Question

A Proell governor has equal arms of length 300 mm. The upper and lower ends of the arms are pivoted on the axis of the governor. The extension arms of the lower links are each 80 mm long and parallel to the axis when the radii of rotation of the balls are 150 mm and 200 mm. The mass of each ball is 10 kg and the mass of the central load is 100 kg. Determine the range of speed of the governor.

(a) 20 rpm

(b) 30 rpm

(c) 10 rpm

(d) 25 rpm

I have been asked this question in an interview for job.

This intriguing question comes from Principles of Governor in chapter Governor of Farm Machinery

Answer 1

Right answer is (c) 10 rpm

The best explanation: sin α = sin β = 150 / 300 = 0.5 or α = β = 30°

and, MD = FG = 150 mm = 0.15 m

FM = FD cos β = 300 cos 30° = 260 mm = 0.26 m

IM   = FM tan α = 0.26 tan 30° = 0.15 m

BM = BF + FM = 80 + 260 = 340 mm = 0.34 m

ID = IM + MD = 0.15 + 0.15 = 0.3 m

FC – m (ω 1)^2 * r1 – 10 \([\frac{2πN}{60}]\)^2 – 0.0165 (N1)^2

N1 = 170 rpm

h = PG = (PF)^2 – (FG)^2 = (300)^2 – (200)^2 = 224 mm = 0.224 m

FM = GD = PG = 224 mm = 0.224 m

BM = BF + FM = 80 + 224 = 304 mm = 0.304 m

Range of speed = N2-N1 = 10 RPM