Analysis of acoustic characteristics according to design parameter of diaphragm

Journal of Materials Processing Technology 187–188 (2007) 442–446

Analysis of acoustic characteristics according to design parameter of diaphragm J.H. Kwon, S.M. Hwang ∗ Department of Mechanical Engineering, Pusan National University, Jangjun-dong San 30, Busan 609-735, Republic of Korea

Abstract The recent cellular phones provide various functions such as satellite TV receiver, motion picture player and MP3 player. For these multimedia effects, the acoustic quality through the microspeaker is important. Thus, the functions of microspeakers are included in the preference index of the cellular phones and more powerful and high-performance microspeakers are required. A typical microspeaker is composed of magnetic circuit, voice coil, and diaphragm. Among these components, diaphragm is closely related to acoustic characteristics. Acoustic performance of the microspeaker is evaluated by frequency range and sound pressure level (SPL). In case of microspeakers, it is hard to have good performance in lower frequency region due to size. The microspeaker whose first resonance is low can make high SPL in lower frequency region. Also, SPL in higher frequency region is hardly affected by the first resonance. Therefore, in this paper, the first resonance frequency is optimized in order to investigate acoustic performance in lower frequency region as the design parameters of diaphragm are varied. A performance evaluation for each setting of parameters is simulated using finite element method (FEM). The simulated result of the proposed analysis is also compared with the experimental. © 2006 Elsevier B.V. All rights reserved. Keywords: Microspeaker; Diaphragm; SPL; First resonance frequency

1. Introduction With the growth in electronics, the remarkable advance in wireless communication technology and mobile devices such as mobile phones and PDAs, functional performance of these devices are incessantly improved. Lighter weight and smaller size has been gradually accomplished by recent circuit integration technology resulting in rapid growth in the number of mobile phone subscribers. Driven by customer demand, recent mobile devices are fully capable of realizing a variety of dazzling multimedia effects powered by electro-acoustic parts that have become one of the generic components. However, size effect on performance of such parts with mechanical and acoustical characteristics has been considered to be a bottleneck in size reduction of mobile devices. Considering the size effect, it can be quite predictable that electro-acoustic parts such as microspeaker and dynamic receiver are intrinsically hard to achieve high sound pressure level within limited volume, thus there needs a high-performance microspeaker of broad band capacity. In this paper, for the performance improvement, a complete

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Corresponding author. Tel.: +82 51 510 2468; fax: +82 51 582 3104. E-mail address: [email protected] (S.M. Hwang).

0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.11.139

analysis of a microspeaker considering mechanical, electrical and magnetic coupling effects was performed using FEM and its validity was confirmed as well by experiments. Through electromagnetic field analysis, two-dimensional (2D) FEM model was implemented to calculate electromagnetic force that excites diaphragm. For the prediction of acoustic characteristics of diaphragm, free and forced vibration analysis considering coupling effect was performed and confirmed by experiments. Generally, acoustic performance of the microspeaker is evaluated by frequency range and SPL. In case of microspeakers, it is hard to have good performance at lower frequency region due to size. Therefore, the frequency range of microspeaker is limited by the first resonance. In this paper, seven design parameters of diaphragm are selected in order to analyze sensitivity to the first resonance. For previous research, most work in electro-acoustic devices is concerned with high-performance loudspeakers, which are typically driven beyond their linear output range [1,2]. 2. Operating principle Microspeaker is a transducer which converts electrical energy into mechanical energy. There are several ways to accomplish the transformation from electron motion to air motion such as

J.H. Kwon, S.M. Hwang / Journal of Materials Processing Technology 187–188 (2007) 442–446

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Fig. 1. Schematic of dynamic microspeaker.

electrostatic, plasma, ionic, and Corona Wind. The most successful types, however, are dynamic and electrostatic. Dynamic microspeakers function by utilizing the interaction of a varying electromagnetic field, generated in the voice coil and a fixed magnetic field provided by a permanent magnet. As electric current from the amplifier passes through the voice coil, a similarly changing electromagnetic field is projected by the voice coil, expanding and contracting as the signal varies. This evanescent magnetic field pushes and pulls against the fixed magnetic field of the speaker magnet, repelling and attracting the diaphragm in like fashion, thus making vibrations in the air which we hear as sound. Fig. 1 shows a schematic of dynamic microspeaker. 3. Method of analysis 3.1. Electromagnetic system Magnetic circuit of microspeaker consists of top plate, permanent magnet, yoke, and voice coil. For the magnetic field analysis, a 2D FEM model can be implemented utilizing Maxwell’s equations with axisymmetric boundary conditions. Voice coil current can be also determined by solving voltage equation of the equivalent circuit as in Eq. (1), where V, R, I and L denote applied voltage, coil resistance, coil current and inductance, respectively. The voice coil motion generates the back electro motive force (BEMF), Bl(z)˙z, where l, z and z˙ are the voice coil length, the voice coil displacement and velocity. The magnetic exciting force resulting from the interaction between the magnetic field and the total electric currents can be expressed as in Eq. (2). Fig. 2 shows flux line and flux density analyzed by FEM: V = IR + L

 Fcoil =

dI + Bl(z)˙z, dt

Idl × B .

where f, ρ, c, S and σ rad are the frequency of vibration, density of the air, the velocity of the propagation of sound in air, area of the diaphragm surface contributing to sound radiation and the radiation efficiency, respectively. The sound radiation efficiency is calculated by a simplified equation, in which the diaphragm is considered as a monopole source, and is given as in Eq. (5) [3]: (kr)2

(1)

σrad (f ) =

(2)

where k (=2πf/c) is the wave number and r is the diaphragm radius. The sound pressure level at distance d from the source can be expressed as in Eq. (6):

The mechanical model of the vibrating diaphragm including voice coil can also be developed using FEM. Displacement and surface velocity of the diaphragm can be obtained by solving mechanical vibration equation as in Eq. (3), where [M], [C], [K] and {Fcoil (t)} denote mass matrix, damping coefficient matrix, stiffness coefficient matrix and magnetic exciting forces acting on voice coil, respectively:

(5)

1 + (kr)2

Lp = 10 log

3.2. Mechanical system

[M]{¨z} + [C]{˙z} + [K]{z} = {Fcoil (t)}.

Fig. 2. Flux line and magnetic force: (a) flux line of the microspeaker; (b) magnetic force of microspeaker.

Wrad + 20 log W0

d d0

+8

The normalized value for d0 is 1 m. Fig. 3 shows mode shapes of diaphragm.

(3)

For an acoustical analysis, the sound power radiated by a microspeaker vibrating in a mean rms surface with the spatial velocity of V0 (f)2, can be calculated as in Eq. (4): Wrad = ρcσrad (f )sV0 (f )2 

(4)

(6)

Fig. 3. Mode shapes of diaphragm: (a) first; (b) second; (c) third.

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Fig. 4. Design parameters of diaphragm.

4. Optimization The first resonance frequency has important meaning for acoustic characteristics. In this paper, design parameter is determined to minimize first resonance frequency using response surface methodology. Generally, RSM consists of three steps [4]. First, a series of experiments, i.e., designs of experiments (DOE), are performed in order to gather adequate and reliable measurements of the identified responses. Then, a mathematical model that best fits the data collected from the execution of DOE is determined. By testing several hypotheses concerning the model’s parameters, the fitting accuracy of the model will be analyzed. Finally, the maximum (or minimum) value of the identified responses will be determined. In this paper, the objective function of RSM is the first resonance frequency of diaphragm. A quadratic approximation model is commonly used to construct the fitted response surface. In general, the response model

Fig. 5. Main effect of first resonance frequency.

can be written as y = β0 +

2  i−1

βi xi +

2  i−1

γi xi2 +

2  

bij xi xj + ε

(7)

i
where bi , gi , bij are coefficients for the control variables and ε is a random error. Instead of the 3 k full factorial experiment scheme, the central composite design (CCD) is applied to construct the experiments. CCD usually consist of three distinct portions: (1) a complete 2k or fractional 2k-m (when k ≥ 5) first-order factorial design in which the factor levels are coed into usual −1 and +1 values; (2) axial points or “star” points, the points on the axis of each design variable at a distance α from the design center, such as

Fig. 6. Surface plot of first resonance frequency: (a) by H3 and D1; (b) by H2 and D1; (c) by H2 and H3.

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(±α, 0, 0, . . ., 0), (0, ±α, 0, . . ., 0), . . ., (0, 0, 0, . . ., ±α). For a rotatable CCD, the value of α is chosen as, where k denotes the number of factorial points in the design; (3) one or more center points. Seven parameters are selected in order to analysis sensitivity as in Fig. 4. Designs of experiments are performed. Experiments are simulated using finite element (FE) analysis in each trial. In Fig. 5 the design parameters H2, H3 and D1 are the key control variables, which are the main influences on the first resonance frequency. The first resonance frequency is optimized in order to investigate acoustic performance at lower frequency range as the design parameters H2, H3 and D1 are varied. A performance evaluation for each setting of parameters is simulated. One alternative is to build polynomial approximation models for the functional relationships between the performance characteristics and the design variables using RSM. The first-order model is used in Fig. 5. Fig. 6 shows the response surfaces of H2, H3 and D1. The second-order model is used in Fig. 6. Using the experimental response values along with the setting of the coded variables, the fitted second-order model is

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Table 1 Condition of forming process Mctsrid Thickness Temperature Pressure Time

Polyetherimide 30 ␮m 210 ◦ C 14.7 N/m2 10 s

y = 1861.55 − 46.57x1 + 148.952x2 − 81.027x3 − 42.5411x12 − 72.8411x22 − 760x32 + 106.66x1 x2 + 2.5525x1 x2 − 13.665x3 x1

(8)

To minimize first resonance frequency, parameters H2, H3 and D1 are 0.2, 0.3 and 8 mm, respectively. 5. Manufacture of diaphragm Fig. 7 shows a schematic of diaphragm manufacturing process. The Diaphragm is formed at high temperature and pressure. The process conditions such as temperature, pressure and time vary according to the material of diaphragm film.

Fig. 8. Experimental setup and SPL: (a) experimental setup; (b) SPL.

Table 1 shows forming condition of polyetherimide. The polyetherimide film on cast at 210 ◦ C is deformed into the exact shape of diaphragm by high pressure. Fig. 8(a) shows the schematic of an experimental setup to measure SPL of the microspeaker. Fig. 8(b) is a graph simulated and experimental SPL. Simulated results match well with the experimental results. Some discrepancy at higher frequency regions results from the complicated acoustic impedance characteristics of the surface hole of the microspeakers. Noting that the frequency range of 500 Hz to 4 kHz in SPL characteristics is the most important range in mobile phones, the proposed analysis is good enough to predict the performance of the microspeakers. 6. Conclusion

Fig. 7. Schematic of diaphragm forming process and cast: (a) diaphragm forming process; (b) diaphragm cast.

To meet the customer demand in multimedia era, microspeakers in mobile phones need to be smaller with better performances, such as higher SPL and broader frequency range. This paper analyzes microspeakers considering electromagnetic, mechanical, acoustical and their coupling effects. The shape of diaphragm for broadband microspeaker is designed

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using RSM to lower the first resonance. Simulated results match well with the experimental results. Acknowledgements This work was supported by the Ministry of Education and Human Resources Development (MOE), the Ministry of Commerce, Industry and Energy (MOCIE) and the Ministry of Labor (MOLAB) through the fostering project of the IndustrialAcademic Cooperation Centered University (MES-08).

References [1] M. Rausch, et al., Optimization of electrodynamic loudspeaker-design parameters by using a numerical calculation scheme, Acoustica 85 (1999) 412–419. [2] D.J. Murphy, Axisymmetric model of a moving-coil loudspeaker, J. Audio Eng. Soc. 41 (1993) 679–690. [3] L.E. Kinsler, Fundamentals of Acoustics, Wiley, New York, 1982. [4] A.I. Khuri, J.A. cornell, Response Surface: Design and Analyzes, Marcel Dekker, New York, 1966.