# Integrated Thermal and Dynamic Analysis of Dry Automotive Clutch Linings
## 1 Introduction  
Take-up judder is a low frequency torsional rigid body dynamic response of the clutch system which is experienced by vehicle occupants during the clutch engagement at vehicle take-off. The frequency range is usually 5-20 Hz, leading to vehicle kangaroo-type fore and aft oscillations which are quite disconcerting [1]. [PERSON] [2] investigated the effect of frictional performance of the clutch lining material on the generated torsional vibrations. He concluded that friction-induced torsional vibrations of the clutch system appear with low drivetrain damping and particularly with a negative gradient for the coefficient of friction variation with clutch facing slip speed, whilst the clamp load, torsional stiffness and mass moment of inertia of the clutch showed slight effects. [PERSON] et al. [3] used a dedicated clutch dynamometer to investigate the self-excited vibrations during clutch engagement. They determined that judder arises due to the thermo-elastic distortion of contacting surfaces, or misalignments in the drivetrain, as well as a negative coefficient of friction of clutch lining material with interfacial slip speed. The engine torsional torque fluctuations (engine orders) are another known factor, affecting the clutch take-up judder phenomenon, which has been studied by several authors [4; 5]. [PERSON] et al. [6; 7] and [PERSON] et al. [8] developed detailed multi-body dynamic models, including measured clutch interfacial frictional characteristics. They showed that in addition to the clutch lining negative coefficient of friction slope characteristics with interfacial slip, loss of clamp load due to hurried release of clutch pedal increases the propensity to judder. [PERSON] and [PERSON] [9] reported their combined experimental test rig and dynamic modelling for the investigation of the clutch judderphenomenon. They concluded that the major cause of judder is the variation in axial (clamp) load resulting from any misalignment of the driveline system. Additionally, judder was shown to be influenced by the clutch friction characteristics, the engagement time and the position of the bottom of the depression in the friction-sliding speed variation. The simulation results indicated that judder occurs at a position, where the axial load reaches its maximum value, and the flywheel velocity drops just prior to the full engagement. [PERSON] et al. [10; 11] used lumped parameter modelling to investigate clutch judder. Two models were developed, one with four degrees of freedom (4-DOF) and another with 12 degrees of freedom, including an automatic transmission, differential gearing, and the driveline. It was shown that the clutch facing frictional characteristics plays a key role in the generation of clutch torsional vibrations. It was also reported that increasing the static coefficient of friction is likely to decrease the tendency to stick-slip. [PERSON] et al. [12] also created a 4-DOF clutch engagement model, incorporating the measured clutch friction lining characteristics through use of pin-on-disc tribometry in line with SAE (Society of Automotive Engineers) and ASTM (American Society for Testing and Materials) standards [13]. [PERSON] et al. [12] also showed that stick-slip friction, caused by a negative slope of coefficient of friction variation with slip at the clutch plate interface, is the main cause of clutch take-up judder. They also showed that the judder response spectrum is broader than that previously reported but is more discernible with higher amplitudes of oscillation in the range 8-20 Hz. The above investigations studied clutch judder under cold or isothermal contact conditions. It has been shown by a number of authors that prolonged engagement times increase the quantity of generated heat in the contact, in time altering the interfacial lining characteristics, increasing the propensity to judder as well as causing dry clutch failures [14; 15; 16].