Question

A pair of bevel gears has the velocity ratio equal to (1.5). The driven gear
has 20 teeth of (15.71) circular pitch and runs at 600 r.p.m. Calculate accurately
all dimensions and make working drawing showing the gears engaged. The shaft
diameters of driver and driven gears are 30 mm and 25 mm respectively.
Additionally, make the hub diameter equal to (1.7) from the shaft diameter.
Backing for driver and driven are 28 mm and 22 mm respectively

Answer 1

Solution:

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Given,

Driving bevel gear as pinion and suffix of p

Driven bevel gear as gear and suffix of g

Thus,

Number of teeth on pinion, z_p = 20

Circular pitch of teeth for pinion, p_p = 15.71 mm

Pitch circle diameter of Pinion, D_p = z_p X p_p = 20 X 15.71 = 314.2 mm

Speed Rpm of pinion, n_p = 600 rpm

Shaft diameter of pinion, d_p = 30 mm

Hub diameter of pinion, h_p = 1.7 X 30 = 51 mm

Backing at pinion, B_p = 28 mm

Likewise,

Number of teeth on gear, z_g = To Find

PCD of gear, D_g = To Find

Rpm of gear, n_g = To Find

Shaft diameter of gear, d_g = 25 mm

Hub diameter of gear, h_g = 1.7 X 25 = 42.5 mm

Backing at gear, B_g = 22 mm

Note - Backing is the distance of pitch point from the back of hub.

Also we have following data,

Velocity ratio, VR = 1.5

Using the data we have

we get

Velocity Ratio = n_p / n_g = D_g / D_p = z_g / Z_p

Therefore,

1.5 = z_g / 20

z_g = 30 teeth

.

VR = D_g / Dp

1.5 = D_g / 314.2

D_g = 471.3 mm

n_g = n_p / VR = 600 / 1.5 = 400 rpm

.

Also we have

tan() = Z_p / Z_g = D_p / D_g

= tan^-1(20/30) = 33.69^o

Where, = Pitch angle, it is the angle made by pitch line with the axis of gear.

The cone distance, A_o = [(D_p / 2)² + (D_g / 2)² ] =  [(314.2 / 2)² + (471.3 / 2)² ] = 283.21 mm

A_o is shown in figure

Note - Tooth thickness is always equal to circular pitch

Refer following figure for working drawing of the engaged gears -