Assessing the vibro-acoustic radiation characteristics of a compact consumer appliance

Transcription

1 Assessing the vibro-acoustic radiation characteristics of a compact consumer appliance Daniel TAYLOR 1 and John LAMB 2 Dyson Ltd, Malmesbury, England ABSTRACT Customer acceptance and regulatory requirements require manufacturers to develop quieter, more pleasant sounding consumer appliances. In developing and deploying noise mitigation strategies, it is important to understand the transfer functions from a source of noise or vibration to the external environment. This study looks to investigate the low frequency vibro-acoustic transfer function of a curved shell, loaded with a spatially varying forced vibration. To better understand the vibro-acoustics of the compact system of sub-wavelength dimensions, the radiation characteristics of the curved shell under vibration loading is investigated. By then correlating the average surface velocity of the curved shell with far field acoustic measurements the vibro-acoustic characteristics can be obtained. This is then compared to a three dimensional scan performed with a pressure/velocity (PU) intensity probe to interrogate the developing sound field at different distances. Keywords: vibro-acoustics, radiation efficiency, consumer appliance 1. INTRODUCTION The drive from consumers and regulatory bodies for quieter domestic appliances as well as the general trend towards compact, lightweight construction, presents challenges for noise control engineering. To inform the correct engineering decisions it is becoming increasingly important for the structural vibration and radiation characteristics of a realistic geometry to be understood at the design stage, to aid in the reduction of radiated noise. Although prototypes provide a platform upon which accurate measurements can be performed the further these components diverge from classical problems (e.g. baffled plates), the less intuitive they become to understand. This can be particularly problematic when rapid development cycles require time efficient measurement procedures that are still sufficiently accurate to direct the design process. For example, without performing in-depth analysis it is difficult to know in advance where best to perform a coarse set of vibration measurements in order to obtain representative vibration profiles. In this regard, the radiation efficiency is a useful construct to collapse the effects of spatially varying vibration profiles and modal behaviour into a single correction factor for a compact source model. One limitation of this approach is that a radiation efficiency is specific to a single operating point of the machinery under test. As a result it cannot be applied generally to different operating points of the device, especially if the vibration profile varies strongly between these operating conditions. Obtaining analytic expressions for the radiation efficiency of classical structures such as baffled, flat plates has been studied in depth [1 3]. Work has also been conducted on curved shells to obtain suitable approximations for the radiation efficiency of these structures. This work has mainly been focused on applications in aerospace where the radius of curvature is large compared to the dimensions of the panel under consideration [4 7]. For more complex geometries the radiation efficiency must usually be determined experimentally. The ISO standard ISO 7849:2 [8] provides guidelines for determining the radiation efficiency (radiation factor) experimentally as well 1 Daniel.Taylor@dyson.com 2 John.Lamb@dyson.com 7513

2 as outlining procedures for using it to estimate the radiated sound power level from a coarse set of vibration measurements. Revel and Rossi [9] proposed an approach for predicting the pressure field at a given position which involves a linear superposition of small radiating elements distributed over the surface of the enclosure. As this method accounts for spatial variations in the velocity profile over the radiating surface, it offers a more generally applicable technique. Acquiring the data with sufficient resolution can be a time consuming process. In their work Revel and Rossi compared the superposition method to the ISO 7849:2 standard approach and found that they agreed well for a simplistic test case. In this work the ISO 7849:2 standard approach and the piecewise linear summation approach are compared in their ability to predict the sound power radiated from the compact curved shell of a Dyson vacuum cleaner head. During operation the beater bar within the cleaner head (Figure 1) is subjected to high levels of spatially varying vibration as a result of the interaction of the beater bar s bristles with the floor. This vibration excites the compact curved shell of the cleaner head assembly through the mounting points and is subsequently radiated as low frequency sound. As the enclosure dimensions are smaller than the acoustic wavelength in air, simple transfer function expressions such as the compact source model [10] with a suitable radiation efficiency term should provide reasonable engineering approximations. However, the strongly varying spatial vibration response may make this approach sensitive to measurement position. Figure 1: Typical Dyson cleaner head with beater bar. A pressure/velocity PU intensity probe was used to measure the intensity field radiated by the curved shell. The visualization provides qualitative insight to the developing sound field. In Section 2 the experimental procedure for obtaining the high resolution laser Doppler vibrometry scan required for the linear patch summation method is discussed along with the methodology for measuring the acoustic response of the system. The methodologies used to determine the linear summation method and the radiation efficiency are presented in Sections 3 and 4 respectively. The accuracy of these methods are compared in Section 5 along with a brief investigation into the sensitivity of the ISO standard approach with respect to measurement position. The results for the intensity scan are also presented followed by a discussion of the accuracy of the two methods. 2. EXPERIMENTAL PROCEDURE The experimental procedures used to capture the vibration of the light weight curved shell using a laser Doppler vibrometer is described in this section, as well as the configuration used in the hemi-anechoic chamber to accurately capture the radiating sound field of the appliance. 2.1 Laser Doppler-vibrometry To replicate the intended operating conditions of the appliance, the system was placed on carpet and air flow introduced by a slave vacuum pump to generate the equivalent suction force. Power was supplied to the beater bar motor to provide the in-use vibration loading. A photograph of the experimental configuration is shown in Figure 2. To determine an appropriate spatial sampling frequency, the expression for the transverse wavelength on a flat plate [11] was used to calculate an approximate value for the bending wavelength at the 7514

3 Figure 2: The vibration measurement setup. highest frequency of interest, fmax = 1000 Hz, λb,max = 1 fmax s 4 Bω 2, m (1) where B is the bending stiffness of the material and m the mass per unit area of the casing. Using the material parameters of the shell, a wavelength (λb,max ) of 70 mm was calculated. A spatial sampling rate of 20 mm was deemed adequate to capture at least three measurements per wavelength of the highest frequency of interest. Following this, the surfaces of the enclosure were discretised into 159 measurement points. The vibration of the shell was captured using a Polytech 100 portable digital vibrometer [12]. The rig was mounted onto an X-Y traverse system which was used to accurately position the LDV over the surface of the curved shell. Normal incidence of the laser with the surface of the enclosure was achieved using an adjustable angled mount and measurements were captured for each of the 159 positions. The error in positioning the vibrometer was less than ±2 mm. An accelerometer was placed on the upper surface of the shell to provide a phase reference. Data acquisition was performed using National Instruments hardware and a Labview measurement framework. 2.2 Acoustic testing The experimental configuration as shown in Figure 2 was transferred to a hemi-anechoic chamber to acquire the acoustic response of the system. The acoustic response of the system could not be measured simultaneously with the laser vibrometry scan as the X-Y traverse system was not portable and could not be located within the hemi-anechoic facility. A 10 microphone setup on a 2 m hemisphere was used to determine the sound power level of the system in accordance with IEC [13]. Experimental determination of the radiation efficiency requires the measured sound power to be a function solely of the forced vibration of the structure. Contamination from airborne noise sources, such as aero-acoustic noise or that produced by a motor would reduce the accuracy of the derived radiation efficiency and limit its efficacy as a predictive tool. It is therefore paramount that all efforts are made to isolate the structure borne noise from the airborne sources during testing. To minimize unwanted noise, the slave vacuum was situated outside of the chamber and an inlet silencer used to reduce the airborne noise in the airflow. 7515

4 While the airflow through the cleaner head generates noise, at low frequencies the predominant source of noise is due to the vibro-acoustic response of the enclosure. With the airflow on, acoustic measurements were made with and without the beater bar running. Figure 3 presents the sound power level in Constant Percentage Bandwidth (CPB) for these two cases. With the beater bar engaged, the sound power level is >10 db above that for the flow noise over much of the frequency range of interest. The airflow noise therefore contributes a negligible amount to the total sound power of the system at lower frequencies, however above 600 Hz its contribution increases. Figure 3: Comparison of CPB for the beater bar on and off. 3. LINEAR SUMMATION METHOD As shown by Revel and Rossi [9], sound pressure level estimates of the sound radiated by a vibrating source can be obtained through discretization of the vibrating surface and treating each patch or element as an independent radiator. The sound field at a given position may be calculated by performing a linear superposition over each of these independent sources. Although similar to a boundary element approach, the transfer function from each patch to the field position does not satisfy the true boundary conditions of the enclosure. Therefore diffraction and shadowing by parts of the structure are not taken into account. The consequence is that in general, unlike a boundary element approach, as the patch size becomes infinitesimal the result will not converge to an exact solution. Using the naming system defined in Figure 4 the sound pressure level at a given position may be estimated by calculating the linear summation SP L mic,n = jρ ock 2π I i=1 S i V i,rms e j( k r i,n φ i ), (2) r i,n where V i,rms is the RMS velocity magnitude at each discrete patch, k is the wavenumber in air, φ i is the relative phase, I is the total number of elements and r i,n is the magnitude of the position vector between the i th element and the field location r i,n = ((x mic,n x i ) 2 + (y mic,n y i ) 2 + (z mic,n z i ) 2 ). (3) To replicate the acoustic sound power level measurement, the geometry of the experimental arrangement was simulated and the sound pressure level calculated at the equivalent locations of each of the 10 microphones in the hemisphere. To calculate the pressure at a single microphone position SP L mic,n the measured velocity and phase at each of the 159 LDV measurement positions was used. The measured response using the LDV at each position was assumed to be representative of the vibration response across the surface of each element and each element was given an equal area weighting S i with 159 i=1 S i = S total. No interpolation or smoothing was performed between measurement positions. 7516

5 Figure 4: Discretisation of the curved shell. 4. RADIATION EFFICIENCY The radiation efficiency of a structure provides an engineering solution to assess the radiated sound power of a system with a low resolution set of vibration data. As used in this work, the radiation efficiency matches the experimental acoustic measurements with the average surface velocity over the radiating system, condensing contributions of the modal behavior and different radiating surfaces into a frequency dependent transfer function. In the strictest sense, it is valid only when considering similar sources under identical measurement and operating conditions. However, in circumstances where changes in operating conditions are unlikely to dramatically effect the radiation characteristics of the system the radiation efficiency provides a convenient framework for coarse prediction and diagnostics. The radiation efficiency is calculated from experimental data using σ rad = W rad ρ o cs v 2, (4) where W rad is the radiated sound power of the structure, v 2 is the space averaged normal surface velocity of the structure, ρ o is the density of air, c the equilibrium speed of sound and S the radiating surface area of the structure [14]. The spatial average of the RMS velocity v 2 was calculated using all 159 measurement positions over the total surface of the shell S = S total. This quantity, along with W rad, the sound power determined from the 10 microphone hemisphere was used to calculate the radiation efficiency for the curved shell. 5. RESULTS This section outlines the initial observations from the surface vibration measurements as well as a comparison with measured SWL for the linear summation method and the radiation efficiency procedures. 5.1 Shell vibration response A MATLAB routine was used to post-process the vibration signals for each of the 159 measurement positions. Figure 5 compares the velocity magnitude for the upper curved face of the enclosure at 100, 200 and 1000 Hz. It can be seen that the response has high spatial dependence even at low frequencies. Figure 5a shows the vibration response at the lowest frequency of interest, 100 Hz. The strongest vibration can be seen at the edges of the upper surface corresponding to the mounting points of the beater bar. In Figure 5b, the uneven vibration loading is shown to introduce strong 7517

6 asymmetry into the modal response. At 1000 Hz, Figure 5c demonstrates that the complex modal response of the shell is captured. (a) 100 Hz. (b) 200 Hz. (c) 1000 Hz. Figure 5: Spatial distribution of velocity magnitude across the top surface of the curved structure at different frequencies. 5.2 Linear summation method The estimated sound power level of the linear summation approach was determined by first calculating the sound pressure level at each of the 10 simulated microphone positions. These estimates were averaged and the sound power level determined in accordance with IEC The difference in db compared to the actual measured value is shown in Table 1. The comparison between the measured and estimated sound power level in CPB is shown in Figure 6. The agreement of the total sound power level calculated between 100 and 1000 Hz is very good, although it can be seen in Figure 6 for frequencies above 600 Hz, the fit between the estimate and actual radiated sound power begins to diverge. 5.3 Radiation efficiency The radiation efficiency determined for the curved shell is shown in Figure 7, along with a quadratic curve fit to this data. From baffled plate theory, the radiation efficiency tends to unity at frequencies above the coincidence frequency. This is when the bending wave speed matches the speed of sound in air. From the known material properties of the curved shell this was approximated to be above 20 khz, well away from the frequency region of interest. The quadratic fit is in good agreement with the 20 db/decade increase expected for the subsonic bending wave regime [14]. To assess the accuracy of the approximated radiation efficiency the sound power level was calculated using the surface averaged RMS velocity for all 159 LDV measurement points and the radiation efficiency derived using the quadratic best fit. The radiated SWL predicted using the approximated radiation efficiency with the full LDV data set gives good accuracy for the measurement at <0.5 db, 7518

7 Figure 6: Comparison of sound power level prediction for the linear summation method with the measured sound power level in CPB for the curved shell. Figure 7: The calculated radiation efficiency of the curved shell. see Table 1. This demonstrates that the approximated radiation efficiency shown by the purple line on Figure 7 is a good description of the radiation characteristics. The ISO 7849:2 standard recommends that for sound power level estimation at least 10 measurement positions are used for applications where the surface area is <1 m 2. A subset of 10 evenly distributed measurement points i.e every 16 th element, was selected from the 159 LDV measurements. This was used to generate a new surface averaged vibration magnitude from which a sound power level calculation could be performed. The predicted sound power level in CPB, made using this measurement subset and the approximated radiation efficiency is shown in Figure 8 alongside the measured data. The difference between the measured and predicted total sound power level integrated over 100 to 1000 Hz is shown in Table 1, showing good agreement. Table 1: Comparison between the measured SWL, and two prediction methods. Method Predicted SWL ( db) Linear summation -1.1 Radiation efficiency (σ rad,approx ), with 159 points +0.3 Radiation efficiency (σ rad,approx ), with 10 points

8 Figure 8: Comparison between the predicted result using the ISO 7849:2 procedure with the quadratic fit radiation efficiency and the measured SWL. A subset of 10 evenly distibuted measurements from the 159 LDV data set was used to provide a surface averaged velocity profile Sensitivity to measurement position As shown in Section 5.1 the vibration profile of the enclosure is spatially dependent. The ISO standard suggests that the number of vibration measurements should increase until the surface averaged velocity profile v 2 converges. It is not always possible to evaluate v 2 during a measurement session so it is of interest to evaluate the sensitivity of the approach to the measurement position when using a reduced data set. To evaluate the sensitivity as a function of measurement position the sound power level was calculated using a subset of 10 measurements selected randomly from the 159 LDV data points. This process was first performed for the exact radiation efficiency calculated with all 159 LDV data points and the 10 randomly selected measurements, see Figure 9 (red marker). This was also undertaken with the 10 random measurement subset using the approximated radiation efficiency (purple markers). Figure 9 presents the mean and spread of the 10 repeats using each procedure. The sound power level calculation can be seen to be more accurate when using the approximated radiation efficiency when a reduced measurement set is selected, however both efficiency terms provide very reasonable predictions. Extending the sensitivity investigation further, the number of data points in each subset was reduced to 5 and 3 and the approximated radiation efficiency was used in the calculation. Reducing the number of data points increases the average error and spread of results, although the predictions remain suitably accurate even with 3 data points, for many engineering applications. 6. INTENSITY FIELD SCAN A PU intensity probe was used to measure the intensity field around the shell up to a radius of 0.5 m from the structure. The resulting visualisation allows a qualitative analysis of the developing sound field to be made. Contour plots of the intensity fields at 100, 200 and 1000 Hz are shown in Figure 10. In all three cases strong asymmetry is observed close to the shell, however as the sound field develops the intensity begins to homogenise. 7520

9 Figure 9: Sensitivity study results using randomly sampled elements. The impact of using the measured radiation efficiency and the approximated radiation efficiency is shown. (a) 100 Hz. (b) 200 Hz. (c) 1000 Hz. Figure 10: Sound intensity scan of the developing sound field at different frequencies. 7. DISCUSSION Both the linear summation method and the radiation efficiency approach were able to provide very good estimates of the sound power despite a spatial vibration profile that varied strongly across the surface of the shell. The patch summation method provided a very good agreement in terms of total sound power level and reasonable agreement in certain CPB center frequency bands. As the vibration data was recorded during a separate session to the acoustic measurement, it is possible that some of the differences might be as a result of variations in the operating conditions during the two experiments. Figure 6 shows that the agreement between the prediction and measurement diverges for frequencies above 600 Hz. Referring to Figure 3 the aero-acoustic noise due to flow through the structure was seen to contribute increasingly to the SWL in this frequency region which may account for this discrepancy. The radiation efficiency appears to provide a robust and accurate method to predict the sound 7521

10 power level from a coarse set of measurements. The 10 measurement positions recommended by the ISO standard appears to provide suitable resolution. If a greater trade off in accuracy is acceptable, reasonable agreement can be achieved with even lower sample sizes, however the sensitivity with respect to the choice of measurement position increases. The radiation efficiency shown in Figure 7 is highly oscillatory, this suggests that this quantity would be sensitive to changes in the system. One would expect that the implicitly smooth gradient of the quadratic fit, while less accurate in specific cases, would offer a more robust quantity for general use. The intensity field visualisation highlights that the vibration profile results in an asymmetrical sound intensity in the near field, however this does not persist strongly into the far field. Qualitatively this helps to explain why the two methods provide similarly accurate predictions. For a compact enclosure with sub-wavelength dimensions the spatial dependence of the vibration profile does not translate into the far field. The simple compact source transfer function is therefore a good description of the far field pressure. 8. CONCLUSIONS Two methods for determining the sound power level from vibration measurements were compared for a compact curved shell with high levels of spatial variation in the vibration profile. Both the linear superposition method and the ISO 7849:2 standard approach were found to provide accurate sound power level estimates. Approximating the radiation efficiency to provide a function with smooth frequency variation was shown to be more robust to choice of measurement position than the exact expression. It is reasonable to assume that approximated radiation efficiency terms that vary smoothly with frequency will be more generally applicable when system operating conditions vary, however more work would be needed to validate this. The linear superposition method takes the spatial variation of the vibration profile into account. The prediction made using this approach was accurate, providing a closer match across the frequency range, however the data collection and post processing requirements are more intensive than the radiation efficiency approach. An intensity probe was used to measure and visualise the intensity field radiated by the vibrating curved shell. As the radiating structure is much smaller than the acoustic wavelengths of interest in air, the spatial dependence of the vibration profile does not persist into the far field. 7522

11 REFERENCES [1] C. Wallace. Radiation resistance of a rectangular panel. Journal of the Acoustical Society of America, 51(946), [2] G. Squicciarini, D. J. Thompson, and R. Corradi. The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates. Journal of Sound and Vibration, 333(17): , [3] A. Putra and D. J. Thompson. Sound radiation from perforated plates. Journal of Sound and Vibration, 329(20): , [4] G. Maidanik. Radiation Properties of Cylindrical Shells. Journal of the Acoustical Society of America, 36(1691), [5] W. Graham. The Influence of curvature on the sound radiated by vibrating panels. Journal of the Acoustical Society of America, 98(1581), [6] J. Bevan. Piezoceramic actuator placement for acoustics control of panels. NASA technical report, [7] B. Liu. Acoustical characteristics of aircraft panels. Doctoral Thesis, Marcus Wallenberg Laboratory, [8] DD ISO/TS :2009. Acoustics- determination of airborne sound power levels emitted by machinery using vibration measurement - Part 2: Engingeeing method including the determination of the adequate radiation factor. ISO Standard, [9] G. Revel and G. Rossi. Sound power estimation by laser doppler vibration measuement techniques. Journal of Shock and Vibration, 5(5/6): , [10] L. Kinsler et al. Fundamentals of Acoustics. Wiley, [11] F. Fahy and P. Gardonio. Sound and Structural Vibration. Elsevier, [12] Polytech 100 laser Doppler Vibrometer [13] IEC Household and similar electrical appliances - Test code for the determination of airborne acoustical noise - Part 2-1: Particular requirements for vacuum cleaners. IEC Standard, [14] L. Beranek. Noise and Vibration Control. McGraw - Hill,