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Chapter 12: Problem 65

The pinion of an internal gearset has pitch radius \(r_{p}=30 \mathrm{~mm}\) and the gear has pitch radius \(r_{g}=150 \mathrm{~mm}\). If the pinion is the input member of the set, determine the velocity ratio, the torque ratio, and the gear ratio of the set.

Short Answer

Expert verified
The velocity ratio of the gear set is 5, the torque ratio is 0.2, and the gear ratio is also 0.2.

Step by step solution

01

Calculate the velocity ratio

The velocity ratio, \(VR\), of a gear set can be calculated using the formula: \( VR = \frac{r_g}{r_p} \), where \(r_g\) is the pitch radius of the gear and \(r_p\) is the pitch radius of the pinion. For this task, \(r_g = 150 mm\) and \(r_p = 30 mm\). So, \( VR = \frac{150 mm}{30 mm} = 5 \). This indicates that the velocity of the gear is 5 times higher than that of the pinion.
02

Calculate the torque ratio

The torque ratio, \(TR\), is calculated in a similar way to the velocity ratio. The formula for it is \(TR = \frac{1}{VR}\). Using the VR calculated in Step 1, we find that \(TR = \frac{1}{5} = 0.2\). This suggests that the torque on the gear is 0.2 times the torque on the pinion.
03

Calculate the gear ratio

The gear ratio, \(GR\), is simply the reciprocal of the velocity ratio; so \(GR = \frac{1}{VR} = 0.2\). This means that for every rotation of the pinion, the gear rotates 0.2 times.

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Most popular questions from this chapter

A 21-tooth pinion rotating at 1800 rpm meshes with a 33-tooth gear in a spur gear reducer. Both pinion and gear are manufactured to a quality level of 9 . A reliability of \(0.9\) has been specified, and the transmitted tangential load is \(2800 \mathrm{lb}\). Conditions are such that \(K_{m}=1.7\). It is proposed that standard \(25^{\circ}\), full-depth teeth be used, with both pinion and gear hobbed from an AISI 4140 nitrided steel. The diametral pitch is 6, and the face width \(2.000\) in. Estimate the number of cycles of bending stress (using the AGMA equations) that the gearset can withstand.

A 78-tooth spur gear is in mesh with a 27-tooth pinion. The \(p_{d}=6\) and \(\phi=20^{\circ}\). Find the contact ratio.

A 22-tooth pinion rotating at 1650 rpm meshes with a 66-tooth gear in a spur gear reducer. Both pinion and gear are manufactured to a quality level of 10 . A reliability of \(0.9\) has been specified, and the transmitted tangential load is \(5000 \mathrm{lb}\). Conditions are such that \(K m=1.7\). It is proposed that standard \(25^{\circ}\), full-depth teeth be used, with both pinion and gear hobbed from an AISI 4340 nitrided steel. The diametral pitch is 5 , and the face width \(2.500\) in. Estimate the number of cycles of bending stress (using the AGMA equations) that the gearset can withstand.

A \(20^{\circ}\) pressure angle, 23-tooth spur gear has a diametral pitch of 6. Find the pitch diameter, addendum, dedendum, outside diameter, and circular pitch.

A gearset with full-depth teeth is designed to have a pinion with 24 teeth, a gear with 54 teeth, and a diametral pitch of 6. Compare the contact ratio for this set for pressure angles of \(14.5,20\), and \(25^{\circ}\).
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