STUDY ON THE VIBRATION REDUCTION OF THE DOUBLE PISTONS HYDRAULIC ENGINE MOUNT

48 Journal of Marine Science Technology, Vol. 11, No. 1, pp. 48-5 (3) STUDY ON THE VIBRATION REDUCTION OF THE DOUBLE PISTONS HYDRAULIC ENGINE MOUNT You-Gang Tang*, Hong-Yu Zheng**, Jia-Yang Gu**, Da-Ning Jiang** Key words: hydraulic engine mount, vibration reduction, dynamic stiffness, transfer function. ABSTRACT A novelty style metal hydraulic engine mount (HEM) is developed. The HEM designed in this paper consists of hydraulic cylinder, bar, two pistons the spring on the bottom. The mechanical model the dynamic equations are set up by considering kinematics continuous of fluid, the analytical method for dynamic behavior including dynamic stiffness transfer function of HEM are suggested herein. The dynamic characteristics of HEM are investigated. It is shown that the HEM proposed herein can be employed in the practical engineering for vibration reduction. INTRODUCTION The rubber mount is often adopted to reduce vibration noise of cars, but the rubber dampers have poorer performance of vibration reduction in lower frequencies. In order to improve the vibration noise of cars in broad frequencies, the hydraulic rubber mount for engine of a car was presented in 1984, Waliace summarized the constructions of hydraulic mounts mechanism of vibration reduction [8]. In general, there are 4 type of HEM [-4, 6]: HEM with simple orifice; HEM with inertia track; HEM with orifice decouple; HEM with inertia track de-couple. The dynamic performances of HEM with simple orifice depend on the area of orifice rubber element. The optimization theory analytical model of HEM were presented to minize transfer function of vibration [3]. Gau Jeffry [] carried out the theory experiment Paper Submitted 8/7/, Accepted 4/9/3. Author for Correspondence: You-Gang Tang. *Professor, Dr., Department of Naval Architecture Marine Engineering, School of Architecture Engineering, Tianjin University, Tianjin, 37, P.R.C. **Graduate Students, Department of Naval Architecture Marine Engineering, School of Architecture Engineering, Tianjin University, Tianjin, 37, P.R.C. study of the HEM with orifice de-couple, it is shown that the HEM has high damping in 5-15 Hz frequency region, low damping in1-3hz frequency region, whose are suitable for vibration reduction of cars. The HEM with inertia track comprises the primary rubber element the inertia track (long tube), thus it can provide higher damping than HEM with orifice, Kim Singh studied the behaviors of reduction vibration by using the model of engine-mount system, the results of calculation are identical with the experiment datum [4]. The behavior of vibration reduction of HEM with inertia track de-couple were investigated with two freedom model considering the piecewise liner characteristics of de-couple [7]. The HEM mentioned in References [-4, 6-8] can be called as the Rubber Fluid Absorbers (RFA), which are not suitable for vibration reduction of heavy vehicles. The HEM with metal cylinder single piston (MCSP) was designed used in the ambulance stretcher system. The MCSP is composed of metal cylinder one piston with orifice, when a piston moves up down, the fluid flows back forth thus causes the damping effect [5]. There are some weaknesses in the behaviors both impulse fatigue of RFA MCSP. So, it is important to develop novelty HEM for the vibration reduction of heavy machineries heavy vehicles. The paper improved the HEM based on the construction of RFA MCSP. The metal cylinder replaces the primary rubber element, the disc with orifice is fixed inside the cylinder, the two pistons are linked by bar. When the two pistons move up down with bar simultaneously, it forces the fluid to flow through the orifice, which produces higher damping than MCSP. The HEM developed in this paper can be employed in the vibration reduction of heavy vehicles. ANALYTICAL MODEL AND MOTION EQUATIONS OF THE HEM The Fig. 1 shows the HEM with orifice two pistons. The HEM is composed of two pistons, bar,

Y.G. Tang et al.: Study on the Vibration Reduction of the Double Pistons Hydraulic Engine Mount 49 disc with orifice spring on the bottom. The upper piston lower piston are linked by bar, they move with bar simultaneously. Only if the vertical displacement is considered, HEM can be described by the model in Fig.. As a engine moves down, the two pistons move down with bar simultaneously, the upper chamber is compressed, which forces the fluid to flow through the orifice into the lower chamber, it causes the inertia force the damping of fluid inside the orifice, the transfer function of vibration will be reduced by making use of these two forces. In Fig., k s c s are the stiffness coefficient damping coefficient of the bottom spring, respectively; m 1 is the mass including the two pistons the bar; m is the mass on the top of mount; x expresses the inputting deflection; F is the resultant of forces acting on the upper piston. The volume stiffness k(n/m 5 ) of fluid is defined as the ratio of p to v inside the upper chamber, i.e. k = p/ v [6, 8], p denotes the pressure change, v is the volume change inside the upper chamber. k indicates the pressure change induced by unit volume change of upper chamber. p v are induced by pistons motion. The fluid pressure of upper chamber is defined as p; A represents the cross-section area of piston (except the area of bar) is the total area of orifice in the disc; y is the vertical flow of fluid inside the orifice. Based on the continuous condition of fluid, the change of fluid volume inside the upper chamber should equalize the fluid volume flowing through the orifice i.e. A x = y (1) where, A is the volume change of fluid inside the upper chamber; y indicates the fluid volume flowing through the orifice. It is assumed that the fluid pressure p inside upper chamber is uniform, so the fluid pressure can be given as following p = ( y)k () the vibration equation of the construction can be obtained based on the equilibrium of force, (m + m 1 ) x + c s x + k s x + A p = F (3) where, A p is the hydraulic force acting on the piston. The fluid inside the orifice bears the pressure forces p, it can be simplified into the oscillator caused by the acceleration of fluid motion through the orifice, the dynamic equation of the oscillator can be described as following m f y + c f y = p (4) where, m f is the total mass of fluid inside orifice, m f = hρ, h is the height of orifice; ρ denotes the density of fluid; c f expresses the damping coefficient, which depends on the friction between fluid the wall of the orifice the resistance force of orifice. Substituting Eqs. (1), () into Eqs (3), (4) respectively, it is obtained as following (m + m 1 ) x + c s x + k s x + A ( y) k = F (5) m f y + c f y =( y) k (6) Fig. 1. Hydraulic double-pistons mount. Fig.. Analytical model.

5 Journal of Marine Science Technology, Vol. 11, No. 1 (3) according to Eq. (6), one yields y = m fy + c f y k substituting the Eq. (7) into Eq. (5), one has (7) m (m + m 1 ) x + c s x + k s x + A f y + c f y = F (8) according to the continuous condition (1) of fluid, one yields THE NATURAL VIBRATION CHARA- CTERISTICS AND DYNAMIC STIFFNESS OF HEM SYSTEM According to Eq. (13), the natural frequency of HEM without damp is k λ = s (14) M according to Eq. (13), the free vibration equation of HEM is y = A x, y = A x, y = A x so, Eq. (8) can be rewritten as following or (m + m 1 ) x + c s x + k s x +[m f ( A ) x + c f ( A ) x]=f (9) x +ζλ x + λ x = (15) ζ = τa Mλ The natural frequency of HEM with damp is λ d = λ 1 ζ (m + m 1 + m ) x +(c s + τa ) x + k s x = F (1) m e =( A ) m f, c e =( A ) c f = τa where, m e c e are the equivalent mass the equivalent damp coefficient of the fluid flowing through orifice. According to the hydraulic theory, c e can be calculated by Eq. (11) [1] c e = τa (N s/m) (11) τ = 18υρh nπd 4 (N s/m 5 ) (1) where, τ is the resistance force coefficient of orifice; υ is the stick coefficient of fluid, υ = 1 1 6 (m /S) for water; n denotes number of orifices; d is the diameter of orifice; ρ = 1 (Kg/m 3 ) It is known that m e c e depend on the ratio of the A /A 1. The behavior of vibration reduction can be improved by adjusting the ratio of A /A 1 ; the damp of HEM increases with increment of A /A 1. If the damp coefficient of the spring is ignored, the equation of motion (1) can be rewritten as following Mx + τa x + k s x = F (13) where, M = m + m 1 + m e. is, It is assumed that the excitation is harmonic, that x = x e iωt, F = F e iωt (16) where, i = 1 ; ω is the frequency of excitation displacement; x denotes the displacement amplitude of excitation; F indicates the amplitude of resultant forces. Substituting Eq. (16) into Eq. (13), one yields Mω x + τa x iω + k s x = F (17) The dynamic stiffness k d (iω) of HEM is defined as F /x, or k d (iω)= F = Mω x + k s + τa iω (18) also, the amplitude of dynamic stiffness can be given by Eq. (19) where k d = k d (iω) = M ω +( Mk s + τ A 4 ) ω + k s = k s (1 µ ) + η µ (19) µ = λ ω, η = τa =ζ () Mλ It is known from Eq. (19) that the dynamic stiff-

Y.G. Tang et al.: Study on the Vibration Reduction of the Double Pistons Hydraulic Engine Mount 51 ness increases with the increment of stiffness the damp coefficient of HEM. In order to show the effect of fluid inside orifice on the dynamic stiffness of HEM, only m e is considered in Eq. (19), one has where, D(α) = D(iω) = m e ω 4 +( Mk s + τ A 4 ) ω + k s = k s (1 α ) + β α (1) α = ω ; β = τa m e ω ; ω = k s m e () D(α) is called as the dynamic stiffness of equivalent fluid. TRANSFER FUNCTION OF FORCE The amplitude of inputting force is given as following F =( Mω + τa iω + k s ) x (3) the outputting force acting on the foundation is F 1 = m e x + τa x + k s x (4) substituting Eq. (16) into Eq. (4), the amplitude outputting force is F 1 =( m e ω + τa iω + k s ) x (5) the transfer function of force is T(iω)= F 1 = m eω + τa iω + k s F Mω + τa iω + k s = (1 α )(1 γα )+β α (1 γ) βγ + 3 (1 γα ) + β α (1 γα ) + β α i = R e + I m i The amplitude of force transfer function is µ(α)= T(iω) = R e + I m = [(1 α )(1 γα )+β α ] +[(1 γ) βα 3 ] where, α = ω ω ; γ = M m e. [(1 γα ) + β α ] (6) EXAMPLE The parameters of HEM shown in Fig. 1 are: n = 43; d = 4 mm; h = 1mm; the height of cylinder is 75 mm. According to the parameters, one has A = 34. cm =43 (.3 ) 3.14 = 3.4 cm A / A 1 = 15.8 m f = 3.4 1-4.1 1 =.64 kg m e = 15.8.64 =.8 kg m 1 =.957 kg, m = 1 kg Fig. 3. Curve of HEM dynamic stiffness. Fig. 4. Curve of fluid dynamic stiffness.

5 Journal of Marine Science Technology, Vol. 11, No. 1 (3) CONCLUSIONS The metal hydraulic engine mount with orifice two pistons is presented, the analytical method of vibration reduction behavior is developed. The dynamic stiffness of HEM the fluid oscillator are solved. Also, the force transfer function is determined. The analysis shows that the vibration response can be reduced effectively by using the metal hydraulic engine mount designed in this paper. The paper provides the novelty technology for reduction vibration of heavy vehicles. Fig. 5. Curve of force transfer function. M = m + m 1 + m e = 11.76 kg The stiffness of spring on the bottom is calculated by Eq. (7) [9] k s = Gd4 8D 3 (7) i where, G is the shear elasticity modulus, G = 1.68 1 11 (N/m ); d is the diameter of spring wire, d = 4 mm; D denotes the diameter of spring, D = 5 mm; i is the curves of spring, i = 3. The spring stiffness is k s = 1.15 1 5 (N/m). According to Eqs. (1), (14) (), one has λ = 98.9 (1/s), ω = 379 (1/s), τ =.46 1 5 (N.s/m 5 ). Substituting the above datum into Eq. (19), the curve of dynamic stiffness of HEM can be obtained drawn in Fig. 3. Also, Fig. 4 shows the curve of dynamic stiffness of fluid inside the orifices. The curve of force transfer function is obtained according to Eq. (6) described in Fig. 5. It is known from Fig. 5 that the transfer function can be reduced effectively as α > 1 µ > 1 corresponding to the higher frequency. Otherwise, the dynamic stiffness depends on the fluid damping the force transfer function is less than 1 as α < 1 µ < 1 corresponding to the lower frequency. So the HEM has high performance of vibration reduction in broad frequency region. REFERENCES 1. Frolov, K.V., Vibration in Technique, Machinary Press, Moscow (1995).. Gau, S.J. Jeffry, D.C., Experiment Study Modeling of Hydraulic Mount Engine System, Proceeding of the Noise Vibration Conference of SAE, No. 951348, pp. 97-939 (1995). 3. Kazuto, S. Katsuml, E., Optimum Design Method for Hydraulic Engine Mounts, Proceeding of the Noise Vibration Conference of SAE, No. 911 55, pp. 463-47 (1991). 4. Kim, G. Singh, R., A Study of Passive Adaptive Hydraulic Engine Mount System with Emphasis on Nonlinear Characteristics, J. Sound Vib., Vol. 179, No. 3, pp. 47-453 (1995). 5. Qi, J.C., Li, R.X., Liu, Z.G., Xu, X.X., Study on Active Vibration Control for Ambulance Stretcher System Based on Sky-Hook Damper Theory, J. of Vib. Eng., No., pp. 41-44 (1998). (in Chinese) 6. Takao, U., Kazuya, T., Hiroshi, Ko., High Performance Hydraulic Mount for Improving Vehicle Noise Vibration, Proceeding of the Noise Vibration Conference of SAE, No. 8873, pp. 45-458 (1988). 7. Thomas, J.R. Singh, R., Study of Nonlinear Hydraulic Engine Mounts Focusing on Decoupler Modeling Design, Proceeding of the Noise Vibration Conference of SAE, No. 971936, pp. 536-545 (1997). 8. Waliace, C.F., Understing Hydraulic Mounts for Improving Vehicle Noise, Vibration Ride Qualities, Proceeding of the Noise Vibration Conference of SAE, No. 85975, pp. 13-13 (1985). 9. Yang, L.M., Huang, K., Li, A.Z., Cheng, S.X., H Book of Machine Design, National Defense Industry Press, Beijing (1988).