1304 THE BELL SYSTEM TECHNICAL JOURNAL, NOVEMBER 1954 



two test methods. The remaining 1,500 dyne-cm difference can be 

 accounted for by considering the friction in the mechanism before and 

 after the critical velocity. 



Initially the system is accelerating as a simple fly wheel under the 

 influence of the motor spring. At the critical velocity the governor studs 

 engage the case and the dial rotates at virtually constant speed for the 

 rest of the rundown period. This implies that the average speed of the 

 moving parts in the mechanism will be twice as great for the period after 

 the critical velocity as before. By considering the friction which exists 

 in the dial bearings,* one can see the effect of this change in speed on the 

 torque required to drive the mechanism. In sliding bearings with film 

 lubrication the coefficient of friction is a function of speed. Specificalh', 

 as the speed of rotation of the journals increases, the coefficient of fric- 

 tion in the bearings will increase. Since the regulated dial speed is greater 

 than the average speed while accelerating, friction in the system will 

 also be greater. One can, therefore, justify the remaining 1,500 dyne-cm 

 torque difference w^hich exists before and after the critical ^'elocity by 

 considering it to result from the increased friction at the higher speed. 



Therefore, by considering the effect of the pulsing mechanism and 

 friction in the system, it has been possible to account for the difference 

 in torciue determined by the two test methods. Table VI shows the dis- 

 position of the torque. 



Appendix III 



DERIVATION OF CHATTER EQUATION FOR FLY-BAR TYPE GOVERNOR 



Consider the governor rotating in the vertical plane at constant speed 

 CO. Referring to the schematic Fig. 7 and taking moments about B 



FJ) - F,h - Fnd + y.F^c - ml sin /3 = 



* Design of Machine Members, Valence and Doughtie, p. 255. 



