曾群：风扇噪音分析

　　风扇噪音分析

　　曾群

　　Analysis of motor-driven thin blade fan noise

　　Zeng Qun

　　Abstract: For a long time, there is not a method to predicting the noise level of motor-driven blade. In order to satisfy, we developed a method for calculating the sound generated when a rotating blade is excited by the torque pulsation of a motor. The sound pressure values calculated by the new method for a rotating blade were found to correspond well with experimentally measured ones.

　

　　List of symbols

　　ds Reference small area (m2);

　　ri Instantaneous distance from ith node to P (m);

　　j Imaginary unit;

　　S Area of sound radiator (m2);

　　k Free field wave number of plane wave (1/m);

　　V Velocity distribution of sound radiator (m/s);

　　P Field point (m);

　　Vi Amplitude of velocity at ith node (m/s);

　　p Sound pressure level (Pa);

　　øi Phase of velocity at ith node (rad); q Angle of sound radiator (rad);

　　q Mass density (kg/m3); R Observed radius (m);

　　x Angular frequency (rad/s); r Distance from reference small area ds (m);

　　xr Angular velocity of rotating radiator (rad/s);

　　1 Introduction

　　A method for predicting the electromagnetic noise of a thin blade fan driven by an electric motor has been developed.

　　Electric motors are used as actuators in various kinds of machinery. Vibrating motions and noise in the machinery arise when the excitation forces of electric motors act on elastic parts of machinery. For instance, an air conditioner has a fan structure attached to the motor shaft. The thin blade fan vibrates and radiates electromagnetic noise when the torque pulsation acts on the rotating blades.

　　A number of investigators have studied vibration and noise caused by motors. Here we propose a new noise calculation method for rotating blades that are excited by the torque pulsation of a capacitor motor. The calculation method is composed of two main modules, one for analyzing the vibration response of the blades, and one for calculating the electromagnetic noise of a rotating blade.

　　In the analyzing module, the vibration response of a rotating thin blade is analyzed using both torque pulsation and the mesh model of the blade. To calculate the motor’s torque pulsation, we employed an equivalent electric circuit corresponding to the motor. The calculated torque pulsation was used to obtain the vibration response. In measuring the vibration response at various points along the length of the rotating blade, we found that the calculation and experimental results agreed well for each point.

　　This calculation module for electromagnetic noise calculates the sound field caused by sound radiated from the rotating blade excited by the torque pulsation of the motor. It was found that the sound pressure values calculated by the new calculation method for a rotating blade corresponded well with experimentally measured ones.

　　2 Experimental device

　　2.1 Specifications of experimental device. The motor referred to in this paper is a capacitor motor with the specifications shown in Table 1. The main part of the testing system, shown schematically in Fig. 1, primarily consists of a motor, a four-bladed fan, and a high-stiffness block. The high-stiffness block is a steel block 220x220x220 mm in size and 83 kg in mass; its natural frequency is 6.7 kHz. A foam rubber was inserted under the block to prevent vibration from the floor from being transmitted to the motor and blades. The four-bladed fan was attached to the motor shaft. Each blade is an aluminum plate 300x80x3 mm in size. The motor rotates at a slow speed of 210 rpm because of the air resistance of this large fan. An accelerometer and slip ring were used to measure the vibration response of a rotating blade.

　　2.2 Measurement device for radiated noise

　　The system for measuring the sound pressure, shown schematically in Fig. 2, was set up in a semi-anechoic chamber. The blade rotates at a distance of 645 mm.

　　Table 1 Motor specifications

　　-------------------------------------------------------

　　Motor type Capacitor motor

　　Rated power 140 W

　　Power supply frequency 50 Hz

　　Power supply voltage AC 150 V

　　Capacitor 8 l F

　　Pole 6

　　Stator slot 24

　　Rotor slot 34

　　Rotation speed 210 rpm( four-bladed fan)

　　Fig. 1 Experimental device

　　Above the floor to prevent noise from the floor from influencing the results. The points evaluated lie at a distance of 210 mm above the blade.2.3 Characteristics of radiated noise.

　　Figure 3 shows the frequency response of the sound pressure produced by the testing system. In this figure, the microphone is set up at a radius of 200 mm from the rotating center. Many frequency components are shown in this figure, with the blade passage frequency causing a peak frequency component at 14 Hz. The peak frequency components at 100 Hz and 200 Hz are the result of electromagnetic noise caused by torque pulsation.

　　

　　3 Calculation method for radiated noise

　　3.1 Basic formula

　　Figure 4 shows the analytical model of radiated sound. The sound pressure p of a field point P caused by sound radiated from a plane radiator with area S and velocity distribution V(x, y) in an infinite baffle wall can be evaluated with the following equation.

　　Where r is the distance from a reference point ds on the radiator to the field point P, x is angular frequency, q is mass density, and k is the free field wave number of a plane wave.

　　3.2 Calculation method for radiated electromagnetic noise from a rotating blade.

　　We developed a calculation method when a plane radiator rotates. Figure 5 represents the plane radiator rotating about the z-axis with angular velocity xr. In this method, we can calculate sound pressure p(t) from the rotating blade based on Eq. (1). The value of sound pressure p(t) at fixed field point P is calculated by

　　where, vi= the amplitude of the velocity at the ith node/i= the phase of the velocity at the ith nodeq= angle of plane radiator. The vibration response vi and its phase /i of the rotating blade can be calculated by using the finite-element method (FEM).The directivity factor can be calculated by both the size of sound radiator and the point source’s frequency. At 100 Hz, the wave length is about 3.4m and the size of the blade is comparatively small. As a result, in the calculation of the electromagnetic noise component it may be assumed that acoustic directivity at100 Hz is negligible.4 Sound field analysis of rotating blade.

　　4.1 Modeling

　　To analyze vibration response, we created a mesh model of a blade. The natural frequencies and modes of the mesh model were determined by using the program MSC/NASTRAN. At the same time, experimental modal analysis of the blade was performed. Table 2 lists the measured and calculated natural frequency values for five different vibration modes. For each mode the measured and calculated values were in agreement.

　　Figure 6 shows examples of measured and FEM calculated vibration modes; agreement between the two was obtained in this case as well. As a result, we can conclude that the thin blade was modeled sufficiently well using the mesh model.

　　4.2 Vibration response

　　Acceleration response of the blade excited by the motor torque pulsation was determined by using the mesh model. Only the 100 Hz frequency component, at which the fundamental component of torque pulsation occurs, was used in this calculation. The fundamental component of torque pulsation can be calculated by using an equivalent electric circuit analysis .

　　Figure 7 shows both the calculated and experimentally measured vibration responses. The horizontal axis shows the points along the blade length at which vibration response was measured. The solid line and solid circles are measured accelerations, and the gray line is the equivalent calculated values. It is clear that both lines match well from beginning to end.

　　4.3 Sound field analysis.

　　In the experimental measurement of electromagnetic noise, the measured value consists of the sound radiated from the rotating blades and the motor. As the four bladed fan is symmetrical about the rotating axis, the sound radiated from each blade is canceled at its rotating center. To measure only the sound from the motor, we measured sound on the rotating center (R=0 mm).

　　We used Eq.(2) to analyze the sound field caused by sound radiated from the thin blades excited by the torque pulsation. In this analysis, we used previously obtained data of the vibration response of blades excited by torque pulsation and the experimentally measured sound of a motor.

　　Figure 8 shows the calculated and measured time wave form of the electromagnetic noise at evaluated radiuses of 0, 200 and 300 mm. As can be seen in this figure, the closer the evaluated point is to the rotating center, the larger is the influence of the electromagnetic noise of the motor. Put the other way, the farther the evaluated point is from the rotating center, the larger is the influence of noise radiated from the rotating blades. These results show that there is a beat of time wave form caused by the blades’ rotation when the measurement radius was increased from 0 mm to 200 mm to 300 mm. The calculation results are in good agreement with the measured values and their character.

　　Figure 9 shows both the calculated and measured sound pressure level (SPL) of the electromagnetic noise. The horizontal axis shows the radius from the rotating center of the four-bladed fan, shown schematically under the graph. The solid circles are measured SPL, and the solid line is the calculated values of SPL. Additionally, the blade acceleration amplitude is represented a slight or dark, where dark means low acceleration.

　　The acceleration amplitude was reflected in the SPL at each evaluated point as shown in this figure. It is clear that both dots and line match well from beginning to end. Therefore, we can conclude that calculating the torque pulsation using the equivalent circuit allows us to accurately determine the electromagnetic noise of the rotating blade.

　　5 Conclusion

　　We developed a method for calculating the electromagnetic noise of a rotating thin blade fan driven by an electric motor. With this method, we successfully obtained the vibration response of a thin blade excited by torque pulsation. The calculated electromagnetic noise values of a rotating blade fan agreed well with experimentally measured ones.