The speed of the crankshaft is found to vary between 120 r.p.m. and 150 r.p.m. during one cycle of operation. What is the coefficient of fluctuation of speed?

Concept:

Maximum Fluctuation of Speed:

The difference between the maximum and minimum speeds during a cycle is called the maximum fluctuation of speed i.e. (N1 - N2).

Coefficient of Fluctuation of Speed (C_s):

The ratio of the maximum fluctuation of speed to the mean speed is called the coefficient of fluctuation of speed.

\({C_s} = \;\frac{{{N_1} - \;{N_2}}}{N} = \;\frac{{2\left( {{N_1} - \;{N_2}} \right)}}{{{N_1} + \;{N_2}}}\)

N = Mean speed in r.p.m. \(= \frac{{{N_1} + \;{N_2}}}{2}\)

Coefficient of steadiness (m):

The reciprocal of the coefficient of fluctuation of speed is known as the coefficient of steadiness.

\(\begin{array}{l} m = \frac{1}{{Coeff.\;of\;fluctuation\;of\;speed}}\\ = \frac{{{N_{mean}}}}{{{N_{max}} - {N_{min}}}} = \frac{{{N_1} + \;{N_2}}}{{2\left( {{N_1} - {N_2}} \right)}} \end{array}\)

Calculation:

Given:

N1 = 150 rpm and N2 = 120 rpm

N  = Mean speed in r.p.m. \(= \frac{{{N_1} + \;{N_2}}}{2}=\frac{{{120} + \;{150}}}{2} =135\ rpm\)

Maximum fluctuation of speed = 150 - 120 = 30 rpm

and \({C_s} = \;\frac{{{N_1} - \;{N_2}}}{N} =\frac{30}{135}\)

∴ CS = 0.22.