Question

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A new design of an automotive disk clutch (as shown in Figure 18.2) is to be fitted with nine springs, each compressed at 5mm to provide a clamping force of 1.8 kN. The clutch is to have two driving surfaces and two driven surfaces. The moulded friction material provides a conservatively estimated coefficient of friction 0.39 when in contact with the flywheel and the pressure plate. The outer ring radius is set to 276 mm when the engine produces a maximum torque of 208279 Nmm. Determine resulting factor of safety with respect to slippage of a brand new clutch assuming ideal usage of the surface area. Answer to 2 decimals. Your answer must be accurate within 5%.

Answer 1

Given For Spring

No. of spring 9 Clamping force of one spring 1.8 kN 1.8x 103 N Clamping force of 9 springs 9x1.8x103 N 16200 N Compression of each spring,6 5 mm

For Clutch

Co-efficient of friction, u0.39 Outer ring radius of the clutch, D 276 mm Maximum engine torque, M, 208279 mm The clutch is new

To find: Factor of safety (FOS)

Solution Since, as per question the clutch is new, therefore we will use Uniform Pressure Theory. d Therefore for maximum torque capacity, the optimum ratio is 0.577 where,dis the inner ring diameter of the clutch d 0.577 d 0.577xD

d 0.577x276 d159.25 mm

Now as per question there are two pairs of contacting surfaces pair between the flywheel and the friction disc a) one b) one pair between the friction disc and the pressure plate Maximum torque transmitted by the engine 208279 N_mm 208279 Torque transmitted by one pair,M, 2 104139.5 N mm

Now we know Torque transmitting capacity or permissible torque of the clutch from Uniform Pressure Theory is xFx(D-d3 М, 3x(D2-d2 tper 0.39x 16200x(276 -159.25 3x(2762 159.252 M, per

6318x(21024576-4038669.6) 3x(76176-25360.6) 6318x(16985906.4) 3x(50815.4) M, per M, per 1.073169566x101 M, per 152446.2 M, =703966.098 N mm per

Factor of safety (FOS)=lorque transmitting capacity Torque transmitted М, per М, 703966.098 104139.5 6.7598 6.75

Hence, when the clutch is new, the Factor of safety (FOS) with respect slippage is 6.75