【正文】
e pads at a constant velocity V. We will investigate the conditions under which a spatially sinusoidal perturbation in the temperature and stress fields can grow exponentially with respect to the time in a similar manner to that adopted by Lee and Barber. It is evidenced in their work [7] that it is sufficient to handle only the antisymmetric problem. The perturbations that are symmetric with respect to the midplane of the disc can grow at a velocity well above the sliding velocity V thus being made uninteresting. Let us introduce a coordinate system ( x1。Frictionally excited thermoelastic instability in disc brakes— Transient problem in the full contact regime Abstract Exceeding the critical sliding velocity in disc brakes can cause unwanted forming of hot spots, nonuniform distribution of contact pressure, vibration, and also, in many cases, permanent damage of the disc. Consequently, in the last decade, a great deal of consideration has been given to modeling methods of thermo elastic instability (TEI), which leads to these effects. Models based on the finite element method are also being developed in addition to the analytical approach. The analytical model of TEI development described in the paper by Lee and Barber [Frictionally excited thermo elastic instability in automotive disk brakes. ASME Journal of Tribology 1993。 Disc brake。 y) to move together with the perturbated field. Then we can write V = c1 c2。is the imaginary unit. The parameter m=m( n) =2pin/cir =2pi/L, where n is the number of hot spots on the circumference of the disc cir and L is wavelength of perturbations. The symbols T0m and p0m in the above formulae denote the amplitudes of initial nonuniformities (. fluctuations). Both perturbations (2) and (3) will be searched as plex functions their real part describing the actual perturbation of temperature or pressure field. Obviously, if the growth rate b0, the initial fluctuations are damped. On the other hand, instability develops if B〉 0. . Temperature field perturbation Heat flux in the direction of the xaxis is zero when the ribbed portion of the disc is considered. Next, let us denote ki = Ki/Qicpi coefficient of the layer i temperature diffusion. Parameters Ki, Qi, cpi are, respectively, the thermal conductivity, density and specific heat of the material for i =1,2. They have been recalculated to the entire volume of the layer (i = 3)