95%
Example
Data
Actuating pressure: 300 kPa
Outer diameter primary piston: 140 mm
Inner diameter primary piston: 80 mm
Friction coefficient: 0.05
Outer diameter plate: 140 mm
Inner diameter plate: 120 mm
Number of plates: 6
Question What is the maximum transferable torque?
Calculation
Pressure
The actuating pressure is behind the primary piston.
300 kPa = 30 N/cm²
Area
The outer diameter of the primary piston is 140 mm
(= 14 cm).
$$A_1 = 1/4 \times \pi \times d^2 = 1/4 \times \pi \times 14^2 = 153.94 cm^2$$
The inner diameter of the primary piston is 80 mm
(= 8 cm).
$$A_2 = 1/4 \times \pi \times d^2 = 1/4 \times \pi \times 8^2 = 50.27 cm^2$$
Calculating the area of the primary piston:
$$153.94 - 50.27 = 103.67 cm^2$$
Clamping force
The force exerted on the area of the piston is
calculated by multiplying the pressure and the area
(in cm²).
$$F_{clamp} = p \times A = 30 \times 103.67 cm^2 = 3110.1 N$$
Friction circle
Both $$r_1$$ and $$r_2$$ of the plates are known.
$$r_f = 0.5 \times (r_1 + r_2) = 0.5 \times (0.07 + 0.06) = 0.065$$
Frictional force
$$F_f = \mu \times F_{clamp} \times z = 0.05 \times 3110.1 \times 12 = 1866.06 N$$
Maximum transferable torque
$$T_m$$ can now be calculated by substituting $$F_f$$ and $$r_f$$:
$$T_m = F_f \times r_f = 1866.06 \times 0.065 = 121.29 Nm$$
Behind this primary piston, the oil pressure is 400 kPa.
What's the force the piston exerts on the clutch
pack ($$F_{clamp}$$)?