Common transmission failures result from the glazing of clutch surfaces by deposition of oil oxidation and decomposition products. Both the oxidation and decomposition processes depend on temperature histories of the surfaces. Because it is difficult to measure these surface temperatures during operation, it is useful to develop models to predict clutch-interface thermal behavior. The relative velocity between mating clutch plates, from the initial engagement to the zero-sliding (lock-up) condition, generates heat that is transferred to the plates. The relative velocity decreases at a constant rate during this period, producing a heat flux that is initially very large and decreases linearly with time, until lock-up occurs. Accordingly, q"f; = q"o [1 - (t/t1u)], where q"o = 1.6 x 107 W/m2 and t1u = 100 ms is the lockup time. The plates have an initial uniform temperature of T; = 40°C, when the prescribed frictional heat flux is suddenly applied to the surfaces. The reaction plate is fabricated from steel, while the composite plate has a thinner steel center section bonded to low-conductivity friction material layers, The thermo physical properties are Ps = 7800 kg/m J , C s = 500 J/kg . K, and ks = 40 W/m ∙ K for the steel and Pfm = 1150 kg/m3, Cfm = 1650 J/kg ∙ K. and kfm = 4 W/m ∙ K for the friction material.

(a) On T - t coordinates, sketch the temperature history at the mid plane of the reaction plate, at the interface between the clutch pair, and at the mid-plane of the composite plate. Identify key features.

(b) Perform an energy balance on the clutch pair over the time interval ∆t = t1u to determine the steady-state temperature resulting from clutch engagement. Assume negligible heat transfer from the plates to the surroundings.

(c) Compute and plot the three temperature histories of interest using the finite-element method of FEHT or the finite-difference method of IHT (with ∆x = 0.1 mm and ∆t = 1 ms). Calculate and plot the frictional heat fluxes to the reaction and composite plates, q"rp and q"cp, respectively, as a function of time. Comment on features of the temperature and heat flux histories. Validate your model by comparing predictions with the results from part (b). Note: Use of both FEHT and IHT requires creation of a look-up data table for prescribing the heat flux as a function of time.

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0.5 mm ** -2 mm -+1 mm Tx, 0) = T; Friction Steel Steel Reaction plate (rp) material Composite plate (cp) = 1.6 x 10' Wim? 4= 100 ms Time, r(s) b + b = 4)b %3!