Analytical model and material equivalent methods for steady state heat partition coefficient between two contact discs in multi-disc clutch

The heat partition coefficient between two finite thickness contact discs during long-time sliding is studied with a coupled finite element method. Results show that the heat partition coefficient varies from its initial value to another steady state value rapidly instead of being a constant all the time. An analytical solution of the temperature field under invariant heat flux input is deduced, which tells that there exists a unique critical thickness ratio between the contact discs that keeps the heat partition coefficient a constant. An equivalent method for single-material contact bodies is proposed that is capable of calculating the steady state heat partition coefficient for any thickness ratio. It reveals that the steady state heat partition coefficient only has relationship with the mass density and the heat capacity of the materials and the thickness ratio. Based on this method, a two-step material equivalent method is further proposed for the contact discs that have friction linings on them. The solution shows that the steady state heat partition coefficient in this situation is also only determined by the material properties and the layer thicknesses. A test bench of multi-disc clutch is set up and a series of sliding experiments are conducted to validate the proposed equivalent methods and solutions of steady state heat partition coefficient. The measured experimental temperature variations show that the temperature level of the separator disc in the clutch is overestimated with the constant heat partition coefficient of semi-infinite model, while it is close to those calculated results with steady state heat partition coefficient. Therefore, the temperature fields of the contact discs during long-time sliding with constant speed can be figured out efficiently using the steady state heat partition coefficient with only small error, and these equivalent methods benefit the multi-disc clutch design and temperature estimation in practical applications.