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DECELERATION AND DEFORMATION DURING DYNAMIC LOADING OF MODEL CAR BODY PARTS AFTER POST-ACCIDENT REPAIR

KONIECZNY, Łukasz

TRANSPORT PROBLEMS                                                                                2020 Volume 15 Issue 3 
PROBLEMY TRANSPORTU                                                                      DOI: 10.21307/tp-2020-032 
 
 
Keywords: shock absorber; damping characteristic; shock absorber with by-pass 
 
Łukasz KONIECZNY 
Silesian University of Technology, Faculty of Transport and Aviation Technologies 
Krasińskiego 8, Katowice, 40-019, Poland 
Corresponding author. E-mail: lukasz.konieczny@polsl.pl 
 
 
 
EFFECT OF FAIL-SAFE MODE ON THE DAMPING 
CHARACTERISTICS OF A BYPASS-CONTROLLED SHOCK ABSORBER 
 
Summary. The article provides and discusses results of tests of a bypass-controlled 
hydraulic shock absorber studied at a test stand (mechanical inductor), making it possible 
to plot work charts and determine velocity characteristics. Measurements of the shock 
absorber performance were conducted at different values of velocity and forced travel.  
The measurements were carried out for two statuses, i.e. for the emergency power failure 
condition and for normal setting. The results thus obtained can be used in simulation tests 
as input shock absorption characteristics for different technical conditions. 
 
 
1. INTRODUCTION 
 
The suspension system of the assembly is used to support the weight of the vehicle, to absorb road 
shocks, as well as to maintain the movement of the tires with the road. During mechanical work, the 
suspension system is in a dynamic balance, still adaptation to changing driving conditions. The vehicle 
suspension must be analyzed before production and its parameters selected. This requires an analysis 
of the shock absorber system under dynamic load conditions to see how it works in the worst-case 
scenario. 
A safe vehicle must be able to operate and maneuver in a wide range of road conditions. Good 
contact with the road should be maintained while fast maneuvering. Suspension is the term given to a 
system of springs, shock absorbers, and rods connecting a vehicle with wheels. The shock absorber 
has a significant effect on handling and safety. Shock absorbers are also critical to the interaction of 
tires off the road, which includes the tendency of tires to slip off the road. It affects braking, steering, 
cornering, and overall stability. Generally, shock absorbers should be replaced when the mileage 
exceeds a certain value. To make sure what the technical condition is, the best solution is to check the 
condition of the shock absorber. There are several methods for testing the damper condition. One of 
the tests is the analysis of damping characteristics using a dynamic test on a special stand. It is 
complicated and expensive because the machine is very expensive but provides reliable test results. 
Tests of shock absorbers are performed at test stands which enable measurement of motion 
parameters (displacement and input function velocity) as well as the force (shock absorber resistance) 
with which a shock absorber responds to a kinematic input function. Such stands are typically used in 
shock absorber durability tests. Testing of shock absorbers at such a stand makes it possible to 
establish graphs depicting the damping forces in the function of displacement and linear velocity of 
the shock absorber’s piston rod against its housing (Fig. 1). 
44   L. Konieczny 
 
 
 
Fig. 1. Theoretical diagram of shock absorber operation (damping force in function of displacement 2R and 
linear velocity 2ωR [8] 
 
In many cases, it is enough to simplify the damping characteristics of a shock absorber so as to 
bring them down to a linear coefficient to study the dynamics of suspension systems in automotive 
vehicles.  The said coefficient (shock absorber damping constant c) equals the ratio of the force given 
by the point of intersection of the work curve and the axis of abscissae (see Fig. 1) to a product of 
forced angular frequency ω and arm length R.  Symbol A on fig.1. is amplitude of force. 
 
(1) 
where c -shock absorber damping constant, ω - forced angular frequency, F4 - force -point 4 on 
diagram, and R - arm length.  
The value of conventional elasticity constant ku equals the tangent of the inclination angle of a line 
cutting through the beginning of the coordinate system and through the point of tangency of the 
characteristic curve with lines parallel to the X-axis (see Fig. 1) for the extreme forced travel values. 
 
 (2) 
where ku - conventional elasticity constant, F3 - force - point 3 on diagram, and R - arm length.  
Regarding the tests of shock absorbers of contemporary cars with non-symmetrical damping 
characteristics adjusted by overflow valves, one obtains work graphs that diverge from the ellipsis. In 
many cases, the force of the shock absorber’s resistance against displacements can be described with 
satisfactory accuracy by polynomials of the nth order (typically 2nd or 3rd) [1-4, 12-17].  
 
+ 
Fig. 2. Sample graphs of automotive shock absorber operation and corresponding damping characteristics 
(progressive, degressive, and linear): x-displacement, v-linear velocity, and F-force 
 
The apparatus used to study shock absorbers is commonly referred to as test stands, and they make 
it possible to measure the values of forces, displacements, and velocities on variable input function 
parameters (angular velocity and/or piston rod travel values). Such a test stand is to be found at the 
b
ww
w tg
R
F
R
cRc === 4
atg
R
Fku == 3
Effect of fail-safe mode…  45. 
 
Laboratory of Motor Vehicle Dynamics of the Faculty of Transport of the Silesian University of 
Technology [8-10].  
The aim of the work was to determine the damping characteristics established for the two operating 
statuses, including for the emergency status, to make it possible to run simulations by taking the shock 
absorber’s technical condition into account. 
 
 
2. METHODS AND MATERIALS 
 
The object of the tests was a shock absorber by Monroe, typically installed on Audi A6. The 
measurements were performed in the fail-safe mode, i.e., when the solenoid valve controlling the oil 
flow through the bypass was not in operation, and for comparison, with the 1.7 A and 9 V power 
supply on, i.e. close to the level theoretically defined by the manufacturer as the near-maximum 
damping value. The current value limitation below the maximum of 2 A was owing to the test object 
considerably heating up (caused by the operating parameters that were more encumbering than those 
of standard vehicle operation and on account of replacing the PWM control signal with direct current) 
[5-7, 11]. The shock absorber subject to the tests as well as the bypass control valve has been 
schematically shown in Fig. 3. 
 
 
 
Fig. 3. Bypass-controlled shock absorber subject to tests and control valve 
 
 
3. MEASURING STATION 
 
In the measurement system addressed in the paper, a type CL 16 bidirectional strain gauge with the 
operating range of ±2.5 kN was used for direct force measurements, whereas the PTx 100 series 
transformer-type linear displacement transducer together with the MPL 104 displacement gauge was 
used to measure displacements. The signals received from the transducers were recorded using the 
SigLab 20-220A two-channel analyzer and stored on a computer hard drive in a format compatible 
with the Matlab software. A diagram schematically representing the measurement system used to 
measure the changes in the forces generated by the shock absorber and the instantaneous displacement 
values at the test stand has been provided in Fig. 4. 
piston rod 
   inner tube 
         outer tube 
               bypass  
electro controlled valve 
                                coil solenoid 
46   L. Konieczny 
 
 
 
Fig. 4. Measurement system diagram 
 
Once the bypass-controlled shock absorber had been mounted on the test stand, the shock absorber 
was warmed up before the actual measurements were taken. The test procedure first involved heating 
up the shock absorber by running it for two minutes. Depending on the different input function 
velocities changed according to the frequency, the time of a single measurement ranged between 20 
and 60 s, thus ensuring that at least 20 operating cycles were recorded. The tests were performed on 
the shock absorber travel of 60 mm. The bypass-controlled shock absorber mounted on the test stand 
has been shown in Fig. 5. 
 
 
 
Fig. 5. Bypass-controlled shock absorber mounted on the test stand 
 
For the shock absorber mounted on the test stand, time curves of force signals and of linear 
displacement were recorded. The signals thus recorded were smoothed using a low-pass filter. For 
signal filtering in Matlab, FIR1 function was used. FIR1 implements the classical method of 
windowed linear phase FIR digital filter design. Lowpass, linear phase FIR filter with cutoff frequency 
and Hamming-windowed was used. The time curves recorded for the signals before and after filtering 
have been shown in Fig. 6. 
Effect of fail-safe mode…  47. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 6. Time curves recorded for force signals and displacement before (red) and after filtering (blue) 
 
Further proceedings included determination of averaged loops depending on the input function 
velocity, each time based on at least 15 complete recorded operating cycles comprising the motion of 
compression and expansion. Fig. 7 depicts the averaged loops of force changes in the function of 
displacement (a) and of linear velocity (b).  
 
Fig. 7a. Averaged loops of force changes in the function of displacement  
 
 
4. RESULTS  
 
According to the procedure discussed in this paper, tests were performed for selected frequencies 
and travel values for two statuses, i.e. the fail-safe status, in which the solenoid valve controlling the 
oil flow through the bypass was not in operation, and – for comparison – in a condition with the 1.7 A 
power supply enabled. Some typical results thus obtained have been provided in Figs. 8–11. 
The tests were performed for selected frequencies (Tab. 1) and constant amplitude value (stroke) 
60 mm. The maximum values of the linear velocity of excitation resulting from these parameters are 
48   L. Konieczny 
 
presented in Table 1. The colors of loops in Figs. 8-11 correspond to the frequency of excitations 
shown in Table 1. 
 
Fig. 7b. Averaged loops of force changes in the function of linear velocity 
Table 1 
Values of input selected parameters  
 
Frequency [Hz] Angle velocity [1/s] Amplitude [m] Linear velocity [m/s] 
0,440 2,761 0,06 0,1598 
0,684 4,296 0,06 0,2651 
0,919 5,770 0,06 0,3612 
1,148 7,210 0,06 0,4496 
1,382 8,681 0,06 0,5341 
1,618 10,160 0,06 0,6123 
1,853 11,639 0,06 0,6831 
 
Based on the plotted graphs of force changes in the function of linear velocity, point characteristics 
were determined as force values corresponding to the maximum linear velocity. The characteristics 
thus established were approximated by polynomials functionally describing changes to the damping 
force (Fig. 12). The characteristics described by that means can be used for purposes of simulation 
tests, e.g. in multibody system analyses.  
 
 
5. DISCUSSION 
 
Currently, among the test methods for shock absorbers installed in automotive vehicles, the 
EUSAMA method is most often used. The advantage of its use is the unification of construction of test 
stands, large statistical material, and no need for comparative database. Its disadvantage is a simplified 
multi-state qualification system, and therefore a simple system for assessing the technical condition of 
the shock absorber, large width of individual condition ranges, no damage identification, and 
ambiguity of results for rear axle shock absorbers, especially for vehicles with low own weight. 
Other methods (BOGE, MAHA, and HOFFMAN) currently have limited applications. The 
recommendation in some cases of ambiguous assessment is the control of shock absorbers at test 
stands allowing for verification and comparison with reference characteristics. This is the only method 
Effect of fail-safe mode…  49. 
 
that allows for unambiguous qualitative and quantitative verification. However, it is difficult in 
practical application because it requires disassembly of the shock absorber from the vehicle and testing 
on an expensive test stand. 
 
Fig. 8. Graph of force changes in the function of displacement for the shock absorber operating in the fail-safe 
mode; colors correspond to values of input function frequency (red - 0,44 Hz, dark blue - 0,68 Hz,  
orange - 0,92 Hz, yellow 1,15 Hz, magenta-1,38 Hz, green - 1,62 Hz, and light blue – 1,85 Hz) 
 
Fig. 9. Graph of force changes in the function of linear velocity for the shock absorber operating in the fail-safe 
mode; successive colors correspond to increasing values of input function frequency (red - 0,44 Hz, dark 
blue - 0,68 Hz, orange - 0,92 Hz, yellow – 1,15 Hz, magenta-1,38 Hz, green -1,62 Hz, and light blue – 
1,85 Hz) 
50   L. Konieczny 
 
 
 
Fig. 10. Graph of force changes in the function of displacement for the shock absorber operating in the power 
supply mode; successive colors correspond to increasing values of input function frequency (red –  
0,44 Hz, dark blue - 0,68 Hz, orange - 0,92 Hz, yellow – 1,15Hz, magenta-1,38 Hz, green - 1,62 Hz, 
and light blue – 1,85 Hz) 
 
 
Fig. 11. Graph of force changes in the function of linear velocity for the shock absorber operating in the power 
supply mode; successive colors correspond to increasing values of input function frequency (red –  
0,44 Hz, dark blue - 0,68 Hz, orange - 0,92 Hz, yellow – 1,15 Hz, magenta-1,38 Hz, green -1,62 Hz, 
and light blue – 1,85 Hz) 
Effect of fail-safe mode…  51. 
 
 
 
Fig. 12. Established point characteristics and polynomials approximating these characteristics – colors red and 
blue represent the fail-safe mode, whereas yellow and gray correspond to the power supply mode 
 
 
6. CONCLUSIONS 
 
The tests performed under the study in question made it possible to plot the graphs of changes to 
the damping force of a bypass-controlled shock absorber in the function of displacement and in the 
function of linear velocity. With reference to the graphs thus obtained, damping characteristics were 
determined as functions approximating the damping force against linear velocity. The characteristics 
described in this way are most frequently used in simulation studies of dynamics of automotive 
vehicles. The vibration damping characteristics thus obtained can be described as non-linear and 
asymmetrical. The graphs plotted with reference to the tests imply that the shock absorber’s resistance 
force is lower during compression than during expansion, which stems from the characteristics 
assumed for the condition of reduction of the forces occurring in the shock absorber compression 
motion phase to be fulfilled. The characteristics established for the two operating statuses, including 
for the emergency status, make it possible to run simulations by taking the shock absorber’s technical 
condition into account. The description of the approximating functions envisaged in the form of 
polynomials may be a description of damping characteristics, e.g. in simulations of multibody-type 
systems (Adams /Car, etc.). 
 
 
References 
 
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Received 22.03.2019; accepted in revised form 26.08.2020 


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