Sensitivity analysis and optimal design of conventional and magnnetorheological fluid brakes

Mechanical and electrical brakes have dominated the braking industry for many years and will most likely continue to do so for the foreseeable future due to their low cost and adequate operating performance, wide range of applications, vehicle engineering, civil engineering, and biomedical engineering. Simple mechanical drum brake and magnetorheological (MR) fluid brake have presented in the current work. The main objective of this work is to increase braking torque, and to develop a new optimal design of MR fluid brake with better design and design control of the MR fluid design. To do so, four important steps have been accomplished. In the first step, a mathematical modeling of the conventional frictional brake and MR fluid brake has been developed to study and specify all design parameters. In the second step, a nondimensional, closedform analysis and a Taylor series expansion have used to examine the effects of perturbing dimensionless design parameters on the overall brakes performance. In the third step, two optimal designs for MR fluid brakes have been developed by taking advantage of sensitivity analysis and the design of experiments method also known as the Taguchi method. In the fourth step, controlling a MR fluid brake is performed by using two parallel PI controls for controlling the magnetic current and MR fluid thickness simultaneously. It was concluded that sensitivity analysis is a good method for identifying the parameters that have the greatest impact on brake performance and can be used as one method for the designer to obtain an optimal design. Four nondimensional design parameters were successfully used to describe the conventional frictional brake and seven nondimensional design parameters for MR fluid brake. Only two parameters for the conventional brake and five parameters for the MR fluid brake affect the performance and the others can be neglected. Two new designs for the MR fluid brake are presented and shown to be very simple in design, low in cost by removing a lot of additional auxiliaries for the frictional brake, and easy for control. By simultaneously controlling the MR fluid thickness and the electric current, a large range of brake torque is achieved without increasing the radial envelop for the brake, and saturation conditions in one controller are compensated for by the other controller. High angular velocities of the brake are primarily controlled by increasing the MR fluid thickness, while low angular velocities are primarily controlled by increasing the electric current. Good transient responses for regulating a constant speed (high, moderate, and low), and good stability while seeking to track a sinusoidal input have been achieved. In summary, the proposed control system for the MR fluid brake has demonstrated good controllability for the MR fluid brake.Includes bibliographical reference

Dynamic Analyses of Two-Dimensional Functionally Graded Timoshenko Beam using Finite element Method

In this work, dynamic analyses of a functionally graded beam are presented. The governing equations of the beam is found based on the displacement field defined by Timoshenko beam theory, then solved by using finite element method based on Hamilton’s principle. The beam is assumed to be free-clambed boundary condition (F-C). The PL index is used for describing the distribution of the beam properties in both transverse and longitudinal directions. A parametric study is accomplished to investigate effect of several parameters on the natural frequency, mode shapes and transient response of the beam., such as the PL indexes (nx and nz) for x and z axis, respectively, and the elasticity modulus ratio (Eratio). To valid the present results and current mathematical formulation, some of the findings are compared with another research. A good agreement is noticed. It is noted that the response of the beam is more sensitive to the variations of the PI in the longitudinal axes than that corresponding in the transverse one. For specific design requirements, the dynamic response of the beam can be adjusted by chose a proposal indexes and modulus ratios

Transient analysis of transversely functionally graded Timoshenko beam (TFGTB) in conjunction with finite element method

In this work, transient and free vibration analyses are illustrated for a functionally graded Timoshenko beam (FGM) using finite element method. The governing equilibrium equations and boundary conditions (B-Cs) are derived according to the principle of Hamilton. The materials constituents of the FG beam that vary smoothly along the thickness of the beam (along beam thickness) are evaluated using the rule of mixture method. Power law index, slenderness ratio, modulus of elasticity ratio, and boundary conditions effect of the cantilever and simply supported beams on the dynamic response of the beam are studied. Moreover, the influence of mass distribution and continuous stiffness of the FGM beam are deeply investigated. Comparisons between the current free vibration results (fundamental frequency) and other available studies are performed to check the formulation of the current mathematical model. Good results have been obtained. A significant effect is noticed in the transient response of both simply supported and cantilever beams at the smaller values of the power index and the modulus elasticity ratio