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机械系统信号处理 211 (2024) 111181

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测量识别 滚动轮胎 平面内动态行为

伊万诺·帕利亚 a * 卢卡·拉皮诺 a 弗朗切斯科·里帕蒙蒂 a 西蒙娜·巴罗 b Roberto Corradi a
伊万诺·帕利亚a*卢卡·拉皮诺a弗朗切斯科·里帕蒙蒂a西蒙娜·巴罗b,RobertoCorradia

a Politecnico di Milano, Department of Mechanical Engineering, Via La Masa 1, 20156 Milano, 意大利 b Pirelli Tyre S.p.A., Viale Piero e Alberto Pirelli 25, 20126 米兰, 意大利
PolitecnicodiMilano,Department ofMechanicalEngineering,Via LaMasa 1,20156Milano,意大利PirelliTyreS.p.A.,VialePieroAlbertoPirelli25,20126米兰,意大利

A R T I C L E I N F O 传达 John E. Mottershead Key的话:
ARTCLENFO传达John E.Mottershead Key的话:

滚动轮胎动力学 实验夹板测试 传播解决方案 识别算法 结构噪声

A B S T R A C T

作用在轮胎可以提高道路车辆的 NVH 性能 轮胎 起着至关重要的作用 结构噪声 振动传输到 机舱最高可达 500 Hz。 本文 旨在 研究 滚动轮胎 平面内动力学 频率范围。 轮胎径向振动测量是通过 专用的实验装置进行的 基于 激光 三角测量传感器扫描滚动轮胎 胎面 实验数据是在夹板测试期间收集的,考虑了不同的滚动速度 充气压力,研究它们轮胎动力学的影响 然后,数据处理 算法 提出的目的是 识别 传播的渐进波和退 锁片撞击后的 轮胎周长 最后,为了解释 结果,确定轮胎响应进行了比较 通过 简化平面内轮胎模型获得的分析结果
作用在轮胎可以提高道路车辆的 NVH性能轮胎起着至关重要的作用结构噪声振动传输到机舱最高可达500Hz。本文旨在研究滚动轮胎的平面内动力学频率范围。轮胎径向振动测量是通过专用的实验装置进行的基于激光三角测量传感器扫描滚动轮胎胎面实验数据是在夹板测试期间收集的,考虑了不同的滚动速度和充气压力,研究它们轮胎动力学的影响然后,数据处理算法提出的目的是识别传播的渐进波和退锁片撞击后的轮胎周长最后,为了解释结果,确定轮胎响应进行了比较通过简化平面内轮胎模型获得的分析结果

1. 引言

汽车行业 车辆舒适性的关注 显著 增加。 因此 人们开始关注 车辆 NVH(噪声、 振动声振粗糙度)性能 [1,2]。 此外, 近年来 电动汽车 越来越 受欢迎,因此 轮胎/路面相互作用当今 影响 整体噪声的最重要因素,并且 在车辆感知到的振动水平 [3]。 此外, 乘客 机舱 感知也在发生变化因为 引入 自动驾驶 功能。 在这种情况下 必须 提高道路车辆 NVH 性能尤其是 <b 上<b1197> 1198>轮胎, 结构性座舱噪声振动 着重要作用 500 Hz [4,5]。
汽车行业车辆舒适性的关注显著增加。因此人们开始关注车辆NVH(噪声、振动声振粗糙度)性能[1,2]。此外,近年来电动汽车越来越受欢迎,因此轮胎/路面相互作用当今影响整体噪声的最重要因素,并且在车辆感知到的振动水平[3]。此外,乘客机舱感知也在发生变化因为引入自动驾驶功能。在这种情况下必须提高道路车辆NVH 性能尤其是在 1198>轮胎,结构性座舱噪声振动着重要作用500Hz[4,5]。

可以 采用 不同的方法来研究 轮胎 动态行为 方面, 建模的角度来看 有几种解决方案可能是 根据所需的复杂程度 进行考虑 分析模型计算 效率高,可在短时间内 提供结果; 然而,它们 提供了这种现象的一般理解 [6]。 有限模型需要苛刻的计算工作,但实现了这种可能性 轮胎设计的影响进行预测参数分析 参数 [7]。

另一方面 可以 进行实验研究并且可以使用特定的信号处理技术 用于 识别 模型标定 NVH 有用的参数 分析。 为此文献提出了 不同的方法 固有频率、振型 模态阻尼系数可以通过 Experimental 来确定 模态分析
另一方面可以进行实验研究并且可以使用特定的信号处理技术用于识别模型标定 NVH 有用的参数 分析。为此文献提出了不同的方法固有频率、振型模态阻尼系数可以通过实验来确定模态分析

* 通讯作者。

电子邮件地址ivano.lapaglia@polimi.it (I. La Paglia)。

https://doi.org/10.1016/j.ymssp.2024.111181

接收日期 2023 年 6 月 22 ; 2023 年 12 月 20 修订接收; 接受日期 2024 年 1 月 23 日在线提供 2024 年 2 月 4
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I. La Paglia et al.Mechanical Systems and Signal Processing 211 (2024) 111181
I.La Paglia人机械系统信号处理211(2024)111181

(EMA). This analysis can be performed in static conditions, where the tyre is excited at one location through an impact hammer or a shaker, and accelerations are measured at different positions along the tyre circumference. The Frequency Response Functions (FRFs) of the system are computed and used in the extraction of the modal parameters. Several test bench configurations have been proposed in literature to carry out the EMA of a static tyre, such as in [8,9]
(欧洲药品管理局 (EMA))。这种分析可以在静态条件下进行,其中轮胎通过冲击锤或振动器在一个位置被激发,并在沿轮胎圆周的不同位置测量加速度。计算系统的频率响应函数 (FRF) 并用于模态参数的提取。文献中已经提出了几种测试台配置来执行静态轮胎的 EMA,例如 [8,9]
.

Although tyre vibrations have been deeply studied in static conditions, difficulties arise when dealing with a rolling tyre. At first, vibration measurements cannot be easily performed with conventional accelerometers placed on the tyre outer surface. Therefore, other measuring systems such as laser Doppler vibrometer should be considered [10]. Furthermore, the dynamic response at the contact patch cannot be measured. Secondly, a reliable identification of the input force becomes challenging. This prevents the execution of the classical EMA, and other identification techniques must be considered. In literature, most of the authors rely on the Operational Modal Analysis (OMA) to identify the modal parameters of the rolling tyre [9,1114]
尽管在静态条件下对轮胎振动进行了深入研究,但在处理滚动轮胎时会出现困难。起初,使用放置在轮胎外表面的传统加速度计无法轻松进行振动测量。因此,应考虑其他测量系统,如激光多普勒测振仪[10]此外,无法测量接触贴片处的动态响应。其次,可靠地识别输入力变得具有挑战性。这会阻止经典 EMA 的执行,并且必须考虑其他识别技术。在文献中,大多数作者依靠业务模态分析(OMA)来确定滚动轮胎的模态参数[9,11\u201214]
.

Regarding the test configuration, one of the typical solutions adopted to excite a rolling tyre in indoor conditions relies on a cleat test, where the tyre rolls over an obstacle providing an impulsive-like excitation. This test is suitable for understanding the tyre low frequency dynamic behaviour, given that the maximum frequency excited by the cleat impact is approximately 300 Hz [2]. For instance, a cleat test was carried out in [15] mounting the obstacle on the surface of a 2 m diameter steel drum, with a perpendicular inclination with respect to the tyre rolling plane. The tyre hub forces were measured and used to tune an in-plane ring model. A similar test setup was used in [9], where a laser Doppler vibrometer was adopted to measure the tyre radial surface vibrations. An alternative cleat test setup was proposed in [13], constituted by two identical tyres which rotate one against the other. The undriven wheel is mounted on a dynamometric hub which allows the measurement of the forces generated during the test. The excitation is provided by an aluminium cleat mounted on the driven wheel, and a laser Doppler vibrometer was used to measure the surface vibrations.
关于测试配置,室内条件下激励滚动轮胎的典型解决方案之一依赖于防滑钉测试,其中轮胎obstacle提供类似冲动激励。测试适用于了解轮胎低频动态行为,因为锁片撞击激发的最大频率约为300Hz[2]对于例如,直径2m表面进行夹板测试[15],使其垂直倾斜轮胎滚动平面。测量轮胎轮毂用于调整平面内模型。类似的测试装置用于 [9]其中采用激光多普勒测振仪测量轮胎径向表面振动。[13] 提出了一种替代的防滑钉测试装置,由两个相同的轮胎组成,它们相互旋转无驱动安装在测功轮毂,可以测量测试过程中产生的激发安装在从动上的铝制夹板提供并使用激光多普勒测振仪测量表面振动。

A phenomenon that has been observed by many authors during rolling tyre tests is the bifurcation effect [16]. In static conditions, input forces generate progressive and regressive waves that propagate along the tyre structure at the same speed. Consequently, their superposition results in standing wave vibration modes. In rolling conditions, progressive and regressive waves travel at different propagation speeds due to Coriolis accelerations. Moreover, a Doppler frequency shift is present if the tyre rotation is observed in a fixed reference system. The Coriolis effect prevents the realization of standing waves, and the resulting modes will be complex; thus, they will present a propagation velocity [9,13,1618]. The bifurcation effect depends on the tyre rolling speed, the considered mode number and the corresponding mode shape. Based on these considerations, the classical definition of mode shape cannot be applied to rotating systems, and identification techniques should be based on wave propagation models.
许多作者滚动轮胎测试观察到的一个现象分岔效应[16]静态条件下,输入会产生渐进回归它们相同的速度沿轮胎结构传播因此,它们的叠加导致振动模式。滚动条件下,由于科里奥利加速度进波回归不同的传播速度传播。此外,如果在固定参考系统中观察到轮胎旋转则存在多普勒科里奥利效应阻止驻波的实现产生的模式复杂;因此,它们呈现传播速度[9,13,1618]效应取决于轮胎滚动速度、所考虑模态相应的振型基于这些考虑,经典的振型定义不能应用于旋转系统,识别技术基于传播模型。

This paper aims at investigating the in-plane dynamic behaviour of a rolling tyre in the frequency range below 300 Hz through an indoor experimental approach. A measuring setup specifically designed to this purpose is presented. A cleat test is performed on a steel drum, and tyre radial vibration measurements are carried out through a laser triangulation sensor scanning the tread of the rolling tyre. Data are collected at different rolling speeds and inflation pressures to investigate the influence of both parameters on the tyre dy- namics. Secondly, starting from the tyre surface vibration at several positions along the tyre circumference, a strategy to identify the wave propagation field is proposed. With respect to previous publications, in this paper experimental data are fitted using a wave propagation formulation. Through this approach, no Complex Modal Testing [19] or Operational Modal Analysis techniques are
本文旨在通过室内实验方法研究滚动轮胎低于300Hz的频率范围内的平面内动力学行为提出了一种专门为此目的设计的测量装置进行夹板测试并通过扫描制胎面激光三角测量传感器进行轮胎径向振动测量轮胎。在不同滚动速度和充气压力收集数据以研究这两个参数轮胎动态的影响其次,轮胎沿轮胎圆周多个位置的轮胎表面振动出发,提出了一种识别传播的策略相对于以前的出版物,本文使用传播公式拟合实验数据通过这种方法没有复杂模态测试[19] 操作模态分析技术

Fig. 1. Measurement grid: 50 nodes regularly spaced every 5 , from 33 to +212 (their position is defined in the fixed reference system). For visualization purposes, only nodes 1, 10, 30 and 50 are highlighted.
无花果。1.测量网格:50个节点5节点从 33 +212 间隔(它们的位置固定参考系统中定义)。出于可视化目的,突出显示节点1、10、3050

2

I. La Paglia et al.Mechanical Systems and Signal Processing 211 (2024) 111181
I.La Paglia人机械系统信号处理211(2024)111181

applied; no analytical model is involved during the identification procedure, such as in [11,12]. The discontinuity in tyre radial vi- bration due to the contact patch is taken into account enabling the identification of real circumferential mode numbers. In addition, to interpret the results, the test data have been compared to the analytical results obtained with a simplified in-plane tyre model, showing a satisfactory degree of correlation.
应用的;识别过程中涉及任何分析模型例如[11,12]中,由于接触引起的轮胎径向振动不连续性被考虑在内启用模式数的标识此外,为了解释结果测试数据使用简化的面内轮胎模型获得的分析结果进行了比较显示出令人满意的程度相关性。

The paper is organized as follows. In Section 2, the experimental setup realized to measure the tyre response during a cleat test is described. In Section 3, the data processing technique to synchronize data and extract the tyre vibration out of the recorded time histories is described; then, the wave propagation algorithm is presented and details on the fitting procedure are provided. In Section 4, different datasets are compared in order to investigate the influence of speed and inflation pressure; in addition, the results are compared with those of a tyre analytical model. Eventually, Section 5 draws the conclusions of this work.
本文的组织结构如下2 节中,描述了防滑钉测试期间测量轮胎响应实验设置3 节中,描述了同步数据并从记录的时中提取轮胎振动数据处理技术;然后,给出了传播算法,并详细介绍了拟合过程4 节中,比较不同的数据集研究速度和充气压力的影响;此外,还将结果轮胎分析模型的结果进行比较最终,5得出了这项工作结论

2. Experimental setup
2.实验装置

In order to measure the vibration of the tyre in rolling conditions, a dedicated experimental setup has been designed and installed in an existing facility, where cleat tests are carried out. The test rig is made up of a steel drum driven by an electric motor. A laser triangulation sensor (MEL Microelectronics M7L 50) is adopted to scan the tyre surface. The sensor has a measuring range of 50 mm around the focus distance of 95 mm. It is kept at a fixed distance from the tyre by the supporting structure, and it measures the tyre response after the cleat impact. The vibration measurements have been performed at 50 positions (nodes) along the tyre circumfer- ence. A measurement grid of 5 has been adopted, with a total covered angle of 245. Due to the contact patch and the contiguous regions that could not be reached by the laser beam, given the presence of the drum, no measurements could be performed over 115. For the sake of clarity, Fig. 1 shows the measurement grid: for visualization purposes, only few nodes are reported. The centre of the contact patch is located at the angle position 270, while the first measuring position is in correspondence of the angle 327. The blue arrows on Fig. 1 show the adopted convention for the reference system and the tyre rolling direction. In this work, a transversal cleat (perpendicular to the x-y plane) was used, and we refer to radial vibrations occurring in the x-y plane as the in-plane tyre response.
为了测量轮胎滚动条件下振动已经设计了一个专门的实验装置,并在现有设施安装了防滑钉测试装置执行测试电动驱动的组成采用激光三角测量传感器 (MELMicroelectronicsM7L50) 扫描轮胎表面。传感器95mm 的焦周围具有 50mm测量范围通过支撑结构轮胎保持固定距离测量轮胎在锁碰撞后的响应振动测量沿轮胎圆周50个位置(节点)进行采用了 5测量网格覆盖245由于接触贴片相邻区域可以激光束无法到达鉴于滚筒的存在无法进行超过115测量为了清晰起见,无花果。1测量网格:出于可视化目的,报告了少量节点接触的中心位于角度位置270第一测量位置角度327 相对应图 1 上的蓝色箭头1显示了参考系统和轮胎滚动方向的采用约定在这项工作使用了横向夹板(垂直x-y平面),我们将发生在x-y平面上的径向振动称为平面内轮胎响应。

The structure that carries the sensor was designed to be stiff and stable in order to measure the tyre vibration, reducing as much as possible any disturbance. To this end, the structure was installed on supports that are dynamically decoupled from the test rig basement by means of a suspended foundation. Fig. 2 shows a 3D CAD model of the designed system, that is constituted by two set of elements: a fixed rigid frame (supporting structure), which carries the loads and provides the required stiffness; a moving structure connected to the fixed frame, that supports the laser sensor and which can be fixed at different angular positions around the centre of the tyre.
承载传感器的结构被设计坚硬和稳定以便测量轮胎振动,尽可能减少任何干扰。为此结构安装在通过悬空基础测试地下室动态解耦支架无花果。图 2显示了所设计系统的 3DCAD模型它由元件组成:一个承载载荷的固定刚性框架(支撑结构)并提供所需的刚度;一种所述固定框架相连移动结构,所述固定框架支撑所述激光传感器,且该结构可以固定在所述激光传感器中心周围的不同角度位置轮胎。

Considering the moving structure, it is positioned at the centre of the horizontal beam, aligned with the centre of the tyre. The
考虑到移动结构,位于水平的中心轮胎的中心对齐

rotation of the structure (red dashed line in Fig. 2b) is provided by an electric motor. At each position, the tyre vibration is acquired for
结构旋转图 1 中的红色虚线)。2b)电动提供在每个位置,获取轮胎振动

30 s at a sampling frequency of 5 kHz. Once the acquisition is completed, the sensor automatically moves to the subsequent position. To reduce the effect of the oscillations induced by the arm rotation, before to start the next acquisition, further 30 s are considered so as to reach a static condition. At the end of the test, 50 time histories are collected.
采样频率为 5 kHz 30采集完成后,传感器会自动移动到后续位置。为了减少机械臂旋转引起的振荡的影响开始下一次采集之前,