Thiết kế, mô hình hóa và điều khiển hệ thống giảm chấn cho máy giặt cửa trước sử dụng vật liệu thông minh TT TA

MINISTRY OF EDUCATION AND TRAINING HCMC UNIVERSITY OF TECHNOLOGY AND EDUCATION BUI QUOC DUY DESIGN, MODELING AND CONTROL OF A SUSPENSION SYSTEM FOR FRONT–LOADED WASHING MACHINE FEATURING SMART MATERIALS Major: Engineering Mechanics Major code: 9520101 SUMMARY OF PHD DISSERTATION HO CHI MINH CITY – 2022 This work was completed at HCMC University of Technology and Education Supervisor 1: Assoc Prof PhD Nguyen Quoc Hung Supervisor 2: PhD Mai Duc Dai Reviewer 1: Reviewer 2: Reviewer 3: The dissertation will be defended in front of the Council for evaluation of PhD dissertation at room HCMC University of Technology and Education on / / ABSTRACT This dissertation investigates and develops new semi–active suspension systems featuring smart materials (shape memory alloy and magneto–rheological fluid) to effectively control vibration of front–loaded washing machines Relying on the ability to tune characteristics flexibly to external excitations, the performance and reliability of the smart material–based suspension systems are significantly improved The overall aims of the dissertation are: − Investigation of a new damper using shape memory alloy (SMA): design and modeling of the nonlinear hysteresis phenomenon of the damper − Investigation of a new damper using magneto–rheological fluid (MRF): design, identification of the hysteresis phenomenon and proposal of a new parametric dynamic model to predict the damper behavior − Design of a semi–active control system for the dampers − Development of two self–adaptive MRF dampers: self–powered and stroke– by–activated MRF dampers − Experimental validation of the dampers on a prototype washing machine The novel contributions of this dissertation can be listed as follows: New dampers in shear–mode featuring smart materials, SMA and MRF; A new parametric dynamic model that can predict accurately the nonlinear hysteresis behavior of the dampers; A control system for the dampers with simple structure and low cost; A MRF damper with self–powered ability that can adapt itself to external excitations to produce appropriate damping levels without any control; Development of a novel self–adaptive MRF damper with stroke–by–activated ability that has low cost and possesses displacement–dependent damping characteristic consisting well with operation of washing machines Firstly, an overview of front–loaded washing machine suspensions and smart material dampers is introduced Based on the quasi–static model and dynamic modeling of the tube assembly, the smart material dampers are configured The first researched smart material is SMA A prototype SMA damper is designed, manufactured and experimentally evaluated on a test rig Three models, including Bingham, Bouc–Wen models and the proposed model in the author’s published paper [3], are employed to predict the nonlinear hysteresis behavior of the damper MRF is the second studied smart material To achieve the best performance, the MRF damper design is optimized considering active damping force, off–state force, size, installability and cost Based on the optimal solution, a MRF damper prototype is designed, manufactured and tested A new dynamic model is proposed to predict the hysteresis phenomenon of the damper The proposed model is compared with the general Spencer’s model and the original Pan’s model A simple and economical semi–active control system for the washing machine installed with the MRF dampers is then designed, simulated and assessed From the aspects of compact structure and low cost, two self–adaptive MRF dampers are developed in the subsequent part of the dissertation These dampers can adjust damping force itself to external excitations to suppress vibration without any control The first type is the self–powered MRF damper that comes from the idea of converting wasted system vibration into electrical energy to power the damper The second type is the stroke–by–activated MRF damper that possesses displacement–based damping characteristic Both are optimized to obtain the best performance The prototypes of the dampers are also fabricated and assessed on the test rig All the dampers are installed and tested on a prototype front–loaded washing machine to evaluate their operating efficiency The experimental results show that the vibration of the washing machine featuring the smart material dampers is considerably reduced as compared with that using commercial passive dampers, thereby certificating the feasibility of the proposed dampers PREFACE Rationale Vibration of washing machines is a challenging issue for scientists Especially in front–loaded washing machines, the vibration is harder to be controlled due to the gravity impact of unbalanced laundry mass Commercial passive suspensions can reduce the resonance at low frequencies but increase the transmitted force from the tube to the frame at high frequencies because their damping coefficient is unchangeable Therefore, in order to effectively mitigate the vibration of washing machines during operation process, a suspension system with controllable damping coefficient should be developed Along with development of science and technology, smart materials have entered society Smart materials provide devices with the ability to adjust characteristics versatilely and are the key for the above semi–active suspension system Research aim To develop a suspension system featuring smart materials that can effectively control vibration of front–loaded washing machines during operation process Research tasks To design dampers using smart materials, to propose a dynamic model, to design a control system, to develop self–adaptive dampers, to test the dampers on a prototype front–loaded washing machine and compare their damping performance with that of passive dampers Research scope Dampers for front–loaded washing machines, two smart materials SMA and MRF, quasi–static model for design and parametric dynamic model for behavior of the dampers at steady state, control via communication with computer Research approach and methods Research approach: − Applications of SMA and MRF to suspensions are first analyzed, then their advantages and disadvantages are clarified, and an improvement is proposed appropriately for the vibration problem of front–loaded washing machines − From the mathematical model, the design problem is analyzed, numerically simulated and optimized The results are then verified by experiments − The performance characteristics of the proposed dampers are compared with those of commercial passive dampers currently installed in washing machines Research methods: Legacy and expert interviews, analysis and review, analytical and numerical modeling, experience statistics, trial and error, experiments Scientific and practical significance of the research theme Scientific significance: − The SMA and MRF help to solve the vibration problem of washing machines − The precise hysteresis model is a contribution to control design − The low–cost optimized self–powered and stroke–by–activated MRF dampers provide effectiveness for operation of washing machines − The feasibility is validated via experiments on a prototype washing machine Practical significance: − The proposed hysteresis model in the dissertation can be applied for accurate control of force feedback systems or robotic aims − Low–cost self–adaptive MRF dampers are applicable not only to washing machines but also to motorcycles, cars, landing gears or building construction Dissertation outline Preface, Chapter 1: Overview, Chapter 2: Theoretical basis, Chapter 3: Shape memory alloy damper, Chapter 4: Magnetorheological fluid damper, Chapter 5: Self–adaptive magnetorheological fluid dampers, Chapter 6: Conclusions and future works, References, List of publications Chapter 1.1 OVERVIEW Introduction Vibration of washing machines is a challenging issue for scientists Washing machines often experience resonance at low frequencies, around 100 – 300 rpm [1–3] When the spindle speed increases to 900 rpm or more, the exciting force is transferred from the tube assembly to the floor through the suspension causing vibrations and noises Passive dampers Fig 1.1: Force transmissibility under different damping levels can reduce the vibration at low frequencies but increase the transmitted force and noises at high frequencies Thus, a suspension system with controllable damping coefficient should be developed (Fig 1.1) In this dissertation, two smart materials, magneto–rheological fluid (MRF) and shape memory alloy (SMA), will be investigated and applied to dampers for effective vibration suppression 1.2 1.2.1 a) Literature review Researches on vibration control of washing machines First approach: to control the tube balance Dynamic balancers [2, 3] can significantly mitigate the vibration However, the tube structures are complex, and the production and maintenance cost are high b) Second approach: to reduce the vibration based on suspension systems Many researches on SMA have been performed [5, 6] There were several works of SMA dampers [7, 8] but most are conducted for civil engineering with complex design, large size, high maximum and off–state forces Studies and applications of SMA in washing machine suspensions have been not found yet MRF has been investigated in many fields [9, 10] MRF sponge dampers [11] well suppress vibration, but gradual decreasing durability and wearing are main obstacles Aydar [12], Nguyen [13] proposed flow–mode MRF dampers; however, their disadvantages are high off–state force, complex structure and high cost Because the required force for washing machines is not so high, shear–mode MRF dampers are conformable Cha [14], Nguyen [15] studied shear–mode MRF dampers with simple structure but had no test yet on a washing machine for assessment Consequently, the researches on MRF damper for washing machines still have restrictions, the dynamic models have not been established effectively, and especially a creation should be made to leave the beaten track of traditional control systems – the main impediment for commercial objectives 1.2.2 a) Researches on modeling of dampers First group: quasi–static models Bingham [16, 17] and Herschel–Bulkley [18, 19] models are beneficial to design but insufficient to describe the damper behavior under dynamic loads b) Second group: dynamic models Non–parametric dynamic models [20, 21] flexibly capture the damper hysteresis; however, they are quite complicated and cannot reflect the parameters’ meanings Parametric dynamic models [22–24] are adaptive and receive more attention due to obvious meanings but require initial assumptions and appropriate constraints for solution divergence Spencer’s model [25] based on Bouc–Wen model is widely studied relying on its well prediction but cannot fully express the behavior under continuously varying excitations and the inverse model is difficult to solve Thus, a precise hysteresis model should be established to effectively predict the damper responses in rather extreme operating cases such as washing machines 1.2.3 Researches on control system of dampers Classic controllers [26, 27] are short of robustness under disturbances but favorable due to their simplicity and low computational cost Advanced controllers [28, 29] overcome the disadvantage; however, they are sophisticated and expensive Hybrid controllers [30, 31] can be used in complicated systems For commercialization, a low–cost simple controller for the washing machines installed with smart material dampers should be investigated in this dissertation 1.3 Research imperative Vibration of washing machines causes noises, unpleasant feelings and gradual decrease of machine life–span This dissertation aims at a suspension system featuring smart materials to effectively control the vibration of washing machines during operation process, thereby improving the life quality of customers 1.4 Scientific and practical significance of the research work Scientific significance: Solution for the vibration problem of washing machines Proposal of a precise hysteresis model for control design Low–cost optimized self–adaptive dampers The feasibility is validated by experiments Practical significance: The hysteresis model can be applied for feedback systems or robotic aims The self–adaptive dampers have many practical applications 1.5 Research aim and subjects Research aim: to develop a suspension featuring smart materials that can effectively control vibration of front–loaded washing machines during operation Research subjects: smart material suspensions for front–loaded washing machines, hysteresis model for the dampers under dynamic loads, control system for the dampers, self–adaptive dampers 1.6 Research tasks and scope Research tasks: to design dampers using smart materials, to propose a dynamic model, to design a control system, to develop self–adaptive dampers, to test the dampers on a prototype front–loaded washing machine and compare their damping performance with that of passive dampers Research scope: dampers for front–loaded washing machines, two materials SMA and MRF, quasi–static model for design and parametric dynamic model for behavior of the dampers at steady state, control via interaction with computer 1.7 Research methods Legacy and expert interviews, analysis and review, analytical and numerical modeling, experience statistics, trial and error, experiments Chapter 2.1 2.1.1 THEORETICAL BASIS Shape memory alloy (SMA) Introduction SMA is an unique shape memory material with the ability to recover its original shape when heated, thereby producing large actuating energy [32] 2.1.2 Shape memory effect (SME) Fig 2.4: Stress–strain–temperature data exhibiting SME for a typical while in the Twinned Martensite phase NiTi SMA [32] and then unloaded at a temperature SMA exhibits the SME as it is deformed below As When heated above Af, SMA will regain its original shape by transforming back into the parent Austenite phase (Fig 2.4) 2.1.3 Pseudo–elasticity The pseudo–elastic behavior of SMA is associated with the stress–induced transformation, which leads to the Fig 2.5: Thermo–mechanical loading strain generation during loading and path exhibits SMA pseudo–elasticity [32] subsequent strain recovery upon unloading at temperatures above Af (Fig 2.5) 2.1.4 Behavior of SMA spring actuators The behavior of compression and tension SMA springs are described in Fig 2.7 Fig 2.7: Behavior of SMA spring actuators 5.2.3 Modeling of the stroke–by–activated MRF damper The active damping force Fd and off– stated force F0 are determined by Eqs (4.1, 4.2) In this design, Lon  6lp and Loff  3lm where lp and lm are respectively the lengths of each pole piece and magnet Three types of MRF, including 122–2ED, 132–DG and 140–CG, are considered The design optimization is conducted and Fig 5.19: Modeling of the stroke–by– activated 140–CG MRF damper the optimal results are presented in Table 5.5 and Fig 5.19 It is observed that the performance of the 140–CG MRF is better than the two others, so it is chosen for this work The outer radius of the 140–CG MRF damper is reduced considerably as compared with the conventional and self–powered MRF dampers Table 5.5: Optimal solutions of the stroke–by–activated MRF dampers Parameters (mm) 122–2ED 132–DG 140–CG Magnet Length lm 2,4 2,4 Radius rm 13,5 10,2 Pole piece lp 9,1 9,1 9,1 Thin wall tw 0,8 0,8 0,8 Radius rs 14,3 11 9,8 Length L 34,6 34,5 33,3 Thickness tg 0,8 0,8 0,8 Thickness to 4,2 4,5 Outer radius R 20 16 15,1 Max damping force Fd (N) 80,1 80,1 80,1 Off–state force F0 (N) 31,7 24,4 22 Shaft MRF gap Housing Performance 21 5.2.4 Experimental evaluation of the stroke–by–activated MRF damper The experimental responses of the stroke–by–activated MRF damper at Hz frequency are shown in Fig 5.21 It is seen that the experimental damping force increases with the displacement, which correlates well to the theoretical analyses The force–displacement curve expresses a clockwise hysteresis, especially at the stroke ends The test results on the prototype washing machine in Fig 5.23 show that the vibration suppression of the proposed damper is much better than that of passive dampers, thereby certificating its practical feasibility 5.3 Summary In this chapter, two self–adaptive shear–mode MRF dampers were optimized in design, manufactered and tested on the prototype washing machine These dampers are self–adaptable to excitations to mitigate vibration without any control, thereby remarkably reducing cost The research results were published in ISI journals [49, 50], Scopus journal [51] and Proceeding [52] Fig 5.21: Experimental responses of the stroke– by–activated MRF damper at Hz frequency Fig 5.23: Responses of the washing machine featuring the stroke–by– activated MRF dampers 22 Chapter 6.1 CONCLUSIONS AND FUTURE WORKS Conclusions The dissertation provided the vision and investigation of the suspension systems integrated with smart material to effectively control the vibration of front–loaded washing machines With the ability to versatilely adjust and control operating characteristics corresponding to external excitations, the proposed suspension systems marked a new advance of the automation industry The research results clarified these main points: The first smart material that was studied and applied to the suspension of front–loaded washing machines is SMA The experimental responses of the SMA damper agreed well with the simulation as the active damping force could reach up to 76.5 N (95% of the calculated value), which is high enough to mitigate most vibration of washing machines Against the MRF dampers, the SMA damper has simpler structure, lower cost and smaller off–state force (about N), thereby showing its potential The test results on the prototype washing machine also expressed its better vibration suppression as compared with that of passive dampers However, with high state changing time (about 25 second), the SMA damper is initially suitable for on–off control only The experimental data indicated a hysteresis phenomenon of the SMA damper, especially at the stroke ends The proposed model in [37] (publication [3]) and two typical Bingham and Bouc–Wen models were used to predict the nonlinear behavior of the damper The simulated results showed that against the others, the Bingham model cannot capture accurately the hysteresis behavior of the SMA damper, especially at small velocities; however, its simple structure is beneficial to design and initial estimation Contrarily, the Bouc–Wen and proposed models better reflect the damping force variation but at the same time are more complicated and hence are suitable for control design, feedback or system identification problems 23 The second smart material that was explored in the dissertation is MRF The shear–mode MRF damper was optimized in design to achieve the best performance considering the criteria of damping force, size, installability and cost The experimental and analysis results were correlative as the max damping force reached to 76.6 N (96% of the simulated value) and off–state force was 19.1 N – a little higher than the theoretical calculation (about 104%) The force–velocity and force–displacement data of the MRF damper indicated a strong hysteresis in the pre–yield region Based on the Magic Formula and Pan’s models, a new dynamic model was proposed to describe this nonlinear hysteresis behavior, in which the damping force is defined as a function of displacement, velocity, current and frequency The simulated results showed that, against the Spencer’s and Pan’s models, the proposed model not only predicts more precisely the asymmetric hysteresis characteristic and sharpness of the curve but also is more adequate to different operating conditions The model has clear physical meanings and is favorable for approach, also it is absolutely possible to apply the model in other semi–active control systems An open–loop control system based on the sky–hook algorithm was designed to assess the efficiency of the proposed model The experimental results showed that the proposed model controlled the damping force corresponding to the desired damping force better than the Spencer’s and Pan’s models A semi–active vibration control system was developed for the washing machine installed with the MRF dampers, consisting of a system controller and a phase–lead damper one The sensor component of the system is an induction coil integrated into the rear damper to simplify structure and reduce cost From the simulated and experimental results, it was observed that the proposed control system combines the advantages of the uncontrolled and constant current control states The proposed control system showed the effective vibration suppression at low frequencies, especially in the resonance region, while still well preventing the force transmission at high frequencies 24 Although the MRF damper showed its ability to solve the vibration problem of washing machines, the complex structure and high cost coming from the associated equipment are the obstacles for commercialization Therefore, a new type of MRF damper with self–powered ability was subsequently developed based on the idea of reusing wasted mechanical vibration energy of washing machines to power itself Two configurations of and induction coils of the EH part were studied and optimized in design for integration in washing machines The research results showed that the max damping force of both configurations was almost similar to that of the conventional MRF damper, but the 4–coil one has the advantages of smaller size, easier connection and lower cost of manufacturing and maintenance The remarkable point is that the self– powered MRF damper can adapt itself to excitations to generate corresponding damping level without any control, thereby considerably reducing cost This is an important criterion for commercial development The test results on the prototype washing machine also showed that the 4–coil self–powered MRF damper well mitigated the vibration at all frequencies against passive dampers With magnetic winding coils, the self–powered MRF damper to some extent has a conventional mark as it cannot thoroughly deal with the structural complexity Still based on the idea of self–adaptation, a new type of shear–mode MRF damper with stroke–by–activated ability was developed The experimental data showed that the damping force increases with the vibratory excitation amplitude, which correlates to the theoretical analyses As compared with the conventional and self–powered MRF dampers, this displacement–based damping characteristic is very compatible with operation of washing machines In addition, the stroke–by–activated MRF damper possesses compact structure and lower cost than the other MRF dampers, which can make a breakthrough for commercialization The test results of the proposed damper on the prototype washing machine also showed its better performance against passive dampers, thereby certificating its feasibility and potential in practical applications Comparison between the four dampers that were studied in this dissertation: 25 − The pin–to–pin lengths of the four dampers are correlative (about 200 mm) to satisfy the assembly space in the washing machine However, the stroke–by– activated MRF damper has smallest outer radius − The smart materials used for the four dampers are imported from abroad with a minor difference in cost of each damper With respect to structure, the three MRF dampers need the O–rings to seal the fluid and the coils to generate magnetic field but not does the SMA damper, so its design is simpler However, the SMA and conventional MRF dampers require the power source and controller and hence they are more complex and expensive The self–powered and stroke– by–activated MRF dampers are both self–adaptive type, but the stroke–by– activated one has the advantages of compactness and favorableness of manufacturing, assembly, maintenance and cost due to the replacement of the coils with the magnets, also it possesses displacement–based damping characteristic which is more conformable to operation of washing machines − There were correlations of damping force between the four dampers and the simulations The off–state force of the stroke–by–activated MRF damper is somewhat higher than the two other MRF dampers due to the impact of the magnets while that of the SMA damper is smallest However, the high state changing time of the SMA damper is an issue that should be further investigated − When tested on the prototype washing machine, the vibration suppression of the four dampers were better than passive dampers The z–direction vibration was not much mitigated as compared with the x– and y–direction vibrations because of the in–plane distribution of the dampers The results can be improved as the frame structure of the suspension is modified Each smart material damper in the dissertation has its own advantages and disadvantages The above comparison is for summary and orientation purposes for the damper consideration in accordance with each specific application 6.2 Future works The dissertation significantly contributed to the vibration control problem of front–loaded washing machines However, the work still has some certain 26 restrictions First, since the SMA damper has high actuating time, the study stopped at design and on–off control Lowering this quantity will improve the SMA damper efficiency and allow the close–loop control Second, the hysteresis model of the dampers was established in steady state and did not consider the transience from off– to active–states as well as did not associate the design and modeling Studying a model that can reflect the physical nature of the dampers and predict both states will help to complete the system dynamic modeling Third, the axial magnetization magnets of the stroke–by–activated MRF damper cannot maximize the active MRF length in the gap The replacement with radial magnets will be a better choice Fourth, the smart material dampers are distributed in–plane, which restricts the z–direction vibration reduction Modifying the suspension frame will be an improvement Fifth, to simplify the design process, the dynamic modeling of front–loaded washing machines was implemented on the 2D plane containing the unbalanced mass and suspension system; therefore, the impacts of pitching, displacing and rolling with regard to the third dimension were neglected Although considering these factors is more sophisticated, the performance evaluation will be more obvious and accurate From the above analyses, the dissertation can be developed as follows: − Researches on heating and initial heat treatment methods for SMA, design of SMA damper considering the pseudo–elasticity, application of magnetic shape memory alloy to the damper based on the fast response ability of magnetic field − Modeling with the connection between the quasi–static frame and hysteresis factors − Study of a model for both the steady and transient states − Improvement of the stroke–by–activated MRF damper using radial magnetization magnets − Modifying the assembly structure of the suspension to improve the vibration mitigation effectiveness of the dampers in all three directions − Solutions of the design, modeling and vibration control of washing machines based on the 3D dynamic model of the tube assembly 27 REFERENCES [1] H T Lim, W B Jeong and K J Kim Dynamic modeling and analysis of drum–type washing machine International Journal of Precision Engineering and Manufacturing, Vol 11, Issue 3, pp 407–417, 2010 [2] S Bae, J M Lee, Y J Kang, J S Kang and J R Yun Dynamic analysis of an automatic washing machine with a hydraulic balancer Journal of Sound and Vibration, Vol 257, Issue 1, pp 3–18, 2002 [3] E Papadopoulos and I Papadimitriou Modeling, design and control of a portable 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for washing machines Smart Materials and Structures, Vol 30, Issue 3, 037001, 2021 [51] Q D Bui, L V Hoang, D D Mai and Q H Nguyen Design and testing of a new shear–mode magneto–rheological damper with self–power component for front–loaded washing machines Lecture Notes in Mechanical Engineering, pp 860–866, 2021 [52] D Q Bui, T B Diep, V L Hoang, D D Mai and H Q Nguyen Design of a self–power magneto–rheological damper in shear mode for front–loaded washing machine Hội nghị khoa học toàn quốc lần thứ Động lực học Điều khiển, Da Nang City, Vietnam, 2019, pp 297–303 LIST OF PUBLICATIONS ISI journals Q D Bui, Q H Nguyen, T T Nguyen and D D Mai Development of a magnetorheological damper with self–powered ability for washing machines Applied Sciences, Vol 10, Issue 12, 4099, 2020 Q D Bui, Q H Nguyen, L V Hoang and D D Mai A new self–adaptive magneto–rheological damper for washing machines Smart Materials and Structures, Vol 30, Issue 3, 037001, 2021 Q D Bui, Q H Nguyen, X X Bai and D D Mai A new hysteresis model for magneto–rheological dampers based on Magic Formula Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, Vol 235, Issue 13, pp 2437–2451, 2021 Q D Bui, X X Bai and Q H Nguyen Dynamic modeling of MR dampers based on quasi–static model and Magic Formula hysteresis multiplier Engineering Structures, Vol 245, 112855, 2021 Scopus journals D Q Bui, V L Hoang, H D Le and H Q Nguyen Design and evaluation of a shear–mode MR damper for suspension system of front–loading washing machines Lecture Notes in Mechanical Engineering, pp 1061–1072, 2018 Q D Bui, L V Hoang, D D Mai and Q H Nguyen Design and testing of a new shear–mode magneto–rheological damper with self–power component for front–loaded washing machines Lecture Notes in Mechanical Engineering, pp 860–866, 2021 Q D Bui, Q D Do, L V Hoang, D D Mai and Q H Nguyen Design and experimental evaluation of a novel damper for front–loaded washing machines featuring shape memory alloy actuator and wedge mechanism Lecture Notes in Mechanical Engineering, pp 873–878, 2021 D Q Bui, H Q Nguyen, V L Hoang and D D Mai Design and hysteresis modeling of a new damper featuring shape memory alloy actuator and wedge mechanism Lecture Notes in Mechanical Engineering, pp.125–136, 2021 Q D Bui and Q H Nguyen A new approach for dynamic modeling of magneto–rheological dampers based on quasi–static model and hysteresis multiplication factor Mechanisms and Machine Science, Vol 113, pp 733–743, 2021 Other journals 10 D Q Bui, T B Diep, H D Le, V L Hoang and H Q Nguyen Hysteresis investigation of shear–mode MR damper for front–loaded washing machine Applied Mechanics and Materials, Vol 889, pp 361–370, 2019 11 Q D Bui and Q H Nguyen Design and simulation of a new self–adaptive MR damper for washing machines featuring shear–mode and radial permanent magnets Science and Technology Development Journal, Vol 4, Issue 3, pp 1– 13, 2021 Conference proceedings 12 D Q Bui, T B Diep, V L Hoang, D D Mai and H Q Nguyen Design of a self–power magneto–rheological damper in shear mode for front–loaded washing machine Hội nghị khoa học toàn quốc lần thứ Động lực học Điều khiển, Da Nang City, Vietnam, 2019, pp 297–303 13 Q D Bui, Q H Nguyen and L V Hoang A control system for MR damper–based suspension of front–loaded washing machines featuring magnetic induction coils and phase–lead compensator The 1st International Conference on Advanced Smart Materials and Structures, Ho Chi Minh City, Vietnam, 2021, pp 79–88 ... under Hz frequency, 20 mm amplitude and different current excitations 4.4 Experimental evaluation of the MRF damper The experimental data of the MRF damper under Hz frequency, 20 mm amplitude and... passive dampers However, with high state changing time (about 25 second), the SMA damper is initially suitable for on–off control only The experimental data indicated a hysteresis phenomenon... the simulated and experimental results, it was observed that the proposed control system combines the advantages of the uncontrolled and constant current control states The proposed control system