Gear Train Application (continued)

 

Step 5:  Calculate   φA/B:     Here:   φA/B  =  T1 L / J G  =  TA L / J G 

 

 

Step 6:  The total angle of rotation of the shaft at A  =   φA  =  φA/B  +  φgear 1 

 

   φA  =   TA L / J G  +  [TA (R2 / R1)2 L] / J G  =   TA L [ 1 + (R2/R1)2 ] / J G       (result)

 

 

 

For the Given Data:

 

Shearing modulus of elasticity, G, of 10 x 106 psi.   Shaft length, L, is 100 inches.

Each shaft  diameter is 5 inches.  T = 5,000 ft lb.  R1 = 12 in,  R2 = 4 in.

 

 

 

   φA  =   (5,000)(12) lb in (100 in) [1 + 9 ] / [π(5)4/32 in4][107 lb/in2 ]

 

   φA  =   0.0978 rad  =  5.6 o     (result)

 

 

 

Maximum shear stress in shaft 1:

 

                       τ1max  =  T1(d/2)/J  =  TA(d/2)/J  =  16 TA/ (π d3 )                (result)

 

                      τ1max  =  (16)(5,000)(12) / (π 53 )  =  2445  psi                     (result)

 

 

 

Maximum shear stress in shaft 2:

 

                       τ2max  =  T2(d/2)/J  =  TA(R2/R1)(d/2)/J  =  16 TA(R2/R1)/ (π d3 )     (result)

 

Thus               τ2max  =  (R2/R1)  τ1max  

 

                       τ2max  =  3 τ1max  =  7335  psi                    (result)

 

 


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