Design of a self-power magneto-rheological damper in shear mode for front-loaded washing machine

Nội dung text: Design of a self-power magneto-rheological damper in shear mode for front-loaded washing machine

1. Tuyển tập Hội nghị khoa học toàn quốc lần thứ nhất về Động lực học và Điều khiển Đà Nẵng, ngày 19-20/7/2019, tr. 297-303, DOI 10.15625/vap.2019000293 Design of a self-power magneto-rheological damper in shear mode for front-loaded washing machine Duy Quoc Bui1,2,a, Tri Bao Diep1,2,b, Vuong Long Hoang2,c, Dai Duc Mai3,d and Hung Quoc Nguyen4,e * 1 Faculty of Civil Engineering and Applied Mechanics, HCMC University of Technology and Education, Ho Chi Minh City, Vietnam 2 Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam 3 Faculty of Mechanical Engineering, HCMC University of Technology and Education, Ho Chi Minh City, Vietnam 4 Faculty of Engineering, Vietnamese-German University, Binh Duong Province, Vietnam E-mail: a duybq.ncs@hcmute.edu.vn, a buiquocduy@iuh.edu.vn, b tridb.ncs@hcmute.edu.vn, b diepbaotri@iuh.edu.vn, c hoanglongvuong@iuh.edu.vn, d daimd@hcmute.edu.vn, e hung.nq@vgu.edu.vn Abstract drum to the frame and next to the floor causing acoustic In this research work, a self-power shear-mode noises, uncomfortable feeling for human and gradual magneto-rheological (MR) damper that can replace decrease of the machine life-span. conventional passive damper of a front-loaded washing machine is designed and experimentally evaluated. The self-power damper consists of two main components: the damping component and the self-power one. The damping component is composed of an inner housing with a thin wall, on which the coils are wound directly, and an outer housing to cover the coil and to create a closed magnetic circuit of the damper. The gap between the inner housing and the shaft is filled with MR fluid to create damping force. The self-power component consists of magnetized permanent magnets fastened together on the moving shaft and a slotted stator core covered by an outer housing. The coils are wound directly on the slots of the stator core and connected to the coils of the damping component to generate the required current when the shaft moves reciprocally. After an introduction to suspension system for front-loaded washing Figure 1. Control of washing machine vibration machine, the configuration of the self-power MR damper for featuring semi-active suspension system front-loaded washing machine is proposed. Optimization of the proposed self-power MR damper is then performed considering The vibration of washing machine is mostly due to required damping force, off-state friction force, size, power the unbalanced mass of laundry disposed in the drum. consumption and low cost of the damper. From the optimal Particularly, in a front-loaded washing machine, the results, simulated performance of the optimized MR damper is impact of gravity makes the unbalance more serious. obtained and a detailed design of the MR damper is then conducted and presented with discussion. Various suspension methods have been developed to control the vibration of washing machine. In this study, Keywords: Front-loaded washing machine, Self-power MR the vibration of front-loaded washing machine is damper, Suspension system, Optimal design. suppressed based on the damping control of suspension system. It is found that during the spinning process, the 1. Introduction first resonance usually appears at quite low frequency, around 100-250 rpm while another one occurs at high It is well-known that a washing machine is one of speed, usually above 1000 rpm. In a conventional helpful equipment in human life as it releases people suspension system, since passive dampers (constant from hard washings for more free time. Recently, in order damping coefficient) are applied, there is a tradeoff to satisfy the upgrading demand of customers, the laundry between the probability of vibration suppression at low capacity and the spin speed are increased, while the frequency and its increased transmissibility at high machine weight and cost are reduced. With these, the frequency. Consequently, in order to effectively attenuate vibration of washing machine becomes a more the vibration of washing machine at low resonance challenging issue that should be under consideration. The frequency whereas the one at high excitation frequency is vibration of washing machine is transferred from the well isolated, a semi-active suspension system with
2. Duy Quoc Bui, Tri Bao Diep, Vuong Long Hoang, Dai Duc Mai and Hung Quoc Nguyen controllable damping coefficient should be employed, as and the design optimization is carried out considering shown in Figure 1. For that, in this paper, a shear-mode required damping force, sealing ability, power magneto-rheological (MR) damper is designed. consumption, available space and cost of the system. MR fluid is a type of smart material consisting of From the optimal results, simulated performance of the spherical or ellipsoid magnetic particles suspended within optimized MR damper is obtained and a detailed design carrier oil. When an external magnetic field is applied, of the MR damper is then conducted and presented with these particles form chains along the lines of magnetic discussion. flux resulting in solidification of MR fluid. Applications 2. Dynamic modeling of washing machine of MR fluid can be found in various industry fields such as brake, clutch, valve, damper due to its possibilities of rapid response, easy control and reverse. There are some research works on semi-active suspension system for front-loaded washing machines featuring MR fluid. Michael and Carlson [1] have developed a low-cost MR fluid sponge damper for washing machines. Although the sponge MR damper can well eliminate the vibration of washing machine at low frequency [2], wearing and durability of the sponge are still significant challenges. Aydar et al. [3] have researched on design and application of a flow-mode MR damper to control vibration of washing machine. However, the optimal design of the MR damper has not been considered, and the zero-field Figure 2. 2D simplified schematic of the prototype friction force (the damping force when no current is washing machine applied to the coils of the damper), also called the off-state force, is still very high, which may cause a grave In this work, the front-loaded washing machine vibration of washing machine at high frequency. object is a prototype based on the Samsung Furthermore, because a large amount of MR fluid is WF8690NGW washing machine manufactured by required for flow-mode, the cost of the damper is also Samsung Electronics. A 2D simplified schematic of the high. Recently, Nguyen et al. [4] have developed a washing machine is shown in Figure 2. According to [4, shear-mode MR damper for front-loaded washing 7], the drum and the tub were modeled as rigid bodies machines. It is potential that the MR damper can provide with 3 degrees of freedom in consideration of the a damping force up to 120 N while the zero-field friction rotational motion in x-direction and the translational force can be considerably small. Yet, this MR damper has motions in y and z-directions. From the figure, the not been verified on a front-loaded washing machine, governing equation of the washing machine can be where sealing and assembly of the damper are significant expressed problems that should be completely taken into account. mu cu  sin22  sin  21 To overcome this drawback, an optimal design of ku sin22 sin F ( t ) (1) shear-mode MR damper considering the sealing ability 12u and the assembly space in the washing machine has been where m is the mass of the suspended tub assembly proposed by Bui et al. [5], and also the hysteresis including the drum, laundry, shaft, counter weight, rotor behavior of MR damper has been investigated [6]. and stator; c is the damping coefficient of each damper; k However, the application of a controller based on this is the stiffness of each spring; φ is the angle of an nonliner hysteresis model will meet a lot of difficulties in arbitrary direction, i, in which the vibration is considered; algorithm and make the operating system more complex. u is the displacement of the tube center in the i-direction; The main contribution of this research is to design a and Fu is the excitation force due to an unbalanced mass self-power MR damper in shear-mode which can operate in the i-direction, defined by Fu = F0cos(ωt) = 2 by itself in front-loaded washing machine without muω Rucos(ωt), where mu and Ru are the mass and radius external power supply, making the control of suspension from the rotation axis of the unbalanced mass, system easier. Firstly, a suspension system for respectively. From equation (1), the damped frequency of front-loaded washing machine featuring MR dampers is the suspended tub assembly is calculated by introduced. The configuration of the self-power MR  1 2 (2) damper for front-loaded washing machine is proposed dn
3. Design of a self-power magneto-rheological damper in shear mode for front-loaded washing machine in which the natural frequency is the self-power MR damper consists of two main 22 components: the damping component and the self-power k sin sin 12 one (energy-harvesting device). n (3) m The damping component is composed of an inner and the damping ratio is housing with a thin wall, on which the coils are wound c sin22  sin  directly, and an outer housing to cover the coil and to 21  (4) create a closed magnetic circuit of the damper. The gap 2sinsinmk 22 12 between the inner housing and the shaft is filled with MR It can be observed that the damped frequency, natural fluid to create damping force. The section of the thin wall frequency and damping ratio of the tub assembly in the is designed to have a small area so that the magnetic flux i-direction are functions of the angle φ. Therefore, the tub going through it promptly reaches to saturation and hence assembly exhibits different resonant frequencies in is drived across the MR gap. In response to the magnetic different directions of vibration. This causes the vibration field, the MR fluid solidifies and resists the relative to become more severe and hard to control. In the design movement between the shaft and the housing, producing of the suspension system for the tub assembly, the the damping force. In the literature, a configuration with frequency resonance in all directions should be restricted more than two coils can be used in order to increase the as much as possible. From this, it is easy to realize that, magnetic flux density across the MR gap. However, this by choosing α1 = α2 = β1 = β2 = 45° considering increases the length of the damper and so the assembly manufacturing and available space, equation (1) can be space will not be satisfied. On the other hand, more coils simplified as follows means more applied powers required, which results in high cost of operation and the rising of heat emission. mu cu  ku F() t (5) u Taking all above issues into account, the configuration Then, the damped frequency, natural frequency and with two coils is recommended for the damping damping ratio of the tub assembly do not depend on the component. i-direction of the vibration and we have The self-power component consists of magnetized kc permanent magnets and spacers alternately fastened  ; (6) together on the moving shaft and a slotted stator core n m 2 mk covered by an outer housing. Each one magnet and one 3. Configuration of self-power MR damper adjacent spacer are grouped into one pole pair. The in shear-mode magnets are placed in cross-pole positions in order to force the flux going through the spacers and across the air gap. The coils are wound directly on the slots of the stator core and connected to the coils of the damping component. Under external excitation caused by the vibration of the washing machine, the relative movement between the shaft end carrying magnets and the stator core appears, the coils experience a change in flux Figure 3. Schematic configuration of proposed linkage and electrical power is generated for the damping self-power shear-mode MR damper component. Figure 3 shows the configuration of proposed 4. Optimal design of MR damper self-power shear-mode MR damper. As shown in the In this work, optimal design of the proposed figure, the shaft of damper moves reciprocally due to the shear-mode MR damper is performed based on the vibration of washing machine, developing damping force quasi-static model of the MR damper and the dynamic via direct shearing of the MR fluid. Among three equation of the washing machine presented in “Dynamic operational modes of MR damper (shear-mode, modeling of washing machine”. From the Figure 3, by flow-mode and their combination, mixed-mode), this assuming a linear profile of velocity of the MR fluid in shear-mode is proposed for our study due to its simple the duct between the shaft and the housing, the damping design, small off-state friction force and low cost. force Fsd and the zero-field friction force Fs0 can be Compared with traditional MR damper using external respectively determined by current applied to the coils, the self-power MR damper v operates based on energy harvested from its operating F 2( RL )2 F F (7) sdseyormfd environment via an energy-harvesting device. In general,
4. Duy Quoc Bui, Tri Bao Diep, Vuong Long Hoang, Dai Duc Mai and Hung Quoc Nguyen v Fs 000 2( RLsd y )2 F or F mf (8) on a non-magnetic aluminium shaft end. The length of d magnets and spacers are both 7 mm. The number of where Rs is the shaft radius, d is the gap size of the MR magnets and coils on the stator core is designed to be, fluid duct, v is the relative velocity between the shaft and respectively, 2 and 7 based on the available assembly the housing,  and y are, respectively, the space of dampers in the washing machine. By this way, field-dependent post-yield viscosity and yield stress of the maximum number of coils in the electromagnetic the active MR fluid in the duct, Ld is the length of the MR working state will be 4 out of 7 coils. Assuming the fluid duct, and Le is the effective length of the active MR reluctance of stator core and spacers are neglected for fluid in the duct. For the proposed MR damper, Le can be their high magnetic permeability, the magnetic flux of the approximated by Le  Ld. Fmf is the friction force caused air gap between the magnets and the stator core Φg is by the magnetism of the permanent magnets and is found given as [10, 11] to be around 19 N in this study. For is the coulomb Bl HA  rem m0 coe gm (11) friction force between the shaft and the o-ring which can g 2tBgm rem l m0 H coe A gm A m be approximately calculated by [8] in which Brem is the remanent flux density of magnet, Hcoe F fL fA (9) or c r h r is the coercive magnetic field intensity of magnet, µ0 is -7 in which Lr is the length of seal rubbing surface, fc is the relative magnetic permeability and equals 4µ*10 2 friction per unit length due to o-ring compression, Ar is N/A , lm is the length of the permanent magnets, tgm is the the projected area of seal, and fh is friction force due to thickness of air gap, Agm is the surface area of cylindrical fluid pressure on a unit projected area of seal. It is air gap, and Am is the cross-section area of magnet. Agm noteworthy that for the shear-mode MR damper, the and Am can be determined by, respectively pressure on the o-rings is very small and thus can be t gm plmm Ar 2 (12) neglected, fh  0. Moreover, the compression of o-rings gm m1 22 should be set at a moderate ratio so that the off-state force 22 is not too high while the sealing of the MR damper is Ammm rr12 (13) well ensured during the operation of washing machine. where rm1 and rm2 are, respectively, the outer and inner Therefore, in this paper, 70-durometer rubber o-rings are radii of magnet, and pm is the pitch of pole pair. The used and the compression of o-rings is set by 10%. With induced voltage 𝐸 in the inducing coil is defined as these, it can be found that f = 116.75 N/m. c dx The MR fluid 132-DG made by Lord Corporation EN sin x (14) g 0 pp dt is employed for our proposed MR damper. Based on mm Bingham model, the rheological properties of MR fluid in which N is the number of turns of inducing coil, x and depend on applied magnetic field and can be estimated by dx/dt are, respectively, the displacement and velocity of the following equation [9] shaft, and φ0 is the intinial phase angle of inducing coil. BB 2 SY SY Since the pitch of pole pair pm is double the pitch of coil YY ()(2) YY0 e e (10) slot pcm, the phase angle is π/2 between each nearby coil. where Y represents one of the rheological parameters of Therefore, the induced voltages in four working coils are MR fluid such as yield stress and post-yield viscosity. dx The value of parameter Y tends from the zero applied EN  sin x (15) 1 g field value Y0 to the saturation value Y∞. αSY is the ppdtmm saturation moment index of the Y parameter. B is the dx EN  cos x (16) applied magnetic density. The values of Y0, Y∞, αSY are 2 g ppdtmm determined from experimental results using curve-fitting method and the results are presented in Table 1. EE31 (17) EE (18) Table 1. Rheological properties of MR fluid 132-DG 42 In order to increase the efficiency of generating Bingham model parameters power, the coils of phase angle 0 and π/2 are connected -1 μ0 = 0.1 pa•s τy0 = 15 pa αsμ = 4.5 T together and feed the first coil of the damping component. -1 μ∞ = 3.8 pa•s τy∞ = 40,000 pa αsτy = 2.9 T Similarly, the π and 3π/2 phase coils are connected together and feed the second coil. It is noted that the For the self-power component, the stator core and the current applied to two coils of the damping component spacers are made of C45 steel. The permanent magnets must be cross to make sure the magnetic flux goes made of NdFeB grade N35 and the spacers are mounted
5. Design of a self-power magneto-rheological damper in shear mode for front-loaded washing machine correctly, thus bridge rectifier is employed in this design. study, the first order method with golden section Another problem should be under consideration in algorithm of ANSYS optimization tool is used. The the MR damper design is the available space of the detailed procedure to obtain the optimal solution of MR washing machine. From assembly aspects, with the fluid devices based on FEA has been mentioned in required maximum stroke of damper set by 40 mm, the several researches [12, 13]. available length of MR duct is approximately calculated Figure 4 shows the flow chart to achieve optimal by 50 mm. Despite no strict constraint on the outer radius design parameters of the MR damper. Firstly, an analysis of MR damper, it should be as small as possible in order ANSYS file for solving the magnetic circuit of the to reduce its cost and weight. Since the outer radius of damper and calculating the objective function is built conventional damper is around 20 mm, the one of MR using ANSYS parametric design language (APDL). In the damper is restricted to be smaller than this value. For the analysis file, the design variables (DVs) such as the possibility of machining the bushing cylinder without length of MR duct Ld, the outer radius R, the radius of warping, the height of coil grooves should not be so small. shaft Rs, must be coded as variables and initial values In this case, it is set to be larger than 5.45 mm. are assigned to them. The geometric dimensions of the Furthermore, the 0.34 mm-diameter coil wires are damper structure are varied during the optimization employed for both damping and self-power components process; the meshing size therefore should be specified of MR damper due to their popularity and good ability of by the number of elements per line rather than the filling slots. In order to ensure the durability of these element size. Because the magnetic density is not coils, the generated current is limited to 1 A. In summary, constant along the duct length, it is necessary to define the optimization of MR damper design for washing paths along the MR active volume where magnetic flux machine can be expressed as follows: Find optimal values passes. Based on the induced voltages obtained from of significant geometric dimensions of the proposed MR Equations 15-18, the average magnetic density across the damper that maximize the damping force Fsd, subjected to MR ducts Bmr is calculated by integrating the magnetic the length of MR duct Ld is smaller than 50 mm, the outer density along the defined path then divided by the path radius of the damper R is smaller than 20 mm, the height length. Thus, the magnetic density is determined as of coil grooves hc is greater than 5.45 mm, and the follows: L generated current is smaller than 1 A. 1 d BBsds () (19) mr Ld 0 where B(s) is the magnetic flux density at each nodal point on the defined path. From the figure, it is observed that the optimization is started with the initial value of DVs. By executing the analysis file, first the magnetic density is derived. Then the yield stress, post-yield viscosity, and objective function are respectively calculated from Equations 10 and 7. The ANSYS optimization tool then transforms the optimization problem with constrained design variables to an unconstrained one via penalty functions. The dimensionless, unconstrained objective function f is formulated as follows: OBJ n f ()xPx ( ) (20)  xii OBJ 0 i 1 where OBJ0 is the reference objective function value that is selected from the current group of design sets. Pxi is the exterior penalty function for the design variable x . For i the initial iteration (j = 0), the search direction of DVs is Figure 4. Flow chart to achieve optimal design assumed to be the negative of the gradient of the parameters of the MR damper unconstrained objective function. Thus, the direction vector is calculated by In order to obtain the optimal solution, a FEA code 00 integrated with an optimization tool is employed. In this dfx  (21)
6. Duy Quoc Bui, Tri Bao Diep, Vuong Long Hoang, Dai Duc Mai and Hung Quoc Nguyen The values of DVs in the next iteration (j + 1) is in the “Optimal design of MR damper” section. Figures 5 obtained from the following equation: and 6 show the voltage and current generated in the jj 1 j self-power MR damper at the resonance excitation and x xsd (22) j frequency, respectively. The optimal results of the where the line search parameter sj is calculated by using a combination of the golden section algorithm and a local self-power MR damper are then obtained based on these quadratic fitting technique. The analysis file is then results and the optimization problem developed above. executed with the new values of DVs, and the From commercial aspects, the C45 steel is employed for convergence of the objective function is checked. If the magnetic components of the MR damper. The MR fluid convergence occurs, the values of DVs at this iteration gap size and air gap size are set from 0.5 mm to 1 mm are the optimum. If not, the subsequent iterations will be based on the consideration of manufacturing, amount of performed. In the subsequent iterations, the procedures MR fluid and size of o-rings. The optimal solutions of the are similar to those of the initial iteration except for that proposed MR damper are summarized in Table 2, and the the direction vectors are calculated according to the magnetic flux distribution of the optimized damper is Polak-Ribiere recursion formula as follows shown in Figure 7. It is observed from the figure that the magnetic flux density in the thin wall of the damping dfxrd jjj  1 (23) j 1 component reaches to saturation, which agrees well to the jj 1 T j theoretical analysis.  fx fx fx where r (24) j 1 2 fx j 1 Table 2. Optimal parameters of the proposed shear-mode MR damper 5. Results and discussions Parameters Off-state force Fs0 (N) 37.34 Coil width wc0 (mm) 2.5 Max damping force Fsd (N) 72.3 Axial chamfer ch1 (mm) 3.12 MR duct length Ld (mm) 50 Shaft radius Rs (mm) 8.25 Outer radius R (mm) 20 MR duct gap tg (mm) 0.8 Coil groove height hc (mm) 5.62 Thin wall ti (mm) 0.8 Coil height hc0 (mm) 3.93 Sliding housing t0 (mm) 4.53 Radial chamfer ch (mm) 1.7 Coil to centerline tfi (mm) 8.13 Figure 5. The voltage generated in each coil of the self-power MR damper at the resonance excitation and frequency Figure 7. Magnetic flux density of the proposed optimized MR damper 5. Conclusions This paper focused on the design a shear-mode self-power MR damper for suspension system of front-loaded washing machine to eliminate vibration due Figure 6. The current generated in each coil of the to an unbalanced laundry mass occurring in the washing self-power MR damper at the resonance excitation and drum. Firstly, a suppression system for washing machine frequency featuring MR dampers was introduced and the configuration of the self-power MR damper was proposed. In this section, by using a MATLAB code, the results Optimization of the proposed MR damper was then of induced voltage and current applied to the coils of the performed considering required damping force, off-state damping component are presented based on the analysis friction force, size, manufacturing and low cost. From the
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