LossyGearGear with mesh efficiency and bearing friction (stuck/rolling possible) 
This information is part of the Modelica Standard Library maintained by the Modelica Association.
This component models the gear ratio and the losses of a standard gear box in a reliable way including the stuck phases that may occur at zero speed. The gear boxes that can be handled are fixed in the ground or on a moving support, have one input and one output shaft, and are essentially described by the equations:
flange_a.phi = i*flange_b.phi; (flange_b.tau  tau_bf_b) = i*eta_mf*(flange_a.tau  tau_bf_a); // or flange_b.tau = i*eta_mf*(flange_a.tau  tau_bf_a  tau_bf_b/(i*eta_mf));
where
The loss terms "eta_mf", "tau_bf_a" and "tau_bf_b" are functions of the absolute value of the input shaft speed w_a and of the energy flow direction. They are defined by parameter lossTable[:,5] where the columns of this table have the following meaning:
w_a  eta_mf1  eta_mf2  tau_bf1  tau_bf2 
...  ...  ...  ...  ... 
...  ...  ...  ...  ... 
with
w_a  Absolute value of angular velocity of input shaft flange_a 
eta_mf1  Mesh efficiency in case that flange_a is driving 
eta_mf2  Mesh efficiency in case that flange_b is driving 
tau_bf1  Absolute resultant bearing friction torque with respect to flange_a
in case that flange_a is driving (= tau_bf_a*eta_mf1 + tau_bf_b/i) 
tau_bf2  Absolute resultant bearing friction torque with respect to flange_a
in case that flange_b is driving (= tau_bf_a/eta_mf2 + tau_bf_b/i) 
With these variables, the mesh efficiency and the bearing friction are formally defined as:
if (flange_a.tau  tau_bf_a)*w_a > 0 or (flange_a.tau  tau_bf_a) == 0 and w_a > 0 then eta_mf := eta_mf1 tau_bf := tau_bf1 elseif (flange_a.tau  tau_bf_a)*w_a < 0 or (flange_a.tau  tau_bf_a) == 0 and w_a < 0 then eta_mf := 1/eta_mf2 tau_bf := tau_bf2 else // w_a == 0 eta_mf and tau_bf are computed such that der(w_a) = 0 end if; flange_b.tau = i*(eta_mf*flange_a.tau  tau_bf);
Note, that the losses are modeled in a physically meaningful way taking into account that at zero speed the movement may be locked due to the friction in the gear teeth and/or in the bearings. Due to this important property, this component can be used in situations where the combination of the components Modelica.Mechanics.Rotational.IdealGear and Modelica.Mechanics.Rotational.GearEfficiency will fail because, e.g., chattering occurs when using the Modelica.Mechanics.Rotational.GearEfficiency model.
useSupport 
Value: false Type: Boolean Description: = true, if support flange enabled, otherwise implicitly grounded 

useHeatPort 
Value: false Type: Boolean Description: =true, if heatPort is enabled 
ratio 
Value: Type: Real Description: Transmission ratio (flange_a.phi/flange_b.phi) 
lossTable 
Value: [0, 1, 1, 0, 0] Type: Real[:,5] Description: Array for mesh efficiencies and bearing friction depending on speed 
flange_a 
Type: Flange_a Description: Flange of left shaft 


flange_b 
Type: Flange_b Description: Flange of right shaft 

support 
Type: Support Description: Support/housing of component 

heatPort 
Type: HeatPort_a Description: Optional port to which dissipated losses are transported in form of heat 
Modelica.Mechanics.Rotational.Examples Example to show that gear efficiency may lead to stuck motion 

Modelica.Mechanics.Rotational.Examples Example to show combination of LossyGear and BearingFriction 

Modelica.Mechanics.Rotational.Examples Example that failed in the previous version of the LossyGear version 

Modelica.Mechanics.Rotational.Examples Demonstrate the modeling of heat losses 
Modelica.Mechanics.Rotational.Components Realistic model of a gearbox (based on LossyGear) 