Maximum power in V-belt drive with varying friction and groove angle

[oxon88]

Homework Statement

1. A pulley 150 mm diameter is driven directly by an electric motor at 250 revs min–1. A V-belt is used to transmit power from this pulley to a second pulley 400 mm diameter against a load of 200 Nm.

The distance between the centre of the pulleys is 600 mm, the included angle of the pulley groove = 40°, the coefficient of friction between the belt and pulley is 0.4 and the ultimate strength of the belt is 8 kN.

What would be the effect of the following factors on the maximum power which can be transmitted (give reasons for your answer):

(i) increasing the coefficient of friction

(ii) increasing the included angle of the pulley groove.

Homework Equations

F1 / F2 = e^{µθ/ sinα}

The Attempt at a Solution

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Increasing the coefficient of friction would increase the power up to a certain point. graph 1 shows this. however I'm having some trouble explaining why this is.

Increasing the included angle of the pulley groove will have the effect of decreasing the power. again i have a graph which shows this, but cannot really explain why.

can anyone advise?

 

[Bystander]

Increasing the included angle of the pulley groove will have the effect of decreasing the power.

What's coeff. of friction as a function of angle?

 

[oxon88]

not really sure, would that be F1 / F2 = e^{µθ/ sinα}

but solved for sinα?