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Shocks absorbers with inertial valve in vertical dynamic behavior of a passenger car Guilherme Caravieri de Abreu Magneti Marelli
ABSTRACT This study is intended at investigating the possible benefits of the use of shock absorbers with inertial valves in terms of ride quality and safety. This is aimed to provide a theoretical framework for decision making before large investments are made in experimental evaluations, which are costly. A comparative study of the dynamic response resulting from a car suspension equipped with shock absorber with inertial valves and the one resulting from a suspension with conventional shock absorbers is conducted. For this objective, mathematical models have been developed to investigate the influence of acceleration sensitive shock absorbers on the vertical dynamics of passenger vehicles in terms of ride and handling criteria. A quarter car model with 2DoF is used for an analysis of the dynamic response of the vehicle under different road quality conditions and utilizing performance criteria quantifying comfort and safety. The results reported in this manuscript indicate a good potential for the use of shock absorbers with inertial valves, showing improved ride comfort without sacrificing safety.
INTRODUCTION For physical reasons, comfort and stability are antagonistic in the design of the vehicle suspension. A vehicle with great performance in stability is not comfortable on bumpy roads. The converse of this statement is that the extremely comfortable vehicle, does not have proper grip of the tire to the ground. The dampers and springs of the suspension plays an essential part in this relation, because they determine the compromise between comfort and safety. These two components determine the relative movement between the wheels and the ground and between the wheels and the vehicle body, aiming to keep the wheels as much time in contact with the ground and with minimal disturbance in body, increasing safety and improving comfort, respectively. For some time are applied for suspension systems which use shock absorbers with characteristics of the variable damping coefficient depending on driving conditions, the weight carried and various other information using electromagnetic valves or magneto-rheological fluids. These are called semi-active systems, however, have the disadvantages of very high cost and the need to use sensors in the vehicle suspension and complex electronic controllers. There are also shock absorbers that do not use electronic modulation of damping, but valves which are sensitive to the stroke, frequency or acceleration. One of these shock absorbers that have an internal device that is excited by the movement of the sprung mass or even by the unsprung mass change the damping coefficient for more appropriate level to the current acceleration of the sprung mass in a passive way. These dampers are called shock absorbers with inertial valves and promise a performance positioned between passive and semi-active suspension, but with lower cost and complexity than the latter. The purpose of this study is to provide an objective evaluation of the performance potential of a suspension that uses a system with inertial valves through computer simulations. Through the development and use of relatively simple mathematical models, it is expected to evaluate the potential of a vehicle suspension equipped with shock absorbers with inertial valves subjected to typical situations on the track, using objective performance criteria found in the literature and specific standards used by the vehicles manufacturer.
MAIN SECTION A simple model can point to trends, to elucidate phenomenon observed and provide important guidance on the way forward in developing a more complex model, possibly with more degrees of freedom and with some nonlinearities. INERTIAL VALVE MODELING - A conventional linear shock absorber exerts damping forces fa proportional to activation speed.
(1)
where: fa - damping force C - damping coefficient va - speed of activating the shock absorber
The construction of a completely linear shock absorber through simple valve would result in impractical for vehicular application size. In order that linear characteristic of the eq. 1 is obtained, the resource used is a set of valves operating in series and in parallel approximate the response of a linear damper behavior. Figure 1 shows a valve concept is applied in the most extensive vehicular shock absorbers with and additional inertial device represented by mass mi, spring ki, damper ci and orifice As2.
Figure 1 - Concept of a constructive with inertial shock absorber valve.
The fluid flows from P1 to P3 and the oil velocity va ∝ Q (oil flow), the damping coefficient is built by three stages: Stage 1: orifice AV fully closed by the spring, so that the entire stream flows through the orifices AL and AP and the 2 damping behavior is P3-P1 ∝ Q , where Q is the fluid flow. Stage 2: Orifice AM partially open, dependent of the pressure difference between P2 and P3. Stage 3: Opening of the AV orifice reaches a maximum value AM, so that the shock absorber exhibits behavior 2 P3-P1 ∝ Q again. The figure 2 illustrates the behavior of the valve assembly and the red dashed line shows the approximation for fa = Cva:
Figure 2 – Typical damping curve The change of the orifice As2 causes a variation of the average slope of the damping curve in stage 2, as shown in figure 3. This dependence was explored to propose the concept of an acceleration dependence for the inertial valve damping coefficient.
As2 <
As2 >
Figure 3 – Typical damping curve
Assuming â&#x2C6;&#x2020;AS2â&#x2C6;? (Zi â&#x20AC;&#x201C; ZB), the shock absorber force equipped with inertial valve can be approximately expressed by:
f C
â&#x2C6;?
| |.
v
(2)
Where ι and β are proportionality factors. The figure 4 shows the damper coefficient variation for some different As2 values:
fa
Shock absorber force
Figure 4 â&#x20AC;&#x201C; Force of the inertial valve shock absorber
The parameters of the inertial valve (mi, Ki and Ci) as well as an accelerometer, it must be designed so that the operating frequency is a fraction of the natural frequency of the instrument and the damping factor Îś is situated around 0.7.
2GdL MODEL - Application of valve inertial shock absorber to model 2GdL The shock absorber with inertial valve allows two options on positioning in the vehicle simply inverting the damper, the piston rod connected to the sprung mass (figure 5) or the piston rod connected to the unsprung mass (figure 6).
Sprung mass inertial shock absorber model - The mass of the inertial valve mi is much lower than the sprung mass ms, so it can despised the direct influence of oscillation of the mass of the inertial valve on the dynamics of the sprung mass. Dynamically will only change the damping coefficient CS of the shock absorber, therefore the dynamical equation for sprung mass can be writen considering CS variable and dependent on the relative motion of the inertial valve (Zi-Zs).
Figure 5 â&#x20AC;&#x201C; Representation of 2 GdL system with inertial damping connected to the sprung mass.
The damping coefficient CS is deduced from eq. 2:
C C
(3)
#Z$% & Z$ ' K Z% & Z
(4)
| |.
Therefore the dynamical equations are: m Z" C
For the sprung mass mS:
For the unsprung mass mU:
m% Z"% C
where: ZS - displacement of the sprung mass; ZU - displacement of the unsprung mass; Zi - displacement of the inertial mass; ZR - excitation from the ground; mS â&#x20AC;&#x201C; sprung mass;
| |.
| |.
#Z$ & Z$% ' K Z & Z% K % Z) & Z%
(5)
mU - unsprung mass; mi - inertial mass; KS - stiffness of the suspension spring; KU - stiffness of the tire; Ki - stiffness of the inertial system; C1 - damping coefficient. Ci - damping coefficient of the inertial system.
Unsprung mass inertial shock absorber model â&#x20AC;&#x201C; Analogously the sprung mass inertial shock absorber model, it can be written despising the direct influence of oscillation of the mass of the inertial valve on the dynamics of the unsprung mass.
Figure 6 â&#x20AC;&#x201C; Representation of 2 GdL system with inertial damping connected to the unsprung mass.
The damping coefficient CS is deduced from eq. 2:
C C
| * + |.
(6)
Therefore the dynamical equations are:
For the sprung mass mS:
m Z" C
For the unsprung mass mU:
m% Z"% C
#Z$% & Z$ ' K Z% & Z
(7)
#Z$ & Z$% ' K Z & Z% K % Z) & Z%
(8)
| * + |.
| * + |.
where: Zn - displacement of the inertial mass; mn - inertial mass; Kn - stiffness of the inertial system; Cn - damping coefficient of the inertial system.
RESULTS OF SIMULATIONS â&#x20AC;&#x201C; The 2GdL model allows the delimitation in standards used to evaluate both comfort as well as safety of vehicles. Through simulations with frequency and amplitude characteristics of tracks with different roughness, it can be evaluated whether there is the potential of the shock absorber with inertial valve to bring significant gains in terms of comfort and safety compared to conventional linear dampers. The criteria selected for evaluation are: 1. Effect of vibration on the human body â&#x20AC;&#x201C; ISO2631; 2. The r.m.s. value of the acceleration of the sprung mass normalized by dividing by g;
-.
/012 3
(9)
3. The r.m.s. value of the vertical force fluctuations divided by the mean vertical force.
-4
â&#x2C6;&#x2020;678 012 67819 :
(10)
The chosen tracks follow the standard ISO8606:1995 Class D and E, which represent paved runways, with less roughness class D and class E more roughness. Each track has been tested at speeds of 20km/h, 60km/h e 120km/h to evaluate the influence of this parameter.
Parameters of the model: mS = 315 kg; mU = 39 kg; KS = 20000 N/m; KU = 200000 N/m; C = 1600 N.s.m-1 (model with conventional shock absorber).
Parameters for the inertial valve shock absorber connected to sprung mass (MS): C1 = 400 N.s.m-1; α = 1200 N.s.m-1 β = 10000 m-1 mi = 0,05 kg; Ki = 5000 N/m; Ci = 22,2 N.s.m-1; Parameters for the inertial valve shock absorber connected to sprung mass (MñS): C1 = 200 N.s.m-1; α = 1300 N.s.m-1 β = 100000 m-1 mn = 0,01 kg; Kn = 89000 N/m; Cn = 42,2 N.s.m-1.
The values of C1, α and β were determined by a process of trial and error to provide significant gains in performance of the vehicle without perform a formal optimization.
Evaluation according ISO2631 - Effect of vibration on the human body causing reduced physical efficiency.
Track class D:
Figure 7 – R.M.S. vertical acceleration x limit physical efficiency – Track class D
Track class E:
Figure 7 – R.M.S. vertical acceleration x limit physical efficiency – Track class E
DP index:
Track class →
Class D
Class E
Shock Absorber →
Conventional
Inertial MS
Inertial MñS
Conventional
Inertial MS
Inertial MñS
20 km/h
0,143
0,135
0,135
0,287
0,263
0,266
60 km/h
0,275
0,245
0,247
0,549
0,475
0,487
120 km/h
0,436
0,370
0,376
0,871
0,722
0,746
DT index:
Track class →
Shock Absorber →
Class D
Conventional
Inertial MS
Class E Inertial MñS
Conventional
Inertial MS
Inertial MñS
20 km/h
0,090
0,091
0,091
0,182
0,185
0,184
60 km/h
0,158
0,159
0,159
0,320
0,325
0,320
120 km/h
0,225
0,225
0,225
0,450
0,465
0,461
CONCLUSION The suspension analyzed in this paper is a possible way to improve vehicle performance without an increase in cost that unviable implantation. Shock absorbers variables without the use of electromagnetic valves or magneto rheological fluids, sensors and computers are being developed to enter this gap between the technology used 40 years ago and still costly electronic sophistication. It is not common to find the acceleration sensitive variable shock absorber being used in the vehicles available in the market, but according to the study presented here, has the potential to raise the quality of driving. The greatest contribution of this work was to have shown the potential of this kind of shock absorbers provided with inertial valve suspension objectively even using simple models. For all track conditions and vehicle speed analyzed according to the standard ISO2631, models with shock absorbers with inertial valves showed similar or better performance in comfort in relation to conventional damper. This evaluation, though far from covering all the points of subjective evaluation by a human being driving a vehicle, shows a trend that a significantly higher level of comfort can be achieved by replacing the conventional shock absorber by one equipped with
inertial valve. Furthermore, it was observed that this type of shock absorber provides significant reduction in magnitude of the acceleration between the frequencies of 3 and 10 Hz, a significant range for human comfort. The evaluation of the "DP" index follows the same trend of evaluation with the ISO 2631 standard, that vehicles with inertial valve shock absorbers tend to be more comfortable than the conventional shock absorber. As the "DP" index takes into account the entire spectrum of the frequency at which the model was submitted, these results are a further indication that the car could become more comfortable when equipped with inertial valve shock absorbers. According the "DT" indices, models with shock absorbers with inertial valve does not have a tendency to a higher safety performance but also did not show a deterioration this criterion compared to the conventional damper. Due to better performance in comfort, it can be concluded that the shock absorber with inertial valve has the potential to bring about improvements in comfort without damaging the security. Finally, the car is a complex system and therefore still holds many opportunities for improvement, even if the improvement is still with merely mechanical parts such as damper having an inertial valve often considered simple but creative, going contrary to the growing escalation of electronics in vehicles that bring gains in comfort and safety more significant, but still has the disadvantages of cost, complexity and power consumption.
ACKNOWLEDGMENTS The authors would like to thank Magneti Marelli Cofap and Centro Universitário da FEI.
REFERENCES ABREU, Guilherme Caravieri de. Estudo de amortecedores com válvula inercial na dinâmica vertical de um veículo. 2014. 110 f. Dissertação (Mestrado em engenharia mecânica) – Centro universitário da FEI, São Bernardo do Campo. DIXON, John C. The Shock Absorber Handbook. 2. ed. United Kingdom: John Wiley & Sons Ltd, 2007. DOEBELIN, Ernest O. Measurament Systems: Application and Design. International student edition. 4. ed. New York, St. Louis, San Francisco Dusseldorf, London, Mexico, Panama, Sydney, Toronto: McGraw-Hill Book Company, 1966. GENTA, Giancarlo; MORELLO, Lorenzo. The Automotive Chassis. v.2, New York: Springer, 2009. GILLESPIE, Thomas D. Fundamentals of Vehicle Dynamics. Warrendale: Society of Automotive Engineers, 1992.
CONTACT Guilherme Caravieri de Abreu R&D Product Engineer at Magneti Marelli Cofap E-mail: guilherme.abreu@magnetimarelli.com Phone: +55 11 2144-1271 Bachelor (UMC – Mogi das Cruzes) and Master of Science (FEI – São Bernardo do Campo) in mechanical engineering. MBA in business management Specializations in Suspension, Steering and Vehicle Dynamics. 6 Sigma level Black Belt. Works at Magneti Marelli COFAP since April 2001 in Research and Development of shock absorbers and suspension.