.001 -inch micrometer scale. The vernier, thimble, and barrel scales are shown in flattened view.

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Problem 7

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Circular Pitch }=1.5708^{\sim} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 8

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=10 & \text { Circular Pitch } & \\
\hline
\end{array}
$$

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Problem 9

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=5.2000^{\prime} \\
\text { Number of Teeth }=26
\end{array} & \text { Circular Pitch } & \\
\hline
\end{array}
$$

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Problem 10

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=12.5714^{\prime \prime} \\
\text { Number of Teeth }=44
\end{array} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 11

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch }=7 \\
\text { Number of Teeth }=26
\end{array} & \text { Pitch Diameter } & \\
\hline
\end{array}
$$

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Problem 12

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Circular Pitch }=0.3142^{\prime \prime} \\
\text { Number of Teeth }=12
\end{array} & \text { Pitch Diameter } & \\
\hline
\end{array}
$$

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Problem 13

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=18 & \text { Circular Pitch } & \\
\hline \begin{array}{l}
\text { Pitch Diameter }=0.7273^{\prime} \\
\text { Number of Teeth }=16
\end{array} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 14

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=0.7273^{\prime} \\
\text { Number of Teeth }=16
\end{array} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 15

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch }=12 \\
\text { Pitch Diameter }=1.1667^{\prime \prime}
\end{array} & \text { Number of Teeth } & \\
\hline
\end{array}
$$

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Problem 16

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Circular Pitch }=0.6283^{\prime} \\
\text { Pitch Diameter }=8.4000^\gamma
\end{array} & \text { Number of Teeth } & \\
\hline
\end{array}
$$

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Problem 17

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number of Teeth }=56 \\
\text { Pitch }=8 \\
\end{array} & \text { Outside Diameter } & \\
\hline
\end{array}
$$

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Problem 18

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=14 & \text { Addendum } & \\
\hline
\end{array}
$$

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Problem 19

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=1.3333^{\prime} \\
\text { Dedendum }=0.0643^{\prime \prime}
\end{array} & \text { Root Diameter } & \\
\hline
\end{array}
$$

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Problem 20

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=3.4 & \text { Whole Depth } & \\
\hline
\end{array}
$$

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Problem 21

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Circular Pitch }=0.2856^{\prime} & \text { Working Depth } & \\
\hline
\end{array}
$$

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Problem 22

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Circular Pitch }=1.4650^{\prime} & \text { Clearance } & \\
\hline
\end{array}
$$

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Problem 23

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=20 & \text { Tooth Thickness } & \\
\hline
\end{array}
$$

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Problem 24

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=3.5000^{\circ} \\
\text { Addendum }=0.1818^{\circ}
\end{array} & \text { Outside Diameter } & \\
\hline
\end{array}
$$

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Problem 25

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Circular Pitch }=0.0954^{\prime \prime} & \text { Dedendum } & \\
\hline
\end{array}
$$

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Problem 26

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Circular Pitch }=0.8976^{\prime \prime} & \text { Addendum } & \\
\hline
\end{array}
$$

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Problem 27

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Addendum }=0.1429^{\prime \prime} \\
\text { Dedendum }=0.1653^{\prime}
\end{array} & \text { Whole Depth } & \\
\hline
\end{array}
$$

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Problem 28

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=4 & \text { Dedendum } & \\
\hline
\end{array}
$$

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Problem 29

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Circular Pitch }=0.3076^{\prime \prime} & \text { Whole Depth } & \\
\hline
\end{array}
$$

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Problem 30

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=17 & \text { Clearance } & \\
\hline
\end{array}
$$

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Problem 31

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit for each of the following gearing problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Pitch }=9 & \text { Working Depth } & \\
\hline
\end{array}
$$

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Problem 32

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Addendum }=0.0857^{\prime \prime} & \text { Circular Pitch } & \\
\hline
\end{array}
$$

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Problem 33

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Addendum }=0.0666^{\prime \prime} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 34

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Addendum }=0.2000^{\circ} \\
\text { Outside Diameter }=4.8000^{\circ}
\end{array} & \text { Pitch Diameter } & \\
\hline
\end{array}
$$

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Problem 34

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Addendum }=0.2000^{\circ} \\
\text { Outside Diameter }=4.8000^{\circ}
\end{array} & \text { Pitch Diameter } & \\
\hline
\end{array}
$$

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Problem 35

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Outside Diameter }=2.7144^{\prime} \\
\text { Number of Teeth }=17
\end{array} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 36

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Outside Diameter }=4.3750^{\prime \prime} \\
\text { Circular Pitch }=0.3927^*
\end{array} & \text { Number of Teeth } & \\
\hline
\end{array}
$$

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Problem 37

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Working Depth }=0.0769^{\prime \prime} & \text { Pitch } & \\
\hline
\end{array}
$$

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Problem 38

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Working Depth }=0.4500^{\prime \prime} & \text { Circular Pitch } & \\
\hline
\end{array}
$$

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Problem 39

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. The formula in terms of the unknown is not given. Choose the formula that consists of the given parts, rearrange in terms of the unknown, and solve.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Outside Diameter }=4.7144^{\prime \prime} \\
\text { Pitch Diameter }=4.4286^{\prime \prime}
\end{array} & \text { Addendum } & \\
\hline
\end{array}
$$

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Problem 40

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number ofTeeth }=72 \\
\text { Pitch Diameter }=6.0000^{\circ}
\end{array} & \text { Addendum } & \\
\hline
\end{array}
$$

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Problem 41

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number ofTeeth }=44 \\
\text { Pitch Diameter }=3.6667^*
\end{array} & \text { Dedendum } & \\
\hline
\end{array}
$$

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Problem 42

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number ofTeeth }=10 \\
\text { Pitch Diameter }=2.5000^{\prime \prime}
\end{array} & \text { Whole Depth } & \\
\hline
\end{array}
$$

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Problem 43

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number ofTeeth = } 90 \\
\text { Pitch Diameter }=12.8571^{\prime \prime}
\end{array} & \text { Working Depth } & \\
\hline
\end{array}
$$

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Problem 44

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=1.0625^{\prime \prime} \\
\text { Pitch }=16
\end{array} & \text { Outside Diameter } & \\
\hline
\end{array}
$$

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Problem 45

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=2.9167^{\prime \prime} \\
\text { Pitch }=12
\end{array} & \text { Root Diameter } & \\
\hline
\end{array}
$$

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Problem 46

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number ofTeeth }=29 \\
\text { Pitch Diameter }=2.0714^{\prime \prime}
\end{array} & \text { Root Diameter } & \\
\hline
\end{array}
$$

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Problem 47

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Number ofTeeth }=75 \\
\text { Pitch Diameter }=6.8182^{\prime \prime}
\end{array} & \text { Clearance } & \\
\hline
\end{array}
$$

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Problem 48

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \text { Addendum }=0.1429^{\prime \prime} & \text { Tooth Thickness } & \\
\hline
\end{array}
$$

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Problem 49

Refer to the Decimal-Inch Spur Gears Table under the heading "Gearing-Diametral Pitch System" earlier in this unit. No single formula is given that consists of the given parts and the unknown. Two or more formulas, some in rearranged form, must be used in solving these problems.
$$
\begin{array}{|c|c|c|}
\hline \text { GIVEN VALUES } & \text { FIND } & \text { ANSWER } \\
\hline \begin{array}{l}
\text { Pitch Diameter }=1.0455^{\prime \prime} \\
\text { Addendum }=0.0455^{\prime \prime}
\end{array} & \text { Number of Teeth } & \\
\hline
\end{array}
$$

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Problem 50

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears. Determine the average backlash of each of the following using this formula.
$$
\text { Average backlash }=\frac{0.030}{P}
$$
A 7-pitch gear

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Problem 51

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears. Determine the average backlash of each of the following using this formula.
$$
\text { Average backlash }=\frac{0.030}{P}
$$
A 20 -pitch gear

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Problem 52

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears. Determine the average backlash of each of the following using this formula.
$$
\text { Average backlash }=\frac{0.030}{P}
$$
A 3.5 -pitch gear

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Problem 53

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears. Determine the average backlash of each of the following using this formula.
$$
\text { Average backlash }=\frac{0.030}{P}
$$
A gear with a whole depth of $0.2696^{\prime \prime}$

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Problem 54

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears. Determine the average backlash of each of the following using this formula.
$$
\text { Average backlash }=\frac{0.030}{P}
$$
A gear with a working depth of $0.1176^{\prime \prime}$

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Problem 55

Backlash is the amount that a tooth space is greater than the engaging tooth on the pitch circles of two gears. Determine the average backlash of each of the following using this formula.
$$
\text { Average backlash }=\frac{0.030}{P}
$$
A gear with a pitch diameter of $4.800^{\prime \prime}$ and 24 teeth

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Problem 56

The center distance of a pinion and a gear is the distance between the centers of the pitch circles. Determine the center distance of each of the following using this formula.
$$
\text { Center Distance }=\frac{\text { Pitch Diameter of Gear }+ \text { Pitch Diameter of Pinion }}{2}
$$
A pinion with a pitch diameter of 2.8300 inches and a gear with a pitch diameter of 4.1667 inches

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Problem 57

The center distance of a pinion and a gear is the distance between the centers of the pitch circles. Determine the center distance of each of the following using this formula.
$$
\text { Center Distance }=\frac{\text { Pitch Diameter of Gear }+ \text { Pitch Diameter of Pinion }}{2}
$$
A pinion with a pitch diameter of 4.8889 inches and a gear with a pitch diameter of 8.6752 inches

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Problem 58

The center distance of a pinion and a gear is the distance between the centers of the pitch circles. Determine the center distance of each of the following using this formula.
$$
\text { Center Distance }=\frac{\text { Pitch Diameter of Gear }+ \text { Pitch Diameter of Pinion }}{2}
$$
A 9-pitch pinion and gear; the pinion has 23 teeth and the gear has 38 teeth

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Problem 59

The center distance of a pinion and a gear is the distance between the centers of the pitch circles. Determine the center distance of each of the following using this formula.
$$
\text { Center Distance }=\frac{\text { Pitch Diameter of Gear }+ \text { Pitch Diameter of Pinion }}{2}
$$
A 16-pitch pinion and gear; the pinion has 18 teeth and the gear has 44 teeth

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Problem 60

The center distance of a pinion and a gear is the distance between the centers of the pitch circles. Determine the center distance of each of the following using this formula.
$$
\text { Center Distance }=\frac{\text { Pitch Diameter of Gear }+ \text { Pitch Diameter of Pinion }}{2}
$$
A gear and pinion with a circular pitch of 0.1745 inch; the gear has 55 teeth and the pinion has 37 teeth

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Problem 61

Refer to the Metric Spur Gears Table under the heading "GearingMetric Module System" earlier in this unit and determine the values in the following table.
$$
\begin{array}{|l|c|c|c|c|c|c|c|}
\hline \text { Module } & \begin{array}{c}
\text { Number } \\
\text { of Teeth }
\end{array} & \begin{array}{c}
\text { a. Pitch } \\
\text { Diameter }
\end{array} & \begin{array}{c}
\text { b. Circular } \\
\text { Pitch }
\end{array} & \begin{array}{c}
\text { c. Outside } \\
\text { Diameter }
\end{array} & \text { d. Addendum } & \begin{array}{c}
\text { e. Working } \\
\text { Depth }
\end{array} & \begin{array}{c}
\text { f. Tooth } \\
\text { Thickness }
\end{array} \\
\hline 6.5 \mathrm{~mm} & 18 & & & & & & \\
\hline
\end{array}
$$

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Problem 62

Refer to the Metric Spur Gears Table under the heading "GearingMetric Module System" earlier in this unit and determine the values in the following table.
$$
\begin{array}{|l|c|c|c|c|c|c|c|}
\hline \text { Module } & \begin{array}{c}
\text { Number } \\
\text { of Teeth }
\end{array} & \begin{array}{c}
\text { a. Pitch } \\
\text { Diameter }
\end{array} & \begin{array}{c}
\text { b. Circular } \\
\text { Pitch }
\end{array} & \begin{array}{c}
\text { c. Outside } \\
\text { Diameter }
\end{array} & \text { d. Addendum } & \begin{array}{c}
\text { e. Working } \\
\text { Depth }
\end{array} & \begin{array}{c}
\text { f. Tooth } \\
\text { Thickness }
\end{array} \\
\hline 9 \mathrm{~mm} & 24 & & & & & & \\
\hline
\end{array}
$$

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Problem 63

Refer to the Metric Spur Gears Table under the heading "GearingMetric Module System" earlier in this unit and determine the values in the following table.
$$
\begin{array}{|l|c|c|c|c|c|c|c|}
\hline \text { Module } & \begin{array}{c}
\text { Number } \\
\text { of Teeth }
\end{array} & \begin{array}{c}
\text { a. Pitch } \\
\text { Diameter }
\end{array} & \begin{array}{c}
\text { b. Circular } \\
\text { Pitch }
\end{array} & \begin{array}{c}
\text { c. Outside } \\
\text { Diameter }
\end{array} & \text { d. Addendum } & \begin{array}{c}
\text { e. Working } \\
\text { Depth }
\end{array} & \begin{array}{c}
\text { f. Tooth } \\
\text { Thickness }
\end{array} \\
\hline 2.5 \mathrm{~mm} & 10 & & & & & & \\
\hline
\end{array}
$$

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Problem 64

Refer to the Metric Spur Gears Table under the heading "GearingMetric Module System" earlier in this unit and determine the values in the following table.
$$
\begin{array}{|l|c|c|c|c|c|c|c|}
\hline \text { Module } & \begin{array}{c}
\text { Number } \\
\text { of Teeth }
\end{array} & \begin{array}{c}
\text { a. Pitch } \\
\text { Diameter }
\end{array} & \begin{array}{c}
\text { b. Circular } \\
\text { Pitch }
\end{array} & \begin{array}{c}
\text { c. Outside } \\
\text { Diameter }
\end{array} & \text { d. Addendum } & \begin{array}{c}
\text { e. Working } \\
\text { Depth }
\end{array} & \begin{array}{c}
\text { f. Tooth } \\
\text { Thickness }
\end{array} \\
\hline 3.75 \mathrm{~mm} & 16 & & & & & & \\
\hline
\end{array}
$$

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Problem 65

Refer to the Metric Spur Gears Table under the heading "GearingMetric Module System" earlier in this unit and determine the values in the following table.
$$
\begin{array}{|l|c|c|c|c|c|c|c|}
\hline \text { Module } & \begin{array}{c}
\text { Number } \\
\text { of Teeth }
\end{array} & \begin{array}{c}
\text { a. Pitch } \\
\text { Diameter }
\end{array} & \begin{array}{c}
\text { b. Circular } \\
\text { Pitch }
\end{array} & \begin{array}{c}
\text { c. Outside } \\
\text { Diameter }
\end{array} & \text { d. Addendum } & \begin{array}{c}
\text { e. Working } \\
\text { Depth }
\end{array} & \begin{array}{c}
\text { f. Tooth } \\
\text { Thickness }
\end{array} \\
\hline 10 \mathrm{~mm} & 26 & & & & & & \\
\hline
\end{array}
$$

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Problem 66

Compute the whole depth of a 5-millimeter module gear designed with a clearance of $0.157 \times$ module.

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Problem 67

What is the number of teeth on a 4-millimeter module gear with a pitch diameter of 120 millimeters?

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Problem 68

What is the module of a gear that has a working depth of 13 millimeters?

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Problem 69

Compute the dedendum of a 7-millimeter module gear designed with a clearance of $0.1667 \times$ module.

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Problem 70

What is the module of a gear with 38 teeth and an outside diameter of 220 millimeters?

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