how to solve 12

Question

1. An epicyclical gear train consists of an annulus A, having 100 teeth, a sun gear B having 40 teeth and a planetary gear C, having 30 teeth that are mounted on arm D. 1.1. if arm D rotated at calculate the speed of sun gear B, when annulus A is fixed. 1.2. Determine the speed of annulus A, when the sun gear B is fixed and arm D rotates at 30 r/min.

Answer 1

1.1)

Speed of arm D is  30 r/min .

When annulus A is fixed , we have calculate speed of sun gear .

Let us consider the case where planetary gear is driven by sun gear 

The ratio of revolutions can be given by S/(A+S) .

Where A is number of teeths on annulus = 100 .

         S is number of teeth for sun gear = 40

Ratio of revolutions ⇒40/(100+40) ⇒ 40/140 = 2/7

This means that to get one complete rotation on the output side, the input side needs to make  three and half rotations.

Speed of the arm is 30 r/min .

So the speed of the sun gear is 30 * 2/7 = 8.5714 RPM .

The speed of the sun gear is 8.5714 RPM .

Answer 2

1.2)

Ratio of revolutions of sun gear to annulus gear is 2/7 .          [Form 1.1]

Speed of the arm is 30 r/min .

So the speed of the annulus gear is = 30 * (7/2)

                           = 30 * 3.5 = 105 RPM .

The speed of the annulus gear A is 105 RPM .