液粘离合器摩擦热弹性不稳定性及其热失效机理研究

项目来源

国家自然科学基金(NSFC)

项目主持人

崔红伟

项目受资助机构

太原理工大学

项目编号

51805351

立项年度

2018

立项时间

未公开

研究期限

未知 / 未知

项目级别

国家级

受资助金额

22.00万元

学科

工程与材料科学-机械设计与制造-传动与驱动

学科代码

E-E05-E0502

基金类别

青年科学基金项目

关键词

热失效 ; 热弹性不稳定性 ; 热屈曲特性 ; 液粘离合器 ; 热失效 ; 热弹性不稳定性 ; 热屈曲特性 ; 液粘离合器

参与者

龙日升;廖瑶瑶;王其良;乔一军;刘强

参与机构

沈阳化工大学;太原理工大学;太原科技大学

项目标书摘要:液粘离合器广泛应用于大功率机械设备的调速和软启动,是节能降耗和提高设备可靠性的有效手段。然而大量的摩擦损耗经常导致摩擦副出现局部高温甚至发生烧蚀或翘曲变形等热失效问题。预先研究表明摩擦副的非均匀温度场及其热屈曲变形是导致热失效的直接原因,而控制油压动态变化和非均匀接触压力引起的摩擦副瞬态热弹性不稳定性及热失效临界条件难以预测。因此,本项目构建液粘离合器湿式摩擦副热弹性不稳定性三维有限元模型,探寻主模态下的扰动增长系数和热弹性失稳临界速度,揭示控制油压动态变化条件下的热点形成机理及温度场动态分布规律,耦合求解摩擦副的热弹性不稳定性和热屈曲特性,最后试验研究摩擦副的温度场分布和波动特性。通过本项目的研究,有望揭示摩擦副瞬态热弹性不稳定性和局部高温形成机理,阐明温度场非均匀分布和热屈曲特性耦合机制,掌握摩擦副发生热失效的判断方法,为改善液粘离合器调速和软启动性能及提高机械设备可靠性提供理论依据。

Application Abstract: Hydro-viscous clutch is widely applied to the high-power mechanical equipment for speed regulation and soft starting.It is an efficient method to energy-saving,reduce consumption,and improve the reliability of equipment.However,the local high temperature of friction pairs and even thermal failures such as ablation or warpage deformation will occur because of a large number of frictional heat dissipation.Our pre-research demonstrates that the non-uniform temperature field and thermal buckling deformation of friction pairs are the direct causes of thermal failure.But the transient thermoelastic instability and critical conditions of thermal failure which are caused by dynamic change of control pressure and non-uniform contact pressure are difficult to be predicted.Therefore,a three-dimensional finite element model for thermoelastic instability of friction pairs will be established.The perturbation growth coefficient and critical velocity in the main mode will be explored.The mechanism of hot spot and dynamic distribution of temperature field under dynamic change of control pressure will be revealed.The effect of thermoelastic instability on thermal buckling characteristics will be solved.Finally,the distribution and fluctuation characteristics of temperature will be got by experimental research.Through the project,it is expected to reveal the mechanism of transient thermoelastic instability and local high temperature,clarify the coupling mechanism of non-uniform distribution of temperature field and thermal buckling characteristics,and get the judgment method for thermal failure of friction pairs.The research results can provides the theoretical and technical support for improving the speed regulation and soft starting performance of hydro-viscous clutch and the reliability of mechanical equipment.

项目受资助省

山西省

项目结题报告(全文)

液黏离合器具有无级调速、软启动、过载保护及可靠性高等功能和优点,广泛应用于大型设备的调速以及重型刮板输送机的软启动,然而长时间滑摩过程中摩擦副大量的瞬态热积聚导致的出现局部高温甚至发生烧蚀或翘曲变形等热失效现象,而摩擦副的热失效和工作品质不稳定一直是困扰传动性能提高的瓶颈问题,性能优异的湿式摩擦副仍然需要进口,且价格昂贵,成为制约我国液黏离合器领域发展的“卡脖子”问题。因此,针对液黏离合器软启动瞬态滑摩过程,采用理论建模、数值模拟与试验研究等现代化方法,建立了基于扰动法的摩擦副热弹性不稳定性理论模型,考虑摩擦副厚度求解对称—反对称模态下的热弹性不稳定性系统矩阵,获得了临界速度、扰动增长系数、表面扰动压力场及温度场的瞬态分布及变化规律,探明了摩擦副热点形成机理及热点个数对扰动增长系数的影响规律;建立了摩擦副的三维瞬态热传导模型,利用有限元法对摩擦副非均匀温度场的分布特性进行了求解;构建了摩擦副三维瞬态热机耦合模型,探寻了热载荷和机械载荷共同作用下的应力应变变化规律;建立了三维热屈曲壳模型,揭示了热屈曲临界条件及相应的屈曲变形模态;搭建了液黏离合器摩擦副综合试验台,确定了摩擦副温度场的测试方案,验证了仿真模型的有效性。通过本项目的研究,完善了摩擦副瞬态热弹性不稳定性和热机耦合基础理论,阐明了摩擦副表面扰动压力场和非均匀温度场变化规律及热点形成机理,形成了热弹性不稳定性和热机耦合特性共同作用下的热屈曲及热失效判断方法,最终实现了工程实践应用,提高了大功率机械设备的工作品质、使用寿命和可靠性。研究过程中共发表学术论文14篇,其中SCI7篇,EI1篇,参加国际国内学术会议10余次,出版专著1部,申请发明专利2项,培养博士研究生3人,硕士研究生5人,研究成果成功应用于重型刮板输送机的可控启动装置,取得了显著的经济和社会效益。

  • 排序方式:
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  • 1.组合式湿式离合制动器控制下的热模锻压力机工作性能分析

    • 关键词:
    • 组合式湿式离合制动器;热模锻压力机;动力学;工作性能;摩擦副打滑;转矩
    • 崔红伟;李冬辉;梅碧舟;李琦;张玲卿
    • 《锻压技术》
    • 2026年
    • 期刊

    组合式湿式离合制动器作为压力机传动系统的核心组成部分,其质量性能直接决定压力机能否可靠安全地运行。为研究组合式湿式离合制动器对热模锻压力机工作性能的影响,对热模锻压力机传动系统进行了动力学分析,引入修正的平均流量模型和粗糙接触模型,建立了湿式摩擦副接合过程中传递转矩模型;基于组合式湿式离合制动器液压控制原理,利用AMESim与Simulink联合仿真技术,构建了热模锻压力机传动系统仿真模型。仿真结果表明,通过对组合式湿式离合器活塞油压软离合-硬离合-软制动-硬制动变化的控制,实现离合制动器传递转矩和曲轴行程角度变化。接合压力降低、摩擦盘磨损、制动弹簧力降低均会导致离合器、制动器打滑,进而导致压力机发生闷车、滑块超程等故障,最后,针对此故障原因提出了预防与解决措施。研究结果对实现压力机可靠控制及维护安全生产具有指导意义。

    ...
  • 2.Numerical simulation and experimental investigation on the thermal-fluid-solid multi-physical field coupling characteristics of wet friction pairs considering cavitation effect

    • 关键词:
    • Wet friction pairs; Cavitation effect; Thermal-fluid-solid coupling;Maximum temperature; Convective heat transfer coefficient;CONVECTIVE HEAT-TRANSFER; DISK SYSTEM; BRAKE; CLUTCH; FLOW; BEHAVIOR
    • Wang, Qiliang;Zhang, Xingbo;Wang, Dagang;Cui, Hongwei;Zhang, Shuai;Wang, Jianmei
    • 《APPLIED THERMAL ENGINEERING》
    • 2025年
    • 260卷
    • 期刊

    The coupling characteristics of thermal-fluid-solid multi-physical fields are crucial in determining the operational performance and service life of wet clutches. However, the underlying mechanism behind the influence of cavitation effect on these coupling characteristics remains unclear. Therefore, we propose a numerical solution method for considering cavitation effect in the coupling characteristics based on the multi-physical field coupling platform MPCCI combined with ABAQUS and FLUENT. The distribution patterns and intercoupling relationships among temperature field, flow field, and stress-strain field are comprehensively analyze. The influence of relative speed, cross-sectional shape of oil grooves, and oil flow on the coupling characteristics is investigated. Experimental validation confirms that the proposed model accurately predicts temperature variation by accounting for cavitation effect. The temperature distribution of steel discs is notably affected by the cavitation effect, leading to an elevation in the maximum temperature and uneven distribution characterized by localized hot spots along the circumferential direction. Accounting for the cavitation effect reduces errors between calculated and experimental values of temperature rise. The convective heat transfer coefficient gradually decreases radially, with a more pronounced decrease in the cavitation region. An increase in relative speed and a decrease in oil flow both lead to greater cavitation volume, resulting in higher temperature of steel discs. Among three different crosssectional shapes of oil grooves investigated, rectangular grooves exhibit larger areas affected by cavitation compared to triangular grooves. These research findings provide a theoretical basis and technical support for accurate prediction of thermal characteristics within high-power wet clutches.

    ...
  • 3.Numerical investigation into thermal buckling of friction pairs in hydro-viscous drive under nonlinear radial temperature distribution

    • 关键词:
    • Hydro-viscous drive; thermal buckling; nonlinear radial temperature;eigenvalue; critical buckling temperature;FINITE-ELEMENT-ANALYSIS; CLUTCH
    • Wang, Qiliang;Wang, Jianmei;Cui, Hongwei;Wang, Jun;Zhang, Fan
    • 《PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART J-JOURNAL OFENGINEERING TRIBOLOGY》
    • 2021年
    • 236卷
    • 6期
    • 期刊

    Thermal buckling deformation can significantly impact the operating performance of hydro-viscous drive. A thermal buckling finite element shell model was established with the nonlinear radial temperature as the thermal loading condition. The thermal buckling behavior of friction pairs was investigated under three different boundary constraints. Moreover, the influence of thickness and material parameters on the critical buckling temperature was discussed. The simulation results coincide with the failure modes of friction pairs in practice, and the most common ones are the coning mode and the potato chip mode. The ability to resist thermal buckling deformation can be improved as the thickness increases. In addition, the steel disc with outer edge simply supported is more prone to thermal buckling, because the critical temperature is minimum. The thermal expansion coefficient is the primary factor in thermal buckling study, which is inversely proportional to the critical temperature. These provide a theoretical basis for avoiding thermal failure of friction pairs in a hydro-viscous drive.

    ...
  • 4.液黏摩擦副马鞍形屈曲变形接触及温度场分布特性研究

    • 关键词:
    • 液黏离合器;摩擦副;马鞍形屈曲变形;赫兹接触;温度场
    • 姜宇宇;崔红伟;乔一军;孙浩;宁敬威
    • 《机械传动》
    • 2022年
    • 5期
    • 期刊

    马鞍形屈曲变形是液黏离合器摩擦副最主要的热屈曲变形方式。为获取变形摩擦副的接触特性及温度场分布规律,基于椭球体赫兹点接触理论与屈曲变形规律,建立了摩擦副接触变形等效模型,获得了软启动工况下变形摩擦副接触应力的分布与变化规

    ...
  • 5.Finite Element Analysis on Thermoelastic Instability of Multidisc Clutches Involving Deformation Modes of Multilayer Material Friction Disc

    • 关键词:
    • Ductile fracture;Elastic moduli;Finite element method;Fourier series;Friction;Multilayers;Stability;Thermal conductivity;Thermoelasticity;Critical speed;Deformation modes;Friction disks;Friction pair;Multilayer material friction disk;Multilayer materials;S ratio;Steel disks;Symmetrics;Thermoelastic instability
    • Suo, Yiran;Cui, Hongwei;Mei, Bizhou;Li, Donghui;Jiang, Yuyu;Sun, Hao;Zhang, Lingqing
    • 《Journal of Tribology》
    • 2024年
    • 146卷
    • 4期
    • 期刊

    A two-dimensional finite element model was developed to investigate thermoelastic instability in multilayered friction discs with finite thickness, considering the deformation modes of the steel core. The model was used to simulate four unstable modes that can occur during the engagement process, and the Fourier reduction was applied to calculate the change in critical speed under these modes. Additionally, the influence of thermal physical parameters, including the elastic modulus, thermal expansion coefficient, Poisson’s ratio, and thermal conductivity of the friction pair, on thermoelastic instability was examined. The findings indicate that the critical speed of the friction pair is lower under the symmetric (friction disc)–antisymmetric (steel disc) mode compared to the other three modes. Consequently, the symmetric–antisymmetric mode is the first to be excited and serves as the dominant mode during thermoelastic instability. Moreover, there exists a specific wave number at which the system exhibits the lowest critical speed and poorest stability. Enhancing the thermal conductivity of the friction disc and steel disc, as well as reducing the thermal expansion coefficient of the steel disc and the elastic modulus and Poisson’s ratio of both discs, can improve the thermoelastic stability of the friction pair. Notably, the thermal expansion coefficient of the friction disc has minimal impact on thermoelastic instability. These results provide a theoretical foundation for exploring the relationship between the thermal failure of friction pairs and rotational speed, as well as optimizing overall performance design. © 2024 by ASME.

    ...
  • 6.考虑结构参数影响的液黏离合器锥形摩擦副非线性承载特性研究

    • 关键词:
    • 液黏离合器;锥形变形;结构参数;承载特性
    • 孙浩;崔红伟;梅碧舟;李冬辉;索一然;张玲卿
    • 《机械传动》
    • 2024年
    • 2期
    • 期刊

    为研究不同结构参数对锥形变形摩擦副承载特性的影响,建立不同结构参数下锥形变形摩擦副等效接触模型,采用Ansys Workbench进行屈曲变形仿真,结合Matlab数值模型分析,得到不同结构参数下摩擦副油膜厚度变化规律;基于油膜压力与微凸峰粗

    ...
  • 7.液黏离合器软启动瞬态热机耦合特性及热屈曲变形规律研究

    • 关键词:
    • 液黏离合器;摩擦副;非均匀温度场;热机耦合;热屈曲特性
    • 王其良
    • 指导老师:太原理工大学 廉自生
    • 学位论文

    液黏离合器广泛应用于刮板输送机、带式输送机的软启动和风机、水泵的无级调速,具有节能降耗、高效及可靠性高等优点。摩擦副是液黏离合器的核心部件,在刮板输送机软启动过程中摩擦副长时间的相对滑摩会产生大量的摩擦热损耗,经常发生局部高温引起的摩擦材料烧蚀和剥落、对偶钢片屈曲变形等问题,从而导致摩擦副的热失效,直接影响液黏离合器的工作性能、可靠性及使用寿命。因此,有必要对软启动过程中摩擦副的瞬态热机耦合特性和热屈曲变形规律开展深入研究。以液黏离合器软启动过程为研究对象,建立了油膜剪切转矩和微凸峰接触转矩模型,利用摩擦转矩和负载转矩的动态平衡关系,求解了软启动过程中油膜厚度、油膜压力及微凸峰接触压力,获得了摩擦副接触压力的动态变化规律。结果表明:当启动速度遵循S型曲线变化时,油膜厚度按反S型曲线逐渐减小,接触压力按S型曲线增大,为摩擦副温度场的预测提供了必要的边界条件。为了探明软启动过程中摩擦副的热特性,考虑接触压力和相对转速的时变性,构建了摩擦副瞬态热传导模型,获得了软启动过程摩擦副非均匀温度场的动态分布规律,在此基础上深入研究了启动时间对热特性的影响。结果表明:对偶钢片温度先缓慢上升后快速上升,在达到最大值后逐渐下降;摩擦片温度在启动结束时达到最大值,接触表面上每个菱形区域中心的温度高于四周区域;启动持续时间越长,温升越高,径向温度梯度越大。研究结果可为后续的热机耦合特性和热屈曲变形规律的研究提供基础。为了揭示热载荷和机械载荷共同作用下温度、应力及应变场之间的耦合关系,基于非均匀温度场动态分布特性构建了摩擦副瞬态热机耦合模型,分析了启动过程中摩擦副应力、应变及位移场的分布规律,阐明了径向位移约束位置对热弹塑性变形规律的影响。结果表明:对偶钢片应力沿内径至外径方向先上升后下降,周向应力是最主要的应力分量,可作为判断摩擦副是否发生塑性变形的重要依据,热载荷和径向位移约束位置对应力及应变的分布起到至关重要的作用。针对摩擦副热屈曲特性,基于摩擦副非线性径向温度分布构建了热屈曲有限元模型,探明了摩擦副的热屈曲变形规律,得到了屈曲特征值、临界温度及相应的变形模态,揭示了影响抵抗屈曲变形能力的主要因素。结果表明:锥形屈曲变形和马鞍形屈曲变形是失效摩擦副常见的两种变形模态;自由边界条件下,临界屈曲温度与厚度呈近似二次方关系;热膨胀系数是热屈曲研究中的关键因素,热膨胀系数越大,越容易发生热屈曲变形。根据摩擦副热特性试验的需求,研制了专门的液黏离合器摩擦副综合试验台,测量了软启动过程中摩擦副温度的动态变化,探明了摩擦副接触压力、相对转速和润滑油流量对温度的影响规律。仿真结果和试验结果具有较好的吻合性,验证了数值仿真模型的准确性,表明可利用仿真模型对摩擦副的实际温度进行准确地预测。

    ...
  • 8.Research on Load Matching Characteristics and Torque Experiment of Soft Start for Hydro-Viscous Drive

    • 关键词:
    • Conveyors;Friction;Function evaluation;Tools;Comprehensive evaluation;Condition;Evaluation function;Hydro-viscous drives;Improved radar charts;Load matching;Matching characteristic;Matchings;Scraper conveyor;Soft start
    • Li, Long;Cui, Hong-Wei;He, Bai-Yan;Zhu, Dong-Jie;Cui, Jia-Ru;Guo, Yan-Dong
    • 《9th International Conference on Fluid Power and Mechatronics, FPM 2023》
    • 2023年
    • August 18, 2023 - August 21, 2023
    • Lanzhou, China
    • 会议

    In order to study the load matching characteristics of the hydro-viscous drive soft start of scraper conveyor under different working conditions, a mathematical model of load torque, hydraulic viscous clutch bearing capacity, and hydro-viscous drive torque are established, the influence of different load starting speed on the soft start characteristics of scraper conveyor are revealed. Based on the improved radar chart method, the matching evaluation system consisting of matching evaluation indexes and evaluation functions is established, and the matching schemes of four starting speeds under different working conditions are quantitatively evaluated. The results show that as the load increases, the matching effect between S-type start and sinusoidal start with hydro-viscous drive is better. Simultaneously, a torque testing platform for hydro-viscous drive is established, the torque and friction characteristics of the friction pair of the controllable starting device are analyzed, and the control characteristics of different starting target speeds are studied. Through experimental research, it can be concluded that under heavy load conditions, the speed curves of S-type start and sinusoidal start have good compliance with the theoretical speed, short response time, and quickly reach a stable state. Under light load conditions, the torque required by the load is small, and the clutch fully meets the system torque requirements, and the matching effect of using linear start and parabolic start is better. By reasonably controlling the starting speed of the load and using the comprehensive evaluation function determined by the improved radar chart evaluation method, the advantages and disadvantages of the soft start matching scheme can be accurately quantified. The research results provide a theoretical basis for the optimal control scheme of the soft start of the scraper conveyor under different working conditions. © 2023 IEEE.

    ...
  • 9.液黏离合器摩擦热流分配及温度场分布特性研究

    • 关键词:
    • 液黏离合器;摩擦副;对流换热系数;温度场分布
    • 代吉超
    • 指导老师:太原理工大学 常宗旭
    • 学位论文

    液黏离合器利用油膜剪切力和摩擦表面间的相互接触传递动力来实现设备的软启动,在相对滑摩过程中会产生大量的摩擦热,使得摩擦副温度急剧升高,尤其是不均匀的温升易导致摩擦副变形,从而影响液黏离合器的工作性能。要减小液黏离合器摩擦副的热弹性变形,首先要准确预测摩擦副的温度场。本文以液黏离合器双圆弧油槽摩擦副为研究对象,首先采用有限元仿真分析求得摩擦副与工作油之间的对流换热系数,然后以此为边界条件得到了一组摩擦副的温度场分布,并通过仿真获得了多组摩擦副在轴向方向的温度场分布情况。最后,通过试验验证了数值模拟方法的有效性。为了得到摩擦副准确的对流换热系数,利用CFX建立了摩擦副流固耦合有限元模型,综合考虑换热表面形状,摩擦片转速、油液入口压力和油液物理性能等参数,得到各影响因素与对流换热系数之间的关系。结果表明,对流换热系数从内径到外径随油槽横截面积变化而变化;油液黏度越小,入口压力越大,对流换热系数越大。为了得到摩擦副的温度场分布,在ABAQUS中建立了摩擦副温度场模型,根据理论计算求得的热分配系数输入热流密度作为热源,以求出的对流换热系数为边界条件,得到了摩擦副的温度场分布。结果表明,摩擦片和对偶钢片温度从内径到外径逐渐升高,油槽间的菱形区域中心温度比四周高,易形成热斑;摩擦副法向载荷会影响摩擦元件的温度值,但对温度场的分布规律影响不大。采用数值模拟的方法求得了多组摩擦副的温度场分布情况。结果表明,在轴向方向摩擦副的温度先升高后下降,在活塞侧第5片摩擦元件区域温度值达到最大;外径区域温度明显高于内径区域。摩擦副之间材料属性的差异导致对偶钢片的温度整体比摩擦片高,摩擦副温度在轴向方向呈现高低交替分布。花键处摩擦力使得摩擦副在轴向方向压力递减,导致轴向温度产生梯度。搭建了液黏离合器摩擦副热负荷特性试验台架。采用给定驱动电机转速,给定负载电机转矩的方法模仿软启动过程。在对偶钢片中嵌入了温度传感器,利用计算机数据采集系统对滑摩状态下对偶钢片的温度进行监测,得到了不同离合器压力、不同滑摩时间下的温度场分布情况,试验与仿真得出的结果基本一致。

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  • 10.液黏离合器摩擦副瞬态热弹性不稳定性研究

    • 关键词:
    • 液黏离合器;热弹性不稳定性;临界速度;热点;非均匀温度场
    • 乔一军
    • 指导老师:太原理工大学 王铁
    • 学位论文

    液黏离合器广泛应用于矿用重型刮板输送机、皮带输送机的软启动,车辆的液力变矩器和锁止离合器等。摩擦副是液黏离合器的核心部件,经常发生局部高温问题导致的热失效,直接影响液黏离合器的工作性能、可靠性及使用寿命。热弹性不稳定性理论考虑了周向非均匀温度场、热流密度、热弹性应力等物理量的相互耦合作用,是研究局部高温问题的重要手段。因此,有必要对液黏离合器摩擦副的热弹性不稳定性进行深入的研究,为提高液黏离合器摩擦副的可靠性和使用寿命奠定理论基础。针对液黏离合器摩擦副,建立了考虑多层材料摩擦片厚度的热弹性不稳定性二维理论模型,得到了摩擦片和对偶钢片分别为对称或反对称模态下的热弹性不稳定性系统矩阵,研究了四种变形模态下的临界速度变化规律,确定了摩擦片对称-对偶钢片反对称为系统的热弹性不稳定性主模态。基于热弹性不稳定性二维理论模型,提出了利用系统矩阵确定扰动增长系数与相对滑摩速度定量关系的方法,确定了主模态下不同半径处的临界线速度及扰动增长系数,得到了摩擦副接触表面扰动压力场及扰动温度场的动态分布规律,确定了滑摩时间和初始压力扰动幅值等因素对扰动场的影响规律,为液黏离合器变速滑摩过程瞬态热弹性不稳定性研究提供了先决条件。以液黏离合器变速滑摩过程为研究对象,基于平均流量模型及粗糙接触模型,得出了摩擦副的平均接触压力,利用扰动增长系数与相对滑摩速度的关系,得到了变速滑摩过程中的扰动增长系数,获得了扰动压力及热点总压力;建立了摩擦副三维瞬态热传导模型,得出了摩擦副的径向非均匀温度场分布,结合摩擦副热弹性不稳定性导致的周向温度场扰动,得到了液黏离合器变速滑摩过程中摩擦副的热点温度。为了研究磨损规律对热弹性不稳定性的影响,在热弹性不稳定性理论模型基础上引入磨损定律,建立了磨损对热弹性不稳定性影响的有限元模型。利用双材料半平面解析方法,验证了有限元方法所得数值解的有效性,得到了摩擦副磨损率和厚度对热弹性不稳定性的综合影响规律。根据摩擦副热弹性不稳定性试验的需求,搭建了液黏离合器摩擦副热弹性不稳定性试验台,测量了滑摩过程中摩擦副温度的动态变化,整理出摩擦副相对转速、接触压力和润滑油流量对扰动温度场的影响规律。理论结果与试验结果具有较好的吻合性,验证了理论方法的有效性,表明可利用所提出方法对摩擦副的热弹性不稳定性进行较为准确的预测。

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