Audio Engineering Society Convention Paper 5886
音频工程学会大会论文 5886

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Mark Dodd 马克-多德

Celestion Int. Ltd. Ipswich, Suffolk, United Kingdom.
Celestion Int.Ltd.英国萨福克郡伊普斯维奇。

The application of these FEM techniques to the optimisation of compression driver performance is discussed and illustrated with results. The limitations of plane-wave tube measurements are also mentioned and illustrated with FEM and measured results.
讨论了这些有限元技术在优化压缩驱动器性能方面的应用，并用结果进行了说明。此外，还提到了平面波管测量的局限性，并用有限元和测量结果进行了说明。

This paper is about the development of a compression driver, during which a variety of FEM techniques were applied to help optimise the design in respect to its acoustic, magnetic and thermal behaviour. In previous work, fully coupled vibroacoustic has been used to simulate the constant force response of a driver, and magnetostatic FEM has been used to calculate magnetic flux in the gap [1]. In more recent work transient magnetic analysis has been used to predict coil motion while taking eddy currents into account.
本文介绍的是压缩驱动器的开发过程，在此期间应用了多种有限元技术，以帮助优化声学、磁学和热学行为方面的设计。在以前的工作中，全耦合振动声学 用于模拟驱动器的恒力响应，磁静力有限元用于计算间隙中的磁通量[1]。在最近的工作中，瞬态磁分析被用于预测线圈运动，同时将涡流考虑在内。
Thermal FEM models have also been investigated but they need experimental data to give accurate results.
对热有限元模型也进行了研究，但这些模型需要实验数据才能得出准确的结果。

The ideal FEM software for loudspeaker design would provide full coupling between magnetic, structural, acoustic, and thermal FEM models together with electrical circuits. However, to the author's knowledge, such a system does not exist and
用于扬声器设计的理想有限元软件将提供磁性、结构、声学和热学有限元模型与电路之间的完全耦合。然而，就作者所知，这样的系统并不存在，而且
furthermore if it did, the full coupling would result in very long solution times making the model unwieldy.
此外，如果这样做，完全耦合将导致很长的求解时间，使模型变得臃肿。
In this paper, a new approach has been used in which a one-dimensional coupling between magnetic and vibro-acoustic FEM results has allowed the simulation of a driver response driven by a voltage source.
本文采用了一种新方法，通过磁场和振动声学有限元结果之间的一维耦合，可以模拟由电压源驱动的驱动器响应。
Thermal FEM has been applied as a separate analysis to provide qualitative results to aid material choice.
热有限元分析作为一项单独的分析，可提供定性结果，帮助选择材料。

The aim of the work described in this paper was to produce an economic compression driver with a oneinch diameter throat capable of producing maximum SPL with low distortion over an extended bandwidth.
本文所述工作的目的是生产一种经济型压缩驱动器，其喉管直径为一英寸，能够在扩展带宽内产生最大声压级和低失真。
It was also a requirement that the unit should be easy to crossover and should couple to practical horns, giving good dispersion at higher frequencies.
此外，还要求该装置易于分频，并能与实用的喇叭耦合，在较高频率下具有良好的扩散性。

The most recent versions of front loaded compression drivers use a one-inch voice coil to drive a PETP diaphragm loaded by a single slot phase-plug (Mylar and Melinex are well known trade names of PolyEthyleneTetraPhalate, PETP).
最新版本的前置式压缩驱动器使用一英寸音圈来驱动由单槽相位插头加载的 PETP 振膜（Mylar 和 Melinex 是聚四氟乙稀（PETP）的著名商品名称）。
Magnetic fluid cannot be used to aid coil cooling, however, since it damps the mechanical resonances used to extend the high frequency bandwidth, negating the thermal benefits of the fluid.
不过，磁性流体不能用于帮助线圈冷却，因为它会抑制用于扩展高频带宽的机械共振，从而抵消了流体的热效应。
Compared to conventional 'one inch' compression drivers, these drivers are very economic to manufacture, but handle relatively low power and must be used with a high crossover frequency.
与传统的 "一英寸 "压缩驱动器相比，这些驱动器的制造非常经济，但处理功率相对较低，而且必须使用高分频。

Our requirements for extended bandwidth and high maximum SPL point to the use of a larger diaphragm and voice coil.
我们对扩展带宽和高最大声压级的要求表明，需要使用更大的振膜和音圈。
Rather than extending the high frequency bandwidth by means of structural resonances, it was decided to try and keep the structure moving as a rigid body within the working range. After some initial analysis, a diameter deep drawn aluminium dome with voice coil wound directly on the dome skirt was chosen. This dome is supported by a wide elastomer suspension to allow large excursions without failure due to fatigue. This moving structure is sufficiently rigid for magnetic fluid to be added to the gap with little effect to the frequency response.
与其通过结构共振来扩展高频带宽，不如尝试在工作范围内保持结构作为刚体运动。经过初步分析，我们选择了直径为 的深拉铝球顶，音圈直接绕在球顶裙边。该球顶由 宽的弹性体悬挂架支撑，以便在大偏移时不会因疲劳而失效。这种移动结构具有足够的刚性，在间隙中加入磁性流体对频率响应的影响很小。

Unsuppressed Bessel-type cavity modes between phase-plug and diaphragm result in severe response dips; these dips are both deep and wide. The larger diameter diaphragm chosen here places both the first and second order cavity modes in our bandwidth.
相位塞和振膜之间未抑制的贝塞尔型空腔模式会导致严重的响应骤降；这些骤降既深又宽。此处选用的较大直径振膜将一阶和二阶空腔模式都置于我们的带宽内。
Suppressing these two modes requires a two-slot phase-plug [3].
要抑制这两种模式，需要使用双槽相位插件 [3]。
It is a major limitation of 'front loading' that the phase-plug must either have only a single slot or face the difficulty of having to produce an acoustic delay in one or more slots to correct the path-length differences.
前端加载 "的一个主要限制是，相位插头要么只有一个插槽，要么必须在一个或多个插槽中产生声学延迟，以校正路径长度差异。
As we shall see later in the paper, the exact shape of these slots must be chosen to produce the desired wavefront shape at the driver exit.
正如我们在本文后面将看到的，必须选择这些槽的确切形状，才能在驱动器出口处产生所需的波面形状。

Compression drivers are inevitably used with some type of horn.
压缩驱动器不可避免地要与某种类型的喇叭配合使用。
The response without a horn is of little practical value, although in the past it has been used to validate modelling results [1][2] Since both horn throat impedance and dispersion vary strongly between individual horn designs, it is common practice to use a plane-wave tube in an attempt to evaluate the driver performance loaded with an acoustic resistance.
没有号角的响应几乎没有实用价值，尽管在过去它曾被用来验证建模结果[1][2]。由于号角喉部阻抗和频散在不同的号角设计中差异很大，通常的做法是使用平面波管来评估加载声阻抗的驱动器性能。
However, while compression drivers are often intended to produce plane waves, this limits the high frequency dispersion. The new driver is designed to produce a spherical cap with a 25 degree included angle to give good dispersion in a wide variety of practical horns.
然而，虽然压缩驱动器通常旨在产生平面波，但这限制了高频的扩散。新型驱动器的设计目的是产生一个包含 25 度角的球形盖，为各种实用喇叭提供良好的扩散效果。
When coupled to a plane-wave tube, this wave-front shape will result in cross-modes being excited above the cut off frequency of the plane-wave tube.
当耦合到平面波管时，这种波面形状会导致交叉模式在平面波管的截止频率以上被激发。

However, the plane-wave tube is ideal for examining the low frequency lumped element behaviour, so we decided to investigate the limitations of this method when used with a non-planar source.
然而，平面波管是检查低频块状元素行为的理想工具，因此我们决定研究这种方法在使用非平面源时的局限性。
To this end, two FEM models were made of an infinite tube driven firstly by a planar source and secondly by a pulsating spherical source. In both cases, the source
为此，我们制作了两个有限元模型，一个是由平面源驱动的无限管，另一个是由脉动球形源驱动的无限管。在这两种情况下，源
is defined to have constant amplitude sinusoidal volume-acceleration, equivalent to applying a constant driving force with a mass load.
定义为具有恒定振幅的正弦体积加速度，相当于施加一个恒定的带质量负载的驱动力。
The modelled tube is terminated by coupling the FEM region with a series solution obtained using the separability of the Helmholtz equation in cylindrical coordinates [4]. SPL data was extracted at a node from the source as in a real plane-wave tube, and this data is shown in Figure 1. As we can see, the pulsating sphere excites modes above giving strong peaks and dips in the response curve. The wavefront shapes at are shown in Figure 3 for both source types. The plane source produces plane waves at all frequencies. The pressure distribution produced by the spherical source is a linear combination of plane waves and radial modes so has a somewhat complex shape.
通过将有限元区域与在圆柱坐标中利用亥姆霍兹方程的可分离性[4]获得的串联解耦合，模拟管被终止。在距离声源 的节点处提取声压级数据，就像在实际平面波管中一样，这些数据如图 1 所示。我们可以看到，脉动球激发了 以上的模式，在响应曲线上产生了强烈的峰值和骤降。图 3 显示了两种声源在 处的波面形状。平面源在所有频率上都产生平面波。球形声源产生的压力分布是平面波和径向模式的线性组合，因此形状有些复杂。

Figure 2. 图 2.

Shaded pressure plot of sound pressure due to a planar source radiating into an infinite tube
平面声源辐射到无限大导管所产生声压的阴影压力图

Figure 3 图 3

Shaded pressure plot of sound pressure due to a pulsating spherical source radiating into an infinite tube
脉动球形声源辐射到无限大导管所产生声压的阴影压力图

As a consequence, plane wave tube data must be treated with great caution at frequencies around and above the first cut-off.
因此，在第一截止频率上下的频率范围内，必须非常谨慎地处理平面波管数据。

Vibro-acoustic FEM gives the ability to find the pressure/velocity/displacement at any point in the model. In the frequency range of interest, axial modes of the former are not excited. Hence, it is sufficient to excite with an axial force at a particular position.
振动-声学有限元法能够求出模型中任意点的压力/速度/位移。在感兴趣的频率范围内，前者的轴向模态不会受到激励。因此，只需在特定位置施加轴向力即可。
The mechanical impedance can be determined as the ratio of the known force and the computed axial velocity. Due to the fully coupled nature of the FEM model, this mechanical impedance will include radiation and enclosure loading.
机械阻抗 可以根据已知力与计算出的轴向速度之比来确定。由于有限元模型的完全耦合性质，该机械阻抗将包括辐射和外壳负载。
The transfer function between the displacement at the above position and the SPL at the measurement point are also extracted.
此外，还提取了上述位置的位移与测量点 SPL 之间的传递函数。

The force arises from the current in the magnetic field. The current can be computed using and the force factor BL, where B is the mean radial flux and is the length of wire. The applied voltage can be computed using the blocked voice coil impedance Ze, but taking account of the back-emf due to coil motion.
力来自磁场中的电流。电流可通过 和力系数 BL 计算得出，其中 B 为平均径向磁通量， 为导线长度。外加电压可使用阻塞音圈阻抗 Ze 计算，但要考虑到音圈运动产生的反电势。
Using the linearity of the system, the results can be scaled to give a transfer function between input voltage and SPL at the measurement point.
利用系统的线性度，可对结果进行缩放，从而得出输入电压与测量点声压级之间的传递函数。

Figure 4 图 4

Block diagram of magneto-electrical-vibroacoustical-model
磁电振动声学模型框图

A parametric model of the magnet was produced using the Flux2D package CEDRAT. The model domain was axisymmetric with second order elements see Figure 5. The model boundary is defined with an 'infinite region' to avoid errors due to modelling only a small region of space [5][6].
磁体的参数模型是使用 Flux2D 软件包 CEDRAT 制作的。模型域为轴对称，采用二阶元素，见图 5。模型边界被定义为 "无限区域"，以避免由于只对一小块空间建模而产生误差[5][6]。
This software package allows the problem to be solved over a range of variables defining the geometry. With respect to plate and magnet dimensions, the optimum geometry was selected to obtain the desired static magnetic field.
该软件包允许在定义几何形状的变量范围内解决问题。根据磁板和磁铁的尺寸，选择了最佳几何形状，以获得所需的静磁场。
The field in the gap was evaluated over a line of constant radius through the centre of the coil to give B, the average flux density in the gap. The length of wire in the coil
在通过线圈中心的恒定半径线上对间隙中的磁场进行评估，得出间隙中的平均磁通密度 B。线圈中导线的长度
can then be used to calculate BL, the force factor of the coil.
然后就可以用它来计算 BL，即线圈的力系数。

Figure 5 图 5

Ring magnet structure used for static and transient analysis. Static lines of constant flux shown
用于静态和瞬态分析的环形磁体结构。所示为恒定磁通量的静态线

Having obtained the BL, the blocked coil impedance must be calculated.
获得 BL 后，必须计算阻塞线圈阻抗。
This has been achieved by using Transient Magnetic FEM with the same geometry defining the structure, but re-meshed with a suitable 'skin' of conductive elements, and with a voltage source coupled to the voice coil region [5].
这是通过使用瞬态磁场有限元模型实现的，该模型采用相同的几何形状定义结构，但使用适当的导电元件 "表皮 "重新混合，并将电压源耦合到音圈区域[5]。
After sufficient time-steps for the starting transient to settle, a steady-state waveform of current versus time may be extracted from the solution files, along with the driving voltage.
在经过足够的时间步长使起始瞬态稳定后，可从解算文件中提取电流随时间变化的稳态波形以及驱动电压。
This analysis includes the effect of eddy currents induced in the pole and the copper sleeve; these may be seen in Figure 6.
该分析包括磁极和铜套中感应的涡流效应；这些效应可参见图 6。

Figure 6 图 6

Transient magnetic FEM current density in poles and copper cap for sinusoidal input. Light indicates high current, dark indicates low current
正弦输入时，磁极和铜帽中的瞬态磁场 FEM 电流密度。浅色表示大电流，深色表示小电流

The current waveform flowing through the coil is extracted by evaluating the current through the coil at each timestep, a typical result is shown in Figure 7.
流过线圈的电流波形是通过评估每个时间步长流过线圈的电流提取的，典型结果如图 7 所示。

Figure 7 图 7

Transient Magnetic FEM output for sinusoidal input (black curve) and derived Current through voice coil (grey curve) plotted against time
正弦输入的瞬态磁场有限元输出 （黑色曲线）和通过音圈得出的电流（灰色曲线）与时间的关系图

Subsequently the voice coil's 'blocked' electrical impedance may be calculated by applying Ohm's law. The real and imaginary parts of the example coil are plotted in Figure 8 for a range of frequencies.
然后，就可以应用欧姆定律计算出音圈的 "阻塞 "电阻抗。图 8 中绘出了示例线圈在一定频率范围内的实部和虚部。
The four calculated values of blocked coil impedance shown were used to calculate SPL and driver input impedances throughout this paper.
本文通篇使用所示的四个闭锁线圈阻抗计算值来计算声压级和驱动器输入阻抗。

Figure 8 图 8

Magnitude (upper curve) and Phase (lower curve) components of voice coil electrical impedance. Solid line measured, circles modelled
音圈电阻抗的幅值（上曲线）和相位（下曲线）分量。实线为测量值，圆圈为模拟值

The new compression driver was modelled on a plane-wave tube, terminated by coupling the FEM region with the series solution, obtained using the separability of the Helmholtz equation in cylindrical coordinates.
新型压缩驱动器以平面波管为模型，通过将有限元区域与系列解耦合而终止，系列解是利用圆柱坐标中亥姆霍兹方程的可分离性而获得的。
A 2D axisymmetric model domain was used to give best computational speed for the axisymmetric structure.
采用二维轴对称模型域，以获得轴对称结构的最佳计算速度。
Quadratic elements are used for acoustic and structural regions; they require only three elements per wavelength, unlike the six required by the first order elements described in [7]. An example of the type of mesh used is shown in Figure 9.
四阶元素用于声学和结构区域；与[7]中描述的一阶元素需要六个元素不同，它们每个波长只需要三个元素。图 9 举例说明了所使用的网格类型。

Figure 9 图 9

Mesh used for Vibro-Acoustic analysis of driver on plane-wave tube
用于对平面波管上的驱动器进行振动声学分析的网格

Initial work with the model was hampered by a lack of data for the rubber suspension used. The results shown in this paper have used values of Young's modulus and loss factor adjusted to give "best fit" to measured data.
由于缺乏所用橡胶悬架的数据，该模型的初步工作受到了影响。本文中显示的结果使用了杨氏模量值和损耗因子，并根据测量数据进行了 "最佳拟合 "调整。
It was also found necessary to include volume absorption to give the correct modal damping due to the viscous properties of air between the phase-plug and the diaphragm.
此外，由于相位塞和隔膜之间空气的粘性特性，有必要加入体积吸收，以获得正确的模态阻尼。

The air-cavity in the voice coil gap and within the magnet is neglected in this model due to the presence of ferrofluid in the gap. This avoids the magnet cavity modes found in the 'generic front loaded' benchmark driver which does not use ferrofluid, see Figure 21.
由于音圈间隙中存在铁流体，该模型忽略了音圈间隙和磁体内部的气腔。这避免了不使用铁流体的 "通用前置 "基准驱动器中出现的磁体空腔模式，见图 21。

The measured and modelled frequency response of the driver on a plane-wave tube are shown in Figure 11. The electrical impedance, which may also be derived, was calculated and is shown in Figure 12.
图 11 显示了平面波管上驱动器的测量频率响应和模拟频率响应。电子阻抗也可以通过计算得出，如图 12 所示。

Figure 10 图 10

Pressure contour plot of pressure in compression driver and start of plane-wave tube at
压缩驱动器和平面波管起始处的压力等值线图

These results are very encouraging; the FEM derived SPL matches the measured results within from to . This good match might have been more difficult to achieve in a less "well behaved" driver. It is interesting to note that the model does not predict every mode; perhaps non-axisymmetric modes and spurious structural modes in the tube could be responsible for these features.
这些结果非常令人鼓舞；有限元得出的声压级与测量结果的匹配度在 范围内，从 到 。这种良好的匹配对于 "表现 "较差的驱动器来说可能更难实现。值得注意的是，模型并不能预测所有的模式；也许管内的非轴对称模式和杂散结构模式可能是造成这些特征的原因。

The match between real and modelled impedance results is very close. The impedance curve has a maximum value of and a minimum of 6.7 Ohms reflecting the high degree of mechanical damping provided by the driver.
实际阻抗结果与模拟阻抗结果非常接近。阻抗曲线的最大值为 ，最小值为 6.7 欧姆，反映了驱动器提供的高度机械阻尼。

Figure 12 图 12

Modulus of electrical input impedance plotted against frequency for real driver (dotted ) versus modelled driver (solid)
真实驱动器（虚线）与模拟驱动器（实线）的电输入阻抗模量与频率关系图

It now seems instructive to illustrate the design process with some results from example geometries. These are re-worked with the same material values used in the validation presented above.
现在似乎可以用一些几何图形的结果来说明设计过程。这些几何图形是用上述验证中使用的相同材料值重新设计的。
Throughout this paper 'parametric geometries' were used enabling many design iterations to take place for little extra cost in time or money. The actual geometry used was a result of about 50 acoustic models and a similar number of magnetic models.
本文自始至终使用 "参数几何图形"，这样就可以进行多次设计迭代，而几乎不需要额外的时间或金钱成本。实际使用的几何图形是大约 50 个声学模型和类似数量的磁学模型的结果。

Unlike horns with their various dispersion characteristics, the plane wave tube gives an absolute efficiency of a compression diver. However, we have seen that the high-frequency response is flawed.
与具有各种扩散特性的喇叭不同，平面波管具有压缩潜水员的绝对效率。然而，我们已经看到高频响应存在缺陷。
Consequently, during the driver development, we also modelled the driver on an axisymmetric horn to allow evaluation of the high frequency driver response. While these results are not illustrated here a non-axisymmetric test horn is illustrated and discussed in section 9 .
因此，在驱动器开发过程中，我们还在轴对称号角上建立了驱动器模型，以评估驱动器的高频响应。第 9 部分将对非轴对称测试号角进行说明和讨论，此处不对这些结果进行说明。

Firstly, we will look at the effect of doubling the distance between the phase-plug and the diaphragm. This geometric perturbation has been achieved by altering a parameter defining the position of the coordinates of the points associated with the diaphragm.
首先，我们将研究将相位塞与膜片之间的距离增加一倍的效果。这种几何扰动是通过改变一个参数来实现的，该参数定义了与膜片相关的点的坐标位置。
The geometry may then be re-meshed and re-analysed.
然后可以对几何图形重新进行网格划分和分析。

Figure 13 图 13

Driver with phase-plug to diaphragm spacing doubled (dotted lines)
相位插头与隔膜间距加倍的驱动器（虚线）

The resulting response curve, see Figure 14, shows the decreasing frequency of the HF roll-off, as we would expect from lumped element analysis [8]. However, from the FEM analysis, we can also see changes of magnitude and frequency of some cavity modes.
由此得出的响应曲线（见图 14）显示高频滚降的频率在下降，正如我们从块元分析[8]中所预期的那样。不过，通过有限元分析，我们还可以看到一些空腔模式的幅度和频率发生了变化。
Should we wish to investigate the effect of this change in geometry on, for example, the pressure at any point in the air or the displacement of any part of the structure it is a simple matter to extract the results from the analysis.
如果我们想研究这种几何形状的变化对空气中任何一点的压力或结构任何部分的位移等的影响，从分析中提取结果是一件非常简单的事情。

Figure 14 图 14

Frequency response of driver with phase-plug to diaphragm spacing doubled (dotted lines)
相位插头与隔膜间距加倍后驱动器的频率响应（虚线）

One of the major features of the design is the use of a curved inner path through the phase plug. The intention of this path is to produce the correct wavefront shape to radiate into a 25 degree conical horn. The straight slot version is illustrated below.
设计的主要特点之一是通过相位塞使用弯曲的内部路径。这条路径的目的是产生正确的波面形状，以辐射到 25 度的锥形喇叭。直槽版本如下图所示。

Figure 15 图 15

Simplified driver with straight inner slot
内槽平直的简化驱动装置

As one could expect, the mismatch between the phase-plug slots path length results in a number of severe response dips. These are shown in Figure 16.
正如我们所预料的那样，相位插槽路径长度之间的不匹配导致了一些严重的响应骤降。如图 16 所示。

Frequency response of driver with straight slots (dotted) compared to reference design (solid)
直槽驱动器（虚线）与参考设计（实线）的频率响应对比

For this work, it was decided to produce a static thermal FEM model of the driver with a similar method to that used in previous work [9]. Due to the high frequencies being considered, the omission of forced convection within the driver seems an acceptable simplification.
在这项工作中，我们决定采用与先前工作[9]中类似的方法来制作驱动器的静态热有限元模型。由于考虑到频率较高，省略驱动器内部的强制对流似乎是一种可以接受的简化方法。
This model was intended to determine the thermal effect of various materials and the effect of including a heat-sink. There was no driver available at the time of analysis, so the results are qualitative rather than absolute.
该模型旨在确定各种材料的热效应以及加入散热器的效果。分析时没有驱动程序，因此结果是定性的，而不是绝对的。

Figure 17 图 17

Thermal model of driver showing static temperature contours
显示静态温度等值线的驱动器热模型

The results tabulated in Table 1 are in the form of thermal resistance between coil and environment, together with materials used. It is not surprising to find that the driver with the magnetic fluid, metal components and heat-sink will achieve the coolest coil temperature.
表 1 所列结果是线圈与环境之间的热阻以及所用材料。我们不难发现，使用磁性流体、金属部件和散热器的驱动器能达到最冷的线圈温度。
We must also take into account that the maximum temperature for a voice coil in air is limited by the wire insulation at around 180 degrees Celsius. For a fluid-filled gap, maximum temperature is limited by the magnetic fluid itself to 120 degrees Celsius.
我们还必须考虑到，空气中音圈的最高温度受导线绝缘层的限制，约为 180 摄氏度。对于充满液体的间隙，磁性液体本身会将最高温度限制在 120 摄氏度。

Table 1 表 1

Thermal resistance results from thermal FEM
热有限元得出的热阻结果

These results led to the choice of a basic driver with a one-piece aluminium dome, an aluminium diaphragm carrier and a Ferrofluid-filled magnetic gap.
根据这些结果，我们选择了带有一体式铝质球顶、铝质膜片载体和铁氟体填充磁隙的基本驱动器。

If we consider the effect of temperature rise on the voice coil resistance, we could expect that the driver will not achieve the SPL implied by its sensitivity at high input powers. For a ten watt input we could expect power compression from the generic front loaded driver with a one-inch diameter coil; the new design suffers from only of power compression due to the larger coil size and materials chosen.
如果考虑到温度升高对音圈电阻的影响，我们就可以预计，驱动器在高输入功率时将无法达到其灵敏度所暗示的声压级。对于 10 瓦的输入功率，我们可以预期带有一英寸直径音圈的普通前置式驱动器会产生 的功率压缩；而新设计由于采用了更大的音圈尺寸和材料，功率压缩仅为 。

To evaluate the final compression driver model, a 3D FEM model of a horn was produced. This model was somewhat simplified due to the length of time required to solve problems.
为了评估最终的压缩驱动器模型，我们制作了一个喇叭的三维有限元模型。由于解决 问题所需的时间较长，因此对该模型进行了一定程度的简化。

Firstly the two planes of symmetry in the design were used to justify modelling only a quarter of the horn. A further plane of symmetry, in the plane of the horn mouth, was applied to the boundary element to model the baffle.
首先，设计中的两个对称平面被用来证明只对喇叭的四分之一进行建模是合理的。在喇叭口平面上的另一个对称平面被应用到边界元素中，以模拟 挡板。

Secondly, the driver's moving parts were simplified. The dome itself is modelled in 3D semi-loof shell elements. The voice coil, surround and former were modelled as lumped mass, stiffness and damping elements applied to the edge of the dome.
其次，对驱动器的活动部件进行了简化。球顶本身是用 3D 半浮壳元件建模的。音圈、环绕音圈和前置音圈则以块状质量、刚度和阻尼元件建模，并应用于球顶边缘。

Thirdly, the element size was made somewhat larger than for the axisymmetric model. In particular the circumferential element length has been chosen with the assumption that the wavefront shape is approximately parallel to the mouth profile.
第三，元素的尺寸比轴对称模型大一些。特别是在选择圆周元素长度时，假定波面形状近似平行于口轮廓。

The mesh used for this analysis is illustrated in Figure 18. A parametrically defined geometry was used to create the mesh, in terms of the horn length and cut-off frequencies, of the horizontal and vertical sections.
图 18 展示了用于该分析的网格。根据喇叭长度和截止频率，使用参数定义的几何形状创建了水平和垂直部分的网格。
A boundary element is used to model radiation from the finite element modelled fluid within the horn and driver into half-space.
使用边界元素对喇叭和驱动器内的有限元建模流体向半空间的辐射进行建模。

Measurement points may be defined in any position in half- space. For this model, they were defined at a distance from the horn mouth along horizontal and vertical arcs. Directivity plots may be produced from this data and displayed in the usual manner. This data is very useful since no other method of predicting horn directivity exists.
测量点可以定义在半空间的任何位置。在本模型中，它们被定义在距离喇叭口沿水平和垂直弧线的 处。可以根据这些数据绘制指向性图，并以常规方式显示。这些数据非常有用，因为没有其他方法可以预测喇叭指向性。
For the sake of simplicity, only on axis results have been illustrated here.
为简单起见，这里只说明轴上的结果。

Figure 18 图 18

FEM model of horn and driver
喇叭和驱动器的有限元模型

The axial response from the model was calculated and is shown in Figure 19 in comparison to a measured compression driver and horn. The match is quite good but is limited at high and low frequencies by the model simplifications mentioned in the previous paragraphs.
模型的轴向响应经过计算，并与测量的压缩驱动器和号角进行比较，如图 19 所示。两者的匹配度相当高，但在高频和低频方面受到了前面段落中提到的模型简化的限制。

Figure 19 图 19

SPL of horn/driver model for 1 meter distance on axis. (solid curve)
轴线上 1 米距离内喇叭/驱动器模型的声压级。(实心曲线）

Real driver and horn (dotted curve)
真正的驱动器和喇叭（虚线）

To illustrate the 'real world' driver performance on this horn, the driver fundamental and second and third harmonics were measured with a nominal input from to . These results are shown in Figure 20. For the purposes of comparison the benchmark 'generic front loaded' drivers have been measured under the same conditions. These results are shown in Figure 21.
为了说明该号角的 "实际 "驱动性能，在 的额定输入（从 到 ）下测量了驱动的基波和二次、三次谐波。这些结果如图 20 所示。为了进行比较，我们在相同条件下测量了基准 "通用前负载 "驱动器。这些结果如图 21 所示。

Figure 20 图 20

SPL, harmonic distortion of final driver at on axis for 10w input on elliptical horn. Distortion
声压级、 最终驱动器在 轴上的谐波失真，输入功率为 10 瓦，椭圆形号角。失真

raised  提高

Figure 21 图 21

SPL, harmonic distortion of 'benchmark' generic driver at on axis for input on
基准 "通用驱动器在 轴上的声压级、 谐波失真（ 输入）。

elliptical horn. Distortion raised 20dB
椭圆形喇叭。失真提高 20 分贝

The electro-magneto-vibro-acoustic FEM described in this paper allows the response of electro-dynamic drive units to be calculated without the need to make numerous prototypes. All that is required is the geometry, the material properties and suitable FEM software.
本文介绍的电磁-振动-声学有限元模型可以计算电动驱动装置的响应，而无需制作大量原型。所需要的只是几何形状、材料特性和合适的有限元软件。

The thermal FEM has significant limitations but produces results with real practical value.
热有限元模型有很大的局限性，但其结果具有真正的实用价值。

The combination of methods in practice has proved invaluable in the design of a new compression driver.
实践证明，在设计新型压缩驱动器时，将这些方法结合起来是非常有价值的。

I would like to thank the GPAcoustics engineering team for the help and support in writing this paper.
感谢 GPAcoustics 工程团队在本文撰写过程中给予的帮助和支持。

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[2] Geddes, E. "Computer Simulation of Horn Loaded Compression Driver" JAES, vol.35, No. 7, 1987.
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[3] Smith, B.H. "An Investigation of the Air Chamber of Horn Type Loudspeakers." JASA, vol.25, No. 2, 1953.
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[5] Dodd,M. A. "The Transient Magnetic Behaviour of Loudspeaker Motors" Presented at the 111 Convention 2001.
[5] Dodd,M. A.A. "The Transient Magnetic Behaviour of Loudspeaker Motors" Presented at the 111 Convention 2001.

[6] FLUX2D 7.60 User Manual, CEDRAT, Meylan France. 2002.
[6] FLUX2D 7.60 用户手册，CEDRAT，法国梅兰。2002.

[7] Betran, C.I. AES preprint 4787 'Calculated Response of a Compression Driver using a Coupled Field Finite Element Analysis.' September 1998
[7] Betran, C.I. AES 预印本 4787 "使用耦合场有限元分析计算压缩驱动器的响应"。1998 年 9 月

[8] Bie, D. "Design and Theory of a New Midrange Horn Driver" Presented at the Convention 1992.
[8] Bie, D. "Design and Theory of a New Midrange Horn Driver" Presented at the Convention 1992.

[9] Dodd,M. A. "The Application of FEM to the analysis of Loudspeaker Motor Thermal behaviour." Presented at the Convention 2002.
[9] Dodd,M. A. "The Application of FEM to the analysis of Loudspeaker Motor Thermal behaviour".A. "The Application of FEM to the analysis of Loudspeaker Motor Thermal behaviour"。发表于 Convention 2002。