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

**i**is the constant**gear ratio**,**eta_mf**= eta_mf(w_a) is the**mesh efficiency**due to the friction between the teeth of the gear wheels,**tau_bf_a**= tau_bf_a(w_a) is the**bearing friction torque**on the flange_a side,**tau_bf_b**= tau_bf_b(w_a) is the**bearing friction torque**on the flange_b side, and**w_a**= der(flange_a.phi) is the speed of flange_a

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 > 0or(flange_a.tau - tau_bf_a) == 0andw_a > 0theneta_mf := eta_mf1 tau_bf := tau_bf1elseif(flange_a.tau - tau_bf_a)*w_a < 0or(flange_a.tau - tau_bf_a) == 0andw_a < 0theneta_mf := 1/eta_mf2 tau_bf := tau_bf2else// w_a == 0 eta_mf and tau_bf are computed such thatder(w_a) = 0end 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.

- The essential idea to model efficiency in this way is from Christoph Pelchen, ZF Friedrichshafen.
- The article (Pelchen et.al. 2002), see Literature below, and the first implementation of LossyGear (up to version 3.1 of package Modelica) contained a bug leading to a non-converging solution in cases where the driving side is not obvious. This was pointed out by Christian Bertsch and Max Westenkirchner, Bosch, and Christian Bertsch proposed a concrete solution how to fix this bug, see Literature below.

- Pelchen C., Schweiger C., and Otter M.: "Modeling
and Simulating the Efficiency of Gearboxes and of Planetary
Gearboxes," in
*Proceedings of the 2nd International Modelica Conference, Oberpfaffenhofen, Germany,*pp. 257-266, The Modelica Association and Institute of Robotics and Mechatronics, Deutsches Zentrum für Luft- und Raumfahrt e. V., March 18-19, 2002. - Bertsch C. (2009): "Problem with model LossyGear and a proposed solution", Ticket #108, Sept. 11, 2009.

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