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Unformatted text preview: A NONLINEAR SIMULATION OF CAR VIBRATION
BY MSC/NASTRAN Sergey Sergievsky, Ph. D. Sergey Purgin Boris Shatrov, Ph. D. OJ SC “GAZ” ' OJ SC “GAZ” The MacNealSchwendler Lenin avenue Lenin avenue GmbH, Moscow ofﬁce Nizhni Novgorod 603004 Nizhni Novgorod 603004 Lenin avenue, 6 Russia Russia Moscow 117933, Russia Phone (7+8312) 562 145 Phone (7+8312) 561 299 Phone (7+095) 236 61 77 e—mail: email: e—mail: [email protected] [email protected] [email protected]
ABSTRACT Setting the task of creating a modern competitive vehicle, the designers
need the more exact estimation of the degree of their design optimum at the early
stages of the work. According to this, besides the traditional methods of analysis
(static analysis, normal modes analysis and ‘frequency response analysis), the
transient response analysis of the car real loading becomes more interesting. This
type of analysis provides the data, which are the close analogue to the test results
and allows, later on, to go over to the fatigue analysis. In this article the example of the nonlinear simulation of the car vibration 1n
time domain by MSC/NASTRAN 1s considered. INTODUCTION OJ SC “GAZ” is one of the largest companies in Russia. Founded at 1930, at
present time it produces a wide range of all types of automobiles: cars, trucks,
buses and specials (fig. 1). Gorky Automobile Plant (“plant” is “zavod” in
Russian) is one of the leaders in Russian automobile industry. It is also one of the
leaders among other enterprises in the field of science and technology, none of
which anew the model row of its production as frequently, as GAZ does. Every
year OJSC “GAZ” launches a new model into production, which is a record for
Russia at present time. According to weStern standards 0] SC “GAZ” test department is not
developed enough. OJSC “GAZ” realizes that the modern test center is a
necessary component of such company, as Gorky Automobile Plant, and it does
it’s best to develop it. Nevertheless the computer simulation aimed at decreasing
the period of new car designing and developing is used by OJSC “GAZ” more
and more nowadays. ' At present time OJSC “GAZ” is solving the problem of possessing the.
methodologies of the simulation the car loading taking into consideration the
greater number of features of this process, if possible. It tries to make the
computer simulation results as close as possible to the results of similar tests. The
final aim of these efforts is to possess the methodology of durability analysis of
car parts and units. It is wellknown that the loading of the car during its running is the
nonlinear process. The simulation of this process, in principle, is possible by such
codes as MSC/DYTRAN and LS—DYNA3D. But these codes use the explicit
method of integration. It leads to very small time step which results in hours or
even days of CPU time for the simulation of car loading during about 0.2 second
of real time, if the size of the finiteelement model is about 100 thousand
elements. At the same time, for the correct estimation of the random loading
process it is necessary to analyse the stress/strain time realizations of the
accessing precess within the duration of a few seconds (or even dozens seconds
better). The run time for this simulation in some cases may be not acceptable. To solve the above mentioned problem the practical method of the
simulation of the car vibration with nonlinear approach is proposed. It allows to
get the stress and strain time realizations in the car body parts with the duration of
a few seconds within dozens minutes or some hours (wall clock) of workstation
computer using the modal method of solution. DESCRIPTION OF PROBLEM Generally the equation of the dynamical system vibration is stated as: HMHu<t>+Hanan!u<t>+HK[u<t)]\u<t>=Pa), m
B[U(t)] with “M K[U(t)]H — mass, damping and stiffness matrixes respectively; 9 9 11(t)  grid points displacement vector;
P(t) — the vector of the loads. As it can be seen from the equation (1), the damping and stiffness matrixes
depend on the grid points displacements. Taking into consideration, that the size of the vector 11(t) in real problems mounts to hundreds of thousand, it takes much CPU time for the direct solution of this equation.
It is known that the modal method provides the essential decrease of the
CPU time. But it may be used for solving linear problem only. METHOD OF SOLUTION To avoid the problem of applicability of the modal method for solving the
task under consideration, let’s extract the linear part from the assessing dynamical system. In case of the application to the car, it may be done quite easy. For
example, in the simulation of car vibration the nonlinear shock absorber rate is
used. Let’s present this rate as the sum of the linear and nonlinear fractions (ﬁg.
2). Presenting all internal non elastic forces as the sum of the linear and
nonlinear fractions, the second addendum in the left part of the equation (1) will !B[U(t)ll  11(t) = “13* with ”B ~ u(t) + N1[u(t)], — the damping matrix of the linear part of the dynamical system; 1\I1 [ll(t)] — nonlinear fraction of the internal non elastic forces of the dynamical system. The same can be done with the internal elastic forces of the dynamical
system. After that the equation (1) will be restated as: HMHu<t>+HB* .u<t>+uK* u<t)=
=P<t>—N1[u<t>]—N2[u<t)], m with ”K  the stiffness matrix of the linear part of the dynamical
system;
N 2 [11(t )]  nonlinear fraction of the internal elastic forces of the dynamical system. The left part of the equation (2) satisfies the condition of linearity, therefore
this equation may be solved by modal method. It is necessary to note, that the use of the modal method and the constant
time step of integration is the reason which makes the estimation of the current size of the internal nonlinear forces N1 and N2 impossible. Therefore the calculation of these forces is performed based on the vectors 110:) and 11(12), which were obtained as the result of the previous time step of integration. Thus
the final form of the dynamical system vibration equation will be stated as: uMuu<t)+HB* ~u<t>+HK* ~u<t>=
= P(t) — N1[u(t — At)] — N2 [u(t — At)], with At  the time step of integration. This feature of the method enforces to use a smaller time step in
comparison with the case of completely linear problem to ensure the stability and
acceptable accuracy of result. The MSC/NASTRAN code gives the possibility to apply the nonlinear
forces to the finite—element model. If the modal method (SOL 112) is used, it is achieved by the use of EPOINT, TF and NOLINi entries [Reference]. Thus, the above mentioned method is no more than the “widened” application of already
existing MSC/NASTRAN possibilities. STRUCTURAL MODEL In development and tests of the proposed method the finiteelement model
of car, showed in fig. 3, was used. The loading of the model is performed by moving the nodes, which
correspond to the points of contact between tires and road surface, in vertical
direction. A special code is used for input data deck building which allows to
define the required motion of the aforesaid nodes in MSC/NASTRAN run. This
code includes the random digital generators and digital ﬁlters, which provide
producing the digital sequences with the required power spectral density. Grid points location in the ﬁniteelement model corresponds to the car
loaded by the gravity. If special measures are not be taken, the applying of the
gravity will cause additional deformation of the structure, first of all the
suspensions of the wheels. To avoid this the forces, equal to the constant loads,
arising because of the gravity, are applied to the corresponding nodes of the ﬁnite
element model (ﬁg. 4). According to the analysis, the deformation of the finiteelement model
under the gravity and the forces showed in fig.4, is simulated not enough correctly
if only the eigenvectors extracted by the “usual” normal modes analysis are used.
As a result the stress in the finiteelement model parts is not correct either.
MSC/NASTRAN code allows to solve this problem. By the use of the alternative
solution (versions 68 and 69) or by defining the special solution parameters
(version 70 and the following: PARAM,RESVEC,YES [Reference]) the
calculating of the residual vectors is initialize. These vectors are added to the
already calculated eigenvectors and provide correct simulation of the car
deformation under the constant loads. RESULTS The tests of the proposed method were conducted under the following
conditions. The ﬁniteelement model consisted of about 10 thousand elements and most
of them were shell elements. The range of the frequencies, where the eigenvectors
for modal analysis were found, was from 0 Hz to 50 Hz. There were three
nonlinear effects simulated by the tested model: the devices which constrained the
relative displacement of the wheels and the body (i.e. jounce bumpers), the
features of the shock absorbers rates and the possibility of the jumping the wheels over the road surface. The power spectral density of the road profile in the model
corresponded to the profile of the nonsmooth cobblestone track of the Gorky
automobile plant proving ground. The velocity of the car motion was 10 m/s (36
km/hour). The duration of the car loading process was 10 seconds. The time step
of integration was 0.001 second. For the tests the computer IBM RISC/6000 mod. 591 was used and the
working storage space was 150 megabytes. The run time (wall clock) for the considered model was about 1 thousand
seconds. It is necessary to note, that for correct simulation of the car static
deformation under the constant loads MSC/NASTRAN added two residual
vectors to the primary eigenvectors. In fig. 5 the vertical displacements of the road surface under the left front
wheel, the left front wheel itself and the left body rocker (zone near the B—pillar)
are depicted. The vertical displacements of the bottom and top parts of the spring
strut of the left front wheel and the force, acting on the left front jounce bumper,
are shown in fig. 6 and ﬁg. 7 respectively. From the last two figures it can be,
seen, that if the deformation of the suspension exceeds the certain amount, the
jounce bumper acts and a force arises. At present time the proposed method is being tested with utilization of the
already existing calculation results and experimental data, obtained during the
tests of a new car GAZ~3111 “Volga” (ﬁg. 8), which is planning to be produced at
the end of 1999. CONCLUSION The conducted studies with the use of considered ﬁniteelement model have
shown the high efﬁciency of the proposed method of a nonlinear simulation of
car vibration. The possibility to get the durable realization of results, in our
opinion, gives new ways to the almost real Computer simulation of the vibration
and stress/strain analysis of the car parts and units and, in the future, to the
estimation of car durability based on pseudo random loading in time domain with
nonlinear effects. REFERENCE
MSC/NASTRAN Quick Reference Guide. Version 70. The MacNeal
Schwendler Corporation, Los Angeles, CA. Figure 1. Automobiles of OJSC “GAZ” 1 B+03 0.6 0.8 0.4 0.2 Velocity of tension, mm/sec 0.6 0.4 0.2 0 0.8 a) The complete rate ....{_______
x
l l lfl l. l
I ...i..
l
l llllllllll ...»...
l
. _.l.._ r... J—... .i..1_._. ..........
I u
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l 1.... J......_ 'f""" l L.... J... 1 ._ _  . . . _ _
4. u _ _ _ _
x i. _ . u _ _
II. I .. u _ _
1. n . _ . _L______£__
 2 1 B+03 0.4 0.6 0.8 0
Velocity of tension, mm/sec
b) The linear fraction 0.2 0.6 0.4 0.2 0.0 ___}__l_ l
l 1 B+03 0.8 x
0.6 Velocity of tension, mm/sec
c) The nonlinear fraction I
_.1......r... !
F... . ..
l 0.4 l l
, .
l 0.2 I
a
0 y....
I
l 0.2 r...
m 0.6 0.4 ......{.....L.....£.....
0.8 Figure 2. Decomposition of the shock absorber rate d S
.m n
t
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m
e llllll
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am 
e F
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, I/I/I..IIJ%:$~.~.~§~.~%I F F I I»: \. iaﬁmseﬂu
\ i §§~i§» V i ,,_ Figure 4. The static forces in the elastic parts of the suspensions 10 34011. L_.__.l_... .——.._.L___
I
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Time step, sec 0.88 u m
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c) The displacement (T3) of the rocker Figure 5. The displacement of the model parts 1 1 1 3101 Time step, sec parts of the spring strut of the left front wheel _
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ZS .oouom 1 E+01 0.9 Time step, 0.85 .8 SEC Figure 7. The force, acting on the left front jounce bumper Figure 8. New GAZ3111 “Volga” 12. ...
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