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For an involute rack and pinion arrangement, the value of pressure angle and module is kept fixed at 20° and 5 mm. If the addendum of the rack is 6 mm, then minimum number of teeth on pinion to avoid interference is
Correct answer is '21'. Can you explain this answer?
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For an involute rack and pinion arrangement, the value of pressure an...
5AR = 6
⇒AR=
=1.2
=1.2=20.517
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For an involute rack and pinion arrangement, the value of pressure an...
Understanding Involute Rack and Pinion
Involute gear systems, including rack and pinion arrangements, are widely used in mechanical design for their efficient power transmission and smooth motion.
Given Parameters
- Pressure Angle: 20°
- Module: 5 mm
- Addendum of the Rack: 6 mm
Calculating Minimum Number of Teeth
To prevent interference in a pinion, the minimum number of teeth (N) is determined using the following formula, which considers the pressure angle and the module:
N = (2 * Addendum * Cos(Pressure Angle)) / Module
Substituting the values:
- Addendum: 6 mm
- Pressure Angle: 20° (cos(20°) ≈ 0.9397)
- Module: 5 mm
Now plug in the values:
N = (2 * 6 * 0.9397) / 5
This simplifies down to:
N ≈ 21.24
Since the number of teeth must be a whole number, we round up to 21 to avoid interference.
Conclusion
The minimum number of teeth required on the pinion to avoid interference in this involute rack and pinion arrangement is:
- Minimum Teeth on Pinion: 21
This ensures smooth operation and prevents potential mechanical failure due to interference between the teeth of the pinion and the rack.
Involute gear systems, including rack and pinion arrangements, are widely used in mechanical design for their efficient power transmission and smooth motion.
Given Parameters
- Pressure Angle: 20°
- Module: 5 mm
- Addendum of the Rack: 6 mm
Calculating Minimum Number of Teeth
To prevent interference in a pinion, the minimum number of teeth (N) is determined using the following formula, which considers the pressure angle and the module:
N = (2 * Addendum * Cos(Pressure Angle)) / Module
Substituting the values:
- Addendum: 6 mm
- Pressure Angle: 20° (cos(20°) ≈ 0.9397)
- Module: 5 mm
Now plug in the values:
N = (2 * 6 * 0.9397) / 5
This simplifies down to:
N ≈ 21.24
Since the number of teeth must be a whole number, we round up to 21 to avoid interference.
Conclusion
The minimum number of teeth required on the pinion to avoid interference in this involute rack and pinion arrangement is:
- Minimum Teeth on Pinion: 21
This ensures smooth operation and prevents potential mechanical failure due to interference between the teeth of the pinion and the rack.
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For an involute rack and pinion arrangement, the value of pressure angle and module is kept fixed at 20° and 5 mm. If the addendum of the rack is 6 mm, then minimum number of teeth on pinion to avoid interference isCorrect answer is '21'. Can you explain this answer?
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