الفهرس 
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Abstract
This thesis describes a theoretical study from which the performance of vehicle brake is investigated in order to improve their characteristics. The contact and thermal analysis of the
ventilated disc brake are studied after adjusting the model using complex eigenvalue analysis.
A historical review of the available published work related to ventilated disc brake has been
introduced and showed the need for further research work in the area of modal, contact and
thermal analysis. The comprehensive vehicle brake modeling techniques are presented which describe the way of dealing with the performance parameters of vehicle brake and their relation to
contact stiffness and squeal are given.
Finite element background, methodology and program validation are included. However, the steps used in the modal analysis work are detailed, moreover, the description of the modal analysis
for the coupled ventilated disc brake system is also included. The “Ansys 12” un-symmetric solver and procedures in creating the stiffness matrix Matrix27, is presented in details. The linear element Matrix27 that was used in the modal analysis, was transferred to non-linear elements of Targe170 and Conta173 to study the contact analysis between the ventilated disc and the pad.
Furthermore, the modal work is then transferred to the thermal technique by using a replaced element which is solid 90 (thermal element) to the structural element solid45.
The results demonstrated that the finite element model for the coupled ventilated rotor and pad
showed a good interaction between the non-linear contact and the linear modal analysis.
Furthermore, the un-symmetric solver showed that the modes of the coupled disc-pad contained two types of mode. The first type was normal mode, which did not contain an imaginary part
while the second type was complex mode that contained real and imaginary parts. Moreover, Complex eigenvalue analysis predicted always more unstable modes than the number of squeal frequencies that really occur in the brake system. However, the contact analysis showed symmetry
distribution around the centre of piston pressure loading while was symmetrical under the calliper
fist at fist loading at all contact pressures. The results also showed that the maximum temperature
reached during the thermal loading at disc speed of 1400rpm and at a deceleration of 0.5g after 10
seconds of braking time is 435 ℃.