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### Dynamometer Types Equations and Calculators

Dynamometer Types, Equations and Calculators

Torque from large motors and engines is measured by a dynamometer. Absorption dynamometers (e.g., the simple friction brake, Prony brake, water brake, and fan brake) dissipate energy as the torque is measured. Opposing torque in pumps and compressors must be supplied by a driving dynamometer, which has its own power input. Transmission dynamometers (e.g., torque meters, torsion dynamometers) use strain gauges to sense torque. They do not absorb or provide energy.

Using a brake dynamometer involves measuring a force, a moment arm, and the angular speed of rotation. The familiar torque-power-speed relationships are used with absorption dynamometers.

Preview: Dynamometer Types Calculators

Eq. 1, Torque

*T = F · r*

Eq. 2, Power

*P _{ft-lbf/min} = 2 · π · T_{ft-lbf} · η_{rpm}*

Absorption - Brake Dynamometer

Eq. 3a, [SI Units]

*P = T _{m} · η / 9,549
*

Eq. 3b, [US Units]

*P = 2 · π · T · η / 33,000*

Some brakes and dynamometers are constructed with a “standard” brake arm whose length is 5.252 ft. In that case, the horsepower calculation conveniently reduces to

Eq. 4 (standard brake arm)

*P _{hp} = F_{lbf} · η_{rpm} / 1,000 *

If an absorption dynamometer uses a DC generator to dissipate energy, the generated voltage (V in volts) and line current (I in amps) are used to determine the power. Equation 4 and Eq. 5 are used to determine the torque.

*Eq. 5 [absorption]
*

*P*

_{hp}= I · V / [ η (1,000 W/kW) ( 0.7457 w/hp) ]For a driving dynamometer using a DC motor,

Eq. 6 [driving]

*P _{hp} = I · V · η / [ (1,000 W/kW) ( 0.7457 w/hp) ]*

Torque can be measured directly by a torque meter
mounted to the power shaft. Either the angle of twist,
*Φ*, or the shear strain, τ / G, is measured. The torque in a
solid shaft of diameter, d, and length, L, is

Eq. 7

*T = J · G · Φ / L = ( π/32 ) d ^{4} ( G · Φ / L )*

Eq. 8 [solid round]

*T = π / 16 · d ^{3} · τ *

Where

T = torque, ft-lbf (N-m)

F = force, lbf (N)

*r* = radius, in (m)

*η* = efficiency, %

*I* = amps

*V* = Volts

*P _{hp}* = power, hp (kW)

*Φ*= angle of twist, deg.

*J*= polar moment of inertia, in

^{4}(m

^{4})

*G*= shear modulus, lbf/in

^{2}(Pa)

*τ*= shear stress, lbf/in

^{2}(Pa)

L = length of shaft in, (m)

Reference

- Civil Engineering Reference Manual, Fifteenth Edition, Michael R. Lindeburg, PE

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