Hydraulic system modeling and optimization to achieve performance characteristics

As automation technology continues to be integrated into industrial and mobile machinery, more precise control of hydraulic cylinders will assist in the achievement of desired response characteristics. Thus, in designing the cushioning mechanism for a hydraulic cylinder, there is value in predicting the deceleration response due to pressure generated when fluid passes through the cushion orifice. The cushion orifice can be designed to change as a function of piston position to meet a desired velocity response. In practice, determination of the orifice area requires a lengthy iterative process of trial and error. Therefore, to overcome these design process challenges, dynamic models of cylinder cushioning systems were developed that, when solved numerically, predicted the pressure and velocity responses of the cylinder with time. Utilizing these dynamic models, a cushion design optimization procedure was also developed to obtain the dimensions of the cushioning spear that most closely obtains the desired velocity response profile. Simulations of the dynamic cushion model were performed using a cushion spear with a shape designed through a static analysis to produce constant deceleration during the cushioning phase. Spear shapes were fit to the analytically developed common spear profile and their performance was assessed with simulation. The developed optimization procedure was run to compare the performance the spear shapes common to industry. Lastly, to identify the range of results produced by the optimizer, the procedure was run ten times for each spear type with the variation between runs. The performance of each run was quantified by measuring the root-mean square error (RMSE) between the desired velocity profile and the simulated velocity profile. When surrounding system conditions were held constant, the analytical analysis produced a profile leading to nearly constant deceleration with an RMSE of 1.4x10-3 m/s (0.29 feet per minute; fpm) when simulated by the dynamic model. However, attempts to replicate the results of the analytical model with common spear shapes resulted in deviation from the constant deceleration goal with the parabolic and linear regression curves producing RMSE values of 14.9x10-3 and 21.7x10-3 m/s (2.94 and 4.28 fpm) respectively. The optimizer produced a consistent family of results for each spear with an average standard deviation of 2.6x10 -3 m/s (0.51 fpm). This dynamic modeling approach has potential to assist designers in the development of cushioning spears that meet customer cushion response specifications.