I am currently working on building the mathematical model, but got stuck. Can anyone site a publication so that i can get an idea how to proceed.
You need to be clear on what the model is for? Is it to be a parametric model to accurately represent the physical system or a simple behavioral model?
If you want it to aid in developing detailed clutch control algorithms then it will need to be complex and include actuation mechanism characteristics - in which case the fact that it is a wet multi-plate clutch will be important. If you just want it to be a basic behavioral model as part of a general vehicle simulation then a simpler approach is possible.
For dynamic simulation purposes where you are interested in calculating the rotating speeds of the engine and the transmission via the torques/forces acting on them and there inertias/masses in response to simple clutch control, you need to model three states:
1. disengaged - where there is no torque transmitted through the clutch and the input and output inertias are uncoupled
2. engaging - where a constant torque acts between the input and output inertias. The sign of the torque opposing the relative motion of the input and output inertias. The level of the constant torque will reflect how hard the rider makes the clutch bite. A constant torque model is reasonable here, more complex models in which the torque is modulated in response to engine speed can be added if required.
3. engaged - where the input and output inertias are coupled and rotate at same speed.
Transition from the engaging to engaged state occurs when the speeds of the input and output elements are equal.
More complex models can include detailed viscous friction characteristics giving a non-constant relationship between slip speed, transmitted torque and actualtion pressure for example, and may also include non-linear torsional damper characteristics.
If you are simulation in the matlab/simuling environment then models are available from:
http://uk.mathworks.com/help/physmod/sdl/ug/specialized-clutches.html
If you want a simple purely kinematic model look at:
http://blog.xogeny.com/blog/part-2-kinematic/
Here is some literature:
R. Zanasi: Simulation of variable dynamic dimension systems: the clutch example
http://www.dii.unimo.it/~zanasi/didattica/Veicolo_OLD/ECC01_Clutch.pdf
M. Mitariu-Faller: Methoden und Prozesse zur Entwicklung von Friktionssystemen mit Ingenieurkeramik am Beispiel einer trockenlaufenden Fahrzeugkupplung
e.g.: https://www.isma-isaac.be/past/conf/isma2010/proceedings/papers/isma2010_0160.pdf
Guang Rao: Modellierung und Simulation des Systemverhaltens nasslaufender Lamellenkupplungen (book)
regards,
Mario
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