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According to Table 1, the max. angular acceleration ratio is

a_max   =0.0306 for b = 10°.
   w˛
w = ( 250)( 2p ) rad/sec. = 26.18 rad/sec.
               60

           Hence, a_max = (0.0306) (26.18)˛ = 21.0 rad/sec˛. The weight, W, of the disc is given by 
W = p r˛ t y, where y denotes the density of steel and is equal to 0.283 lbs/in³.
                    W = p (3)˛ (0.25) (0.283) = 2 lbs.

           Inertia torque = I a_max, where I = polar mass moment of inertia of disc (in-lb-sec˛)
               =    Wr˛ , 
                     2g
and g = gravitational constant = 386 in/sec˛.

Hence, l = (2)(3)˛  = 0.0233 in-lb-sec˛.
                  (2) (386)

           Inertia torque = (21.0) (0.0233) 0A89 in-lbs. This inertia torque is a momentary maximum. The inertia torque fluctuates cyclically at two cycles per shaft revolution oscillating between plus and minus 0.489 in-lbs. 
           When system vibrations and resonances are Important, it may be required to determine the harmonic content (Fourier series development) of the output shaft displacement as a function of the displacement of the input shaft. The amplitude of the m^th harmonic (m> 1) vanishes for odd values of m, while for even values of m it is equal to (2/m) (tan1/2 b )^m, where b denotes the operating angle.

5.0 JOINT SELECTION (Torque Rating)

The capacity of a universal joint is the torque which the joint can transmit. For a given joint, this is a function of speed, operating angle and service conditions.
        Table 2 shows use factors based on speed and operating angle for two service conditions: Intermittent operation (say, operation for less than 15 minutes, usually governed by necessity for heat dissipation) and continuous operation. The torque capacity of a single Cardan joint of standard steel construction is determined as follows:
                  
        i. From the required speed in RPM, operating angle in degrees, and service condition (inter. mittent or continuous), find the corresponding use factor from Table 2.
        ii. Multiply the required torque, which is to be transmitted by the Input shaft, by the use factor. If the application involves a significant amount of shock loading, multiply by an additional dynamic factor of 2. The result must be less than the static breaking torque of the joint.
        iii. Refer to the torque capacity column in the SDP catalogue and select a suitable joint having a torque capacity not less than the figure computed in (ii), above.
         If a significant amount of power is to be transmitted and/or the speed Is high, it is desirable to keep the shaft operating angle below 15°. For manual operation operating angles up to 30° may be permissible.

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