Gearbox efficiency simulation

A number of blocks of the "Mechanics" library are designed to simulate various kinds of gearboxes and gears with friction losses in the gear mesh. The loss rate is characterized by the efficiency of the gearbox. For clarity, the approach to simulate the efficiency of gearboxes will be described on the example of a gearbox, both shafts of which rotate. To generalize, the physical dimensions of the quantities will be omitted, since the described approach is also applicable for the translatory motion of the gear transmission elements.

Dependence of efficiency on the direction of power transmission

The torques on the shafts of a mechanical transmission with a unitary drive ratio are related by the formulas:
  • when transmitting power from the driving shaft to the driven shaft:

  • when transmitting power from the driven shaft to the driving shaft:

where:
  • T1 and T2 – torques on the driving and driven shafts of the gearbox, respectively
  • ν12 – efficiency of the gearbox when transmitting power from the driving shaft to the driven shaft
  • ν21 – efficiency of the gearbox when transmitting power from the driven shaft to the driving shaft
To achieve the stability of the numerical solution when changing the direction of power transmission, the value of the torque ratio KEff smoothly changes from the value ν12 to the value 1/ν12. The torques are calculated by the formula:

The Figure (Figure 1) shows a plot of the dependence of the torque ratio KEff on the transmitted power. The power transmitted from the driving shaft to the driven shaft is considered positive.


Figure 1. Dependence of the torque ratio on the transmitted power

The value of Qth determines the power threshold below which the efficiency value will differ from the specified one.

Ways to define the efficiency

The library blocks allow you to set the value of friction loss in the gear mesh in the following ways:
  • "No loss" – efficiency of the gear mesh is assumed to be equal to 1
  • "Constant efficiency" – gear mesh efficiency has a constant value
  • "Variable efficiency on load" – efficiency value is calculated analytically depending on the current values of torques on the gearbox shafts
  • "Table data efficiency on load" – efficiency value is calculated by linear interpolation of the table data depending on the current values of torques on the gearbox shafts
  • "Table data efficiency on temperature" – efficiency value is calculated by linear interpolation of the table data depending on the current values of torques on the gearbox shafts

Regardless to a way to define gear mesh loss the bearing friction loss of a gearbox may be defined separately using the corresponding coefficients of bearing friction.

Variable efficiency on load

When defining the variable efficiency on load its value is calculated using the formula:

where:
  • ν – calculated efficiency value
  • ν0 – efficiency at the rated load
  • T0 – rated torque at the driven shaft, Nm
  • Tmin – the minimum torque at the driving shaft required for motion start, Nm
  • T – current torque value at the driven shaft, Nm

The calculated efficiency value is limited by zero from below. In this case the driving shaft is that from which the power is being taken, and the driven shaft is that to which the power is transmitted.

The Figure (Рисунок 2) shows a plot of the dependence of the efficiency on the torque at the driven shaft.


Figure 2. Dependence of the efficiency on the torque

The value defines the torque at the driven shaft that corresponds to the torque at the driving shaft.