PHYSICAL MODEL OF VEHICLE ENGINE MOUNT WITH MAGNETORHEOLOGICAL DAMPER

Transcription

1 JACEK MECHANICS SNAMINA, AND BOGDAN CONTROL SAPIŃSKI PHYSICAL Vol. 35 No. 1 MODEL 2016 OF VEHICLE ENGINE MOUNT... ttp://dx.doi.org/ /mec JACEK SNAMINA, BOGDAN SAPIŃSKI* PHYSICAL MODEL OF VEHICLE ENGINE MOUNT WITH MAGNETORHEOLOGICAL DAMPER ABSTRACT A pysical model of a veicle engine mount incorporating a magnetoreological (MR) damper in squeeze mode is investigated and te structural design and operating caracteristics of te MR damper are provided. Te matematical model of an engine mount is formulated. Kinematic excitations are assumed to be tose emulating road profile- -cassis (car body) interactions. Simulations of engine vibration are performed to determine te efficiency of te proposed engine mount. Conclusions are drawn concerning te potential applications of te MR damper in veicle engine mounts. Keywords: MR damper, engine mount, vibration, model MODEL FIZYCZNY ZAWIESZENIA SILNIKA SAMOCHODOWEGO Z TŁUMIKIEM MAGNETOREOLOGICZNYM W pracy opisano budowę modelu fizycznego zawieszenia silnika samocodowego, w którym zastosowano tłumik z cieczą magnetoreologiczną (MR) działającą w trybie ściskania. Sformułowano model matematyczny zawieszenia. Zakładając wymuszenie kinematyczne modelujące oddziaływanie nierówności drogi na karoserię, przeprowadzono symulacje komputerowe drgań silnika. Oceniono efektywność działania zawieszenia oraz sformułowano wnioski dotyczące możliwości zastosowania tłumika MR w zawieszeniu silnika samocodowego. Słowa kluczowe: tłumik MR, zawieszenie silnika, drgania, model 1. INTRODUCTION Semi-active systems are now in widespread use, mostly because teir energy demand is rater low and tey can effectively interact wit passive systems. Te most distinctive feature of semi-active systems is tat teir parameters can be varied in te course of teir operation, tus enabling te control of damping force in te vibration reduction system. Te work performed by a semi-active damper force will always be negative, as te damper will take up energy from te system at eac instant. Vibration reduction systems comprising semi-active components can be provided, inter alia, in systems securing a combustion engine to a cassis. A combustion engine as an intricate sape, it is secured to te cassis via fixing elements wose positions and parameters are derived from analyses of te static and dynamic beavior of te entire driving system. Since te causes of engine vibrations cannot be wolly eliminated, te structure of te engine mount is of particular importance, ensuring te correct engine configuration in te engine bay and minimizing te dynamic forces involved in cassis- -engine interactions. Rubber elements are used for securing te engine in its position, as tey are small in size and relatively ceap. As new car designs were developed, purpose-built ydraulic mounts were introduced (Dol 1991, Ivers, Sing et al. 1992, Flower 1995). Te presently developed mount designs utilize controlled semi-active components (Amadian, An 1999, Yune et al. 2001, Soutern 2009, Craft et al. 2010, Zang et al. 2011, Kim 2012, Sapiński and Krupa 2013, Snamina, Sapiński 2014), as well as active components leading to te more effective reduction of undesired dynamic interactions between te engine and cassis. Te engine mount considered in tis paper incorporates a newly-designed squeeze-mode MR damper. Te work covers a description of te damper, a matematical model of te engine-frame system, numerical simulations of te road profiles for te assumed road category, and an analysis of engine vibrations. 2. MR DAMPER A simplified sceme of te damper is sown in Figure 1. Te damper ousing comprises top and bottom covers and an outer cylinder (1). Te top cover and outer cylinder are made of a ferromagnetic material, and te bottom cover is made of a diamagnetic. Te piston rod (3) integrated wit a non-magnetic ring (9) moves inside te inner cylinder (2), wic is made of a diamagnetic material and press-fitted togeter wit te ring (7) in te outer cylinder (1). In te damper s middle section, te inner and outer cylinders are saped in suc a way tat MR fluid sould flow from underneat te piston to te bottom camber, acting as a fluid container. Tis camber is limited from below by te piston (5) aving a small mass and provided wit sealing. * AGH University of Science and Tecnology, Faculty of Mecanical Engineering and Robotics, Krakow, Poland; snamina@ag.edu.pl, deep@ag.edu.pl 6

2 MECHANICS AND CONTROL Vol. 35 No Te piston is pressed down by a spring (not indicated in te diagram) placed between te lower piston surface and te damper s bottom cover (8). Te spring force gives rise to pressure acting upon te MR fluid in te container. In te damper s middle section, tere is a system generating a magnetic field comprising a coil (6) wound on te core (4). Magnetic flux is conditioned in te damper s magnetic circuit, incorporating a coil core, outer cylinder, top cover, and piston, and te volume underneat te piston is filled wit MR fluid. Dimensions of te magnetic circuit components are cosen suc tat te magnetic flux permeating te volume underneat te piston sould be sufficient to effectively affect te MR fluid moving radially (as a result of piston movement). Fig. 1. Sceme of MR damper. Explanation in text During te damper operation, te eigt of te working gap beneat te piston is a function of time; ence, te magnetic resistance of te circuit will vary, and te magnetic system is non-stationary. A detailed description of te damper s design structure is given elsewere (Sapiński, Gołdasz 2015). Te damper force (Sapiński 2015) acting upon te vibrating object can be approximated as follows: 1 1 (, ) & ( ) ( ) sgn( &) Fd =β1 μ Dp +β 3 2 Dp τ 0 I β3( ρ, Dp) && β4( ρ, Dp) & 2 were: D p te piston diameter, μ te dynamic viscosity of te MR fluid, I te current, ρ te density of te MR fluid, τ 0 te yield stress of te MR fluid, β 1... β 4 te coefficients determined empirically, te eigt of te working gap (te displacement between te piston and core surfaces). Te terms expressing particular force components in Equation (1) ave teir pysical interpretation. Te first term is associated wit fluid viscosity and te second is associated wit tose parameters of te MR fluid tat are related to magnetic induction. Te two remaining terms are associated wit te inertia of te MR fluid during its flow in te camber underneat te piston. Te second term, associated wit te magnetic field induction, appears to be predominant. Te damper force is plotted in Figure 2 assuming sine variable movement of te piston wit respect to te damper ousing (an amplitude of 0.7 mm and frequency of 9 Hz) and te following values of te parameters: β 1 = kg m 3 /s; β 2 = m 3 ; β 3 = kg m; β 4 = kg m. In te static equilibrium position, te eigt of te working gap underneat te piston equals 0. In te context of te damper s design structure, 0 corresponds to te maximal piston displacement in its downward movement wit respect to te ousing because te piston surface in tat position is on te same level as te top surface of te core. (1) Fig. 2. Damper force vs. piston displacement for various current levels; frequency of 9 Hz 7

3 JACEK SNAMINA, BOGDAN SAPIŃSKI PHYSICAL MODEL OF VEHICLE ENGINE MOUNT MATHEMATICAL MODEL OF ENGINE-FRAME SYSTEM Vibrations of te engine and frame associated wit te cassis were analyzed by recalling a simplified 2-DOF model. A scematic diagram of te modeled system is sown in Figure 3. Te model incorporates an engine as well as a frame tat secures te engine in its position in te cassis to wic it is directly mounted. Te pysical model incorporates a prototype MR damper (see MRSQD in Figure 3) as a part of te engine mount, and te applied kinematic excitations emulate interactions caused by road unevenness. use of equivalent viscous damping wit factor b p, modeling te damping force in te frame guides. Te term on te rigt-and side of te first part of Equation (2) is given in te units of force. Designating F(t) = 4 k p z(t), an equivalent sceme of te investigated system (Fig. 4) can be obtained in wic kinematic excitations z(t) are replaced by excitations due to force F(t). Te direction of force applied to te engine frame passes troug te engine s center of gravity. In order to ensure te full model equivalence, te lower spring ends are fixed to te support in equivalent model. Fig. 4. Modified sceme of investigated system Fig. 3. Scematic diagram of investigated system Equations of te system s vibration are given as follows: ( M+ m) && y+ ml ϕ+ && 4b & y+ 4k y= 4k z( t) S p p p 2 Jzϕ+ && mls&& y+ kl ϕ= Fdl were: M te frame mass, m te engine mass, J z te inertia moment of te entire engine (incorporating a cranksaft and piston assembly) wit respect to te rotation axis of te engine mount, F d te force of damper-engine block interaction, l te arm of force F d wit respect to te axis of rotation. Moreover, te damper is assumed to be parallel- -connected to a spring wit stiffness k, l S is te distance between te engine s center of gravity and rotation axis, angle ϕ(t) expresses te rotation of te engine block, and y(t) is te coordinate of te frame position. Coordinates ϕ(t) and y(t) are determined wit respect to te static equilibrium position. Te calculation procedure makes (2) Tus, te equations of te system s vibration can be rewritten as follows: ( M+ m) && y+ ml ϕ+ && 4b & y+ 4k y= F( t) S p p 2 Jzϕ+ && mls&& y+ kl ϕ= Fdl (3) Te introduction of Equations (3) is associated wit te potential ability to use te presented calculations for te construction of te laboratory stand. Te analysis of te sceme presented in Figure 4 sows tat te laboratory exciter induces te vibrations of te engine block and te engine frame only, wile Figure 3 sows tat te laboratory exciter also induces te base frame. Te load of te laboratory exciter is significantly lower in te case presented in Figure SIMULATIONS OF EXCITATIONS Due to road unevenness Road surfaces are not perfect, sporting irregular unevenness wose sizes and frequencies of occurrence are dependent on te quality of te road. Road unevenness occurs regularly, so it as to be andled using a stocastic model. Typically, te power spectral density (PSD) of road unevenness is determined and ten used as te criterion for road categorization. 8

4 MECHANICS AND CONTROL Vol. 35 No In te case of most veicles, te resonance frequencies of teir subassemblies as well as frequencies posing a azard to passengers fall witin a range of 0.5 to 50 Hz. Assuming te effective velocity range to be 10 to 30 m/s, one determines te wavelengts of road irregularities tat vastly contribute to veicle vibrations. Tey fall approximately witin a range of 0.6 to 20 m, and te corresponding wave numbers are 0.31 to 10.5 rad/m. Road irregularities falling witin tese estimated ranges are of key importance in te context of veicle design, passenger safety, ride comfort, and safety of te transported cargo. Road surface categories are defined in te normative standard, specifying te stocastic parameters of road unevenness for eac category of roads. Tese standard reference values are used in estimate calculations of vibrations of veicles and teir subassemblies. In simulations, a stationary stocastic process W(x) tat is te sum of te sinusoidal processes of te determined amplitudes, determined wave numbers, and random initial pases was used. ( ) = jsin( j +Φj) W x A k x (4) j In Equation (4), A j is te amplitude determined from te assumed PSD, k j is te wave number calculated in te following way: k j = j k min ; j = 1,..., 60, were k min is minimal wave number, and Φ j is te random variable wit uniform distribution taking values from interval ( π, π). Te calculation procedure uses te normative power spectral density of road unevenness for A-category roads and involves te simulations of kinematic excitations during a veicle ride at a velocity of 20 m/s. Figure 5 sows a selected road profile, wile Figure 6 plots te kinematic excitations and corresponding PSD values. Fig. 5. Selected road profile corresponding to normative PSD (A-category road) Fig. 6. Kinematic excitation and corresponding PSD Wit reference to Section 3, kinematic excitation z(t) due to road unevenness is equivalent to force F(t) acting upon te engine frame. Force F(t) as a stocastic nature, and its realizations are associated wit te assumed road profile. 5. ANALYSIS OF ENGINE VIBRATIONS Recalling te model of te system and te applied input excitations, calculations were performed to investigate te vibrations of te adopted model complete wit te vibration-reduction system incorporating te MR damper. Te first step involved te calculations of vibration modes and frequency followed by calculations of te engine-frame system under te applied excitations emulating te effects of road surface unevenness. Input data included te parameters obtained from measurements of te individual engine subassemblies and structural design parameters of te MR damper: engine mass and moment of inertia: m = 75 kg, J z = 20 kg m 2 ; mass of te frame M = 60 kg; stiffness of te springs in te frame k p = N/m; stiffness of te springs in te engine mount k = N/m; damping ratio in a factory- -made engine mount b = 641 Ns/m; equivalent damping ratio in frame guides b p = 100 Ns/m; piston diameter in te MR damper D p = m; parameters of MR fluid: density ρ = kg/m 3 ; dynamic viscosity μ = 0.05 Pa s. Te calculated natural frequencies wit no damping are as follows: f 1 = 2.1 Hz; f 2 = 5.3 Hz. In te first mode, te coordinate of te relative displacement of te engine wit respect to te frame is very small; ence, te influence of te damper is rater minor. In te second mode, tese displacements are appreciable. 9

5 JACEK SNAMINA, BOGDAN SAPIŃSKI PHYSICAL MODEL OF VEHICLE ENGINE MOUNT... Simulation results are sown in Figures Te first plot in eac figure presents te relative displacement of te damper piston wit respect to te cylinder. Te displacement is associated wit te engine movement relative to te frame. Te second plot sows te frame displacements. Te simulation results for a factory-made mount in wic te damping is modeled as viscous damping are presented in Figure 7. Fig. 10. Displacement of MR damper piston wit respect to cylinder and frame displacement (tird road profile) Fig. 7. Displacement of viscous damper piston wit respect to cylinder and frame displacement (first road profile; te excitation presented in Figure 6) Fig. 8. Displacement of MR damper piston wit respect to cylinder and frame displacement (first road profile; excitation presented in Figure 6) Fig. 9. Displacement of MR damper piston wit respect to cylinder and frame displacement (second road profile) Figures 8 10 plot te results of te calculations obtained for a suspension complete wit te MR damper. Te excitation due to road unevenness sown in Figure 6 was used in te first two cases of te calculations (results presented in Figures 7 and 8). In te latter two cases of te calculations, additionally generated road profiles (for te same PSD) were used. Te calculation results lead us to some conclusions relating to te effectiveness of te MR damper. Te effects are apparent, particularly wen considering te engine motion wit respect to te frame, wile in qualitative and quantitative terms, te frame vibrations are on a similar level (even wen te MR damper is incorporated). It appears tat te nature of relative motion is canged due to te non-symmetry of te damper caracteristic. Piston motion wen te damper is squeezed involves a muc greater force tan in extension; ence, te displacement distribution is non-symmetrical. Te displacements registered on te squeeze end are considerably smaller tan on te extension end. On te squeeze end, tere is an instantaneous blocking of te damper; only wen te force acting in te opposite direction is sufficiently large can te piston displacements be executed. Actually, te displacements on te extension end can be sligtly larger tan tose registered for a viscous damper. Wen different road profiles are generated for te same PSD levels, te calculation results will resemble tose summarized in Figures 9 and 10. Te sligt attenuation of te relative vibration cannot be considered as wolly positive. Te reduced amplitude of te piston relative motion wit respect to te cylinder leads to negative effects as well, as te amount of dispersed energy will be lower. Obviously, te reduction of engine movements wit respect to te frame is indicative of te strengt of te engine-frame contact. 10

6 MECHANICS AND CONTROL Vol. 35 No CONCLUSIONS Te calculation data summarized in tis study was used to estimate te engine vibration associated wit te veicle ride on a road wose surface profile is described by te power spectral density of road unevenness. Te results can be useful wen designing control algoritms, selecting a system s parameters, and evaluating te performance of te entire vibration reduction system. An obvious disadvantage of te proposed MR damper design is te non- -symmetrical caracteristic of te damper-engine frame interactions. Variations of force acting wen te damper is squeezed can follow different patterns. Te lack of symmetry results in te middle position of te engine frame being sifted wit respect to te static equilibrium position wen vibrations occur. Tese will not be vibrations around te static equilibrium position. Terefore, te proposed MR damper is effective as long as a control system is used wose algoritm sould execute te predetermined vibration reduction metod, taking into account te distinctive properties of te MR damper. Acknowledgement Tis study as been sponsored under te statutory researc grant at AGH-UST, No References Amadian M., An A.K., 1999, Performance analysis of magneto- -reological mounts. Journal of Intelligent Material Systems and Structures, 10, 3, Craft M.J., Amadian M., Farjud A., Burke W., William C.T., Nagode C., 2010, Force caracterstics of a modular squeeze-mode magneto- -reological element. Active and Passive Smart Structures and Integrated Systems, Proceedings of te SPIE, ; doi: / Flower W.C., 1985, Understanding ydraulic mounts for improved veicle noise, vibration and ride qualities. SAE Paper no Ivers D.E., Dol K., 1991, Semi-active suspension tecnology: An evolutionary view. ASME DE-Vol. 40, Advanced Automotive Tecnologies, Book No. H00719, Kim J.H., 2012, Damping control device wit magnetoreological fluid and engine mount aving te same. United States Patent Application Publication US 2012/ A1. Sapiński B., 2015, Teoretical analysis of magnetoreological damper caracteristics in squeeze mode. Acta Mecanica et Automatica, 9, 2, Sapiński B., Gołdasz J., 2015, Development and performance evaluation of an MR squeeze-mode damper. Smart Materials and Structures, 24, 11, Sapiński B., Krupa S., 2013, Vibration isolator wit MR fluid in squeeze mode. Notification of inventive design No. P Sing R., Kim G., Ravindra P.V., 1992, Linear analysis of automotive ydro-mecanical mount wit empasis on decoupler caracteristics. Journal of Sound and Vibration, 158, 2, Snamina J., Sapiński B., 2014, Analysis of an automotive veicle engine mount based on squeeze-mode MR damper. Tecnical Transactions Mecanics, 2-M(13), Soutern B.M., 2009, Design and caracterization of tunable magneto- -reological fluid- elastic mounts. M.S. Tesis, Virginia Polytecnic Institute and State University, Blacksburg. Yune Yu, Nagi G. Naganatan, Rao V. Dukkipati, 2001, A literature review of automotive veicle engine mounting systems. Mecanism and Macine Teory, 36, Zang X., Zang H., Amadian M., Guo K., 2011, Study on squeeze- -mode magnetoreological engine mount wit robust H-infinite control. SAE Tecnical Paper , doi: /