Calculate the bending strength St of the pinion spur gear gi

Calculate the bending strength (S_t) of the pinion spur gear given the following information: W_t = the transmitted tangential load = 500 pounds K_0 = the overload factor = 1.0 K_s = the size factor = 1.0 F = face width = 2.5 inches K_m = load distribution factor = 1.75 K_B = rim thickness factor = 1.0 P_d = diametral pitch = 5 teeth/inch pressure angle: 20 degrees The pinion and gear have 21 and 35 teeth respectively. A quality index \"Q\" of 7 is considered as well as a pitch line velocity of 800 inches/second.

Solution

Given that : Wt = 500 pounds

Ko =1

Ks= 1

F = face width – 2.5 inches

Km = 1.75

Kb= 1

Pd= 5 teeth/inch

Pressure angle= 20 degrees

Pinion and gear ---21 and 35 teeth

Pitch line velocity—800 inches/ sec

Assumptions made in the derivation are:

1. The full load is applied to the tip of a single tooth in static condition.

2. The radial component is negligible.

3. The load is distributed uniformly across the full face width.

4. Forces due to tooth sliding friction are negligible.

Stress concentration in the tooth fillet is negligible.

The Lewis equation indicates that tooth bending stress varies with the following:

(1) Directly with load,

(2) Inversely with tooth width b,

(3) Inversely with tooth size p or m,

(4) Inversely with tooth shape factor y or Y.

= wt/b Ym

modified lewis equation:

= wt/b Ym * kv*ko*km

The modified Lewis equation for bending stress is, = wt/Kv b Ym

where K’_v is known as velocity factor and is given by Barth’s equation below for known pitch line velocity V in m/s and is given by, Kv= 6/6+ V

kv = 6/800+6 =0.007

Factors that influence gear tooth bending stresses are as follows:

Pitch line velocity.

Manufacturing accuracy.

Contact ratio.

Stress concentration.

Degree of shock loading.

Accuracy and rigidity of mounting.

Moment of inertia of the gears and attached rotating Members

Substitute above values in the above equation we get

= wt/b Ym * kv*ko*km= 500/2.5*1.75*0.007*1*1

= 16326