design optimization and development of vibration analysis
TRANSCRIPT
Design Optimization and Development of Vibration Analysis Program
for Engine Mount System
Chang Yong Song
Technical Division, AhTTi Co., Ltd., Suite 904~5 of Sicox Tower 513-14 Sangdaewon1-dong Jungwon-gu
Seongnam-si Gyeonggi-do 462-806 Korea
TEL) 82-31-777-9131
FAX) 82-31-777-9135
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Abstract
Engine mount is purposed to control an excessive motion generated from powertrain system and to isolate
vibration and noise to be transmitted to main system. As vibration design of engine mount is one of the main
items on the phase of vehicle development, the design should be optimized considering various design
variables and uncertainties. In the study, design optimization of engine mount for passenger vehicle is
proposed using MSC.ADAMS based engine mount system analysis program – EMTOOLS. EMTOOLS is
capable of carrying out vibration and static analysis, hydro mount & frequency dependent modeling (FDM),
idle and engine shake analysis for 6-DOF and 16-DOF models. In addition, vibration design optimization is
able to be facilitated by design of experiment (DOE) based sensitivity analysis and optimization algorithm.
Keywords: Engine mount; Vibration design; EMTOOLS; DOE; Design optimization
Introduction
The vehicle engine mounting system generally consists of engine, transmission supplementary systems and
several mount rubbers connected to the vehicle structure. The modern engine mounting systems have been
successfully applied to isolate the driver and passenger from noise, vibration and harshness (NVH) generated
from powertrain system. However, there is still a need to improve the performance of engine mounting
systems for the following two reasons: One reason is that the requirements of vibration and noise isolation
for passenger cars are increased. The second reason is that the modern car designs have a trend for lighter car
bodies and more power-intensive engines. The comfort requirements, the weight reduction and the increased
engine power sometimes have adverse effects on vibratory behavior. These aspects are often conflicting.
Substantial improvement in the performance of engine mounting systems definitely plays an important role
in resolving such conflicting requirements.
There are substantial researches on the dynamic performances of engine mounting system. The current
industrial strategies use a model approach to analyze the harmonic response of the powerplant on resilient
supports attached to ground, and the 6-DOF model used in the modal analysis is interesting insofar as the
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response to an excitation is calculated and interpreted according to the position in frequency and to the form
of the modes (Brach, 1997). To decouple the engine torque roll axis, dynamic decoupling axioms are
presented and compared with the conventional elastic axis mounting and focalization methods (Jeong and
Singh, 2000). The significance of the rigid body modes alignment for grounded powerplant to its vehicle
behavior is handled with the accuracy of NVH vehicle models (Hadi and Sachdeva, 2003). Experimental
method is suggested to evaluate the frequency dependent rubber mount stiffness and damping characteristics
by utilizing the measured complex frequency response function from impact test and by least-squares
polynomial curve fitting the data obtained from the test (Lin et al., 2005). Passive, semi-active and active
control engine mount systems are the important research items for the NVH design of commercial passenger
vehicles requiring a good engine vibration isolation performance (Royston and Singh, 1996; Zhang and
Shangguan, 2006; Ibrahim, 2008; Peng and Lang, 2008). Design sensitivity and optimization analysis of
engine mount system are carried out using FRF based sub-structuring method (Lee et al., 2002).
In this paper, design optimization of engine mount for passenger vehicle is proposed using MSC.ADAMS
based engine mount system analysis program – EMTOOLS. The present paper briefly reviews the theory
with respect to engine mount analysis, and then explains the procedures and contents of EMTOOLS. Using
the EMTOOLS, vibration analysis of 6-DOF engine model is carried out for an initial design specification,
and then the design sensitivity and the optimization analyses are performed to achieve the optimum mount
stiffness and location while design performances such as mode frequency and modal purity are satisfied with
target values. The optimized 6-DOF engine mount design is also able to be applied to 16-DOF vehicle model
to carry out the idle vibration and the engine shake analyses. The present study focuses on how the complex
engine mount design solutions are efficiently found using the proposed process.
Theoretical Background for Engine Mount System
Modeling of Multi Body Dynamics (MBD)
The typical configuration of a powertrain is shown in Figure 1(a). The mounts types are usually rubber
mount, hydro mount and its combination. One end of engine mount connects to the powertrain and another
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end connects to the car body or subframe. Figure 1(b) shows a simplified 6-DOF MBD model that
powertrain is regarded as a rigid body system supported by three or four mounts. A mount is able to be
simplified as spring and damping elements in three orthogonal directions. Even if the consideration of
flexibility shows more accurate vibration analysis results, the 6-DOF model idealized to be rigid body
system is good enough to analyze vibration performances of engine mount system in the preliminary design
phase (Sirafi and Qatu, 2003). A right-hand global coordinate system (GCS), G0-XYZ, which has its origin at
the center of gravity (COG) of the powertrain in its static equilibrium, is built to describe the mechanical
motions of the powertrain. Here, the static equilibrium is defined as the position of the powertrain at rest
under its dead weight. The three orthogonal coordinate axes are set with X- and Y- axes parallel to the
horizontal plane, Z- axis normal to the plane, and the positive direction of X- axis points to the rear of a
vehicle. A Local Coordinate system (LCS), Qi-uivixi, is built for each mount, where the origin is at the
connecting point of the mount and the powertrain, and the three coordinate axes are expressed by ui, vi and wi
(i=1,2,... n, where n is the number of mounts), respectively, which are perpendicular to one another
(Shangguan and Zhao, 2007).
Figure 1 Typical configuration and the simplified 6-DOF MBD model of engine mount system.
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Equation of motion for vibration analysis
Assuming the powertrain is fixed to a rigid structure, the natural frequencies and mode shapes of a
powertrain are obtained from:
02 =− MK ω (1a)
02 =− ii MK ϕω (1b)
where M is the 6×6 mass matrix containing inertia parameters of the powertrain and φi is the 6×6 mode
matrix, in which each column represents translation and angle displacements of the 6-DOF of the powertrain
with respect to its COG in GCS. K is the 6×6 stiffness matrix and is a function of the dynamic stiffness,
locations and orientations of the engine mounts. The dynamic stiffness of a mount for analyzing the natural
frequencies of the powertrain using Eqn. 1(a) equals the static stiffness times a dynamic-to-static ratio of a
mount. Solution of Eqns 1(a) and (b) leads to a set of natural frequencies of the powertrain, fi(=ωi/2π, i=1, 2,
… 6), and the corresponding mode vectors . As the powertrain vibrates at a natural
frequency (fi), the mode kinetic energy distribution (usually defined as the decoupling ratio) in the n(n=1,
2…6) DOF of the powertrain and i-th order mode, E(n,i), is estimated from:
Tiiii ),,,( 621 ϕϕϕϕ K=
→
i
T
i
lii
nini
i
T
ii
lii
ninii
M
m
M
minE
→→
=
→→
=∑∑
==ϕϕ
ϕϕ
ϕϕω
ϕϕω6
1
2
6
1
2
21
21
),( (2)
where φni is the n-th element in the mode vector , and mnl is the element of the mass
matrix, M, in n-th row and l-th column.
Tiiii ),,,( 621 ϕϕϕϕ K=
→
The response of the powertrain COG to the dynamic excitation can be calculated by solving the following
Eqn.:
gddd FFXKMX +=+ (3)
where
5
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
⋅⋅⋅−
⋅−=
∑∑
∑∑
−−
−−n
iiid
Ti
n
iid
Ti
n
iiid
n
iid
d
rKrKr
rKKK
1
*
1
*
1
*
1
*
~~~
~
(4)
⎪⎪⎭
⎪⎪⎬
⎫
⎪⎪⎩
⎪⎪⎨
⎧ Δ=∑ ∑
∑
= =
=n
i
n
ii
n
iid
g
rF
1 1
1
~ (5)
The complex stiffness matrix, Kd, in Eqn. 4 is calculated based on complex stiffness matrix of the individual
mount, , and the location of mount i. The mass matrix M is a constant matrix consisting of inertia
properties. Xd={x, y, z, θx, θy, θz}T is the dynamic displacement vector. F is a vector of excitation force
induced by the engine motion. Fg is a excitation force vector induced by the displacement from the ground.
In the frequency domain, the dynamic displacement vector, Xd, is expressed as:
*idK
( ) ( )( ) ( ) ( )( fFfFfKMffX gdd ++−=−122)( π ) (6)
In Eqn. 6, F( f ) is assumed to be zero if only the excitation from a ground is considered. If the excitations to
the powertrain are only from torque changes due to the output power of changes in the engine, Fg( f ) is set to
zero. The dynamic forces transmitted to mount are then calculated by:
[ ] diididid XrKKF ~** ⋅−= (7)
Vibration Analysis Program for Engine Mount System
6-DOF system
6-DOF system module is developed only for the engine mount design without considering vehicle system. 6-
DOF system is able to embody fore/aft, lateral, bounce, roll, pitch and yaw motions in engine vibration mode
analysis. All input/output procedures are embedded in MSC.ADAMS/View, and the necessary design
information of engine and powertrain such as inertia, weight, location and orientation is inserted through an
exclusively developed menu window. Various engine mount types are realized using the input properties of 4
engine mounts and 2 torque rod mounts. Mounting properties are idealized by linear spring for mode analysis,
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and nonlinear spring for static load analysis respectively. In 6-DOF system, some essential analysis items are
considered such as normal mode frequency, modal purity and static load analysis. Static load analysis
extracts various loading conditions occurring in some road driving events. Results of static load analysis are
utilized in structure analysis and/or strength evaluation of engine mount bracket. In addition, vibration design
optimization focusing on controlling of vibration frequency and decoupling of modal purity is facilitated by
design of experiment (DOE) based sensitivity analysis and optimization algorithm. General analysis
procedure of 6-DOF system is depicted in Figure 2.
Figure 2 Engine mount analysis procedure for 6-DOF system
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16-DOF system
16-DOF system module is able to explore the idle and the engine shake vibrations. 16-DOF system considers
not only fore/aft, lateral, bounce, roll, pitch and yaw motions in engine and vehicle mode analyses but also
bounce in suspension. All input/output procedures are embedded in MSC.ADAMS/View same as 6-DOF
system module, and the necessary design information of vehicle such as inertia, weight, tire and suspension
is inserted through an exclusively developed menu window. Frequency dependent properties or hydro
properties for engine mount are required to perform the idle and the engine shake vibration analyses. In idle
vibration analysis, exciting unbalance force and torque fluctuation are considered using various function
parameters. Body force or wheel displacement is required as excitation force to carry out engine shake
analysis. General analysis procedure of 16-DOF system is also presented in Figure 3.
Figure 3 Engine mount analysis procedure for 16-DOF system
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Vibration Analysis
Engine mount system analyses of a passenger vehicle are carried out to evaluate the effectiveness of
developed vibration analysis program – EMTOOLS, and explore the solution of design optimization with
respect to mode frequency and modal purity. First, normal mode and modal purity analyses are performed for
an initial design specification using 6-DOF system model, which represents a 4 cylinder type gasoline
powertrain. After the evaluation of initial design specification, the DOE based sensitivity and the
optimization analyses are carried out to review the effects of design variables on design performances, and to
satisfy the criteria of mode frequency and modal decoupling.
Normal mode and modal purity analyses
Engine mount design specification is initially set up as shown in Table 1.
Table 1 Initial design specification of engine mount
Type 4 Stroke gasoline
Displacement 1686cc
Power 125PS/4400rpm Engine / Powertrain
Idle rpm 800± 50 rpm
Engine mount 1 (-161, -455.7, 303.2)
Engine mount 2 (-161, 455.7, 303.2)
Engine mount 3 (200, 0, 303.2) Mount location [mm]
Engine mount 4 (-500, 0, 303.2)
Direction : (x, y, z)
Engine mount 1 (175.1, 41.2, 103)
Engine mount 2 (263.5, 62, 155)
Engine mount 3 (100, 100, 300) Mount stiffness [N/mm]
Engine mount 4 (100, 100, 300)
Direction : (Kx, Ky, Kz)
Engine mount 1 (0, 0, 0)
Engine mount 2 (0, 0, 0)
Engine mount 3 (0, 0, 0) Inclined angle [Degree]
Engine mount 4 (0, 0, 0)
Direction : (α, β, γ)
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Inertia properties such as mass, center of gravity and moment of inertia are also represented in Table 2.
Table 2 Inertia properties of powertrain
Mass [kg] 253
x -205.3
y 30.5 Center of gravity [mm]
z 193.8
Ixx 1.61e+07
Ixy -6.5e+05
Iyy 8.69e+06
Izx -6.00e+05
Izy 1.88e+06
Moment of Inertia [kg·mm2]
Izz 1.45e+07
ADAMS based multi body dynamics (MBD) model is generated using Tables 1 and 2 as shown in Figure 4.
Figure 4 ADAMS based MBD model for engine mount analysis
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For the initial design of engine mount, normal mode frequencies and modal purities are calculated in 6-DOF
rigid body motion. All analysis procedures are facilitated with EMTOOLS, and the results are shown in
Table 3 and Figure 5.
Table 3 Analysis results of normal mode and modal purity for initial design conditions
Normal mode Modal purity [%] Mode no.
Frequency [Hz] Fore/aft Lateral Bounce Roll Pitch Yaw Total
1 5.27 0.010 98.299 0.000 1.551 0.000 0.140 100
2 7.24 83.233 0.000 3.596 0.010 12.911 0.250 100
3 9.07 7.198 0.000 89.313 0.000 3.439 0.050 100
4 11.99 8.660 0.258 6.680 8.155 75.639 0.608 100
5 13.21 1.252 1.544 0.543 67.741 9.557 19.364 100
6 14.26 0.082 0.045 0.054 24.408 1.525 73.886 100
Figure 5 Modal purity chart for initial design conditions
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As shown in Table 3 and Figure 5, roll and yaw modes are more coupled than other modes. It seems to be
decoupled in pitch, roll and yaw modes improving the initial mount location and stiffness.
Design sensitivity and optimization analyses
For design sensitivity and optimization analysis, consider the following optimization statement:
Maximize roll modal purity [%] (8)
subject to all modal purities excluding roll [%] ≥ 85
6.0 ≤ bounce mode frequency [Hz] ≤ 9.0
6.0 ≤ fore/aft mode frequency [Hz] ≤ 9.0
4.5 ≤ lateral mode frequency [Hz] ≤ 7.5
9.5 ≤ pitch mode frequency [Hz] ≤ 18.0
13.0 ≤ roll mode frequency [Hz] ≤ 20.0
10.5 ≤ yaw mode frequency [Hz] ≤ 20.0
Optimization of rigid body vibration mode is one of the most effective and general approach to initially
satisfy the vibration performance target of engine mount design (Brach 1997). Vehicle vibration is to be
reduced by means of optimizing rigid body modes of engine because the resonant frequencies and modes of
engine are highly relative to idle and driving vibration. Performance targets of engine modal purities and
mode frequencies are carefully set up considering the vibration characteristics of vehicle, tire and suspension
as well as engine operation mechanism. Design variables and their allowable ranges are represented in Table
4, and applied to explore design sensitivity and optimum design points.
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Table 4 Design variables and their ranges
Design variables Lower limit
(loc. : x, y, z) (stiff. :kx, ky, kz)
Initial design (loc. : x, y, z)
(stiff. :kx, ky, kz)
Upper limit (loc. : x, y, z)
(stiff. :kx, ky, kz)
Engine mount1 (EM1) (-180, -500, 270) (-161, -455.7, 303.2) (-140, -400, 330)
Engine mount2 (EM2) (-180, 400, 270) (-161, 455.7, 303.2) (-140, 500, 330)
Engine mount3 (EM3) (180, -10, 270) (200, 0, 303.2) (220, 10, 330)
Mount location [mm]
Engine mount4 (EM4) (-550, -10, 270) (-500, 0, 303.2) (-450, 10, 330)
Engine mount1 (EM1) (150, 20, 70) (175.1, 41.2, 103) (200, 60, 130)
Engine mount2 (EM2) (230, 30, 130) (263.5, 62, 155) (300, 90, 180)
Engine mount3 (EM3) (80, 80, 270) (100, 100, 300) (120, 120, 320)
Mount stiffness [N/mm]
Engine mount4 (EM4) (80, 80, 270) (100, 100, 300) (120, 120, 320)
Statistical results such as main effect are reviewed via design sensitivity analysis. In this study, DOE design
of Placket-Burman is used with 2 level linear screening strategy. Results of main effect on roll purity are
shown in Figure 6.
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Figure 6 Main effect on roll purity with respect to design variables
From Figure 6, it is clear that the x and z directional stiffnesses of the second and fourth engine mounts are
most sensitive design variables on roll purity performance. Main effects on other responses are able to
analyze in the same way. Based on design sensitivity analysis, it is able to decide which design variables are
important on some responses. Optimization analysis is also performed using Eqn. 8 and Table 4 to find out
optimal design points while Eqn. 8 is satisfied. Results of optimal design points are shown in Table 5, and
results of design performances are represented in Table 6 and Figure 7.
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Table 5 Design optimization results
Design variables Initial design (loc. : x, y, z)
(stiff. :kx, ky, kz)
Optimal design (loc. : x, y, z)
(stiff. :kx, ky, kz)
Engine mount1 (EM1) (-161, -455.7, 303.2) (-173.07, -481.93, 286.15)
Engine mount2 (EM2) (-161, 455.7, 303.2) (-150.79, 441.57, 294.08)
Engine mount3 (EM3) (200, 0, 303.2) (206.80, 7.41, 283.08)
Mount location [mm]
Engine mount4 (EM4) (-500, 0, 303.2) (-531.06, -8.40, 292.86)
Engine mount1 (EM1) (175.1, 41.2, 103) (175.05, 38.9, 72.17)
Engine mount2 (EM2) (263.5, 62, 155) (253.88, 86.89, 130.86)
Engine mount3 (EM3) (100, 100, 300) (97.41, 114.57, 303.89)
Mount stiffness [N/mm]
Engine mount4 (EM4) (100, 100, 300) (97.27, 87.71, 313.68)
Table 6 Analysis results of normal mode and modal purity for optimal design
Normal mode Modal purity [%] Mode no.
Frequency [Hz] Fore/aft Lateral Bounce Roll Pitch Yaw Total
1 4.62 0.050 97.371 0.140 2.429 0.010 0.000 100
2 6.75 94.359 0.080 2.920 0.000 2.600 0.040 100
3 8.97 3.220 0.130 96.480 0.060 0.110 0.000 100
4 18.77 0.011 2.235 0.042 88.413 0.752 8.547 100
5 19.51 2.332 0.020 0.395 1.462 95.485 0.306 100
6 19.57 0.019 0.233 0.009 12.962 0.540 86.236 100
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Figure 7 Modal purity chart for optimal design
As shown in Table 6 and Figure 7, modal purities of roll, pitch and yaw are enhanced by virtue of design
optimization analysis comparing with the initial design conditions. Optimized design of 6-DOF model is
carried over 16-DOF full vehicle model to review the vibration effects on vehicle considering the exciting
sources from engine and tires. Using 16-DOF model, idle vibration and engine shake analyses are able to be
performed evaluating the results of some important measuring points such as seat track. Static analysis is
also able to be carried out to generate loading conditions for structure analysis and/or strength evaluation of
engine mount bracket.
Closing Remarks
The paper discusses the implementation of development of MSC.ADAMS based vibration analysis program
and design optimization for engine mount system. In the present study, the application procedure of vibration
analysis program is explained, and the design optimization is explored for the engine mount system of a
passenger vehicle using that program. The paper emphasizes that complex engine mount design is
conveniently and effectively evaluated by means of using the developed program, and also able to be
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extended to the design optimization. From the evaluation of practical design examples, it proves that the
proposed approach is useful to be applied to vibration design of engine mount as well as vehicle system.
References
Brach, R., Automotive powerplant isolation strategies, SAE Technical Paper Series, No. 971942 (1997).
Hadi, R. and Sachdeva, D., Effect of mounting strategy on vehicle NVH, SAE Technical Paper, No. 2003-01-
1467 (2003).
Ibrahim, R. A., Recent advances in nonlinear passive vibration isolators, Journal of Sound and Vibration
Volume 314, Issues 3-5, 22 July (2008) 371-452.
Jeong, T. and Singh, R., Analytical methods of decoupling the automotive engine torque roll axis, Journal of
Sound and Vibration 234 (2000) 85–114.
Lee, D. H., Hwang, W. S. and Kim, C. M., Design sensitivity analysis and optimization of an engine mount
system using FRF-based substructuring method, Journal of Sound and Vibration, Volume 255, Issue 2, 8
August (2002) 383-397.
Lin, T. R., Farag, N. H. and Pan, J., Evaluation of frequency dependent rubber mount stiffness and damping
by impact test, Appl. Acoust. 66 (2005) 829–844.
MSC.ADAMS User’s Manual, MSC software, 2008.
Peng, Z. K. and Lang, Z. Q., The effects of nonlinearity on the output frequency response of a passive engine
mount, Journal of Sound and Vibration 318 (2008) 313–328.
Royston, T.J. and Singh, R., Optimization of passive and active non-linear vibration mounting systems based
on vibratory power transmission, Journal of Sound and Vibration 194 (1996) 295–316.
Shangguan, W. B. and Zhao, Y., Dynamic analysis and design calculation methods for powertrain mounting
systems, Journal of Automotive Technology, Vol.8 No.6 (2007) 731–744.
17
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Sirafi, M. and Qatu, M., Accurate modeling for powertrain and subframe models, SAE Paper No. 2003-01-
1469 (2003).
Zhang, Y. Q. and Shangguan, W. B., A novel approach for lower frequency performance design of hydraulic
engine mounts, Computers & Structures, Volume 84, Issues 8-9, March (2006) 572-584.