Answer to Question #180506 in Mechanical Engineering for Diocel Ann Heria

Question

8. Figure shown

represents a schematic

diagram of a Porter

governor. Each fly ball

weighs 16.1 lb and the

central weight D is 40 lb.

Determine the rotational

speed in rpm about the

vertical axis AD at which

the weight D begins to

rise.

Answer 1

Given : BP = BD = 250 mm ; m = 5 kg ; M = 30 kg ; r₁ = 150 mm ; r₂ = 200 mm

Minimum and maximum speed of the governor

The minimum and maximum position of the governor is shown in Fig. 1 (a) and (b) respectively. N₁ = Minimum speed when r₁ = BG = 150 mm,

and N₂ = Maximum speed when r₂ = BG = 200 mm. 

Fig.1.

To find Speed range of the governor

Referring Fig. 1 (a), height of the governor, 

Referring fig. 1 (b) height of the governor, 

Speed range when friction at the sleeve is equivalent of 20 N of load (i.e. when F = 20 N). When the sleeve moves downwards, the friction force (F) acts upwards and the minimum speed is given by 

We also know that when the sleeve moves upwards, the frictional force (F) acts downwards and the maximum speed is given by

Speed range of the governor = N₂ – N₁= 210 – 172 = 38 rpm.