Consistent efficiency

 In the simplest model of a lossy transmission, the Efficiency of the gear engagement is denoted by η_12 and is assumed to be constant, independent of the load. Conventional notation is (1,2) = (input shaft, output shaft).

 Friction losses described by the Efficiency property are fully taken into account in the energy balance only when the transmitted power through the transmission exceeds a certain threshold \(p_{прг}\). If the power is below this threshold, a hyperbolic tangent function is used, which smoothly changes the influence of the Efficiency coefficient at low power values.

 If the transmission has different Efficiency when changing the direction of power flow inside the unit, then friction is calculated using the formula (1):

(1)\[M_{f} = \frac{M}{2} \cdot ((ПП+ОП)\cdot \tanh(4p/p_{прг})-ПП+ОП)\]

where:

 \(ПП\) - losses during power transmission from the input shaft (1) to the output shaft (2) (2):

(2)\[ПП= 1-\eta_{21}\]

where \(\eta_{21}\) is the efficiency of torque transmission from the output (2) shaft to the input (1).

 «ОП» - losses during power transmission from the output shaft (2) to the input shaft (1) (3):

(3)\[ОП= \frac{1}{\eta_{12}}-1\]

where \(\eta_{12}\) is the efficiency of torque transmission from the input (1) shaft to the output (2) shaft.

 \(M\) - transmitted torque;

 \(p\) - transmitted power;

 \(p_{прг}\) - power threshold after which total losses begin to take effect.

 For some types of transmissions, for example a gear reducer, it is assumed that the Efficiency is the same for the forward and reverse power flow, i.e. \(η_{12}=η_{21}\). In cases where the transmissions use linear mechanics parameters, a similar formula for determining losses is used.