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采暖水泵房噪声控制研究设计含10张CAD图,采暖,水泵房,噪声控制,研究,设计,10,CAD
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附录1：外文翻译噪声住房优化的数值和实验研究减少轴向柱塞泵摘要 本文提出了一种通过改变壳体结构来减少轴向柱塞泵噪声的方法，结合数值和实验方法。建立了壳体和盖板的有限元模型，并组装在一起。有限元模型使用实验模态分析进行验证和更新。计算组件的频率响应函数，并添加壳体内表面中的壳单元。确定壳单元厚度对频率响应函数的影响。进行拓扑优化，以减少频率响应函数和质量的增加。原型泵制造和组装。进行不同的实验测量，包括测量振动和泵周围声压级的分布。结果表明，通过使用优化的外壳，减轻了振动和噪音。特别是在250 bar的排放压力下，平均声压级降低了约2 dB（A），二次谐波的声压级别显着减少。这里提出的方法也可以用于其他种类的排量泵。 1.简介 轴向柱塞泵由于能够根据实际要求调整其位移，因此广泛应用于液压油动力系统。 然而，它们的噪声水平高于其他类型的位移泵，它们是液压系统中的主要噪声源。 为了满足三重奏法律规则的要求，液压泵的噪音必须减小1，特别是轴向柱塞泵。 提出了一种用于对齿轮泵的振动声学特性进行建模的方法1，有助于降低液压泵的噪音。 轴向柱塞泵产生的噪音分为流体噪声，结构噪声和空气噪声。流动波纹是流体噪声的来源;当流动波动与系统阻抗相互作用时，它会导致软管，阀门和执行器的振动，并且提出了一种测量叶片泵压力波动的方法2。内部激励力和力矩是结构噪声的来源;它们会引起泵的振动。阀板是影响噪声源产生的关键部分3，在泵送动力学建模中考虑了惯性效应。比较了具有不同种类的槽几何形状的阀板4，表明具有三角槽几何形状的阀板对工作条件不太敏感。优化了这种阀板的结构参数（槽长，宽度和高度），以减少基于泵模型的流动波动5,6。该方法不能同时考虑流体噪声和结构噪声源。为了解释流体噪声和结构噪声，采用遗传优化方法7。采用类似的优化方法，找到最优的交叉角，以降低噪声对位移的敏感度8。除了使用的被动方式之外，还采用了几种主动方法来控制流体噪声和结构噪声源，其中高阻尼止回阀9和可变换向阀10被发现是在不同的工作条件下有效。这些调查集中在减少噪声源。 降低噪声的另一种方法是改变传输路径11。 对于轴向柱塞泵，早期的研究表明，通过添加加强肋可以减少噪音12,13，改变了房屋的安装和形状14。然而，这些修改或多或少地通过试验和 错误方法。 即使建立了轴向柱塞泵的振动声学模型，这些模型仅用于在设计阶段评估其振动和噪声。 很难提供如何修改房屋的信息。 此外，与汽车行业相比，更安静的组件的发展落后于流体动力行业。在汽车行业，拓扑，尺寸，形状和地形优化方法已被采用，以找到获得更轻和更安静的机器的最佳结构 15,16。预计流体动力工业可以利用这些技术来推动其进步。 本研究的目的是：（1）建立模型分析的住房和覆盖有限元模型; （2）使用基于模态保证标准的实验模态分析验证和更新有限元模型; （3）开发拓扑优化方法，优化房屋结构，降低频率响应功能; （4）使用不同的实验测量来评估原始和优化泵之间的振动和噪声差异，包括泵周围的振动测量和声压级测量。2. 元素分析 轴向柱塞泵是具有九个活塞的可变排量斜盘式。 泵的额定压力为350 bar，排量为250 cm 3 / r，额定转速为1500 r / min。 在本节中，建立了壳体和盖板的有限元模型，并将其组装在一起。进行有限元模态分析，并进行实验模态分析，以验证和更新有限元模型。 更新的模型将用于第3节中频率响应函数的计算。2.1 有限元模态分析 轴向柱塞泵的壳体和盖子是影响振动传播和噪声发射的主要部件。 建立了有限元模型，用于执行有限元模态分析（FEMA）。 轴向柱塞泵有许多润滑界面。 在这些接口中，拖鞋/斜盘接口，活塞/气缸接口和气缸/阀板接口是最主要的。 尽管使用不同的方法对这些接口进行有限元分析建模，但结果并不好，难以正确地进行分析17。 由于这些原因，这些部分不包括在内。 这不仅可以减少计算时间，而且可以用于识别外壳对轴向柱塞泵的振动和噪声的实际影响。 有限元模型如图1所示。四面体元件用于对外壳和盖板进行建模，共有139,432（92,030 + 47,402）个四面体元件。壳体和盖子之间的螺栓由与实际螺栓（M18）具有相同半径的一维梁元件建模。梁元件使用具有三个平移自由度（Dofs）约束的刚性蜘蛛元件（rbe2）连接到周围元件。外壳和盖由可锻铸铁制成。推荐的材料特性为：q = 7010 kg / m 3，l = 0.274，E = 1.61？ 10 11 N / m 2。在初始阶段，这些属性用于确定外壳和盖板的模态特性。使用这些初始设置的模拟前10个模态频率列于表1中。然后，将进行模态保证标准分析（MACA），以分析模拟和测量的模态特征值之间的校正。后来，这些属性将被更新，以改善纠正。当属性成功更新时，将执行频率响应功能分析。它们的结果在拓扑优化中用作约束，如第3节所述。2.2 实验模态分析 使用冲击试验进行实验模态分析（EMA）。 试验台的原理图如图1所示。 2.在壳体表面上构造了74点（编号1-74），压电加速度计（型号4507-B-001，BrelKjr）连接到点59.锤被移动到每个测量点 激励壳体，并且冲击锤中的集成内力传感器提供测量的输入激励。 连接到泵的加速度计测量加速度，并且加速度计提供动态响应。 测量的输入和输出产生系统传输功能。 当EMA完成时，可以获得模态频率和模态。 EMA需要两个程序，数据采集和数据分析。 数据采集设备为LAN-XI 3050，数据分析在PULSE LabShop 14.1和MEscopeVES中进行。 在数据采集中，输入数据通过线性平均五个测量结果（类型7753，Brel和Kjr）获得。 使用铝锤尖，这是较硬的并且允许更高的可测量的频率范围。 此外，使用指数衰减窗口来最小化泄漏的失真效应。之后，在MEscopeVES中进一步解释数据。 测量的前十个模态频率也列在表1中。2.3 模态保证标准分析 当FEMA和EMA都完成时，可以进行模态保证标准分析（MACA），以分析模拟和测量模态特征之间的校正。 模态保证标准矩阵建立在模式i和j上，使用模式i的测试模态向量，以及方程式j给出的模式j的有限元模态向量w j FE。（1）：其中/呈现复共轭。 MAC ij的值大于0，小于1.如果两个向量是正交的，则MAC ij = 0，并且MAC ij = 1，如果它们相等，则相应的测试和有限元模式应该具有高MAC值。实际上，如果MAC ij 0.8，则两个向量被认为是非常好的相关，如果MAC ij 0.7，则两个向量被认为是可接受的18。在本研究中，测试模态向量是用于验证有限元模型精度和更新材料属性（q，l和E）的参考，以获得更高的MAC值。前十个固有频率的初始MAC值列在表1中。该表显示了模拟和测量模式形状之间的最高模式对。这是通过跟踪最高MAC值（测量模式是固定的，有限元模式是变化的）来实现的。使用这种技术，没有呈现具有较小MAC值的其他模式对，这有助于在优化中定义目标函数以更新材料的属性。它显示使用初始设置，MAC值从0.3到0.6不等，这表明两个向量彼此不相关。因此，需要更新模型，如第2.4节所述。2.4 模型更新在MACA的基础上，需要更多的程序来更新模型，模态保证标准灵敏度分析（MACSA）和优化。 MACSA计算MAC值对材料属性的敏感度，并提供有关明确影响MAC值的最大因素的信息。在优化过程中，应定义设计变量和目标。在这项研究中，设计变量是材料属性（q，l和E），目标是最大化MAC值，并最小化测量模型和模拟模型之间的频率差异。使用顺序二次编程算法（集成在LMS virtual.lab中）进行优化，并使用分析方法计算梯度。进行了九个实验设计。优化过程中材料特性的变化如图1所示。 3.更新的材料性质是：q = 7465.2kg / m 3，l = 0.247，E = 1.53？ 10 11 N / m 2。与原始设定相比，密度增加约6.5，泊松比下降约9.9，杨氏模量下降约5.0。这表示MAC值对材料属性非常敏感。使用更新的材料属性计算的前十个模式频率，频率误差和MAC值也列在表1中。它显示了模拟和测量模型之间的相关性有很大的改善。更新的MAC值大于0.70，小于0.90。尽管第二模式频率误差（3.3），但大多数频率误差小于3。考虑到测试模式形状也受到误差的影响，上述结果被认为是足够的精度。为了进一步改善有限元模型，希望通过不太简化和使用更小的元件尺寸（更大数量的元件）来提高四面体元件的网格质量。然而，实际上，考虑到预处理时间和计算时间的增加，它没有任何优势。结果还表明，使用更新的材料属性的更新模型使用推荐的材料属性比原始模型更精确，并且对以下部分中的有限元分析给出了置信度。3.优化使用更新的有限元模型，进行频率响应函数分析，以调查壳体和盖组件的动力学。为了降低频率响应功能，外壳元件被添加到外壳的内表面。定义了不同厚度的壳单元以调查其对频率响应函数的影响。将显示功率对重量的密度有很大的降低。因此，拓扑优化方法用于优化壳单元，通过约束频率响应函数来减小质量。3.1频率响应函数分析在拓扑优化之前，进行频率响应分析，以研究增加内表面厚度对壳体和盖组件动力学的影响。为了实现这个目标，构造壳单元，这些元件通过使用刚性的蜘蛛元件（rbe2）连接到壳体中的相应元件。这使得可以为壳单元定义不同的厚度。缺点是整个壳单元由相同的属性定义，同样的厚度分配给整个外壳。在有限元模型中如图1所示。如图1所示，激励点定义在节点36183（轴承中心），使用三个平移Dofs约束的插值蜘蛛元素（rbe3）与周围元素连接。需要几个程序来计算频率响应函数。首先，在x方向上的节点36183a处具有1000N的恒定幅度的频率变化（0-5kHz）激励力被定义如图1所示。在实际操作条件下，轴承力沿着x和y方向都有分量。但是为了简单起见，只有沿x方向的力被定义为激励。第二，2.5的值被定义为全局模态阻尼。第三，规定了在0-6kHz范围内的每个谐振频率的0.2和0.8的两个激励频率。最后，定义节点9993处的节点位移的响应（图1）。首先研究壳单元厚度对频率响应函数的影响。在三种不同厚度（0,10和20mm）处获得的频率响应函数如图1所示。这表明频率响应函数随着厚度的增加而减小。最大的值出现在大约370Hz，这是组件的模态频率。具体来说，FRF从3.6？ 105mm / N3.2？ 105mm / N时，当壳厚度增加到20mm时，实现了10以上的压下率。应该注意的是，这种模态频率与第2节所述的模态频率不同，其中第一模态频率为890.2Hz。它还表明，第一模态频率随着壳厚度的增加而增加（368-376Hz）。此外，当频率低于3kHz时，与频率大于3kHz的频率相比，FRF的降低更为明显。在这种分析中，加入的壳元素的总面积为约0.1m 2，如果壳元素的厚度从0增加到10mm，并且20mm，则质量增加约为7.6kg和15.2kg。相对于约77.3公斤的房屋重量，增幅约为10和20。通常，这是不能接受的，因为重量的增加太多，因此在功率重量密度方面损失太多。为此，一个拓扑采用优化方法来优化壳单元的厚度。优化结果将为如何优化住房提供有用的指导：最大程度上减少响应，同时增加最小重量 旋转机械的谐波。 当活塞数为9，速度为1490 r / min（实际为14905 r / min）时，泵的基频为223 Hz。 显然振动随着压力水平的增加而增加。 二次谐波振动对于原始和优化的泵都是最大的。 在大多数情况下，第一和第五次谐波的振动是第二和第三大。 前十次谐波（0-2.5 kHz）的振动大于高次谐波（2.5-5 kHz）时的振动。 相比之下，可以发现通过在多个谐波下使用优化的壳体来减小振动。 具体地说，可以清楚地看到第二和第五谐波（447和1115Hz）的振动的减小。 此外，平均振动速度从约7？ 103m / s6？ 如图2所示，在250巴下为10-3m / s。11。4.3 声压级测量几点振动的比较不足以证明优化泵对噪声发射的影响。因此，进一步测量声压级。 为了测量泵周围声压级的分布，需要在测试泵周围建立几个假想曲面。 在这种情况下，如图1所示的四个测量表面（左，前，右和上）。 如图12所示，假设底表面和后表面都是刚性反射表面。 实际上，底面不完全刚性; 它吸收了一些声能。假设的平行六面体的大小是800？ 1000？ 800mm（长高宽），测量段尺寸为100？ 100 mm，得到304（80？3 + 64）个测量段。 对于每个段，测量时间为10 ms，这允许每个段的平均时间为五。 通过参考ISO 9614-1 19和ISO 16902-1 20来构建声压级测量的测量设置，但是应注意测量不能完全满足两个标准的要求 ，因为条件有限，如测量室的尺寸和声学处理。 然而，用于比较测量准确度等级的方法是可以接受和有用的。 在大多数情况下，声压级用于呈现噪音，而不是使用声压。 声压级由以下公式计算： 其中p 0是参考声压。为了同时测量泵周围的声压级的分布，需要许多麦克风阵列。然而，在本研究中它并没有被用于其高成本。因此，声压级按顺序测量，并且使用具有两个麦克风的声强探测器（型号3599，BrelKjr）测量（4197型， BrelKjr）。两个麦克风之间的距离为12 mm，可测量频率为0.25-5000 Hz。该过程描述如下。首先，在每个段测量声压级，然后当前段的测量结束时，测量进行到下一段。然后，当一个表面的声压级的测量结束时，移动到下一个表面。由于这些表面的全部测量完成，所以可以计算测量面的平均声压级，并且可以计算出频谱。此外，也可以计算一个表面的平均声压级。在50和150巴的排放压力下，原始泵周围声压级的分布如图1和图2所示。 13和14。图图15和16分别示出了优化泵的声压级的分布。首先，可以看出，当排出压力增加时，声压级增加。这是因为如图1所示，在较大的排出压力下振动速度较大。 10（忽略流体噪声源的影响）。其次，不同测量段的声压级相差很大。在图如图13所示，总声压级在左表面和右表面上从约85至95dB（A），前表面上为83至93 dB（A），上表面为83至91 dB（A）。类似的现象可以在图1和图2中看到。 14-16。这表明通过测量几个点的声压级来评估噪声水平是不够的。因此，本研究中使用平均声压级进行比较。平均声压级通过对所有选定测量段的声压级求平均值来计算。表3显示了在三种不同排放压力（50,150和250巴）下原始和优化泵的平均声压级。第三，优化泵比原泵更安静。在50巴时，平均声压级几乎相同（89.4和89.1 dB（A），平均声压级从95.9降低到94.1 dB（A） 在150巴时，在250巴时减少超过2 dB（A）（98.6和96.4 dB（A）。注意到平均声压级通常由最大值（在这种情况下为二次谐波，如图17所示）确定。因此，250巴下的声压级的分布不被比较。相反，二次谐波处的声压级的分布将在图1和图2中给出。 19和20。 通过观察表3，似乎每个表面的平均声压级别都不能全部使用优化的外壳来减少。在50巴时，左表面和前表面的平均声压级减小，而在右上表面上的声压级较大。在150 bar时，前，右和上表面的平均声压级别都会降低。在250巴时，它们在前表面，左右表面上减少。这可以通过如图1和2所示的声压级的分布的比较来解释。这表明测量段具有较高声压的量当使用优化的泵时，在50巴的左前表面和150巴的前，右和上表面上的水平都较小。此外，原始和优化泵的四个测量表面的平均声压级的频谱如图1所示。 17在三种不同的压力（50,150和250巴）下，平均声压级也如图1所示。图片清楚地表明，声压级别降低，平均声压级降低约1-2dB（A）。应注意平均振动速度和平均声压级小于其在二次谐波下的振幅。在所有情况下，二次谐波（447Hz）的平均声压级最大，与振动谱一致，如图1所示。因为总的平均声压级通常由它们在频域中的最大值来确定。因此，有必要检查二次谐波处的声压级的分布。由于已经确定在250巴的排放压力下平均声压级最大降低。比较这个压力下声压级的分布是比较好的，因为差异可以看得更清楚。在左，前，右和上测量表面（250巴）上的二次谐波（447Hz）处的声压级示于图1和图2。在前表面，平均声压级从99.0降低到94.7dB（A）。可以看出，对于原始泵，声压级在大于1/3的测量段上的声压级大于97dB（A），而对于优化的声压级，只有大约两个声压级高于97dB（A）的测量段泵。它还显示，当使用优化的泵时，更多的测量段具有低于85dB（A）的声压级。左右表面观察结果相似。这些结果确定了优化的壳体对轴向柱塞泵的噪声发射的影响，并且表明通过使用优化的壳体来降低噪声。5.结论已经提出了一种方法来优化住房结构，结合数值和实验方法。模态保证标准分析表明，为了获得准确的模态结果，需要更新材料性质。拓扑优化方法能够找到加筋肋的最优布局。实验结果解决了优化的壳体对泵的振动和噪声水平的影响。通过使用优化的壳体结构，证明了在宽范围的压力水平下振动和噪声水平被降低。特别地，平均声压级在250巴的排放压力下降低约2dB（A）。本研究提供了一种有效和有用的方法，可用于降低轴向柱塞泵的噪声，此处提出的方法可用于其他种类的流体动力机械。该研究的局限性在于，优化区域在壳体的内表面上受到限制。因此，由于减小的振动，可以获得降低的噪音。在未来的研究中，将整个房屋和房屋覆盖作为优化目标将会更好，以便不仅要改变振动传播，还要改变噪声的发射。 承认该项目得到了中国国家基础研究计划（2014CB046403）和国家自然科学基金（51375431）的支持。作者想承认叶志华，怀怀军，平吴等Hilead液压有限公司其他工程师制造原型泵，并在振动和声压级测量中提供必要的助手。附录A.补充材料在线版本中可以找到与本文相关的补充数据，网址为/10.1016/j.apacoust.2016.03.022。References1 Mucchi E, Rivola A, Dalpiaz G. 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Acousticsdetermination of sound power levels of noise sources using sound intensitypart 1: measurement at discrete points; 1993.20 ISO 16902-1. Hydraulic fluid powertest code for the determination of sound power levels using sound intensity techniques: engineering methodpart 1:pumps; 2003.附录2：外文原文Numerical and experimental studies on housing optimization for noisereduction of an axial piston pumpABSTRACT This paper presents a methodology to reduce the noise of an axial piston pump through modification of the housing structure, combined with both numerical and experimental methods. The finite element models of the housing and cover are established, and are assembled together. The finite element models are validated and updated using experimental modal analysis. The frequency response function of the assembly is calculated, and the shell element in the inner surfaces of the housing is added. The effects of the thickness of the shell element on the frequency response function are identified. A topology optimization is conducted for the purpose of reducing the frequency response function and the increase of mass. The prototype pump is manufactured and assembled. Different experimental measurements are carried out, including the measurement of the vibration and the distributions of the sound pressure levels around the pump. Results show that the vibration and noise are reduced by using the optimized housing.In particular, the average sound pressure level is reduced by about 2 dB(A) at the discharge pressure of 250 bar, and the sound pressure level at the second harmonic is reduced significantly. The method pro-posed here can also be used for other kinds of displacement pumps.1. Introduction Axial piston pumps are widely used in hydraulic fluid power systems due to their ability of adjusting their displacements to match the actual demands. However, their noise levels are higher than other kinds of displacement pumps, and they are the main noise sources in hydraulic systems. In order to meet the requirement of tricter legal rules,the noise from hydraulic pumps must be reduced 1, particularly the axial piston pumps. A methodology was pro-posed to model the vibro-acoustic characteristics of a gear pump1, and it is helpful in reducing the noise of hydraulic pumps. The noise generated by an axial piston pump is divided into fluid-borne noise, structure-borne noise and air borne noise. Flow ripple is the source of fluid-borne noise; it causes the vibration of the hoses, valves and actuators when flow ripple interacts with system impedances, and a method is proposed to measure the pressure ripple of a vane pump 2. Internal excitation forces and moments are the sources of structure-borne noise; they cause the vibration of the pump. Valve plate is the key part affecting the generation of noise sources 3, and the inertia effects were considered in modeling the pumping dynamics. Valve plates with different kinds of slot geometries were compared 4, demonstrating that the valve plate with triangular slot geometry is less sensitive to working conditions. Structure parameters (slot length,width and height) of this kind of valve plate are optimized to reduce the flow ripple based on a pump model 5,6. This method cannot consider fluid-borne noise and structure-borne noise sources simultaneously. In order to account for both fluid-borne noise and structure-borne noise, a genetic optimization method was used 7. Similar optimization method was employed to find the optimal cross-angle for reducing the sensitivity of noise to dis-placement 8. In addition to the passive methods used, several active methods are also used to control the fluid-borne noise and structure-borne noise sources, among which, the highly damped check valve 9 and variable reversing valves 10 are found to be effective at different working conditions. These investigations focus on reducing the noise sources. The other method to reduce the noise is to change the transmission paths 11. For axial piston pumps, early studies have demonstrated that the noise can be reduced by adding reinforce ribs12,13, changing the mounting and the shape of housing 14.However, these modifications are carried out more or less by trial and error method. Even though the vibro-acoustic models of axial piston pumps were established, these models are merely used to evaluate their vibration and noise at the design stage. It could hardly provide information on how to modify the housing. Besides, comparing to the automotive industry, the development of quieter components falls behind in fluid power industry.In the automotive industry, the topology, size, shape and topography optimization methods are already employed to find the optimal structure for obtaining lighter and quieter machines 15,16.It is expected that the fluid power industry could use these techniques to promote its advancement. The aim of this study includes: (1) build a finite element models of the housing and cover for the modal analysis; (2) validate and update the finite element model using experimental modal analysis based on modal assurance criterion; (3) develop a topology optimization methodology to optimize the housing structure for the purpose of reducing the frequency response function; (4) evaluate the differences of vibration and noise between the original and optimized pumps using different experimental measurements,including vibration measurement and sound pressure levels measurement around the pump.2. Finite element analysis The axial piston pump is of variable displacement swash plate type with nine pistons. The rated pressure of the pump is 350 bar, the displacement is 250 cm 3 /r, and the rated rotational speed is 1500 r/min. In this section, the finite element models of the housing and cover are built, and they are assembled together.The finite element modal analysis is performed, and experimental modal analysis is performed for the purpose of validating and updating the finite element model. The updated model will be used for the calculation of the frequency response function in Section 3.2.1. Finite element modal analysis The housing and cover in the axial piston pump are the main parts affecting the vibration transmission and noise emission. Their finite element models are established for performing the finite element modal analysis (FEMA). There are many lubrication interfaces in the axial piston pump. Among these interfaces, the slipper/swash-plate interfaces, piston/cylinder interfaces and cylinder/valve-plate interface are the most dominant. Even though different method is used to modeled these interfaces for the finite element analysis, the results are not good, making it difficult to perform the analysis correctly 17. For these reasons, these parts are not included. This is acceptable not only for reducing the computing time, but also for identifying the real effects of the housing on the vibration and noise of the axial piston pump. The finite element model is shown in Fig. 1. The tetrahedral element is used to model the housing and cover, there are totally 139,432 (92,030 + 47,402) tetrahedral elements. The bolts between the housing and cover are modeled by 1D beam elements having the same radius with the actual bolts (M18). The beam elements are connected to the surrounding elements using rigid spider element (rbe2) with three translational degree of freedoms (Dofs)constrained. The housing and cover are made of malleable castiron. The recommended material properties are: q = 7010 kg/m 3 ,l = 0.274, E = 1.61 ? 10 11 N/m 2 . In the initial stage, these properties are used to determine the modal characteristics of the housing and cover. The simulated first ten modal frequencies of the housing using these initial settings are listed in Table 1. Then, modal assurance criterion analysis (MACA) will be conducted to analyze the correction between the simulated and measured modal Eigen values. Later, These properties will be updated in order to improve the correction. When the properties are successfully updated, the frequency response function analysis will be performed. Their results are used in the topology optimization as the constraints as it will be presented in Section 3.2.2. Experimental modal analysis Experimental modal analysis (EMA) is performed using impact test. The schematic of the test rig is shown in Fig. 2. There are 74 points (No. 174) constructed on the housing surface, with the piezoelectric accelerometer (type 4507-B-001, Brel & Kj r)attached to point 59. A hammer is moved to each measuring point to excite the housing, and the integrated inner force transducer in the impact hammer provides a measured input excitation. The accelerometer attached to the pump measured the acceleration,and the accelerometer provides the dynamic response. The measured input and output yield the system transfer functions. The modal frequency and mode shape are obtained when the EMA is completed. EMA requires two procedures, the data acquisition and data analysis. The data acquisition equipment is LAN-XI 3050, and the data analysis is performed in PULSE LabShop 14.1 and MEscopeVES. In the data acquisition, the input data is obtained by linear averaging five measurement results (type 7753, Brel & Kj r). The aluminum hammer tip is used, which is harder and allows a higher measurable frequency range. In addition, the exponentially decaying window is used to minimize the distortion effects of leakage.Later, the data is further interpreted in MEscopeVES. The measured first ten modal frequencies of the housing are also listed in Table 1.2.3. Modal assurance criterion analysis When both the FEMA and EMA are finished, the modal assurance criterion analysis (MACA) can be conducted to analyze the correction between the simulated and measured modal characteristics. The modal assurance criterion matrix is built on mode i and j,using the test modal vectors w i test of mode i, and the finite element modal vectors w j FE of mode j as given in Eq. (1): where presents the complex conjugate. The value of MAC ij is larger than 0, and smaller than 1. If the two vectors are orthogonal, MAC ij = 0, and MAC ij = 1 if they are equal.Therefore, the corresponding test and finite element modes should have a high MAC value. In practice, the two vectors are considered to be very good correlation if MAC ij 0.8, and they are uncorrelated if MAC ij 0.7 18. In this study, the test modal vector is the reference used for validating the accuracy of the finite element model and updating the properties ( q , l and E) of the material in order to obtain a higher MAC value. The initial MAC values at the first ten natural frequencies are listed in Table 1. This table shows the highest mode pairs between the simulated and measured mode shapes. This is accomplished by tracking the highest MAC values (the measured mode is fix, and the finite element mode is varying). Using this technique, the other mode pairs having smaller MAC values are not presented, and this helps in defining the objective functions in the optimization for updating the properties of the material. It shows that using the initial settings, the MAC values vary from 0.3 to 0.6, which indicates that the two vectors do not correlate each other well. Therefore, model updating is required as will be presented in Section 2.4.2.4. Model updating On the basis of the MACA, two more procedures are required to update the model, the modal assurance criterion sensitivity analysis (MACSA) and optimization. MACSA calculates the sensitivity of MAC values to material properties, and will provide information on clarifying the biggest factor impacting the MAC value. In the optimization procedure, the design variables and objectives should be defined. In this study, the design variables are the material properties ( q , l and E), the objectives are to maximize the MAC values and to minimize the frequency differences between the measured and simulated models. The Sequential Quadratic Programming algorithm (integrated in LMS virtual.lab) is used to perform the optimization, and the analytical method is used to calculate the gradient. Nine experimental designs are performed. The variations of the material properties during the optimization are shown in Fig. 3. The updated material properties are: q = 7465.2 kg/m 3 ,l = 0.247, E = 1.53 ? 10 11 N/m 2 . Comparing to the original settings,the density increases about 6.5%, the Poissons ratio decreases about 9.9%, and the Youngs modulus decreases about 5.0%. This indicates that the MAC values are quite sensitive to the material properties. The first ten mode frequencies, frequency errors and MAC values calculated using the updated material properties are also listed in Table 1. It shows that the correlation between the simulated and measured models is improved quite a lot. The updated MAC values are larger than 0.70, and smaller than 0.90. Most of the frequency errors are smaller than 3%, despite of the second mode frequency error (3.3%). The results obtained above are considered to be of enough accuracy considering the fact that the test mode shape is also affected by errors. For further improving the finite element model, it is desired to improve the mesh quality of the tetrahedral element, by making less simplification and using smaller element size (larger number of elements). However, in practice, it offers no advantages, considering the increased pre-processing time and computing time. The result also indicates that the updated model using the updated material properties is more accurate than the original model using the recommended material properties,and gives confidence in the finite element analysis in the following sections.3. Topology optimization Using the updated finite element model, the frequency response function analysis is performed to investigate the dynamics of the housing and cover assembly. In order to reduce the frequency response function, shell element is added in the inner surfaces of the housing. Different thicknesses of the shell element are defined to investigate their effects on the frequency response function. It will be shown that the power-to-weight density is reduced quite a lot. Therefore, topology optimization method is used to optimize the shell element to reduce the mass by constraining the frequency response function.3.1. Frequency response function analysis Before the topology optimization, the frequency response analysis is performed to investigate the effects of increasing the thickness of inner surfaces on the dynamics of the housing and cover assembly. In order to achieve this goal, shell element is constructed, these elements are connected to their corresponding elements in the housing by using rigid spider element (rbe2). This makes it possible to define different thickness to the shell elements. The shortage is that the whole shell element is defined by the same property, and the same thickness is assigned to the whole shell. In the finite element model as shown in Fig. 1, the excitation point is defined at node 36183 (center of the bearing), connected with the surrounding elements using interpolation spider element(rbe3) with three translational Dofs constrained. Several procedures are required to calculate the frequency response function. First, the frequency varying (05 kHz) excitation force with a constant magnitude of 1000 N at node 36183along the x direction is defined as shown in Fig. 1. In actual operating conditions, the bearing forces have components along both x and y directions. But for simplicity, only force along x direction is defined as the excitation. Second, a value of 2.5% is defined as the global modal damping. Third, two excitation frequencies with a ratio of 0.2 and 0.8 of each resonant frequency between the range of 06 kHz are specified. Last, the response in terms of the nodal displacement at node 9993 is defined (Fig. 1). At first, the effects of the thickness of the shell element on the frequency response function are investigated. The frequency response functions obtained at three different thicknesses (0, 10and 20 mm) are shown in Fig. 4. It shows that the frequency response function decreases as the thickness increases. The largest value appears around 370 Hz, which is the modal frequency of the assembly. Specifically, the FRF decreases from 3.6 ? 10 ?5 mm/N to 3.2 ? 10 ?5 mm/N, a reduction of more than 10% is achieved when the shell thickness increases to 20 mm. It should be noticed that this modal frequency is different from the modal frequency of the housing as presented in Section 2, in which, the first modal frequency is 890.2 Hz. It also shows that the first modal frequency increases with an increase of the shell thickness (368376 Hz). In addition, when the frequency is lower than 3 kHz, the decrease of the FRFs is more evident than those at frequencies larger than 3 kHz. In this analysis, the total area of the added shell element is about 0.1 m 2 , and the mass increase is about 7.6 kg and 15.2 kg if the thickness of the shell element increases from 0 to 10 mm,and 20 mm. Comparing to the weight of the housing of about 77.3 kg, the increase is about 10% and 20%. In common, this is not acceptable, for too much increase in weight, and consequently too much loss in the power-to-weight density. For this, a topologyoptimization method is employed to optimize the thickness of the shell element. The results from the optimization would provide helpful guidance on how to optimize the housing: decrease in the response most while increase in the weight least. The results from the frequency response function analysis in this section gives several details used in the optimization, and makes the optimization feasible.3.2. Description of topology optimization Topology optimization is a mathematical approach that optimizes material layout. In this study, the density method is used for its efficiency and capability in solving engineering problems.In the density method, the density of the material ranges from 0 to 1. If the density is 1, then the materials are kept. If the density is 0, then the materials are moved. The advantage of the density method is that no much extra memory is required, only one free variable is required for each element. Before performing the topology optimization, the objective and constraints should be defined. The thickness of the shell is defined as the design variable. At first, a thickness of 5 mm is used. The objective is to minimize the whole volume of the assembly defined by the housing, cover and the shell element. The constraint is the frequency response function between node 9993 (response) and node 36183 (excitation), of which, the upper limit is set as 3.35 ? 10 ?5 mm/N. This value is given by analyzing the results from the frequency response function analysis presented in Section 3.1. The magnitude is about 3.2 ? 10 ?5 mm/N when the shell thickness is 20 mm, which is considered to be the largest reduction (the thickness cannot be larger than 20 mm to avoid the0 1 2 3 4 51e-81e-7 Frequency (kHz)FRF (mm/N) T=0 mm T=20 mm 1e-6 1e-4 1e-5 T=10 mm 360 380 370 3.0e-5 3.4e-5 3.8e-5 Fig. 4. Effects of shell thickness on the frequency response function.46 B. Xu et al./Applied Acoustics 110 (2016) 4352occurrence of interference). Because the optimization conducted in this study is not possible to reducing the strength of housing, the static analysis is not conducted.3.3. Optimization resultsThe optimization ended at the 10th iteration. The optimal housing is shown in Fig. 5. In Fig. 5(b), the presented elements have a density larger than 0.5. From this result, several reinforce ribs are recommended to be added on the inner surfaces, two horizontal reinforce ribs on the left inner surfaces and three horizontal reinforce ribs on the right inner surfaces. Two horizontal and vertical reinforce ribs on the bottom inner surfaces. The optimal layout from this optimization will be simplified before the manufacturing of the prototype as presented in Section 4.The FRFs calculated using the original and optimal housings are shown in Fig. 6. This figure shows the FRFs along the x, y and z directions. The FRFs along the x direction are the largest. Whereas,the FRFs along the y directions are the smallest. This is the reason to constraint only the FRF along the x direction in the topology optimization. It should be noticed that even the FRFs along the z direction is equivalent to the FRFs along the x direction, it is not used as the constraint in the topology optimization. It shows that when the optimal housing is used, the FRFs along x, y and z direction decrease. For the FRF along x direction, the peak value decrease from 3.62 ? 10 ?5 to 3.32 ? 10 ?5 mm/N, a decrease of about 8%. The reduction is about 2% smaller compared to that when the thickness of the whole shell element is 20 mm, and the reduction is almost 1% larger compared to that when the thickness is 10 mm. The FRF along the y direction decreases quite a lot. The largest one reduces from about 5 ? 10 ?6 to 0.9 ? 10 ?6 mm/N at the first resonant frequency. When it comes to the mass increase,the increased mass is far smaller when the optimized structure is used. The area of the optimized layout is about 0.042 m 2 , and the mass is about 3.2 kg when the shell element is 10 mm. Comparing to the area of the whole shell element, the area is reduced by almost 60%, and so as the mass reduction. This result shows the effectiveness of the proposed methodology.4. Experimental investigation When the topology optimization is completed, the optimized prototype housing is manufactured with some simplification. This is acceptable for the purpose of this study. As shown in Fig. 7, three vertical reinforce ribs are added on the left and right inner surfaces, respectively, and four horizontal reinforce ribs are added on the bottom inner surface (the definition of surfaces coincides with that shown in Fig. 5). In this section, the vibration measurement and sound pressure level measurement are performed to investigate the differences in the spectrums of the vibrations and sound pressure levels, and the distributions of the sound pressure levels between the original and optimized pumps.4.1. Test rig In order to measure the vibration and noise of the pump at different operating conditions, a test rig is built. The schematic of the hydraulic circuit is shown in Fig. 8, and the details are listed in Table 2. The test rig is designed for energy recovery by using a hydraulic motor with a maximum displacement of 250 cm 3 /r (its actual displacement is adjusted manually to match the specific requirement). This enables an energy recovery of about 7080% when the displacement of the test pump is 250 cm 3 /r. This is valuable to reduce the energy consumptions and its cost. The pressurein the outlet line is regulated by a pressure relief valve with a maximum pressure of 350 bar. The electrical motor has a fixed speed of 1490 r/min, which limits further investigation on the effects of the revolution speed on the vibration and noise. Therefore, the vibration and noise can be measured at a wide range of pressure levels and displacements using this test rig. This is enough for evaluating the noise because the pump with a displacement of 250 cm 3 /r is designated for use with a rated revolution speed of 1500 r/min when the inlet pressure is 1 bar. In addition, only the test pump is in the measurement room, the electrical motor and hydraulic motor are placed outside of the measurement room (as shown in Figs. 9 and 12). This reduces the effects of these noise sources on the measurement results.4.2. Vibration measurement The accelerations at two points on the outer surface of the cover are measured as shown in Fig. 9. The vibration velocity is calculated by integrating the acceleration. The measured vibration velocities using the original and optimized housing structure at point 1 are shown in Fig. 10. The mean vibration velocities are also presented as shown in Fig. 10. The operating conditions for the measurement are as follows: p = 50, 150 and 250 bar, n = 1490 r/min, e = 100%. It is noted that the sound pressure level measurement in Section 4.3 will be performed at the same operating conditions. It is important to compare the contents at differentharmonics for rotating machinery. The fundamental frequency of the pump is 223 Hz, when the number of piston is nine and the speed is 1490 r/min (1490 5 r/min in practice). It is obvious that the vibration increases as the pressure level increases. The vibration at the second harmonic is the largest both for the original and optimized pumps. In most cases, the vibrations at the first and fifth harmonics are the second and third largest. The vibrations at the first ten harmonics (02.5 kHz) are larger than those at higher harmonics (2.55 kHz). By comparison, it can be found out that the vibration is reduced by using the optimized housing at a number of harmonics. Specifically, the reduction in the vibrations at the second and fifth harmonics (447 and 1115 Hz) can be seen clearly. In addition, the mean vibration velocity is reduced from about 7 ? 10 ?3 m/s to 6 ? 10 ?3 m/s at 250 bar as shown in Fig. 11.4.3. Sound pressure level measurement Comparison of the vibrations at several points is not enough to justify the effects of the optimized pump on the noise emission.Therefore, the sound pressure level is measured further. In order to measure the distributions of the sound pressure levels around the pump, several hypothetical surfaces need to be constructed around the test pump. In this case, four measurement surface (left, front, right and upper) as shown in Fig. 12, assuming that the bottom and back surfaces are both rigid reflecting surfaces. In reality,the bottom surface is not fully rigid; it absorbs some sound energy.The size of the hypothetical parallelepiped is 800 ? 1000 ? 800mm (length ? height ? width), with the size of the measurement segment of 100 ? 100 mm, resulting in 304 (80 ? 3 + 64) measurement segments. For each segment, the measurement time is 10 ms,which allows an averaging time of five for each segment. The measurement set-up for the sound pressure level measurement is constructed by referencing to ISO 9614-1 19 and ISO 16902-1 20.However, it should be noticed that the measurement cannot fully satisfy the requirement of the two standards, because of the limited conditions, such as the size of and the acoustic treatment to the measurement room. However, this method used for the purpose of comparisons in the grade of accuracy of survey can be acceptable and useful. In most cases, the sound pressure level is used to present the noise instead of using the sound pressure. The sound pressure level is calculated by:where p 0 is the reference sound pressure. In order to measure the distributions of the sound pressure levels around the pump at the same time, many microphone arrays are required. However, it is not used in this study for its high cost.Instead, the sound pressure level is measured in sequence, and it is measured using the sound intensity probe (type 3599, Brel &Kj r) with two microphones (type 4197, Brel & Kj r). The space between the two microphones is 12 mm, allowing a measurable frequency of 0.255000 Hz. The procedure is described as follows. First, the sound pressure level is measured at each segment, and then the measurement proceeds to the next segment when the measurement at the former segment is finished. Then move on to the next surface when the measurement of the sound pressure level at one surface is finished. As all the measurement for these.four surfaces are completed, the average sound pressure level for the measurement surfaces can be calculated, and the frequency spectrum can be calculated. In addition, the average sound pressure level at one surface can also be calculated. The distributions of the sound pressure levels around the original pump at the discharge pressure of 50 and 150 bar are shown in Figs. 13 and 14, respectively. Figs. 15 and 16 show the distributions of the sound pressure levels for the optimized pump, respectively.Firstly, it is seen that the sound pressure level increases when the discharge pressure increases. This is because that the vibration velocities are larger at larger discharge pressure as shown in Fig. 10 (neglecting the effects of fluid-borne noise sources). Secondly, the sound pressure levels at different measurement segments are quite different from each other. In Fig. 13, the total sound pressure levels vary from about 85 to 95 dB(A) on the left and right surfaces, 83 to 93 dB(A) on the front surface, and 83 to 91 dB(A) on the upper surface. Similar phenomenon can be seen in Figs. 1416. This indicates that it is inadequate to assess the noise level by measuring the sound pressure level at several points.For this reason, the average sound pressure level is used for comparison in this study. The average sound pressure level is calculated by averaging the sound pressure levels at all the chosen measurement segments. Table 3 shows the average sound pressure levels for the original and optimized pump at three different discharge pressures (50, 150 and 250 bar). Thirdly, the optimized pump is quieter than the original pump. At 50 bar, the average sound pressure levels are nearly the same (89.4 and 89.1 dB(A),the average sound pressure level decreases from 95.9 to 94.1 dB(A) at 150 bar, and it is reduced by more than 2 dB(A) (98.6 and 96.4 dB(A) at 250 bar. Noticed that the average sound pressure level is often determined by the largest value (the second harmonic in this case as shown in Fig. 17). Therefore, the distributions of the sound pressure levels at 250 bar are not compared. Instead, the distributions of the sound pressure levels at the second harmonic will be presented in Figs. 19 and 20.By observing Table 3, it seems that the average sound pressure levels on each surface cannot all be reduced using the optimized housing. At 50 bar, the average sound pressure levels on the left and front surfaces decrease, whereas they are larger on the right and upper surfaces. At 150 bar, the average sound pressure levels are reduced on the front, right and upper surfaces. And at 250 bar, they are reduced on front, left and right surfaces. This can be explained by a comparison of the distribution of the sound pressure levels as shown in Figs. 13, 15 and 14, 16. It shows that the amount of measuring segments having higher sound pressurelevels are smaller on the left and front surfaces at 50 bar, and the front, right and upper surfaces at 150 bar when the optimized pump is used. Besides, the frequency spectrums of the average sound pressure levels from the four measurement surfaces for the original and optimized pump are shown in Fig. 17 at three different pressures(50, 150 and 250 bar), and the mean sound pressure levels are also presented as shown in Fig. 18. The pictures clearly show that the sound pressure level is reduced, and the mean sound pressure level is reduced about 12 dB(A). It should be noticed that the mean vibration velocities and the mean sound pressure levels are smaller than their amplitudes at the second harmonic. In all the cases, the average sound pressure levels at the second harmonic (447 Hz) are the largest, which coincides with the vibration spectrum as shown in Fig. 10. Because the total average sound pressure levels are often determined by their largest values in the frequency domain. Therefore, it is necessary to examine the distributions of the sound pressure levels at the second harmonic. As it has been already identified that the average sound pressure levels are reduced most at the discharge pressure of 250 bar. It is better to compare the distributions of the sound pressure levels at this pressure because the difference can be seen more clearly. The sound pressure levels at the second harmonic (447 Hz) on the left, front, right and upper measurement surfaces (250 bar)are shown in Figs. 19 and 20. On the front surface, the average sound pressure level reduces from 99.0 to 94.7 dB(A). It is seen that the sound pressure levels are larger than 97 dB(A) at more than 1/3measurement segments for the original pump, whereas there are only about two measurement segments having a sound pressure level above 97 dB(A) for the optimized pump. It also shows that much more measurement segments having a sound pressure level below 85 dB(A) when the optimized pump is used. Observations tot he left and right surfaces show similar results. These results identified the effects of the optimized housing on the noise emission of the axial piston pump, and it shows that the noise is reduced by using the optimized housing.5. ConclusionA methodology has been presented to optimize the housing structure, combined with numerical and experimental methods.The modal assurance criterion analysis showed the material properties need to be updated for obtaining accurate modal results. The topology optimization method is abl
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