International Journal of Advancements in Mechanical and Aeronautical Engineering
Author(s) : LOKESH BS, NILOTPAL BANERJEE, PAVAN KUMAR AV, VINAYAKA N, YESHODHARA B
Optimisation is a must for every engineering design so as to increase the performance of every mechanical system. Trial and error methods are mostly used to check for stresses and validate the design which is not optimum. A new optimisation technique is found out by using bivariate interpolation method or surface fit method. From multiple variables, the problem is reduced to 3 variables (x, y, z). The variation of x with respect to z, keeping y constant and variation of y with respect to z, keeping x constant are found out. These sampling points are combined to get the relating surface of z= f(x, y) using Bivariate interpolation methods. The surface plot is obtained and for specific value of z, the 3D surface plot is chopped off, the resulting surface will be optimum curve which satisfies all the design considerations. This method is applicable for all types of problems. In this paper, taking an example of spring, keeping the various parameters like free length, effective no of coils, spring stiffness as constant, the variation of spring index and diameter of wire is calculated monitoring deflection and factor of safety. A surface is fit to obtain which relate FOS to diameter of coil and spring index, for a particular value, say FOS=1.5, the obtained surface is chopped off. The surface obtained after chopping off is the optimum curve for which all the design considerations are satisfied. Thus, this method can be effectively used for the optimisation of any 2 variable parameters with respect to the third.