Modeling and Vibration Analysis of a Drum type Washing Machine

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1 Modeling and Vibration Analysis of a Drum type Washing Machine Takayuki KOIZUMI, Nobutaka TSUJIUCHI, Yutaka NISHIMURA Department of Engineering, Doshisha University, 1-3, Tataramiyakodani, Kyotanabe, Kyoto, , Japan Naoto YAMAOKA SANYO Electric Co.,Ltd. 1-1, Seta 1-chome, Otsu City, Shiga, , Japan Nomenclature a : Stroke [mm] c : Equivalent viscous damping coefficient [N s / mm] c t : Viscous damping coefficient for torque [N mm s / rad] F : Force [N] F : Load at max displacement [N] a max k : Sttiffness coefficient [N / mm] k ' : Gradient of load-displacement closed curve k t : Sttifness coefficient for torque [N mm / rad] t : Time [s] T : Torque [N mm] W : Half area of circumscribed quadrangle of load-displacement closed curve [mm 2 ] W : Area of load-diplacement closed curve [mm 2 ] x : Displacement between two parts [mm] x : Free length [mm] δ : Loss angle [rad] θ : Angle [rad] ω : Angular frequency [rad/s] ABSTRACT This paper presents the modeling of a vibration analysis model for a drum type washing machine. This model can analyze the vibrations of the outer tub, the frame, and the force to the floor in the spin-drying stage. The generalpurpose motion analysis software is used to create the analysis model. In order to validate this analysis model, the simulation results and the experimental results are compared in various unbalanced conditions. Using the created model, parameter tests were conducted to reduce the vibration of the drum type washing machine. 1. INTRODUCTION In a fully automatic washing machine, an unbalanced mass of clothes in a spin drum can cause vibration problems. This occurs most frequently in spin-drying stage, because the drum spins at a relatively high speed causing the clothes to be pressed against the inner wall of the spin drum, and these can become a large unbalanced mass until the end of the stage. Accordingly, excessive vibration can occur during the spin-drying stage. In particular, in a drum type washing machine, in which the spin drum rotates on a horizontal axis, the

2 effect of gravity creates an unbalanced mass of clothes, and the vibration problems occur more easily [1]. In a washing machine, vibration of the outer tub causes vibration of the frame and the force transfers from the supports of the frame to the floor. Although springs and dampers between the outer tub and the frame, and rubber cushions have reduced these vibrations, it is difficult to efficiently design the stiffness coefficients and the damping coefficients of these mechanical components. Thus, various washing machine vibration analysis models have been proposed [2]-[6]. An analysis model that is useful enough to optimize the parameters of a washing machine is required that is able to analyze not only the vibration of the outer tub but also the vibration of the frame and the force to the floor. In order to create such a model, modeling of mechanical components and points of connection between each body is important. Because most of the models that have been proposed were created based on the various assumptions such as fixing the frame to the ground to simplify the model, they can t analyze these phenomena in the same time. Therefore, few models are enough useful in the design phase. The purpose of this research is creating a vibration analysis model of a drum type washing machine that can analyze the vibration of the outer tub, the frame, and the force to the floor in various unbalanced conditions. The outer tub, frame, and ground part modeled as rigid bodies are linked by the mechanical components modeled as the working parts consisting of rigid bodies and joints in order to analyze the dynamic behavior of the outer tub and frame. The points of connection between each rigid body are modeled as joints considered the characteristics of the machine subject. The characteristics of the spring damper and rubber cushion investigated experimentally are reflected in each joint. In order to validate the analysis model, the operating tests in spin-drying stage are conducted with an unbalanced mass, and these experimental results and the simulation results are compared in various unbalanced conditions. Finally, using the created analysis model, the design parameters tests to reduce the vibration of the machine subject are conducted. 2. MODELING OF A DRUM TYPE WASHING MACHINE 2.1. Structure of a drum type washing machine Drum type washing machines possess a horizontal spin drum that rotates on a horizontal axis. This machine type possess several advantages such as water and drying efficiency. However, in this type, it is difficult to evenly distribute clothes over the inner wall of the spin drum due to the effects of gravity. Thus, an unbalanced mass of clothes may occur and vibration problems are easily caused. Figure 1 shows the structure of the machine subject and the coordinate system in this research, and Figure 2 shows the appearance of the machine subject. The outer tub that includes the spin drum is linked to the frame by two spring dampers and four springs. Two rubber cushions are attached to the joint between each spring damper and the outer tub or the frame. The frame stands on four rubber supports. Spring Outer tub x z y Fig.1 Structure of the machine subject and the coordinate system 2.2. Modeling of the machine subject Spin drum Frame Spring damper Rubber cushion Rubber support Fig.2 Appearance of the machine subject The vibration analysis model was created using the general-purpose motion analysis software ADAMS. In the

3 software, the simulation is performed with rigid bodies connected by joints. The joints create relative motion between the mutual parts. Figure 3 (a) shows a model of the outer tub containing the spin drum. Figure 3 (b) shows a model of the frame. We regarded the spin drum, the outer tub, and the frame as rigid. Because the spin drum and the outer tub are connected by the revolute joint at the position of the motor shaft, the spin drum can rotate around the joint axis in the outer tub. These rigid parts are linked by the mechanical components modeled as the rigid bodies and joints. Figure 3 (c) shows a jointed model. Figure 4 (a) shows the spring damper and rubber cushions. Figure 4 (b) shows the supports of the frame. The spring dampers are modeled as two rigid bodies linked by translational joints having one degree of freedom. These joints contain linear stiffness and damping properties. The springs suspending the outer tub from the frame are modeled as translational joints linking the outer tub to the frame directly. The equation for the motion of the spring damper and spring can be written as shown in Eq. (1). F = k( x x ) cdx / dt (1) The points of connection between each rigid body are modeled as joints having some degrees of freedom considering the structure of the machine subject. In machine subject, rubber cushions are attached to the points of connection between each spring damper and the outer tub or the frame, and between the frame and the floor as rubber supports. These points are modeled as joints having six degrees of freedom. In order to consider the characteristics of rubbers, these joints contain linear stiffness and damping properties of each direction in the coordinate system applying force and torque to the two parts. The equation for the motion of each force and torque can be written as shown in Eqs. (2) and (3). F = kx cdx / dt (2) T = k θ c dθ dt T T / (3) (a) Outer Tub (b) Frame (c) Jointed Model Fig.3 Rigid parts Outer tub Stiffness Frame Stiffness and and Damping Stiffness Damping (1 DOF) and Damping (6 DOF) Frame (6 DOF) Ground (a) Spring Damper and Rubber cushions (b) Rubber supports of the frame Fig.4 Working parts 2.3. Measurement of dynamic characteristics It s necessary for joints to clarify the dynamic characteristics of the mechanical components experimentally.

4 Excitation experiments were conducted in order to measure stiffness coefficients and damping coefficients of the spring damper, the rubber cushion, and the rubber support of the frame. Experiments on various experimental conditions were conducted to investigate the frequency and displacement characteristics of the dynamic characteristics. Figure 5 shows the experimental environment of the spring damper by way of example. Figure 6 shows an example of the load-displacement relationship from the results of the excitation experiments. Based on the load-displacement relationship, the stiffness coefficients and damping coefficients were calculated. The stiffness coefficient of the spring damper k was calculated using Eq. (4). k = Fa / a max (4) The stiffness coefficients of the rubber cushion and rubber support k were calculated using Eqs. (5) and (6). 2 W sin δ = (5) π W k = k' cosδ (6) The damping coefficients c were calculated as equivalent viscous damping coefficients using Eq. (7). 2π = ω W cω a cos ωtdt = πcωa (7) The damping coefficient of the spring damper had frequency characteristic and displacement characteristic. Figure 7 shows these characteristics. They were considered in the model. Load[N] Displacement[mm] Fig.6 Load - Displacement Relationship Fig.5 Experimental environment of excitation 3. MEASUREMENT OF THE EXPERIMENTAL RESPONSE Fig.7 Characteristic of the damping coefficient of the spring damper An operating tests for the washing machine in the spin-drying stage were conducted in order to verify the analysis model of the drum type washing machine. The horizontal, cross, and vertical displacement of the outer tub and Damping Coefficient[N s / mm] Frequency[Hz] 1.[mm] 3.[mm] 5.[mm] 12

5 the frame as well as the vertical load to the floor from the rubber supports of the frame were measured. At first, the displacement of the outer tub in a steady state vibration and a transient vibration were measured. Figure 8 shows the measurement device of displacement. An accelerometer was attached to the right and left periphery on the outer tub. This measured acceleration signal was passed through a charge amplifier and converted to the displacement signal by a integrator. The measured displacement was displayed on a FFT analyzer. The measurements of the steady state vibration were conducted when the rotation speed of the spin drum was constant. The measured rotation speed of the spin drum was from 6 [rpm] to 8 [rpm]. The measurements of the transient vibration were conducted when the rotation speed of the spin drum was varied from 1 [rpm] to 3 [rpm] during 25 [s]. In order to consider the pattern of the speed up of the motor in the model, the angular speed - time relationship of the motor was measured synchronizing with the measurement of the displacement of the outer tub. Figure 9 shows the measurement device of the angular speed of the motor. Next, the displacement of the frame and the force to the floor in steady state vibrations were measured. An accelerometer was attached to the right and left periphery on the frame. Four load cells were put under each support of the frame. This measured strain signal was passed through a strain amplifier and displayed on a FFT analyzer. Figure 1 shows the measurement device of the floor force. The measured rotation speed of the spin drum was from 6 [rpm] to 8 [rpm]. Unbalanced masses of 3 [g] and 15 [g] were attached to the right and left periphery of the spin drum. Instead of attaching clothes to the inner wall of the spin drum in the spin-drying stage, rubber plates were used. Subject Accelerometer Amplifier Integrator FFT Analyzer Fig.8 Measurement Device of Displacement 4. VALIDATION OF THE MODEL Subject Control Device Resistance Isolating Transformer F-V Converter FFT Analyzer Fig.9 Measurement Device of the Angular speed of the Motor Subject Load Cell Amplifier FFT Analyzer Fig.1 Measurement Device of the force to the floor In this research, the vibration analysis model was validated with experimental results in various unbalanced conditions. At first, the validations about the displacement of the outer tub were conducted. Next, the validations about the displacement of the frame and the force to the floor were conducted. 4.1 Validation of the displacement of the outer tub Figure 11 shows the comparison results of the displacement of the left periphery of the outer tub with an unbalanced mass of 3 [g] at the left periphery of the spin drum. Figures 11 (a)-(c) show the comparison results of the cross, vertical, and horizontal displacement of the outer tub in a steady state vibration. The vertical line indicates the displacement amplitude in millimeters and the horizontal line indicates the frequency in rpm. Figure 11 (d) shows the comparison result of the vertical displacement in a transient vibration. The vertical line indicates the displacement amplitude in millimeters and the horizontal line indicates the time in seconds. As shown in Fig. 11, the simulation results show good agreement with the experimental results. Likewise, on the other unbalanced conditions, the simulation results show good agreement with the experimental results. These results show that this created model can analyze the displacement of the outer tub in various unbalanced conditions.

6 Left_x_experiment Left_x_simulation Left_y_experiment Left_y_simulation (a) Cross Displacement in a Steady state Vibration (b) Vertical Displacement in a Steady state Vibration Left_z_experiment Left_z_simulation Displacement[mm] 12 9 Left_y_experiment 6 Left_y_simulation Time[s] (c) Horizontal Displacement (d) Vertical Displacement in a Transient Vibration in a Steady state Vibration Fig.11 The comparison between the simulation results and experimental results of the Outer Tub 4.2 Validation of the displacement of the frame and the force to the floor Figure 12 shows the comparison results of the displacement of the right periphery of the frame in a steady state vibration with an unbalanced mass of 3 [g] at the left periphery of the spin drum. Figure 12 (a) shows the simulation results of the cross, vertical, and horizontal displacement. Figure 12 (b) shows the experimental results of the cross, vertical, and horizontal displacement. The vertical line indicates the displacement amplitude in millimeters and the horizontal line indicates the frequency in rpm. Figure 13 shows the comparison results of the force to the floor from the each support of the frame in a steady state vibration with an unbalanced mass of 3 [g] at the left periphery of the spin drum. Figure 13 (a) shows the simulation results of the each support. Figure 13 (b) shows the experimental results of the each support. The vertical line indicates the load amplitude in newtons and the horizontal line indicates the frequency in rpm. As shown in Fig. 12 and Fig. 13, the simulation results show good agreement with the experimental results. Likewise, in the other unbalanced conditions, the simulation results show good agreement with the experimental results. These results show that this created model can analyze a steady state vibration of the frame and the force to the floor in various unbalanced conditions Sim_FrameRight_x Sim_FrameRight_y Sim_FrameRight_z Exp_FrameRight_x Exp_FrameRight_y Exp_FrameRight_z (a) Simulation Results (b) Experimental Results Fig.12 The comparison between the simulation results and experimental results of the Displacement of the Frame

7 Load[N] FrontRight RearRight RearLeft FrontLeft Load[N] FrontRight RearRight RearLeft FrontLeft (a) Simulation Results (b) Experimental Results Fig.13 The comparison between the simulation results and experimental results of the force to the floor 5. REDUCING THE VIBRATION Using the created model, the design parameters tests to reduce the vibration were conducted. In this research, the experimental results of steady state vibration were investigated and the vibration problems were clarified. The parameters affecting these vibration problems were verified using the created model. Finally, some improved parameters to reduce the vibrations were proposed. 5.1 Investigation of experimental results The experimental results of steady state vibration were investigated and the vibration problems were clarified. The resonance frequencies of the outer tub were concentrated at low frequencies. At low frequencies, the cross and vertical resonance displacements were larger, and these resonances affected the frame resonances and the force to the floor. Meanwhile, at high frequencies, frame resonances occurred. In particular, the cross and horizontal resonances were larger. These resonances affected the force to the floor. Therefore, at low frequencies, the cross and vertical vibrations of the outer tub were important, and at high frequency, the cross and horizontal vibrations of the frame were important. In this research, these vibrations were forcused on. 5.2 Improvement of the parameters using the created model Using the created model, the design parameters tests to reduce the vibration were conducted. At first, the effect of the design parameters to aforementioned vibrations were investigated. The results of the analyses in various parameters conditions showed the following facts: (1) Increasing the damping coefficients of the spring dampers is effective to reduce the cross and vertical vibrations of the outer tub. (2) Increasing the damping coefficients of rubber supports is effective to reduce the cross and horizontal vibration of the frame. Based on these results, the damping coefficients of spring dampers and rubber supports were increased twice in the created model. Figures 14 (a)-(c) show the simulation results of reducing the vibration using the created model. The horizontal lines indicate the frequency in rpm. Figure 14 (a) shows the results of the left periphery of the outer tub, and Figure 14 (b) shows the results of the right periphery of the frame. The vertical lines indicate the displacement amplitude in millimeters. Figure 14 (c) shows the results of the force to the floor. The vertical line indicates the load amplitude in newtons. In Fig. 14, the unbalanced condition is 3 [g] at the left periphery of the spin drum. As shown in these figures, at low frequencies, the vertical resonance displacement of the outer tub were reduced by about 35%, and the cross resonance displacement of the outer tub were reduced by about 2%. Based on these, the resonances of the force to the floor were reduced. At high frequencies, the horizontal resonance displacement of the frame was reduced by about 5% and the cross resonance displacement of the frame was reduced by about 4%. Based on these, the resonances of the force to the floor were reduced. From these results, the possibility of reducing the vibration of the machine subject according to improve the parameters was indicated.

8 OuterTub_Left_x OuterTub_Left_y OuterTub_Left_z (a) Displacements of the Outer Tub Load[N] FrontRight RearRight RearLeft FrontLeft (c) Force to the floor Fig.14 The simulation results of reducing the vibration Frame_Right_x Frame_Right_y Frame_Right_z (b) Displacements of the Frame 6. CONCLUSION In this research, a vibration analysis model of a drum type washing machine was created. The outer tub, frame, and ground part modeled as rigid bodies were linked by the mechanical components modeled as the working parts consisting of rigid bodies and joints. The characteristics of the mechanical components investigated experimentally were reflected in each joint. Consequently, a model that can analyze not only the vibration of the outer tub but also the vibration of the frame and the force to the floor was created. Using this model, the vibration of the outer tub and the frame can be clarified in various unbalanced conditions, and these can be estimated in terms of the force to the floor. Finally, the design parameters tests to reduce the vibration of the machine subject were conducted. Accordingly, some improved parameters were proposed and the possibility of reducing the vibration of the machine subject according to improve the parameters was indicated. These results show the created model is useful enough to optimize the parameters of a washing machine in the design phase. REFERENCES [1] Y.Yokoi, Y.Sonoda, A.Okonogi, Y.Tomigashi, T Kawaguchi, Vibration Control System for the Drum Type Washer/Dryer, SANYO TECHNICAL REVIEW, Vol. 35 No. 2, (23), pp76-86 [2] O.S.Turkay, I.T.Sumer, A.K.Tugcu, B.Kiray, Modeling and Experimental Assessment of Suspension Dynamics of a Horizontal-Axis Washing Machine, Journal of Vibration and Acoustics, vol. 12, (1998), pp [3] D.C.Conrad, W.Soedel, On the Problem of Oscillatory Walk of Automatic Washing Machines, Journal of Sound and Vibration, Vol. 188 No. 3, (1995), pp [4] E.Papadopoulos, I.Papadimitriou, Modeling, Design and Control of a Portable Washing Machine during the Spinning Cycle, IEEE/ASME International Conference on Advanced Intelligent Mechatronics Proceedings, Vol. 21 No. Vol. 2, (21), pp [5] J.Young Choi, Jong-Min Lee, No-Cheol Park and Young-Pil Park, The dynamic analysis of a pulsator type washing machine and experimental study for the abnormal vibration, APVC Proceedings, Vol. 1, (23), pp63-68 [6] T.Koizumi, N.Tsujiuchi, Y.Nishimura, N.Yamaoka, Vibration Characteristics Analysis of the Fully Automatic Washing Machine, JSME Dynamic & Design Conference 24, No. 259, (24)

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