Method of Measurement for Natural Frequency and Damping Ratio—
Automotive Suspension System
This standard is applicable to measurement of natural frequency and damping ratio of various biaxial automotive suspension systems. The measurement parameters include natural frequency and damping ratio of vehicle body (i.e. sprung weight) and natural frequency of wheels (i.e. unsprung weight). The three parameters are the basic data for analysis of the vibration characteristics of suspension system and for research and evaluation of automotive ride comfort.
1 Test Conditions
1.1 The test is carried out on automobile under full load. No-load test may be added as required. The gross weight of automobile and weights of front and rear axles shall be weighed before the test.
1.2 Suspension elastic element, vibration damper and bumper block shall comply with the technical provisions. Tests with vibration damper and bumper block removed may be added as required.
1.3 The tyre pattern shall be intact and the tyre pressure comply with the values specified by technical provisions.
2 Frequency Response of Measuring Apparatus and Measuring Points
2.1 The frequency of measuring apparatus shall range from 0.3 Hz to 100 Hz.
2.2 Vibration sensors are mounted correspondingly on the front and rear axles and upper part or frame of the automobile.
3 Test Methods
3.1 The following three methods may be applied during the test to make the automotive suspension system produce damped free vibration.
3.1.1 Rolling down method: drive the wheels at test end of automobile to the bump along the slope (the bump section is as shown in Figure 1; it may be 60 mm, 90 mm or 120 mm high depending on the automobile type and suspension structure and it shall be so wide horizontally that the wheels can be placed on the bump entirely), and push them down the bump after parking, idling and turning off the engine. While rolling down, the left and right wheels shall be ensured to touch the ground as simultaneously as possible.
Figure 1 Diagram of Bump Section for Rolling Down Method
3.1.2 Falling down method: raise the middle axle at test end of automobile by 60 mm or 90 mm from the equilibrium position using the falling mechanism, then release the falling mechanism to let the test end of automobile fall on a sudden.
3.1.3 Pulling down method: pull down the vehicle body or middle frame near the axle at test end by 60 mm or 90 mm from the equilibrium position using rope and pulley gear, and then loose the rope suddenly with a releasing device.
Note: during tests by the above three methods, the pull-down displacement, raising height or bump height shall be so selected that the suspension will not impact the stop block in the compression travel and that the vibration amplitude is as approximately long as that under actual operating conditions. For special automobiles, the suspension structure may subject to other values other than 60 mm, 90 mm and 120 mm.
3.2 Record the time course of damped free vibration on the vehicle body and axles using a recorder, 3s at a minimum every time and 3 to 5 times totally, to maintain the integrity of damping vibration curve.
3.3 During the test, the suspension at non-test end generally need not be stuck to limit its vibration, but if the vibration at front and rear ends of the automobile interacts each other greatly, it shall be firmly fixed and noted in the report.
4 Data Processing
4.1 Time course method: based on the damped free vibration curve of vehicle body and axles as recorded (see Figure 2), partial vibration period of vehicle body (T) and partial vibration period of wheels (T') can be obtained by comparison with time scale or reading out the time intervals on the signal processor, then the natural frequency of all parts can be calculated according to the following formulae.
f0=1/T (1)
ft=1/T' (2)
Where,
f0——the natural frequency of vehicle body, Hz;
T——the vibration period of vehicle body, s;
ft——the natural frequency of wheels, Hz;
T'——the vibration period of wheels, s.
a Vehicle body (cut-off frequency of 5 Hz may be selected for low-pass filtering) b Wheels (cut-off frequency of 20 Hz may be selected for low-pass filtering)
Figure 2 Damped Free Vibration Curves
Depending on the half-period vibration attenuation rate of vehicle body τ=A1/A2 (A1 represents the peak-peak value between the second and third peaks, while A2 represents the peak-peak value between the third and fourth peaks), the damping ratio is calculated according to the following formula.
ψ= (3)
Where,
π——the circumference ratio;
ln——the natural logarithm.
If the damping is smaller (A3 represents the peak-peak value between the fourth and fifth peaks, and does not decrease suddenly), the damping ratio may be calculated according to the following formula based on the full-period attenuation rate τ'=A1/A3.
ψ= (4)
4.2 Frequency analysis method: record the acceleration signals, (t) and (t), of damped free vibration on the vehicle body and axles using a tape recorder and then carry out frequency analysis on the signal processor.
4.2.1 Subject the acceleration signals, (t) and (t), of vehicle body and axles to auto-spectrum processing, during which low-pass filtering is carried out at a cut-off frequency of 20 Hz, sampling time interval, , of 20 ms and frequency resolution, , of 0.05 Hz.
a) The peak frequency of acceleration RMS auto-spectrum, , of vehicle body (see Figure 3.a) is the natural frequency, f0, of the vehicle body.
b) The peak frequency of acceleration RMS auto-spectrum, , of wheels (see Figure 3.b) is the natural frequency, f1, of the wheels.
1 Test Conditions
2 Frequency Response of Measuring Apparatus and Measuring Points
3 Test Methods
4 Data Processing
5 Test Report
Annex A Example of Report Format (Supplement)
Additional Explanation:
