Study on two-stage mounting systems having distributed intermediate mass
The design logic and calculation method for determining mount stiffness and damping for

a Powertrain Mounting System (PMS) based on reductions of vehicle vibration and noise

contributed by mounts is proposed in this paper. Firstly, the design target for a PMS with

regard to vibration and noise limitations of vehicle level contributed form mounts is

described. Then a vehicle model with 13 Degree of Freedoms (DOFs) is proposed, which

includes 6DOFs for the powertrain, 3 DOFs for the car body and 4DOFs for the four unsprung

mass, and the dynamic equation for the model is derived. Some widely used models, such as

the 6 DOFs model of the powertrain for the design calculation of a PMS, the 7 DOFs model

(Body’s 3 DOFs; unsprung mass’s 4 DOFs) and the 9 DOFs model (powertrain’s 6 DOFs; Body

’s 3 DOFs) for ride analysis of a vehicle, are the specific cases of the presented model

of 13 DOF. Thirdly, the calculation method for obtaining the vibration of seat track and

evaluation point and the noise at driver right ear is presented based on the mount forces

and the vibration and noise transfer functions. An optimization process is proposed to get

the mount stiffness and damping based on minimization of vehicle vibration and noise, and

the optimized stiffness is validated by comparing the calculated vibration and noise and

limitations. In the end of this paper, the natural frequencies and mode energies for the

powertrain, the body and the unsprung mass are calculated using different models and the

results are compared and analyzed.
Nowadays, two-stage ballast mounting system having integral intermediate mass is widely

applied and researched to attenuate vibration of marine machinery equipment, while two

stage mounting system having distributed intermediate mass which has the feature of

lightweight and installation dimension is rarely used and studied. The theoretical models

of two types of mounting systems are set up and force transmissibility rate of the two

mounting systems are deduced through four-pole parameters method. A scale experimental

prototype is established to test the isolation efficiency of the two-stage mounting system

having distributed intermediate mass. FEMs of the two systems are established to make a

comparison ascertaining the difference between the two about vibration isolation efficiency

at the different frequency. The result shows that two stage mounting system having

distributed intermediate mass achieve better vibration isolation efficiency and take less

space than two-stage mounting system having integral intermediate mass if with equivalent

intermediate mass. Two-stage mounting system having distributed intermediate mass can meet

the requirements of practical projects and provides a new way for engineer to refer to when

meet with machinery equipment vibration problems.
Keywords: two-stage mounting system, distributed intermediate mass, integral

intermediate mass.
1. Introduction
In many segments of industry the trend in the past few years has been towards more

complex equipment and machines, which are lighter and more compact than their predecessors

and which operate at greater speeds and power ratings. To the vibration engineer this trend

has meant more problems associated with vibration isolation problems: i.e., more excitation

available and more components likely to be affected adversely by them so that it has become

increasingly important to provide vibration isolation systems that will retain their

effectiveness [1, 2]. Machinery

ground mounting system is one of the most significant vibration and noise attenuation

technology of mechanical equipment [3-5].
It has been extensively believed that the intermediate mass of two-stage

double

pole mounting system would be better to improve isolation efficiency than one-stage

mounting system [6, 7]. At present, two-stage mounting system having frame structure

intermediate mass like raft mounting system is widely used in the field of naval vessels

which have been gaining widespread attention. In practical application, the intermediate

mass usually takes amount of 20-30 % of the isolated mass [8], but in special cases where

dimensions and weight are strictly limited, this way may not be suitable. Thus, the other

Machinery mounting system that is two-stage mounting system having distributed intermediate

mass which takes less space would play a more important role in the field of vibration

noise controlling.
The simplified theoretical and finite element model of the two kinds of two-stage

mounting systems are analysed in the paper. The equation of two kinds of mounting systems’

isolation effectiveness expressed by transmissibility were deduced through four-pole

parameter method. A comparison between the Single Pole Mounting System to ascertain

the difference about vibration isolation efficiency at different specific frequency through

FEM model analysis was made. A scale experimental platform was established to test the

isolation efficiency of the two-stage mounting system having distributed intermediate mass.
The research results based on the calculation and analysing on the two kinds of

mounting systems can provide a reference for engineer when designing mounting system for

machinery equipment.
2. Mounting system theoretical model
2.1. Basic theory of four-pole parameters method
The behaviour of mounting systems is complicated and extremely hard to predict because

of wave effects. To depict the behaviour of system’ dynamic performance is difficult so

that to simplify practical mounting system is necessary [9, 10].
Four–pole parameters method is an essentially simple idea and for this reason is

helpful in providing a point of view [11]. All of the pertinent properties of a system can

be expressed in terms of four pole parameters which characterize only the system for which

they are determined; their value is not influenced by the preceding or subsequent

mechanical systems.
A linear mechanical system is shown schematically in Fig. 1. The system may be

comprised one or more lumped or distributed elements, or be constructed from any

combination of such elements. The input side of the system vibrates sinusoidally with a

velocity  in response to an applied force . In turn, the output side of the system

exerts a force  on the input side of some further system, sharing with it a common

velocity . Thus the system shown is said to have input and output terminal pairs, a

force  and velocity  at the input terminal pair giving rise to a force  and

velocity  at the output terminal pair, the reaction of any subsequent mechanical

system being accounted for. Forces are considered positive when directed to the right [12,

13].
Isolators made of hard elastic material were used in the upper mount whose natural

frequency were about 8 Hz and stiffness is 1.5×10e6 N/m, damping factor 0.09. Air spring

was used in the lower mount whose natural frequency was about 4 Hz, stiffness is 10e6 N/m

and damping factor 0.05. Intermediate mass amounts about 20 % of the total mass of the

upper body including a vibration generator to simulate vibration source and rack to hold

it. The vibration generator generates vibration at a precise frequency. The isolation

effectiveness expressed by acceleration tested by PULSE exploited by Brüel&Kj?r was shown

in Table 1. All of the measurements summarized here were obtained after post-process using

Pulse Reflex, driven by1/3 octave band filtered white noise, and by measuring 1/3 octave

bands. Experimental results showed that satisfactory isolation effectiveness evaluated by

vibration lever difference could be obtained by using distributed intermediate mass as

frame structure intermediate mass does.
To compare the isolation effectiveness of two-stage mounting system having integral

intermediate mass with distributed intermediate mass. FEMs of the two types of mounting

system was designed based on the scale experimental prototype having distributed

intermediate mass was set up through ABAQUS as is shown in Fig. 10 and Fig. 11. Q235 whose

density  7800 kg/m3, elasticity modulus  200 GPa, Poisson’s ratio  0.3 was

used as the material of foundation, intermediate mass and rack to install a vibration

generator. The upper and lower isolators were simulated by spring with three dimensional

stiffness and both ends of the spring were six degrees of freedom coupling constrained to

the foundation, upper rack and intermediate mass with its actual contract area

respectively. Data of isolators’ three dimensional stiffness was obtained through

practical testing so that can be used as input parameters. The foundation was six degrees

of freedom coupling constrained to the ground.
In this paper, four-pole parameter method and numerical calculation method were used to

analyse the two types of two-stage mounting systems and a scale prototype was designed to

test isolation effectiveness of two-stage mounting system having distributed intermediate

mass. Results showed:
1) Two-stage of mounting system having distributed intermediate mass can satisfy the

criterion of practical projects in isolation efficiency over 40 dB which provide a new way

for designer to choose when making mounting plan.
2) When the carport mounting

system having the same intermediate mass in quality, two-stage mounting system having

distributed intermediate mass would obtain better isolation efficiency.
The usual frame designs, however, incorporate extended structural members which exhibit

modal behaviour at acoustic frequency; thus, such frames do not act as rigid masses at

these frequencies and the advantages of a two-stage mounting system are lost. In many such

installations it is likely that better high-frequency isolation, plus perhaps a saving in

weight, may be obtained essentially by replacing the frame with distributed compact mass

which will act as rigid mass at high frequency like the two-stage mounting system having

distributed intermediate mass I discussed in the paper.
Further research on how the vibration isolation effectiveness fluctuate with increasing

intermediate compact mass and detailed physical explanation on why would distributed

intermediate mass provide as well vibration isolation effectiveness as a frame structure

intermediate masa work will be continued.
The vibration isolation performance of the engine mounting system can be evaluated by

the transmission force. The transmission force characteristics of engine mounting system

are analyzed by simulation and test. The 6-DOF model of engine mounting system is

established by ADAMS software. The results of modal parameters and transmission force of

engine mounting system are obtained by simulation. The force sensor is made with resistance

strain gauge. The sensor is calibrated by chassis dynamometer method. The transmission

force of the engine mounting system is tested under the complete vehicle condition. The

test results of transmission force and acceleration transmissibility are compared. It is

proved that the transmission force is more suitable to evaluate the vibration isolation

performance of the mounting system when the vehicle is running at medium and high speed.
This article is to find optimized placement for an active

solar farm mounting system

suitable for a 6-DOF bar structure with two active paths. When a sinusoidal

excitation force is applied to the structure, secondary force and phase of the two active

supports can be calculated mathematically. When the position changes, the magnitude and

phase of the secondary forces in each path will be analyzed using simulation. If the forces

applied to the two active mounting system are relatively small and the phase does not

change by 180 degrees, these specific positions of paths are considered as optimized

positions of the active mounting system. Based on the simulation results, criteria for

selecting the location are proposed, which will be very useful for proper selection of

actuators for engine mount system.
In automotive industries, engine vibration isolation has been always a difficult task

and due to the trend of lighter weight and higher power of vehicles, it has become a more

serious problem. In order to improve the NVH performance of mounting systems, active

control methodologies have been applied and many research has focused on the position of

the engine mount system to optimally reduce vibration. Genetic algorithms are utilized to

find the optimized locations of piezoelectric actuators and sensors for active vibration

control [1]. For different engine installation positions, vibration characteristics of

heavy commercial vehicles are studied. They demonstrate how to achieve the engine isolation

by arranging the engine isolator in the longitudinal direction of the powertrain [2].

Vibration reduction of a coupled path structure with a piezoelectric laminated actuator and

a rubber bearing is studied and active path interactions are quantified based on the

dynamic characteristics of the passive system [3]. However, under the same excitation

conditions, the vibration reduction could be changed as the position of the movable active

engine mount changes. Thus, this research will focus on optimizing the location of active

elements.
In this study, the experimental setup shown in Fig. 1 is prepared and its numerical

analysis would be presented. Upper and lower bars are representing the vehicle engine and

the sub-frame, respectively. There are two paths made of a piezo-stack actuator and a

rubber mount to provide active vibration isolation between the bars. At first, a parametric

model is proposed for a given laboratory experiment structure and establish a motion

equation. Then, numerical simulation will be performed and the results will be analyzed to

determine the criteria for selecting the best location for the mounting system.