An Improved Non-Intrusive Automotive
Suspension Testing Apparatus with Means to
Determine the Condition of the Dampers.

Reprinted with permission from the SAE Technical Paper Series
960735

Anatoly Tsymberov
Hunter Engineering Company
Bridgeton, Missouri

CONTENTS

[ Introduction | Terminology | Standards | New Measurements
Tester | Summary and Conclusions ]

ABSTRACT

Suspension testing equipment has previously been designed to provide the time-domain response of the automotive suspension. The results of this type of test, although quantitative, are dependent on all suspension components, and are unreliable in determining the safety of the vehicle and condition of the dampers. Frequency domain suspension testers have also been designed; however, they have been limited to the magnitude response of the suspension system. This result, usually referred to as "road" adhesion, is indicative of the safety of the vehicle; however, it is unreliable in determining the performance of the dampers. The present apparatus provides, along with the magnitude response (adhesion), the phase response of the wheel versus the road surface irregularities. This information, including a quantity known as "minimum phase angle," gives valuable information as to the suspension damping value.

INTRODUCTION

An automotive suspension system is meant to provide both safety and comfort for the occupants. When a vehicle encounters a road surface irregularity, the tire deforms and the suspension displaces. Some of the energy caused by the disturbance is dissipated in the tire, some energy is dissipated in the damper, and the remainder of the energy is stored in the spring. The spring then releases this energy as a damped oscillation.

A shock absorber, strut, or damper is a hydraulic mechanism positioned between the sprung and the unsprung masses to dissipate kinetic energy placed into the system by road surface irregularities. For simplicity, the word "damper" is used to represent either a shock absorber or a strut. The term "adhesion" is used to represent the minimum road adhesion. The dampers provide desired ride characteristics, but also play a key role in keeping a good tire-to-road contact that is essential for handling and safety. The dampers control vibration and improve handling and load control. A good suspension system will keep all the wheels in contact with the road surface and make it possible for the driver to keep the vehicle under satisfactory control.

Automotive dampers wear gradually, and dampers that are worn out allow the vehicle to bounce excessively after a disturbance. Some of the signs of worn out dampers are:

The suspension test procedure takes only a few minutes and provides an assessment of the safety, damping characteristics, and comfort of the vehicle suspension system. The suspension tester provides the following information:

TERMINOLOGY

PHASE ANGLE AND MINIMUM PHASE ANGLE - The phase angle is the angular difference between the absolute sinusoidal position of the suspension tester platform and the sinusoidal vertical tire contact force between the tire and the suspension tester platform (relative sinusoidal position of the unsprung mass verses the suspension tester platform). The minimum phase angle is the lowest value of the phase angle between the sprung and unsprung mass resonant frequencies.

ADHESION AND MINIMUM ADHESION - Adhesion is the minimum percentage of remnant vertical tire contact force between the tire and the road surface during vertical oscillation of the wheel. This percentage is calculated by taking the ratio of the minimum remnant vertical load to the static weight (vertical tire contact force) on the suspension tester. The minimum adhesion is the lowest value of adhesion throughout the test.

SIDE TO SIDE ADHESION BALANCE - Side to side (left to right) adhesion balance is a comparison of the minimum adhesion between both wheels of an axle.

RIDE STIFFNESS - Ride stiffness is the relative stiffness measurement of the suspension system, defined by measurement of the accelerations of the suspension system between the frequencies from 4 to 8 Hertz.

TACTILE VIBRATION - Tactile vibrations are those vibrations "felt" by the human body.

HARSHNESS - Harshness is the high frequency (20 Hz and above) vibration of the suspension system that is perceived tactilely and audibly.

RIDE HARSHNESS ISOLATION - Ride harshness isolation is a measurement of the percentage of the suspension tester platform disturbance input between 20 and 25 Hertz that is dissipated by the suspension system.

SPRUNG MASS - The sprung mass is all mass supported by the suspension system, including portions of the suspension members. The sprung mass comprises the mass of the vehicle frame, body and load.

UNSPRUNG MASS - The unsprung mass is the mass of the wheel and components that are supported directly by the wheel, and considered to move with the wheel, but not carried by the suspension system. These components include the wheels, tires, brakes, parts of the axle, suspension links, suspension springs, dampers, and other associated suspension components.

CRITICAL DAMPING - Critical damping is the minimum amount of damping required to prevent a displacement of the system from passing the equilibrium position upon returning from the initial displacement.

DAMPING RATIO OR DAMPING FACTOR - The damping ratio is the ratio of the damping present in the system to the critical damping.

DAMPER - A damper is a device that dissipates energy by forces opposing the motion of a system.

DAMPING VALUE - The damping value is the ratio of the force exerted by a damper to velocity.

WHEEL HOP FREQUENCY OR UNSPRUNG MASS RESONANT FREQUENCY - The wheel hop frequency is the resonant frequency of the unsprung mass relative to the suspension tester platform.

SPRUNG MASS RESONANT FREQUENCY - The sprung mass resonant frequency is the resonant frequency of the sprung mass.

TIRE STIFFNESS OR TIRE SPRING RATE - The tire stiffness is measured by the change of wheel load per unit vertical displacement of the wheel relative to the ground at a specific load and inflation pressure.

STANDARDS

INTERNATIONAL STANDARDS - In 1971 the European Shock Absorber Manufacturers' Association (EuSAMA), was formed. Different suspension testing equipment has been evaluated by EuSAMA. This group established a set of guidelines for vehicle suspension evaluation called "Recommendation for a Vehicle Suspension Performance Test" []. This document standardized the "road adhesion" measurement, which is an excellent vehicle safety comparison.

ADHESION - The European Shock Absorber Manufacturers Association (EuSAMA) established the following guidelines for adhesion:

Table 1: EuSAMA Interpretation of Adhesion. [ 1]
Adhesion Measured EuSAMA Interpretation
61% to 100%
Excellent dynamic wheel contact
41% to 60%
Good dynamic wheel contact
21% to 40%
Fair dynamic wheel contact
1% to 20%
Poor dynamic wheel contact
0%
Bad dynamic wheel contact

Adhesion is the minimum percentage of instantaneous remnant vertical tire contact force between the tire and the road surface. This percentage is calculated by taking the ratio of the minimum remnant vertical load to the static weight (vertical tire contact force) on the suspension tester as shown in the Figure 1.


Figure 1: Graphical Explanation of Adhesion.

(1)

At the resonant frequency of the unsprung mass (wheel hop resonance frequency) the displacement between the unsprung mass and the suspension tester platform is a maximum, or adhesion is minimum. Wheel hop resonance usually occurs between 10 - 20 Hertz, and can be seen graphically as the minimum inflection point on the adhesion verse's frequency graph. If the wheel breaks contact with the platform during a test, the minimum adhesion is zero. The various frequencies range of the adhesion curve can be seen in Figure 2.


Figure 2: Adhesion Curve Showing Wheel hop Frequency and the Resonant Frequency of the Sprung Mass.

NEW MEASUREMENTS

PHASE ANGLES - The phase angle is the angular difference between the absolute sinusoidal position of the suspension tester platform (X3 relative to the ground) and the sinusoidal vertical tire contact force between the tire and the suspension tester platform (sinusoidal position of the unsprung mass (X23) relative to the suspension tester platform) as shown in Figure 3a.

Figure 3a: Explanation of Phase Angle.


Figure 3b: High Phase Angle Compared to Low Phase Angle for Equal Adhesion.

For X23max = 2A: If F23 =0o, X2max = 3A

If F23 = 90o, X2max = 2A

The absolute (relative to the ground) displacement amplitude, X2, of the unsprung mass is:

X2 = X23 + X3 = X23max cos. (F3 - F23)+ A cos.(F3) (2)

Where (ref. Figure 3a):

X3 is the displacement of the suspension tester platform.

A is the amplitude of the suspension tester platform.

F23 is the phase angle.

X23 is the displacement between the unsprung mass and the suspension tester platform.

The displacement between the unsprung mass and the suspension tester platform is proportional to the instantaneous vertical contact force between them. Therefore, the absolute displacement (X2) or acceleration of the unsprung mass is a maximum when the phase angle is zero. The absolute displacement amplitude of the unsprung mass relative to the ground decreases with increasing phase angles even if the measured adhesion value remains the same as shown in Figure 3b. From Figure 3b, we can see that the magnitude of the phase angle for the same adhesion or displacement of X23 significantly effects the unsprung mass acceleration and kinetic energy dissipated by the suspension system.

The resonant frequency of the sprung mass of an automotive suspension falls in the range from 1 to 3 Hertz. At the sprung mass resonant frequency, if no damping is present in the suspension system, the phase angles F23 = F2 - F3 = 180o and F12 = F1 - F3 = 0o, and the displacement (X12) between the sprung mass and the unsprung mass is a maximum. At the resonant frequency of the sprung mass, increasing the damping decreases the displacement amplitudes and the phase angle F23.

The resonant frequency of the unsprung mass of an automotive suspension falls in the range between 10 and 20 Hertz. At the unsprung mass resonant frequency if no damping is present in the suspension system the phase angles F23 = 0o and maximum displacement (X23), or minimum vertical contact force between the unsprung mass and the suspension tester platform occur. At wheel hop resonant frequency, increasing damping reduces wheel displacement and increases phase angle.

When no damping is present in the suspension system at the wheel hop resonant frequency, the immediate (resonant) response of the wheel with respect to the moving platform will be a phase angle of F23 = 0o. A large deviation in responses occurs at lower frequencies and a big phase angle shift F23 occurs, because the wheel attempts to remain at the wheel hop resonant frequency as the moving platform continues to decelerate to lower frequencies, forcing the wheel to slow to lower frequencies.

The phase angle magnitude is indicative of the strength of the damper. The "minimum phase angle" is the lowest magnitude of the phase angle between the sprung and unsprung mass resonant frequencies. When adequate damping is present in the suspension system there will be a smoother response delay of the wheel to the moving platform at the wheel hop resonant frequency. Also, the minimum phase angle (F23) between the sprung and unsprung mass resonant frequencies will remain steady with a magnitude above 90o.

The effect of the damping value in the analytical model on the phase angle vs. frequency graph is shown in Figure 4. From Figure 4, we can see that high damping values have high phase angles with a gradual slope between the sprung and unsprung mass resonant frequencies. When the system has a low damping value it will have steep slopes with a low minimum phase angle.


Figure 4: Analytical Effect of Suspension Damping on Phase Angle: C1=.18 (1), .88 (5), 1.75 (10), 3.5(20), 7 (40) kN sec/m (lb.sec/in.);

M1= 234 kg (515 lbs), M2= 43 kg (95 lbs), K1=56 kN/m (320 lb/in), K2=182 kN/m (1040 lb/in), C2=0 kN sec/m (lb.sec/in.)
Effect of Suspension Damping

RIDE STIFFNESS (LOW FREQUENCY) - The human body is the most sensitive to tactile vibrations in the frequency range from 4 to 8 Hertz and drops rapidly for frequencies above 8 Hertz for the same accelerations [2]. The ride stiffness is highly affected by the damper characteristics, the equivalent spring rate, and the sprung mass.

Ride stiffness is a relative measurement of the accelerations of the sprung and unsprung masses at frequencies between 4 and 8 Hertz and is measured on a scale of 0 to 100%. Ride stiffness is divided into several stages. The lower stage of ride stiffness (less than 30%) represents vehicles with suspension systems that have soft springs and low damping values that give a "cushy" (soft) ride. The preferred stage, (70% ride stiffness 30%), represents a firmer suspension system, which gives a comfortable ride due to properly proportioned spring rates and damping values. The higher stage of ride stiffness (greater than 70%) is characterized by vehicles having a stiff suspension system that gives a firm ride. The ideal ride stiffness varies with individual preference, the type of vehicle and the application in which it will be used. Most passenger vehicles ride stiffness should be in the preferred stage range. The ride stiffness should also be balanced from side-to-side within 20%, where large deviations indicate variation of equivalent spring rates, damping values, and weight distribution. The ride stiffness does not include the effects of the seats.

RIDE HARSHNESS ISOLATION - For frequencies above 20 Hertz the vibrations are perceptible both tactilely and audibly. The frequency range between 20 and 25 Hertz corresponds to both the maximum frequencies of the suspension tester and to the minimum threshold for human hearing [2]. These vibrations are absorbed by the tires, suspension springs, suspension bushings, and friction damping in the suspension systems. Conventional hydraulic dampers have small effect on the ride harshness isolation. Ride harshness isolation depends greatly on the stiffness of the tires, the sprung mass, loose or damage components and friction in the suspension system, depends moderately on the unsprung mass and damping characteristics of the tires. Ride harshness isolation is a measurement of the percentage of the suspension tester platform disturbance input that is dissipated by the suspension system. Higher percentages represent better high frequency road disturbance and road noise isolation. Ride harshness isolation above 80% is considered to be excellent, between 61% and 80% is considered good, between 41% and 60% is considered fair, and under 40% is considered to be poor. Lower numbers indicate stiffer tires and/or excessive friction in the suspension system, and a smaller sprung mass. The ride harshness isolation balance from side-to-side depends on deviations in tire stiffness, tire damping, friction in the suspension system, and the sprung and unsprung masses. Ride harshness isolation does not account for the dynamic effects of the rotation of the tires such as the dynamic tire spring rate, the dynamic tire damping rate, roundness, wheel imbalance, or aerodynamic effects.

QUARTER VEHICLE ANALYTICAL MODEL


Figure 5: Analytical Vehicle Model.

Analytically, the suspension of a vehicle is modeled as a two-degree of freedom system under a forcing vertical sinusoidal oscillation with constant displacement amplitude of the suspension tester platform as shown in Figure 5. This system is modeled by the following force-balance equations:

For m1: Rm1 + Rc1 + Rk1 = 0 (3)

For m2: Rm2 + Rc2 + Rk2 - Rc1 - Rk1 = 0 (4)

For m3: Rm3 + R - Rk2 - Rc2 = 0 (5)

Where: Rm1, Rm2 and Rm2 are the forces due to the masses.

Rc1 and Rc2 are the forces due to the dampers.

Rk1 and Rk2 are the forces due to the springs.

R is the vertical force applied by the platform.

In differential form the equations (3), (4) and (5) are:

This system has been solved and the results were used for the analytical solutions in the following discussions. The units used in the calculated data and the graphs are shown in Table 2:

Table 2: Units used for Analytical and Experimental Results
Quantity Symbol Unit
Weight M kg (lbs)
Damping Value C kN sec / m (lb.sec /inch)
Spring Constant K kN / m (lb. / inch)
Displacement X m (inches)
Force R N (lbs)

EQUIVALENT SPRING RATE () - The equivalent spring rate, , is the change in wheel load per unit displacement of the sprung mass relative to the ground. In the automotive suspension, the tire spring () is in series with the suspension spring (). The equivalent spring rate is found by the following equation:

(9)

The tire spring, however, has a spring constant usually five to ten times greater than the suspension spring constant. This results in an equivalent spring constant equal to approximately 80% to 90% of the suspension spring constant.

SPRUNG MASS () - The sprung mass consists of the vehicle frame, body, and load. The resonant frequency of the sprung mass is usually between 1 and 3 Hertz. The natural frequency of the sprung and unsprung masses relative to the ground are found from equations (3) and (4) where . The natural frequency of the sprung mass is:

(10)

Or approximated by: (11)

UNSPRUNG MASS () - The unsprung mass is composed of the components on a vehicle that move with the suspension as it deflects. These components include the wheels, tires, brakes, parts of the axle, suspension links, dampers, and associated suspension components. The resonant frequency of the unsprung mass usually occurs between 10 and 20 Hertz and is referred to as the "wheel hop frequency." The natural frequency of the unsprung mass is:

(12)

or approximated by:

(13)

MASS OF SUSPENSION TESTER PLATFORM (m3) - The mass of the suspension tester platform (m3) is the mass of the moving components that affect measurements. The force () of the suspension tester platform mass is subtracted from the vertical force of the platform (R) to determine the vertical tire force ( Rk2 + Rc2).

QUARTER VEHICLE SIMULATOR

Figure 6: Quarter-Vehicle Simulator.

A quarter-vehicle simulator, shown in Figure 6, was used to empirically confirm the analytical model with a known suspension spring constant, tire spring constant, suspension damping value, sprung mass, and unsprung mass. The quarter-vehicle simulator rests level on the ground and spans the suspension tester. The tire spring rests directly on the suspension tester platform and is attached directly to the underside of the unsprung mass. The suspension spring and damper are placed between the sprung and unsprung masses. The sprung mass rests directly on top of the suspension spring. The sprung and unsprung masses are guided in the vertical direction.

Weight can be added to both the sprung and the unsprung masses. The tire spring, suspension spring, and the suspension damper can be changed easily to determine their effect on phase angle, adhesion, and comfort. Linear damping was used for the suspension simulator. There is no provision for tire damping on the simulator, but the analytical effect will be discussed.