Development of a Magnetorheological Damper with Self-Powered Ability for Washing Machines
Development of a Magnetorheological Damper with Self-Powered Ability for Washing Machines
Bui, Quoc-Duy;Nguyen, Quoc Hung;Nguyen, Tan Tien;Mai, Duc-Dai
2020-06-14 00:00:00
applied sciences Article Development of a Magnetorheological Damper with Self-Powered Ability for Washing Machines 1 , 2 3 , 4 , 5 6 Quoc-Duy Bui , Quoc Hung Nguyen *, Tan Tien Nguyen and Duc-Dai Mai Faculty of Civil Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 71307, Vietnam; duybq.ncs@hcmute.edu.vn or buiquocduy@iuh.edu.vn Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Ho Chi Minh City 71408, Vietnam Division of Computational Mechatronics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, Vietnam Faculty of Engineering, Vietnamese-German University, Binh Duong Province 75114, Vietnam; tien.nt@vgu.edu.vn Faculty of Mechanical Engineering, Ho Chi Minh City University of Technology and Education, Ho Chi Minh City 71307, Vietnam; daimd@hcmute.edu.vn * Correspondence: nguyenquochung@tdtu.edu.vn; Tel.: +84-938485812 Received: 9 May 2020; Accepted: 10 June 2020; Published: 14 June 2020 Abstract: Magnetorheological (MR) dampers have been widely investigated and proposed for vibration mitigation systems because they possess continuous variability of damping coecient in response to dierent operating conditions. In the conventional design of MR dampers, a separate controller and power supply are required, causing an increment of complexity and cost, which are not suitable for home appliances like washing machines. To solve these issues and to reuse wasted energy from vibration of washing machines, in this study, a self-powered shear-mode MR damper, which integrates MR damping and energy-harvesting technologies into a single device, is proposed. The MR damper is composed of an inner housing, on which magnetic coils are wound directly, and an outer housing for covering and creating a closed magnetic circuit of the damper. The gap between the inner housing and the moving shaft is filled with MR fluid to produce the damping force. The energy-harvesting part consists of permanent magnets fastened together on the shaft and induction coils wound directly on slots of the housing. The induced power from the induction coils is directly applied to the excitation coils of the damping part to generate a corresponding damping force against the vibration. In order to achieve optimal geometry of the self-powered MR damper, an optimization for both the damping part and the energy harvesting part of the proposed dampers are conducted based on ANSYS finite element analysis. From optimal solutions, a prototype of the proposed damper is designed in detail, manufactured, and experimentally validated. Keywords: magnetorheological fluid; self-powered; MR damper; shear-mode MR damper; suspension system; washing machine vibration 1. Introduction Semiactive suspension systems have been widely used in the field of vibration control [1]. Since the 1990s, magnetorheological (MR) dampers have been promisingly studied for these systems due to their attractive features such as high damping force, good adaptability, continuous controllability, and high reliability. MR dampers can be increasingly applied in industrial environments of civil structures [2], automobiles [3], and precision machines [4]. One of the particularly interested applications of MR Appl. Sci. 2020, 10, 4099; doi:10.3390/app10124099 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, x FOR PEER REVIEW 2 of 22 Appl. Sci. 2020, 10, 4099 2 of 21 and high reliability. MR dampers can be increasingly applied in industrial environments of civil structures [2], automobiles [3], and precision machines [4]. One of the particularly interested dampers is to attenuate vibration of washing machines. The distribution of the laundry in the washing applications of MR dampers is to attenuate vibration of washing machines. The distribution of the drum is often out of balance causing the vibration of washing machines. It is found that during laundry in the washing drum is often out of balance causing the vibration of washing machines. It is spinning process, the washing machine usually experiences the first resonance at quite low frequency, found that during spinning process, the washing machine usually experiences the first resonance at around 100–200 rpm [5–7]. This resonance comes from the rigid vibration mode of the washing drum. quite low frequency, around 100–200 rpm [5–7]. This resonance comes from the rigid vibration mode When the spindle speed exceeds 1000 rpm, such as in spinning stage, resonances can appear at the of the washing drum. When the spindle speed exceeds 1000 rpm, such as in spinning stage, rear and side frame panels bringing about noises, uncomfortable feelings, and the shortening of the resonances can appear at the rear and side frame panels bringing about noises, uncomfortable washing feelings, machine and the life sho span. rtening The of dampers the was in hing conventional machine suspension life span. Th systems e dampe could rs in provide conven passive tional damping forces to well eliminate the vibration at low frequency of resonance but raise the force suspension systems could provide passive damping forces to well eliminate the vibration at low transmissibility frequency of resonanc at high e excitation but raise th fre equencies force transm because issibili the ty damping at high excitation coecient fre could quencnot ies beca be changed. use the Therefore, to eectively mitigate the vibration of washing machines at low frequency of resonance damping coefficient could not be changed. Therefore, to effectively mitigate the vibration of washing while machine it is s at still low well freq isolated uency of at reson high ance excitation while fr it equencies, is still welsemiactive l isolated atsuspension high excitatio systems n freque that ncies, can continuously control the damping coecient such as MR dampers-based vibration control systems semiactive suspension systems that can continuously control the damping coefficient such as MR should dampers be -ba employed sed vibration c (Figuront e 1). rol systems should be employed (Figure 1). Figure Figure 1. 1. For Force ce tran transmissibility smissibility of of washing washing m machines achines usin using g d di iff er erent ent vibration vibration c contr ontrol ol systems. systems. Although several studies on MR dampers have been performed to control the vibration of washing Although several studies on MR dampers have been performed to control the vibration of machines [8,9], optimal design of these MR dampers was not considered. Nguyen et al. [10] conducted washing machines [8,9], optimal design of these MR dampers was not considered. Nguyen et al. [10] optimal design of a small MR damper in flow-mode for washing machines. The results showed conducted optimal design of a small MR damper in flow-mode for washing machines. The results that size of the optimized MR damper is well fit for integration in washing machines to replace showed that size of the optimized MR damper is well fit for integration in washing machines to conventional ones. The maximum damping force was up to 150 N, which is greater than expected replace conventional ones. The maximum damping force was up to 150 N, which is greater than damping force for MR damper (from 80 to 100 N). However, o-state force of the damper was quite expected damping force for MR damper (from 80 to 100 N). However, off-state force of the damper high, around 25 N. Later, Nguyen et al. [11] proposed a new shear-mode configuration of MR damper was quite high, around 25 N. Later, Nguyen et al. [11] proposed a new shear-mode configuration of for washing machines. The optimal results indicated that the proposed shear-mode MR damper was MR damper for washing machines. The optimal results indicated that the proposed shear-mode MR able to generate a damping force of about 120 N with much smaller o-state force, around 10 N. It was damper was able to generate a damping force of about 120 N with much smaller off-state force, also pointed out that the proposed damper can be well installed in washing machines to replace around 10 N. It was also pointed out that the proposed damper can be well installed in washing conventional dampers. In addition, no bobbin for coils is used, which facilitate the manufacturing. machines to replace conventional dampers. In addition, no bobbin for coils is used, which facilitate However, no experimental works was conducted in this research. Recently, Bui et al. [12] performed a the manufacturing. However, no experimental works was conducted in this research. Recently, Bui research on optimal design of MR dampers for front-loaded washing machines, considering expected et al. [12] performed a research on optimal design of MR dampers for front-loaded washing damping forces, assembly space, power consumption, and cost as an extension of study carried out machines, considering expected damping forces, assembly space, power consumption, and cost as by [11]. In addition, experimental works on performance characteristics of the damper and eectiveness an extension of study carried out by [11]. In addition, experimental works on performance of implementation of the damper in a prototype washing machine was also implemented. The research characteristics of the damper and effectiveness of implementation of the damper in a prototype results showed a good correlation between the experimental performance and theoretical simulation. washing machine was also implemented. The research results showed a good correlation between Similarly, Ulasyar and Lazoglu [13] developed a MR sponge damper for washing machines with the experimental performance and theoretical simulation. Similarly, Ulasyar and Lazoglu [13] design optimization of geometric parameters; however, stability and lastingness of the sponge are developed a MR sponge damper for washing machines with design optimization of geometric considerable issues. Although the above semiactive systems can well solve the problem of washing parameters; however, stability and lastingness of the sponge are considerable issues. Although the machine vibration control, they require auxiliary equipment such as sensors, control units, and power above semiactive systems can well solve the problem of washing machine vibration control, they sources to enable the operation. This makes the systems more complicated and dicult for maintenance require auxiliary equipment such as sensors, control units, and power sources to enable the with high production cost. Another drawback of the semiactive vibration control systems is that the operation. This makes the systems more complicated and difficult for maintenance with high Appl. Sci. 2020, 10, x FOR PEER REVIEW 3 of 22 production cost. Another drawback of the semiactive vibration control systems is that the vibration Appl. Sci. 2020, 10, 4099 3 of 21 energy is wasted on wearing and heating rather than recovering it to power the dampers. Inspired by those issues, there has been a great deal of research efforts in exploring the area of energy harvesting for MR dampers. Cho et al. [14] proposed a smart passive control system consisting of an vibration energy is wasted on wearing and heating rather than recovering it to power the dampers. MR damper and an electromagnetic induction (EMI) device. Then, Choi et al. [15] and Kim et al. [16] Inspired by those issues, there has been a great deal of research eorts in exploring the area of energy studied the realization of this system by experimental works. However, in this smart passive system, harvesting for MR dampers. Cho et al. [14] proposed a smart passive control system consisting of an the energy-harvesting part is designed apart from the MR damper, so the whole size of the system MR damper and an electromagnetic induction (EMI) device. Then, Choi et al. [15] and Kim et al. [16] would be increased and may not be available for small installation spaces such as those in washing studied the realization of this system by experimental works. However, in this smart passive system, machines. the energy-harvesting part is designed apart from the MR damper, so the whole size of the system would Consequently, this paper aims at the investigation of a self-powered MR damper for the be increased and may not be available for small installation spaces such as those in washing machines. suspension system of washing machines. The self-powered MR damper integrates MR damping part Consequently, this paper aims at the investigation of a self-powered MR damper for the suspension and energy-harvesting part into a single device in order to enable the MR damper to reuse the system of washing machines. The self-powered MR damper integrates MR damping part and wasted mechanical energy from vibration for self-power, and also, it can be well installed in washing energy-harvesting part into a single device in order to enable the MR damper to reuse the wasted machines. Configuration of the damping part is similar to that in previous research [11,12]. The mechanical energy from vibration for self-power, and also, it can be well installed in washing machines. energy-harvesting part is based on electromagnetic induction featuring permanent magnets and Configuration of the damping part is similar to that in previous research [11,12]. The energy-harvesting arrays of coils. With the energy-harvesting part added to the MR damper, the greater the vibration of part is based on electromagnetic induction featuring permanent magnets and arrays of coils. With the the damper shaft is, the higher the power is generated, and the damping level is automatically energy-harvesting part added to the MR damper, the greater the vibration of the damper shaft is, commanded. As a result, the proposed control system can smartly adapt to external excitations by the higher the power is generated, and the damping level is automatically commanded. As a result, itself without any sensors and controllers, which can improve complexity and cost of the suspension the proposed control system can smartly adapt to external excitations by itself without any sensors and system. After the configuration of the self-powered MR damper is proposed, an optimization controllers, which can improve complexity and cost of the suspension system. After the configuration procedure is conducted for both the damping part and the energy harvesting part of the damper. of the self-powered MR damper is proposed, an optimization procedure is conducted for both the From the optimal solutions, a prototype of the proposed damper is designed and manufactured. The damping part and the energy harvesting part of the damper. From the optimal solutions, a prototype performance of each part and the whole damper are then investigated by both simulation and of the proposed damper is designed and manufactured. The performance of each part and the whole experiment. damper are then investigated by both simulation and experiment. 2. Configuration and Operating Principles 2. Configuration and Operating Principles MR dampers typically operate in three modes: shear, flow, and mixed modes (the combination of MR dampers typically operate in three modes: shear, flow, and mixed modes (the combination the first two modes). The flow and mixed modes of MR dampers can provide high damping because of the first two modes). The flow and mixed modes of MR dampers can provide high damping of the pressure generated in the lower and upper chambers. However, they are more complicated because of the pressure generated in the lower and upper chambers. However, they are more and have higher cost than the shear-mode due to a large amount of MR fluid used in the chambers. complicated and have higher cost than the shear-mode due to a large amount of MR fluid used in the It is noteworthy that washing machines do not require a so high damping force, but the zero-field chambers. It is noteworthy that washing machines do not require a so high damping force, but the zero friction -field forfric ce needs tion force nee to be asd small s to be as s as possible mall as po to sussible to suppre ppress the force ss the force tr transmissibility ansmiss at high ibility frequencies. at high Consequently, the shear-mode is implemented in our study. The schematic of the proposed self-powered frequencies. Consequently, the shear-mode is implemented in our study. The schematic of the proposed se MR damperlf-powered in shear-mode MR d isashown mper in inshear Figur -mode e 2. As isshown shown in in Figure the figur 2. e,As thesh shaft own in the figure, of damper moves the reciprocally due to the vibration of washing machines, developing damping force via direct shearing shaft of damper moves reciprocally due to the vibration of washing machines, developing damping fof orce via the MR di fluid. rect shea With ring of this configuration, the MR fluid. the Wi interaction th this config of the urat magnetic ion, the int field erabetween ction of tthe he ma damping gnetic and energy-harvesting parts could be diminished. field between the damping and energy-harvesting parts could be diminished. Figure 2. Schematic of the proposed self-powered shear-mode magnetorheological (MR) damper. Figure 2. Schematic of the proposed self-powered shear-mode magnetorheological (MR) damper. Compared with conventional MR dampers, the self-powered shear-mode MR damper is able to adapt itself based on the mechanical energy produced from its working process via an energy-harvesting Appl. Sci. 2020, 10, 4099 4 of 21 vibration absorber. In general, the self-powered MR damper consists of two main components: the MR damping part and the energy-harvesting one. The MR damping part is composed of an inner housing with a thin wall, on which the exciting coils are wound directly, and an outer housing for covering and creating a closed magnetic circuit of the damper. The MR fluid is fully injected into the gap between the shaft and inner housing. The cross-section area of the thin wall is built to be as small as possible for a quick magnetic saturation of the flux lines. As a result, the magnetic flux is compelled to move across the MR fluid gap. In addition, appropriate chamfers are added to the cross-section of the coils to maximize this magnetic flux. When a magnetic field is applied, the solidification of the MR fluid occurs, and the damping force is produced from the friction between the housing and the shaft. In some researches, the MR damper could be designed with more exciting coils to improve the damping eectiveness. However, this lengthens the damper, which may not satisfy the installation space in washing machines. Furthermore, the more coils are used, the more exciting powers are demanded, which leads to high heat emission and more maintenance cost. Considering the above problems, the design with two exciting coils is proposed for the MR damping part. The energy-harvesting (EH) part consists of magnetized permanent magnets and pole spacers alternately fastened together on the moving shaft and a slotted stator core covered by an outer housing. In this paper, the linear multipole type is proposed for the configuration of the EH part. One magnet and one adjacent pole spacer are grouped into one pole pair. The magnets are ring-shaped and possess axial magnetization; thus, they are placed in cross-pole positions to force the flux going through the spacers and across the air gap. The inducing coils are wound directly on the slots of the stator core and connected to the exciting coils of the damping part. Under linear excitations caused by the vibration of washing machines, the relative movement between the magnets mounted on the shaft end and the stator core appears. This results in an induced electric power supplied to the MR damping part. 3. Energy-Harvesting Part In this section, the EH part is designed to power the MR damping part. Based on the principle of electromagnetic induction, the EH part will convert the kinetic energy resulting from vibration into electricity for the exciting coils of the MR damping part. 3.1. Modeling of the Energy-Harvesting Part Figure 3 shows the schematic of the EH part. The pole spacers and stator core are made of commercial C45 steel, which is a common material with high magnetic permeability. The NdFeB grade N35 ring-shaped magnets are fitted on an aluminum shaft end alternately with the pole spacers. The magnet has an outer diameter of 28 mm, an inner diameter of 6 mm, and a length of 7 mm. In our research, the prototype front-loaded washing machine is the WF8690NGW washing machine produced by Samsung Electronics Co., Ltd., Seoul, Korea. Considering the available assembly space of dampers in the washing machine, the number of magnets and coils on the stator core are chosen to be 2 and 7, respectively. In this way, the maximum number of coils in the electromagnetic working state will be 4 out of 7 coils. Appl. Sci. 2020, 10, 4099 5 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 22 Figure 3. Schematic of the energy-harvesting part. Figure 3. Schematic of the energy-harvesting part. By neglecting the reluctance of pole spacers and stator core, the magnetic flux of the cylindrical By neglecting the reluctance of pole spacers and stator core, the magnetic flux of the cylindrical air gap between the magnets and the stator core is given as [17–20] air gap between the magnets and the stator core Φg is given as [17–20] B l H A Bl rem m μ Hcoe A gm rem m 0 coe gm F = (1) Φ= g λ (1) 2t B + l H A /A gm rem m coe gm m 2tB +l μ0H A A () gmrem m 0 coe gm m where expresses the eciency of the magnetic flux considering leakage eect, B characterizes the rem where λ expresses the efficiency of the magnetic flux considering leakage effect, Brem characterizes magnet remanent flux density, H denotes the magnetic coercivity of the magnet, represents the coe the magnet remanent flux density, Hcoe denotes the magnetic coercivity of the magnet, 0 µ0 represents 7 2 relative magnetic permeability and is equal to 4 10 N/−A 7 , l 2is the length of the magnet, t is the m gm the relative magnetic permeability and is equal to 4π × 10 N/A , lm is the length of the magnet, tgm is thickness of the air gap, A is the cylindrical surface area of the air gap, and A is the sectional area of gm m the thickness of the air gap, Agm is the cylindrical surface area of the air gap, and Am is the sectional the magnet. A and A can be determined by gm m area of the magnet. Agm and Am can be determined by ! ! t p l gm m m pl − gm mm A = 2 r + (2) Ar gm=+ 2π o (2) gm o 2 2 2 2 A = r r (3) A =− π rri () (3) mo i where r and r are the inner and outer radii of magnet, respectively, and p is the pitch of the pole pair. i o m where ri and ro are the inner and outer radii of magnet, respectively, and pm is the pitch of the pole The induced voltage E in the inducing coil is defined as pair. The induced voltage 𝐸 in the inducing coil is defined as dx E = NF sin x + ' (4) ππ dx g 0 p p dt EN =− Φ sin x + ϕ m m (4) g 0 pp dt mm dx where x and are the displacement and velocity of the shaft, respectively, and ' is the initial phase dt dx angle of the inducing coil. The number of winding turns of each inducing coil N is calculated by [17] where x and are the displacement and velocity of the shaft, respectively, and φ0 is the initial dt 2A phase angle of the inducing coil. The number of winding turns of each inducing coil N is calculated N = (5) by [17] 3d where d is the diameter of the copper wire and A is 2A the cross-sectional area of the coil determined by w c N = (5) the product of the coil height h and the coil width w . Since the pitch of the pole pair p is designed cm cm m 3d to double the pitch of the coil slot p , the phase angle is /2 between each nearby coil. Accordingly, cm where dw is the diameter of the copper wire and Ac is the cross-sectional area of the coil determined the induced voltages in four active coils are by the product of the coil height hcm and the coil width wcm. Since the pitch of the pole pair pm is dx designed to double the pitch of the coil slot pcm, the phase angle is π/2 between each nearby coil. E = NF sin x (6) 1 g p p dt m m Accordingly, the induced voltages in four active coils are dx ππ dx E = NF cos x (7) EN 2=− Φ g sin x (6) 1 g p p dt m m pp dt mm Appl. Sci. 2020, 10, 4099 6 of 21 E = E (8) 3 1 E = E (9) In case of low excitation frequencies, by neglecting the coil inductance, the coil is supposed to work as a resistor. The power of four active coils P is obtained by 0 1 2 2 NF BE E C g B C m 1 2 2 B C P = 2(P + P ) = 2 + = 2 v (10) B C 1 2 @ A R R R c c c where P and P are the powers of coils 1 and 2, respectively; R is the resistance of each coil; and v is 1 2 c the velocity of the shaft. Equation (10) describes the generated power of four active coils as a quadratic function of the excitation velocity. From the equation, it is also observed that geometric dimensions of the stator core and the pole spacers considerably aect the power magnitude. Consequently, to achieve the best performance of power generation, an optimization procedure for the design of the EH part should be implemented. 3.2. Optimal Design of the Energy-Harvesting Part As mentioned above, the generated power in Equation (10) should be as large as possible to maximize the eciency of the EH part. In the design of the EH part, the height of coil h , the width of cm coil w , the pitch of coil p , the pitch of pole pair p , and the thickness of housing t are significant cm c m om dimensions and thus set as design variables. Another problem that should be considered is the available assembly space in the washing machine. Since the total length of the damper in equilibrium is approximately 230 mm and the desired maximum damper stroke is established by 40 mm, the length of the shaft end carrying the pole pairs L is restricted to be smaller than 30 mm. From the aspects of compactness and low cost, it would not be ideal to improve the possibility of generating power by increasing the EH part size. Therefore, although the outer radius of the EH part has no restriction, it should not be so much larger than that of commercial passive dampers and conventional MR dampers. In this optimization, the value of 22 mm is chosen to be the upper limit of radius R of the EH part. The final concern is the possibility of machining and assembling the stator core without warping, for which the thickness of the housing t is set to be 2 mm or greater. In summary, the design om optimization of the EH part can be expressed: Determine the optimal geometry of the proposed EH part that maximize the generated power, subjected to the outer radius R is smaller than 22 mm and the length of the shaft end L is smaller than 30 mm. In this work, the finite element model of the EH part is implemented using the 2D-axisymmetric couple element (plane 13) of ANSYS. It is noteworthy that the geometry of the EH part will continuously vary during the optimization process, so the meshing size is defined by the constant number of elements per line rather than the size of each element. Figure 4 shows the finite element model of the EH part. In order to obtain the optimal design of the EH part, the golden section algorithm combined with first-order method of the ANSYS optimization tool is utilized. The procedure in detail based on finite element analysis (FEA) has been presented in some researches [21,22]. The optimal solution of the proposed EH part is specified in Table 1. It is noted that the thicknesses of the air gap t and thin wall t should be as small as possible. In this study, both are set by 0.8 mm gm wm considering the manufacturing cost. Figure 5a,b shows the magnetic flux distribution and magnetic flux density of the optimized EH part, respectively. From Figure 5a, it is observed that the magnetic flux passes through the air gap between the magnets and the stator core. As a result, the induced voltages could be generated in the inducing coils of the EH part to power the exciting coils of the MR damping part. Besides, there is almost a saturation of magnetic flux toward the south poles of the magnets, which is marked in Figure 5b. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 27 Appl. Sci. 2020, 10, 4099 7 of 21 Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 22 Figure 4. Finite element model of the energy-harvesting part. The optimal solution of the proposed EH part is specified in Table 1. It is noted that the thicknesses of the air gap tgm and thin wall twm should be as small as possible. In this study, both are set by 0.8 mm considering the manufacturing cost. Figure 5a,b shows the magnetic flux distribution and magnetic flux density of the optimized EH part, respectively. From Figure 5a, it is observed that the magnetic flux passes through the air gap between the magnets and the stator core. As a result, the induced voltages could be generated in the inducing coils of the EH part to power the exciting coils of the MR damping part. Besides, there is almost a saturation of magnetic flux toward the south poles of the magnets, which is marked in Figure 5b. Figure 4. Finite element model of the energy-harvesting part. Figure 4. Finite element model of the energy-harvesting part. Table 1. Optimal parameters of the energy-harvesting part. Table 1. Optimal parameters of the energy-harvesting part. The optimal solution of the proposed EH part is specified in Table 1. It is noted that the Parameter (mm) Value Parameter (mm) Value thicknesses of the air ga Parameter p tgm and t (mm) hin waV llalue twm should be as Parameter sma(mm) ll as possible. Value In this study, both are Coil height hcm 4.4 Air gap thickness tgm 0.8 set by 0.8 mm considering the manufacturing cost. Figure 5a,b shows the magnetic flux distribution Coil height h 4.4 Air gap thickness t 0.8 cm gm Coil width wcm 4.56 Thin wall thickness twm 0.8 and magnetic flux density Coil width of the op w timized E 4.56H part, Thin respectively. wall thickness From t Figure 0.85a, it is observed that cm wm Coil pitch p 6.74 Housing thickness t 2 Coil pitch pc 6.74 Housing thickness tom 2 the magnetic flux passes through the air c gap between the magnets om and the stator core. As a result, Magnet length l 7 Outer radius R 22 Magnet length lm 7 Outer radius R 22 the induced voltages could be generated in the inducing coils of the EH part to power the exciting Pole pair pitch p 13.48 Generated power P (W) 19.3 Pole pair pitch pm 13.48 Generated power P (W) 19.3 coils of the MR damping part. Besides, there is almost a saturation of magnetic flux toward the south poles of the magnets, which is marked in Figure 5b. Table 1. Optimal parameters of the energy-harvesting part. Parameter (mm) Value Parameter (mm) Value Coil height hcm 4.4 Air gap thickness tgm 0.8 Coil width wcm 4.56 Thin wall thickness twm 0.8 Coil pitch pc 6.74 Housing thickness tom 2 Magnet length lm 7 Outer radius R 22 Pole pair pitch pm 13.48 Generated power P (W) 19.3 (a) (b) Figure 5. Finite element analysis of the optimized energy-harvesting part: (a) magnetic flux lines and Figure 5. Finite element analysis of the optimized energy-harvesting part: (a) magnetic flux lines and (b) magnetic flux density. (b) magnetic flux density. 4. MR Damping Part 4.1. Modeling of the MR Damping Part The MR damping part is coaxial with and in front of the EH part. Figure 6 shows the schematic diagram of the shear-mode MR damping part. The shaft and the housing are made of C45 steel. The O-rings made of 70-durometer NBR rubber are used to seal the MR fluid. (a) (b) Figure 5. Finite element analysis of the optimized energy-harvesting part: (a) magnetic flux lines and (b) magnetic flux density. Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 22 4. MR Damping Part 4.1. Modeling of the MR Damping Part The MR damping part is coaxial with and in front of the EH part. Figure 6 shows the schematic diagram of the shear-mode MR damping part. The shaft and the housing are made of C45 steel. The Appl. Sci. 2020, 10, 4099 8 of 21 O-rings made of 70-durometer NBR rubber are used to seal the MR fluid. Figure 6. Schematic diagram of the shear-mode MR damping part. Figure 6. Schematic diagram of the shear-mode MR damping part. In the design of MR damper-based devices, the damping forces should be first established as In the design of MR damper-based devices, the damping forces should be first established as functions of the applied magnetic field and geometric dimensions. For the proposed MR damping part functions of the applied magnetic field and geometric dimensions. For the proposed MR damping illustrated in Figure 6, it is supposed that if the MR fluid velocity in the gap between the housing and part illustrated in Figure 6, it is supposed that if the MR fluid velocity in the gap between the the shaft is linear, then the generated damping force F and zero-field friction force F are defined by d 0 housing and the shaft is linear, then the generated damping force Fd and zero-field friction force F0 are defined by F = 2r L ( + ) + 2F (11) s e y or F=+ 2( πτ rL η )+2F (11) dse y or F = 2r L( + ) + 2F (12) s or 0 y0 0 where R is the shaft radius; t is the MR fluid gap thickness; v is the velocity between the housing F=+ 2( πτ rL η )+2F s g (12) 00 s yo0 r and the shaft; and are the yield stress and post-yieldg viscosity of the active MR fluid in the gap, respectively; L is the MR fluid gap length; and L is the eective length of the active MR fluid in the where Rs is the shaft radius; tg is the MR fluid gap thickness; v is the velocity between the housing gap. In this configuration, L L. The Coulomb friction force F between the O-ring and the shaft can e or and the shaft; τy and η are the yield stress and post-yield viscosity of the active MR fluid in the gap, be determined by [23] respectively; L is the MR fluid gap length; and Le is the effective length of the active MR fluid in the F = f L + f A (13) or c r r gap. In this configuration, Le ≈ L. The Coulomb friction force For between the O-ring and the shaft can be determined by [23 where L is the seal su ] rface length and in this case, equals to the circumference of the shaft; f is the r c friction per unit length caused by the compression of the O-ring; A is the projected area of the seal; F =+ fL f A (13) and f is the friction force caused by the fluidorpressur c re onha unit r projected area of the O-ring. It is noted that in the configuration of the shear-mode, the pressure on the O-rings could be ignored since it is where Lr is the seal surface length and in this case, equals to the circumference of the shaft; fc is the almost negligible, f 0. Moreover, the O-rings should be compressed moderately so that the zero-field friction per unit length caused by the compression of the O-ring; Ar is the projected area of the seal; friction force is not so high while the sealing ability is still guaranteed during the working process and fh is the friction force caused by the fluid pressure on a unit projected area of the O-ring. It is of washing machines. Accordingly, a compression of 15% is set for the O-rings and f is found to be noted that in the configuration of the shear-mode, the pressure on the O-rings could be ignored since 175.1 N/m. it is almost negligible, fh ≅ 0. Moreover, the O-rings should be compressed moderately so that the For our research, the 132-DG MR fluid produced by Lord Corporation is employed, and the zero-field friction force is not so high while the sealing ability is still guaranteed during the working Bingham model is used to represent the general behavior of the MR fluid. Despite the inconsistency process of washing machines. Accordingly, a compression of 15% is set for the O-rings and fc is with experimental responses at low shear rate, the Bingham model is beneficial to the design of MR found to be 175.1 N/m. damper-based devices due to its simplicity and quick modeling. Based on this model, the dependence For our research, the 132-DG MR fluid produced by Lord Corporation is employed, and the of MR fluid rheological properties on the applied magnetic field are given by [24] Bingham model is used to represent the general behavior of the MR fluid. Despite the inconsistency with experimental responses at low shear rate, the Bingham model is beneficial to the design of MR B 2B SY SY Y = Y + (Y Y )(2e e ) (14) 1 1 damper-based devices due to its simplicity and quick modeling. Based on this model, the dependence of MR fluid rheological properties on the applied magnetic field are given by [24] where B is the applied magnetic density, Y expresses one of the MR fluid rheological properties such as the postyield viscosity and the yield stress , and is the saturation moment of the Y property. y SY The Y value varies from the value of o-state Y to the value of saturation Y . The curve-fitting method is used to estimate the values of Y , Y , and from experimental data, and the results are shown in 0 1 SY Table 2. Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 22 −−BB αα 2 SY SY YY=+() Y −Y(2e −e ) (14) ∞∞ 0 where B is the applied magnetic density, Y expresses one of the MR fluid rheological properties such as the postyield viscosity η and the yield stress τy, and αSY is the saturation moment of the Y property. The Y value varies from the value of off-state Y0 to the value of saturation Y∞. The curve-fitting Appl. Sci. 2020, 10, 4099 9 of 21 method is used to estimate the values of Y0, Y∞, and αSY from experimental data, and the results are shown in Table 2. Table 2. Rheological properties of the magnetorheological (MR) fluid 132-DG. Table 2. Rheological properties of the magnetorheological (MR) fluid 132-DG. Parameters Parameters = 0.1 Pas = 15 Pa = 4.5 T 0 y0 S −1 η0 = 0.1 Pa.s τy0 = 15 Pa αSη = 4.5 T = 3.8 Pas = 40,000 Pa = 2.9 T 1 y1 −1 Sy η∞ = 3.8 Pa.s τy∞ = 40,000 Pa αSτy = 2.9 T 4.2. Optimal Design of the MR Damping Part 4.2. Optimal Design of the MR Damping Part In order to In order to improve the perform improve the performance ance oof f the M the MR R da damping mping part part du during ring the ope the operating rating process of process of washing machines, the maximum damping force (the damping force when a magnetic field is washing machines, the maximum damping force (the damping force when a magnetic field is applie applied) d) determined determined by by Equation Equation (11)(1r1 eaches ) reache tos t a ro equir a requ ed value ired va at l low ue at resonance low resonance frequency fre wher quency eas the zero-field friction force in Equation (12) is minimized at high excitation frequencies. Therefore, whereas the zero-field friction force in Equation (12) is minimized at high excitation frequencies. Therefore the dynamic , thmodel e dyna of mic washing model of w machines ashing should mach be ines sho first analyzed. uld be first The 2D analy mechanical zed. The 2D modeling mechanic of the al washing machine Samsung WF8690NGW is shown in Figure 7. modeling of the washing machine Samsung WF8690NGW is shown in Figure 7. Figure 7. A 2D mechanical modeling of the washing machine. Figure 7. A 2D mechanical modeling of the washing machine. The vibration equation of the washing machine shown in Figure 7 can be represented [10] as The vibration equation of the washing machine shown in Figure 7 can be represented [10] as h i h i .. . 2 2 2 2 22 2 2 mu + cu sin (' + ) + sin ('