# Ride Analysis and Suspension Control

Publish Date: Jun 13, 2011 | 3 Ratings | 4.33 out of 5 |  PDF

## Overview

In this particular tutorial, we will start by analyzing vehicle suspension. We will study the dynamics of a 1/4 car model to analyze vertical vibration of a vehicle. The concepts of controllable suspensions will be discussed and ideal skyhook damping will be introduced. Simulation results using LabVIEW Control Design and Simulation Module demonstrates the effect of skyhook damping.

### 1. Vehicle Suspension

The design of vehicle suspension has a critical functioning role in ground vehicles. Various conflicting functions must be satisfied by the vehicle suspension, namely body attitude and wheel attitude. The suspension needs to provide enough compliance  to cope with uneven terrain and isolate the chassis from the induced forces and vibration. Many vehicle vibration models can be used to analyze the modes of vibrations ranging from a 1 degree of freedom (DOF) to 16 DOF for a complete vehicle model. In this particular tutorial, we will look at the 2DOF 1/4 car model to analyze the vertical vibration of a vehicle.

### 2. Quarter Car Model Simulation

The quarter car model encompasses 1/4th of the sprung mass and incorporating associated un-sprung mass as shown in Figure 1. The dynamics of the sprung mass absorbs excitations from aerodynamics, engine, and drive train where are the imbalanced forces from tire are applied to the un-sprung mass.

Fig 1. Quarter Car Vehicle Model. Vehicle Representation (Left) Simplified Representation (Right)

The dynamics of the quarter car model can be derived by applying Newton's law to each mass and identifying the forces induced on each mass. This leads to the following equations, where W represents road disturbance.

For sprung mass

For un-sprung mass

Using LabVIEW Control Design and Simulation Module, we can build the simulation model from the differential equations above as shown in Figure 2.

Fig 2. Block Diagram of Quarter Car Suspension Model

Let's emulate  the vehicle coming out from a pothole that is 0.1 m. You can see that the masses oscillate quite a bit from Figure 3  . We can determine the natural frequencies for both masses by assuming the response of each variable has the form of

substituting into the undamped and  unforced system will lead us with the characteristic equation with two solutions

where

Using LabVIEW MathScript RT Module shown in Figure 4, we've determined that the natural frequencies for each of the mass is

Fig 3. Quarter Car Suspension Response

Fig 4. Calculating Natural Frequency

Fig 5. Block Diagram of Quarter Car Simulation

### 3. Controllable Suspensions

The simulation result shown above for the 1/4 car model motives the need of having a controllable suspension to minimize oscillation thus improving the rider's experience.  There are several different controllable suspensions which we can categorized by how active they are

• Passive
o There's no external energy needed. This type of suspension utilize the nonlinearity to be able to adjust the suspension system itself.
• Semi-active
o There's little control power which may only be active at some instances. A slow acting load-leveler system may be integrated.
• Hybrid-Active
o These type of systems might be engaged at only low frequencies and utilize passive or semi-active suspension for high frequencies.
• Fully-Active
o These type of systems has high bandwidth and require the most external energy source.

In this tutorial, we will focus on passive suspension design and in particularly, the concept of skyhook damping.

### 4. Skyhook Damping

The concept of skyhook damping or so called fictional absolute damper, is to separate the function of absolute body motion and the relative motion between body and wheels. In another words, there will be an additional damping force Fb added to the sprung mass where

It is important to note that a high pass filter is usually coupled with skyhook damper so the skyhook damper will not respond to constant velocities. The modified quarter car suspension model can be found in Figure 6.

Fig 6. Schematic of Skyhook Damper (Left) Block Diagram of 1/4 Car Suspension with Skyhook Damper (Right)

As shown in Figure 7, the skyhook damper passively reduces the oscillation of the vehicle coming out of the pothole hence improve ride stability.

Fig 7. Quarter Car Simulation Results Comparison

### 5. Conclusion

This article briefly introduces the concept of vehicle suspension and simulate a 2 DOF quarter car suspension using LabVIEW Controls and Simulation Module. The concept of passive suspension is also discussed. By implementing a skyhook damper, the quarter car model reduces its oscillation drastically. It is feasible to implement pitch and bounce dynamics with the quarter car model to simulate a half car response. Notice when performing a half car simulation, it is critical to determine the correct initial conditions.

LabVIEW Control Design and Simulation Module

LabVIEW MathScript RT Module

NI LabVIEW Robotics Starter Kit

NI Automotive Applications

Hybrid Vehicle Test and Simulation using NI's Hardware-In-The-Loop (HIL) Platform

### 7. Reference

ME 390: Vehicle Dynamics and Controls (Spring 2011)

Prof. Raul. G. Longoria, ME, University of Texas, Austin

http://www.me.utexas.edu/~longoria/VSDC/

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