how to solve 13

Question

2. The following specifications apply to a simple gear train having a pinion A and a gear wheel B: Module=10mm Pressure angle=20 degrees Gear ratio=3:2 PCD of pinion=160mm Calculate the following: 2.1. the number of teeth each gear wheel 2.2. the addendum and dedendum of the gear teeth 2.3. the outside diameters of both gears 2.4. the pitch circle diameter of the gear wheel 2.5. the total depth of tooth 2.6. the tooth thickness at the pitch circle.

Answer 1

2.1)

Number teeth of pinion can be calculated using the formula  z = d/m .

Where d is PCD of pinion (d) is =  160 mm .

         m is module = 10 mm .

z = 160 mm / 10 mm = 16 teeth .

So the number of teeth on pinion gear is 16 teeth .

Given the wheel to pinion gear ratio is 3:2 .

so  number of teeth on wheel gear is (16*3)/2

                                              = 48/2  = 24 teeth 

So the number of teeth on wheel gear is 24 teeth .

Answer 2

2.2)

Addendum of the gear teeth can be calculated using the formula  h _a = m .

Where  m is module = 10 mm .

h _a =  10 mm

Hence the addendum of the gear teeth is 10 mm .

Dedendum of the gear teeth can be calculated using the formula  h _f = 1.25 m .

 h _f = 1.25 m = 1.25 * 10 = 12.5 mm

Hence the dedendum of the gear teeth is 12.5 mm .

Answer 3

2.3)

The outside diameter of the pinion gear can be calculated using the formula D _o = (z + 2) x m .

Where z is the number of teeth on pinion gear = 16 .                  [From 2.1]

         m is module = 10 mm .

D _o = (16 + 2) x 10  = 18 x 10  = 180

The outside diameter of the pinion gear is 180 mm .

The outside diameter of the wheel gear can be calculated using the formula D _o = (z + 2) x m .

Where z is the number of teeth on pinion gear = 24 .                 [From 2.1]

D _o = (24 + 2) x 10  = 26 x 10 = 260

The outside diameter of the wheel gear is 260 mm .

Answer 4

2.4)

The pitch circle diameter of the gear wheel is can be calculated using the formula d _g  = z . m .

Where z is the number of teeth on wheel gear = 24 .                  [From 2.1]

         m is module = 10 mm .

d _g  = z . m

d _g  = 24*10

d _g  =  240 mm

So the pitch circle diameter of the gear wheel is 240 mm .

Answer 5

2.5)

Total depth or whole depth tooth can be calculated using the formula  h = 2.25 m .

Where m is module = 10 mm .

h = 2.25 m

h = 2.25 * 10

h = 22.5 mm

So the total depth or whole depth tooth is 22.5 mm .

Answer 6

2.6)

The tooth thickness at the pitch circle can be calculated using the formula  ctt = p/2 .

Where p is  the circular pitch and p = m.π .

So the tooth thickness at the pitch circle is  ctt =  m.π  /2 .

Where m is module  = 10 mm .

 ctt =  m.π  /2  =  10.π  /2  =  10 * 1.5707

 ctt =  15.707 mm .

Hence the tooth thickness at the pitch circle is 15.7 mm .