PSI - Issue 14

Abhijit Kulkarni et al. / Procedia Structural Integrity 14 (2019) 158–167 6 Abhijit Kulkarni a , Rushikesh Nanaware b , Akhilesh Kulkarni c , Vikrant Garud d / Structural Integrity Procedia 00 (2018) 000–000 �� � � �� �� �� � �� �� � �� �� �� �� (20) �� � � � � �� �� �� �� � � �� � � � �� �� (21) 163

Fig. 6.1 Second axle mechanism vector diagram.

By Chace method,

�� � �� �� � � �� � �� �� � �� � �� � ���� �� ���� � (22)

3. Error Optimization An error function is optimization function that gives the value of the deviation of an entity from its ideal value. The objective of the optimization is the minimization of the error function. For a good steering system, the wear on the left and right wheels of the vehicle should be almost equal and less in magnitude. Therefore, error function for the 1st and 2nd axle is considered as the square of difference between the errors of the left wheel and right wheel. For 1 st Axle Line = ��� �� � � � � �� �� � � � � . (23) For 2 nd Axle Line = ��� �� � � � � �� �� � � � � (24) For Tie Rod = (25) The tie rod instead of single link is modelled as 2 rigid links connected by translational joint. This is done to permit the mechanism work without redundant constraints and also to estimate the translational displacement error arising out of 2 inputs for the multi-link hydro mechanical steering mechanism. 4. Genetic Algorithm A genetic algorithm (GA) is a method for solving both constrained and unconstrained optimization problems based on a natural selection process that mimics biological evolution. The algorithm repeatedly modifies a population of individual solutions. At each step, the genetic algorithm randomly selects individuals from the current population and uses them as parents to produce the children for the next generation. Over successive generations, the population "evolves" toward an optimal solution. The optimization is question has many variables and non-linear input function, so the method of optimization was used. MATLAB has inbuilt GA functions and GA toolbox [6] to be readily used for optimization. Functions were written to get required angles (equations 9-11), constrain function