Concept explainers
Figure 21−9 shows a compound gear train. Gears B and C are keyed to the same shaft; therefore, they turn at the same speed. Gear A and gear C are driving gears. Gear B and gear D are driven gears. Set up a proportion for each problem and determine the unknown values, x, y, and z in the table. Round the answers to 1 decimal place where necessary.
(a)
To find the speed of the different gears given in the problem.
Answer to Problem 16A
Speed of gear B is
Speed of gear C is
Speed of gear D is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
13
So,
Hence, speed of gear B is
Since, gear B and C are on same shaft. So, speed of both gear is equal.
Therefore, speed of gear C is
Again,
Hence, speed of gear D is
Thus, speed of gear B is
Speed of gear C is
Speed of gear D is
(b)
To find the number of teeth in the gear and the speed of the gear.
Answer to Problem 16A
Number of teeth in gear B is
Number of teeth in gear D is
Speed of gear C is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Hence, number of teeth in gear B is
Since, gear B and C are on same shaft. So, speed of both gear is equal.
Therefore, speed of gear C is
Again,
Hence, number of teeth in gear D is
Thus, number of teeth in gear B is
Number of teeth in gear D is
Speed of gear C is
(c)
To find the number of teeth as well as speed of the gear.
Answer to Problem 16A
Number of teeth in gear A is
Speed of gear B is
Speed of gear C is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Since, gear B and C are on same shaft. So, speed of both gear is equal. i.e.
Again,
Hence, speed of gear B and gear C is
Putting,
Thus, number of teeth in gear A is
Speed of gear B is
Speed of gear C is
(d)
To find the speed of the different gears and the number of teeth.
Answer to Problem 16A
Number of teeth in gear C is
Speed of gear A is
Speed of gear B is
Explanation of Solution
Given information:
A gear and pinion arrangement is given as below.
Calculation:
We have been given below information,
As we know that in a gear arrangement,
So,
Since, gear B and C are on same shaft. So, speed of both gear is equal. i.e.
Putting
Hence, speed of gear A is
Again,
Hence, number of teeth in gear C is
Thus, number of teeth in gear C is
Speed of gear A is
Speed of gear B is
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Chapter 21 Solutions
Mathematics For Machine Technology
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