Transient Temperature Field Analysis of Brake in Nonaxisymmetric Three-dimensional Model

The disk-pad brake used in automobile is divided i nt o two parts: the disk, geometrically axisymmetric, and the pad, of which the geo metry is three-dimensional. In the course of braking, all parameters of the pro cesses (velocity, load, temperature, physicomechanical and tribological characte ristics of materials of the couple, and conditions of contacts) vary with the ti me. Considerable evidence has show that the contact temperature is an integral f actor reflecting the specific power friction influence at the combined effect of load, speed, friction coefficient, thermo physical and durability properties of materials of a frictional couple. Furthermore, the physic mechanical state of t he interface of the disk and pads is determined not only by the contact temperat ure but also by the nonstationary temperature field. Using the two-dimensional model for thermal analysis implies that the contact conditions and frictiona l heat flux transfer are independent of θ. This may lead to false thermal elast ic distortions and unrealistic contact conditions. An analytical model is presen ted in this paper for the determination of contact temperature distribution on t he working surface of a brake. To consider the effects of the moving heat source (the pad) with relative sliding speed variation, a transient finite element tec hnique is used to characterize the temperature fields of the solid rotor with ap propriate thermal boundary conditions. And the transient heat conduction problem can be solved as a nominal 3-D transient heat transfer problem with an immovab le heat source. Numerical results shows that the operating characteristics of th e brake exert an essentially influence on the surface temperature distribution a nd the maximal contact temperature. The temperature field presents a noaxisymmet ric characteristic (a function of θ) and proves to be strongly localized and po ssesses a sharp gradient in both axial and radial directions.

State vector solutions for nonaxisymmetric problem of multilayered half space piezoelectric medium

A state space formulation is established for the nonaxisymmetric space problem of transversely isotropic piezoelectric media in a system of cylindrical coordinate by introducing the state vector. Using the Hankel transform and the Fourier series, the state vector equations are transformed into ordinary differential equations. By the use of the matrix methods, the analytical solutions of a single piezoelectric layer are presented in the form of the product of initial state variables and transfer matrix. The applications of state vector solutions are discussed. An analytical solution for a semiinfinite piezoelectric medium subjected to the vertical point force P_z, horizontal point force P_x along x-direction and point electric charge Q at the origin of the surface is presented. According to the continuity conditions at the interfaces, the general solution formulation for N-layered transversely isotropic piezoelectric media is given.

Numerical Investigation of a Turbine Stator with Nonaxisymmetric Endwall Profiling

Nonaxisymmetric endwall is an effective method to reduce secondary loss and improve aerodynamic performance.In this paper,a nonaxisymmetric endwall automated optimization process based on the nonuniform rational B-spline surface(NURBS)technique was proposed.This technique was applied for the aerodynamic optimization of the turbine stator shroud endwall to reduce total pressure loss and secondary kinetic energy.The flow fields of the datum endwall design(Datum)and optimization endwall design(Opt)were investigated and compared.Quantitative loss analysis was performed with a loss breakdown method.The entropy generation was classified as profile loss,secondary loss and trailing edge loss,all of which were reduced.The secondary loss was much smaller than the profile loss.In general,the blade row total entropy loss decreased by 11.7%.The results showed that the Opt design reduced total pressure loss and coefficient of secondary kinetic energy by 11.1%and 11.0%,respectively.The decrease in secondary kinetic energy could be attributed to the reduction in the horseshoe vortex and the reduced transverse pressure gradient.When the outlet Mach numbers and inlet incidence angles vary,the performance of the profiled endwall design was always better than the datum design.In the turbine stage simulation,the efficiency was increased by 0.28%with nonaxisymmetric endwall.