Simulation Project

TO: Hope Weiss
FROM: Nap Paholio
DUE DATE: December 11, 2015
SUBJECT: Simulation Project
Introduction
The objective of this lab is to simulate the motion of an untuned vehicle’s suspension driving down an uneven surface. In terms of pitch and bounce, the goal of the simulation is to optimize and tune the car’s suspension to ensure an ideal ride over a bumpy surface for the driver.
Experimental Method The suspension of car works with two- degrees of freedom: the pitch and bounce. The combination of the two determine the longitudinal and vertical vehicle vibrations. With the use of the Lagrange equation, we can initially establish an Equation of Motion which can help preview the motion of suspension. Using Simulink with initial parameters regarding
EOM of Bounce: x ̈(t)=-(((c_f+c_r ))/m) x ̇-(((k_2 c_r-l_1 c_f ))/m) θ ̇-(((k_f+k_r ))/m)x-((〖(k〗_r l_2-k_f l_1))/m)θ+(k_f/m) y_f+(k_r/m)+(c_f/m) y ̇_f+(c_r/m) y ̇_r [6]
EOM of Pitch: θ ̈(t)=(((l_2 c_r-l_1 c_f ))/J) x ̇+(((l_2^2 c_r+l_1^2 c_f ))/J) θ ̇+(((l_2 k_r-l_1 k_f ))/J)x+(((l_2^2 k_r+l_1^2 k_f ))/J)θ=((-k_f l_1)/J) y_f+((k_r l_2)/J) y_r+(-(c_f l_1)/J) y ̇_f+((c_r l_2)/J) y ̇_r [7]
Both figures shows that it takes a significant amount of time for the bounce of the system to reach a steady state as well as the pitch angle looking to be too ample to be ideal. These initial conditions may cause an uncomfortable and irritating motion for the individuals riding in the car, thus a fine tuning is needed. After adjusting the spring constants and damping coefficients, Figures 4 and 6 displays a more ideal motion that has less of a vertical bounce and a smaller pitch angle amplitude. The new tuned coefficients significantly decreased the time it took to reach a steady state as well as controlling the amplitude to a minimal motion. It was found that increasing the damping coefficient to 500 Ns/m and decreasing the spring stiffness value to around 10,000 N/m of the front and rear suspensions will give an ideal response for a much desirable ride. Initially, some will think that increasing only the damping coefficient to a much higher value would tune the response ideally, but taking consideration of the damping ratio, the larger the damping coefficient the smaller the damping ratio will be which will result in a larger pitch angle that will be undesirable for the