Clutch or Brake Engagement Energy and Heat
How much heat a clutch or brake has to soak up each time it engages.
Example
You enter
- Driving-side inertia WR² (lb ft²) 20
- Driven-side inertia WR² (lb ft²) 10
- Driving-side speed (rpm) 1800
- Driven-side speed (rpm, 0 from rest) 0
- Slip torque of the clutch (lb ft, blank to skip) 100
- Weight of metal absorbing the heat (lb, blank to skip) 15
- Specific heat (BTU/lb °F; 0.12 steel or cast iron) 0.12
You get
- Energy turned into heat 3681.1
- Slip time (s) 0.3906
- Common speed after engagement 1200 rpm
- Temp rise f 2.628
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
ScopeTwo spinning masses slip until they turn together, and the energy they lose, I1 I2 (w1 - w2)^2 / (2 (I1 + I2)), goes into the friction faces. It also gives the common speed, the slip time at the clutch torque, and the temperature rise of the metal that absorbs it. Picking up a 10 lb ft2 load from rest with a 20 lb ft2 drive at 1,800 rpm dumps 3,681 ft-lb in 0.39 s at 100 lb-ft of slip and warms 15 lb of steel about 2.6 F per engagement. A design aid; the clutch rating governs.
Formula or tableI = WR^2/g (g = 32.174 ft/s^2); dw = |n1 - n2| x 2 pi/60; E = I1 I2 dw^2/(2 (I1 + I2)) ft lb; E_btu = E/778.169; t_slip = I1 I2 dw/(T (I1 + I2)); n_final = (WR1^2 n1 + WR2^2 n2)/(WR1^2 + WR2^2); dT = E_btu/(C m); average heat = E_btu x engagements per hour.
Source and editionClutch and brake energy considerations (Shigley, Mischke and Budynas, Mechanical Engineering Design, Ch. 16), by name: the kinetic energy lost when two inertias lock together by friction, the slip time at a constant torque, and the temperature rise of the absorbing mass.
Free accessConservation of angular momentum and energy; the inertias, speeds, torque, mass, and specific heat are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namesdriver_wr2_lbft2, driven_wr2_lbft2, driver_rpm, driven_rpm, slip_torque_lbft, absorbing_weight_lb, specific_heat_btu_lbf, energy_ftlb, slip_time_s, final_rpm, temp_rise_f
- Energy lost E = I1 I2 (w1 - w2)^2 / (2 (I1 + I2))Shigley Ch. 16
- Slip time t = I1 I2 (w1 - w2)/(T (I1 + I2)) at constant slip torqueShigley Ch. 16
- Temperature rise dT = E/(C m), C = 0.12 BTU/lb F steel or cast iron, no coolingShigley Ch. 16