曾群：风扇噪音分析

风扇噪音分析

 曾群

Analysis of motor-driven thinblade 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 generatedwhen a rotating blade is excited by the torque pulsation of a motor. The soundpressure values calculated by the new method for a rotating blade were found tocorrespond well with experimentally measured ones.

List of symbols
ds Reference smallarea (m²);  

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

S  Area of sound radiator (m²);
k Free field wavenumber 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 pressurelevel (Pa);            

i   Phaseof velocity at ith node (rad);        q  Angleof sound radiator (rad);         

q   Mass density (kg/m³);                  R  Observedradius (m);                 

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

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

 

1Introduction
Amethod for predicting the electromagnetic noise of a thin blade fan driven byan electric motor has been developed.

Electricmotors are used as actuators in various kinds of machinery. Vibrating motionsand noise in the machinery arise when the excitation forces of electric motorsact on elastic parts of machinery. For instance, an air conditioner has a fanstructure attached to the motor shaft. The thin blade fan vibrates and radiateselectromagnetic noise when the torque pulsation acts on the rotating blades.

Anumber of investigators have studied vibration and noise caused by motors. Herewe propose a new noise calculation method for rotating blades that are excitedby the torque pulsation of a capacitor motor. The calculation method iscomposed of two main modules, one for analyzing the vibration response of theblades, and one for calculating the electromagnetic noise of a rotating blade.

Inthe analyzing module, the vibration response of a rotating thin blade isanalyzed using both torque pulsation and the mesh model of the blade. Tocalculate the motor’s torque pulsation, we employed an equivalent electriccircuit corresponding to the motor. The calculated torque pulsation was used toobtain the vibration response. In measuring the vibration response at variouspoints along the length of the rotating blade, we found that the calculationand experimental results agreed well for each point.
This calculation module for electromagnetic noise calculates the sound fieldcaused by sound radiated from the rotating blade excited by the torquepulsation of the motor. It was found that the sound pressure values calculatedby the new calculation method for a rotating blade corresponded well withexperimentally measured ones.

 

2Experimental device
2.1Specifications of experimental device. The motor referred to in this paper is acapacitor motor with the specifications shown in Table 1. The main part of thetesting system, shown schematically in Fig. 1, primarily consists of a motor, afour-bladed fan, and a high-stiffness block. The high-stiffness block is asteel block 220x220x220 mm in size and 83 kg in mass; its natural frequency is6.7 kHz. A foam rubber was inserted under the block to prevent vibration fromthe floor from being transmitted to the motor and blades. The four-bladed fanwas attached to the motor shaft. Each blade is an aluminum plate 300x80x3 mm insize. The motor rotates at a slow speed of 210 rpm because of the airresistance of this large fan. An accelerometer and slip ring were used to measurethe vibration response of a rotating blade.

2.2Measurement device for radiated noise
The system for measuring the sound pressure, shown schematically in Fig. 2, wasset up in a semi-anechoic chamber. The blade rotates at a distance of 645 mm.

 

Table1 Motor specifications

 

-------------------------------------------------------
Motortype             Capacitor motor
Ratedpower            140 W
Power supply frequency    50 Hz
Power supply voltage      AC 150 V
Capacitor              8 l F
Pole                   6
Statorslot             24
Rotorslot             34
Rotation speed          210 rpm(four-bladed fan) 

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

Fig. 1 Experimental device

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

 

Figure3 shows the frequency response of the sound pressure produced by the testingsystem. In this figure, the microphone is set up at a radius of 200 mm from therotating center. Many frequency components are shown in this figure, with theblade passage frequency causing a peak frequency component at 14 Hz. The peakfrequency components at 100 Hz and 200 Hz are the result of electromagneticnoise caused by torque pulsation.

 

 

3Calculation method for radiated noise
3.1Basic formula
Figure 4 shows the analytical model of radiated sound. The sound pressure p ofa field point P caused by sound radiated from a plane radiator with area S andvelocity distribution V(x, y) in an infinite baffle wall can be evaluated withthe following equation.

 

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

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

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

 

 

where, vi= theamplitude of the velocity at the ith node/i= the phase of the velocity at theith nodeq= angle of plane radiator. The vibration response vi and its phase /iof the rotating blade can be calculated by using the finite-element method(FEM).The directivity factor can be calculated by both the size of soundradiator and the point source’s frequency. At 100 Hz, the wave length is about3.4m and the size of the blade is comparatively small. As a result, in thecalculation of the electromagnetic noise component it may be assumed that acousticdirectivity 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 naturalfrequencies and modes of the mesh model were determined by using the programMSC/NASTRAN. At the same time, experimental modal analysis of the blade wasperformed. Table 2 lists the measured and calculated natural frequency valuesfor five different vibration modes. For each mode the measured and calculatedvalues were in agreement.

 

Figure6 shows examples of measured and FEM calculated vibration modes; agreementbetween the two was obtained in this case as well. As a result, we can concludethat the thin blade was modeled sufficiently well using the mesh model.

 

4.2Vibration response

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

Figure 7 shows boththe calculated and experimentally measured vibration responses. The horizontalaxis shows the points along the blade length at which vibration response wasmeasured. The solid line and solid circles are measured accelerations, and thegray line is the equivalent calculated values. It is clear that both linesmatch well from beginning to end.

4.3Sound field analysis.

Inthe experimental measurement of electromagnetic noise, the measured valueconsists of the sound radiated from the rotating blades and the motor. As thefour bladed fan is symmetrical about the rotating axis, the sound radiated fromeach blade is canceled at its rotating center. To measure only the sound fromthe motor, we measured sound on the rotating center (R=0 mm).      

Weused Eq.(2) to analyze the sound field caused by sound radiated from the thinblades excited by the torque pulsation. In this analysis, we used previouslyobtained data of the vibration response of blades excited by torque pulsationand the experimentally measured sound of a motor.
Figure 8 shows the calculated and measured time wave form of theelectromagnetic noise at evaluated radiuses of 0, 200 and 300 mm. As can beseen 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 theother way, the farther the evaluated point is from the rotating center, thelarger is the influence of noise radiated from the rotating blades. Theseresults 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 300mm. The calculation results are in good agreement with the measured values andtheir character.

Figure9 shows both the calculated and measured sound pressure level (SPL) of theelectromagnetic noise. The horizontal axis shows the radius from the rotatingcenter of the four-bladed fan, shown schematically under the graph. The solidcircles 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.

Theacceleration amplitude was reflected in the SPL at each evaluated point asshown in this figure. It is clear that both dots and line match well frombeginning to end. Therefore, we can conclude that calculating the torquepulsation using the equivalent circuit allows us to accurately determine theelectromagnetic noise of the rotating blade.

 

5Conclusion
Wedeveloped a method for calculating the electromagnetic noise of a rotating thinblade fan driven by an electric motor. With this method, we successfully obtainedthe vibration response of a thin blade excited by torque pulsation. Thecalculated electromagnetic noise values of a rotating blade fan agreed wellwith experimentally measured ones.

 

 

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