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 . Machinery ground mounting system is one of the most significant vibration and noise attenuation technology of mechanical equipment . 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 . 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 , 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 . Four–pole parameters method is an essentially simple idea and for this reason is helpful in providing a point of view . 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 . 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 . 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 . 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 . 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.