基于扩展Stribeck效应的摩擦实验建模及系统动力学研究
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摘要
摩擦是一门十分古老而年轻的科学,已经证实摩擦存在于人类生活的方方面面,在机械领域,摩擦扮演着尤为关键的角色。对摩擦特性及其线性,非线性因素的全面考量和精确控制,对于提高机械加工精度,产品质量,延长运行寿命具有至关重要的作用。
课题从考虑摩擦在机械工程中所起的作用与影响出发,旨在研究含摩擦环节的机械系统实验、建模、识别以及结构的动力学特性。通过对含摩擦系统进行多方实验的基础上,分析研究摩擦的静态和动态特性,并结合实验数据,提出全新的摩擦力模型,使之尽可能多的描述并预测实验中所呈现的摩擦特性,并利用此模型对含摩擦系统低速下的粘滑现象及相关动力学特性进行了分析和探讨。
论文首先概述了摩擦的定义和历史,通过“静、动”两个概念及区别,分类介绍了当前已知的摩擦特性,在此基础上,按照不同的建模思路,分别介绍了静态摩擦模型和动态摩擦模型的原理及优缺点,并简述了含摩擦系统动力学特性并重点关注粘滑、极限环等由摩擦引发的非线性环节的研究进展。
根据机械工程领域的实际研究目标,从宏观角度出发研究摩擦的动静态特性,对电梯导轨与导靴/靴衬间的横向及纵向摩擦特性做了详细的实验研究。通过设计不同的测试装置,采用不同的摩擦材料,通过大量的实验,测试并分析了摩擦力随接触界面间正压力、相对速度、润滑状态变化的情况,研究了摩擦力在预滑动和宏观滑动阶段的静态及动态摩擦特性,发现并提出摩擦过冲(Friction overshoot)概念。对实验得到的Stribeck曲线模型进行了参数化研究,针对界面磨损对摩擦特性的影响,从宏观及微观角度分别进行了实验研究、分析及对比,并得到一些有意义的结果。为后续的摩擦模型的建模和结构系统的动力特性分析提供必要的实验基础。
在实验基础上,提出了一个新的基于Bouc-Wen的单状态变量摩擦力模型(简称SSV)。通过引入规范化的Bouc-Wen模型,可以比较精确的描述摩擦力在预滑动阶段的滞回行为。同时并入一个速度的指数函数以及加速度的线性函数,使得模型可以描述摩擦宏观阶段的Stribeck效应,以及相应的速度滞后特性。根据鬃毛模型平均变形的理念,提出鬃毛平均等效质量的概念,使之可以描述从预滑动到宏观滑动阶段间的摩擦过冲特性,同时实现了两阶段间的光滑过渡。通过与实验数据的对比以及与LuGre模型的比较,此模型可以很好的拟合实测数据,在描述预滑动及摩擦过冲方面,较其他摩擦力模型更加有效。
基于旋转式摩擦试验机,进一步验证了摩擦滞回及速度滞后特性,并实验考察了单向速度激励下,摩擦在宏观滑动阶段的滞后特性。对预滑动范围内的摩擦非局部记忆效应进行了实验研究,发现在润滑条件下,摩擦力与位移在预滑动阶段成近似线性关系。获得了不同正压力下的Stribeck摩擦力曲线及摩擦系数曲线,并扩展了Stribeck曲线的定义范围,使其能够用一个公式预测在不同正压力和相对运行速度下的摩擦力,经实验数据验证具有良好的准确性。考查了摩擦切向与法向间运动的耦合关系,首次发现摩擦在润滑条件下存在法向位移与切线位移间的交叉滞回,及法向位移与切向速度间的滞回特性。从微观角度出发,在物理意义上对此现象进行了阐述及解释,并据此进行了理论建模。模型结构简单,易于识别,并具备进一步扩展的能力。通过模型仿真与实验数据的对比,证实了模型的合理性及有效性。实验以旋转式摩擦实验的研究结果为基础,将实验精度由毫米级提升至微米级,其结果不仅加深了对摩擦机理及特性的理解,并对高精度摩擦模型的发展提供了必要的实验基础。
基于直线往复和旋转式摩擦实验结果,提出一个新的高精度摩擦力模型:广义Bouc-Wen Maxwell-Slip摩擦模型(简称GBM)。在摩擦预滑动阶段,GBM模型用一系列含库仑摩擦的弹簧振子模拟预滑动阶段的摩擦特性;在宏观滑动阶段,则采用了改进的Bouc-Wen模型和含变摩擦系数的扩展Stribeck曲线。通过与四个常用摩擦力模型在描述摩擦特性方面的对比与实验验证,表明GBM模型在描述摩擦滞回、速度滞后、Stribeck效应、摩擦过冲、正压力相关等方面均优于其他模型。而且GBM利用Maxwell-Slip模型中含有多个变量的优点,从而比较好的描述了预滑动阶段非局部记忆效应及非漂移特性。模型在宏观滑动阶段使用的是单状态变量微分方程,在预滑动阶段依靠多变量的代数方程,平衡了效率与性能。另外,通过简化模型参数,GBM模型可以退化为Dahl、LuGre、SSV、GMS及其它模型,具有良好的适应性。总而言之,对于摩擦模型的选择,应根据不同的实际应用需求来进行。当系统精度或实时性需求不高时,Dahl、LuGre甚至库仑摩擦模型即可满足需求;对于高精度及实时性(如精确定位等控制领域)的需求,GBM模型是较为理想的选择。
以单自由度链式模型为研究对象,详细分析了含摩擦机械系统产生粘滑运动的现象与机理。探讨了由粘滑运动引发的两类振动,一是不同的激励速度所导致系统以不同频率做粘滞-滑动-粘滞的反复运动,表现为物体沿相对平衡位置做往复的低频振动,且振动频率与系统固有频率无关;而是伴随往复运动,系统在粘滞阶段还存在高频振动,这与一般认识上的粘滞即停止不同。通过定性、定量及与实验结果的对比分析表明,系统在粘滞阶段的高频振动频率不是单一固定值而是分布在一定宽度的频域内,其来源于摩擦预滑动阶段摩擦界面间不断变化的接触刚度,而摩擦阻尼及系统自身阻尼是高频振动逐渐衰减的原因。当系统发生粘滑运动时,系统响应随激励速度、系统刚度及阻尼的变化而呈周期、拟周期及混沌运动交替变化的形式。当激励速度、刚度及阻尼逐渐增大时,系统均呈现出逐渐从混沌运动状态向稳定的周期运动转变的趋势;伴随这一转变趋势,系统粘滑运动也会随参数值的增大而逐渐衰弱至消失,进而变为摩擦引起的准谐调周期振动,在理论极限情况下,准谐调运动也会消失。
本文的研究方法和结论对于推进摩擦实验研究、摩擦特性研究、摩擦模型的建模以及加深对机械系统粘滑现象的认识,提高系统的工作精度和使用寿命,具有一定的参考价值。
Friction, which belongs to the term of Tribology, is a young scientific discipline with long history. It has been proved to exist in every aspect of daily lives. In mechanical fields, friction acts as an especially important role. The full understand and control of the frictional characteristics is critical for improving machining precisions and product qualities, prolonging service lifetime.
The thesis is initiated from the viewpoint of how friction acts in the mechanical engingeering, aimed to explore the experiments, theoretical modeling, identification, dynamical property of systems with friction. According to profound experiments, the static and dynamic characteristics are analysed and new friction model is provided, which is able to describe and predict those experimentally observed phenomenon as many as possible. In addition, the stick-slip effect of system with frictional parts in low velocity ranges is investigated using the newly provided friction model.
Firstly, the definition and history of friction is summarized. In terms of“static and dynamic”, the state-of-the-art of frictional characteristics is classified. In the light of this point, the static and dynamical friction models and their merits and drawbacks are introduced in this work. The current researching progress on nonlinear reponses of system with frictional parts such as stick-slip and limit cycling are also briefly presented.
Secondly, based on the pratical research target in mechanical engineering field, the lateral/vertical friction characteristics between rail and guide shoe/pad in an elevator system are investigated macroscopically. By designing different test rigs, choosing different friction materials and performing a large amount of tests, the property of friction with respect to the variation of normal loads, relative velocities and lubricational conditions is examined. The static and dynamical properties of friction in the stage of pre-sliding and gross sliding are also studied, which results in the finding of Friction Overshoot property in the transforming stage from pre-sliding to gross sliding. The experimentally obtained Stribeck curve for different normal loads and materials are parameterized. The effects of wear on the frictional properties of surface in contact are carried out and analysed by experiments macroscopically and microscopically. Some meaningful results are visualized which provide a experimental basis for future friction modelings.
Based on the linearly reciprocating friction tests, a new Bouc-Wen based single-state-variable friction model (termed as SSV) is presented. By introducing the normalized Bouc-Wen model, the new model is able to describe the behaviors of friction in the pre-sliding stage precisely. Meanwhile, a exponential function with respect to velocity and a linear function with respect to accerlation are added, which make it possible for the new model to describe the Stribeck effect and friction lag happened in gross sliding stage. According to the definition of average inflection in the bristle theory, the average effective mass of bristle is defined, which is capable to predict the experimentally found friction overshoot property smoothly during the transation from pre-sliding to gross sliding regime. The comparisons between simulation using SSV and LuGre model and the experiment results show that the proposed friction model gives better results than traditional model without losing the flexibility.
Relyed on a rotational tribometer, the friction hysteresis and friction lag are further verified, and the friction lag under the uni-directional velocity excitation in gross sliding regime is also investigated. The non-local memory effect in lubricated condition is evalued as well. The tests show that the frction force varies linearly with respect to displacment in the stage of pre-sliding which is different from the cases of dry frictions. The working range of the Stribeck curve is widened by measuring Stribeck curves under different normal loads. The improved Stribeck curve becomes the function of normal load besides the relative velocity. The coupling relations between tangential and normal motions are investigated, It is the first time to observe a cross hysteretic relations between normal and tangential displacements and a hysteretic relationship between normal displacement and tangential velocity. Based on these results, a theoretical model is proposed from the physically microscopic viewpoint, and is validated by comparing the simulations with the experimental results. The measuring precision of the rotational tribometer is upgraded from the millimeter level to the micrometer level compared with the linearly reciprocating friction test rig, which gives a more profund understanding of friction characteristics and is necessary for developing high precision frition models. Grounded on the linear reciprocating and rotational friction measurements, the generalized Bouc-Wen Maxwell-Slip model (named as the GBM model) is developed.
The GBM model uses a series of parallelly connected spring and friction elements to simulate properties in the pre-sliding stage; while in the gross sliding stage, the extended Stribeck curve and improved Bouc-Wen model is utilized. According to comparisons between four friction models, it is clear that the GBM model performs better on predicting friction hysteresis, friction lag, Stribeck effect, friction overshoot and normal variations than other models. At the same time, GBM model is able to describe the non-local memory and non-drifting property in the stage of pre-sliding because of the incorporation of Maxwell-Slip elements. The model equations used in pre-sliding stage is one signle-state-variable ordinary differential equation. While in the gross sliding stage, it relies on several multi-variable algebra equations which balanced the effieciency and performance of the GBM model. In addition, the GBM is able to boiled down to the Dahl, LuGre, SSV and GMS model by simplifying model parameters, making it quite suitable in the fileds where high precision and real time control abilities are extremely appreciated.
Taking the single degree of freedom train model as the research object, the stick-slip effect and its mechanism in structures with frictional parts are analysed in detail. Two types of vibrations induced by stick-slip motion are dicussed. One is the cycling of stick-slip-stick motion, running in different frequencies being excited by different pulling velocities, taking the form of reciprocating motion along the relative equilibrium position of the object M, and the frequency is irrelevant with the natural frequency. The other is the high frequency vibration in the stage of stick motion. The qualitative, quantitative analyses and experimental verication show that the high frequency of the vibration is not accumulated in single value frequency but a distributed frequency range, which come from the varying stiffness between surfaces in contact. When system is in stick-slip motion, the system response can be periodic, quasi-periodic and chaos with the change of pulling velocities, system stiffness and viscous. When these parameters are increasing, system motion tends to be stabilized periodic motion from chaos. Along with this trend, the stick-slip motion will decrease and vanish, and turns out to be quais-harmonic vibration, which could disappear under extreme theoretical conditions.
The results of this work may provide a scientific path through which one can obtain a better understanding on performing frictional experiments, friction characteristics, friction modeling and stick-slip effect, and then improve operational precison and service lifetime of structures.
课题从考虑摩擦在机械工程中所起的作用与影响出发,旨在研究含摩擦环节的机械系统实验、建模、识别以及结构的动力学特性。通过对含摩擦系统进行多方实验的基础上,分析研究摩擦的静态和动态特性,并结合实验数据,提出全新的摩擦力模型,使之尽可能多的描述并预测实验中所呈现的摩擦特性,并利用此模型对含摩擦系统低速下的粘滑现象及相关动力学特性进行了分析和探讨。
论文首先概述了摩擦的定义和历史,通过“静、动”两个概念及区别,分类介绍了当前已知的摩擦特性,在此基础上,按照不同的建模思路,分别介绍了静态摩擦模型和动态摩擦模型的原理及优缺点,并简述了含摩擦系统动力学特性并重点关注粘滑、极限环等由摩擦引发的非线性环节的研究进展。
根据机械工程领域的实际研究目标,从宏观角度出发研究摩擦的动静态特性,对电梯导轨与导靴/靴衬间的横向及纵向摩擦特性做了详细的实验研究。通过设计不同的测试装置,采用不同的摩擦材料,通过大量的实验,测试并分析了摩擦力随接触界面间正压力、相对速度、润滑状态变化的情况,研究了摩擦力在预滑动和宏观滑动阶段的静态及动态摩擦特性,发现并提出摩擦过冲(Friction overshoot)概念。对实验得到的Stribeck曲线模型进行了参数化研究,针对界面磨损对摩擦特性的影响,从宏观及微观角度分别进行了实验研究、分析及对比,并得到一些有意义的结果。为后续的摩擦模型的建模和结构系统的动力特性分析提供必要的实验基础。
在实验基础上,提出了一个新的基于Bouc-Wen的单状态变量摩擦力模型(简称SSV)。通过引入规范化的Bouc-Wen模型,可以比较精确的描述摩擦力在预滑动阶段的滞回行为。同时并入一个速度的指数函数以及加速度的线性函数,使得模型可以描述摩擦宏观阶段的Stribeck效应,以及相应的速度滞后特性。根据鬃毛模型平均变形的理念,提出鬃毛平均等效质量的概念,使之可以描述从预滑动到宏观滑动阶段间的摩擦过冲特性,同时实现了两阶段间的光滑过渡。通过与实验数据的对比以及与LuGre模型的比较,此模型可以很好的拟合实测数据,在描述预滑动及摩擦过冲方面,较其他摩擦力模型更加有效。
基于旋转式摩擦试验机,进一步验证了摩擦滞回及速度滞后特性,并实验考察了单向速度激励下,摩擦在宏观滑动阶段的滞后特性。对预滑动范围内的摩擦非局部记忆效应进行了实验研究,发现在润滑条件下,摩擦力与位移在预滑动阶段成近似线性关系。获得了不同正压力下的Stribeck摩擦力曲线及摩擦系数曲线,并扩展了Stribeck曲线的定义范围,使其能够用一个公式预测在不同正压力和相对运行速度下的摩擦力,经实验数据验证具有良好的准确性。考查了摩擦切向与法向间运动的耦合关系,首次发现摩擦在润滑条件下存在法向位移与切线位移间的交叉滞回,及法向位移与切向速度间的滞回特性。从微观角度出发,在物理意义上对此现象进行了阐述及解释,并据此进行了理论建模。模型结构简单,易于识别,并具备进一步扩展的能力。通过模型仿真与实验数据的对比,证实了模型的合理性及有效性。实验以旋转式摩擦实验的研究结果为基础,将实验精度由毫米级提升至微米级,其结果不仅加深了对摩擦机理及特性的理解,并对高精度摩擦模型的发展提供了必要的实验基础。
基于直线往复和旋转式摩擦实验结果,提出一个新的高精度摩擦力模型:广义Bouc-Wen Maxwell-Slip摩擦模型(简称GBM)。在摩擦预滑动阶段,GBM模型用一系列含库仑摩擦的弹簧振子模拟预滑动阶段的摩擦特性;在宏观滑动阶段,则采用了改进的Bouc-Wen模型和含变摩擦系数的扩展Stribeck曲线。通过与四个常用摩擦力模型在描述摩擦特性方面的对比与实验验证,表明GBM模型在描述摩擦滞回、速度滞后、Stribeck效应、摩擦过冲、正压力相关等方面均优于其他模型。而且GBM利用Maxwell-Slip模型中含有多个变量的优点,从而比较好的描述了预滑动阶段非局部记忆效应及非漂移特性。模型在宏观滑动阶段使用的是单状态变量微分方程,在预滑动阶段依靠多变量的代数方程,平衡了效率与性能。另外,通过简化模型参数,GBM模型可以退化为Dahl、LuGre、SSV、GMS及其它模型,具有良好的适应性。总而言之,对于摩擦模型的选择,应根据不同的实际应用需求来进行。当系统精度或实时性需求不高时,Dahl、LuGre甚至库仑摩擦模型即可满足需求;对于高精度及实时性(如精确定位等控制领域)的需求,GBM模型是较为理想的选择。
以单自由度链式模型为研究对象,详细分析了含摩擦机械系统产生粘滑运动的现象与机理。探讨了由粘滑运动引发的两类振动,一是不同的激励速度所导致系统以不同频率做粘滞-滑动-粘滞的反复运动,表现为物体沿相对平衡位置做往复的低频振动,且振动频率与系统固有频率无关;而是伴随往复运动,系统在粘滞阶段还存在高频振动,这与一般认识上的粘滞即停止不同。通过定性、定量及与实验结果的对比分析表明,系统在粘滞阶段的高频振动频率不是单一固定值而是分布在一定宽度的频域内,其来源于摩擦预滑动阶段摩擦界面间不断变化的接触刚度,而摩擦阻尼及系统自身阻尼是高频振动逐渐衰减的原因。当系统发生粘滑运动时,系统响应随激励速度、系统刚度及阻尼的变化而呈周期、拟周期及混沌运动交替变化的形式。当激励速度、刚度及阻尼逐渐增大时,系统均呈现出逐渐从混沌运动状态向稳定的周期运动转变的趋势;伴随这一转变趋势,系统粘滑运动也会随参数值的增大而逐渐衰弱至消失,进而变为摩擦引起的准谐调周期振动,在理论极限情况下,准谐调运动也会消失。
本文的研究方法和结论对于推进摩擦实验研究、摩擦特性研究、摩擦模型的建模以及加深对机械系统粘滑现象的认识,提高系统的工作精度和使用寿命,具有一定的参考价值。
Friction, which belongs to the term of Tribology, is a young scientific discipline with long history. It has been proved to exist in every aspect of daily lives. In mechanical fields, friction acts as an especially important role. The full understand and control of the frictional characteristics is critical for improving machining precisions and product qualities, prolonging service lifetime.
The thesis is initiated from the viewpoint of how friction acts in the mechanical engingeering, aimed to explore the experiments, theoretical modeling, identification, dynamical property of systems with friction. According to profound experiments, the static and dynamic characteristics are analysed and new friction model is provided, which is able to describe and predict those experimentally observed phenomenon as many as possible. In addition, the stick-slip effect of system with frictional parts in low velocity ranges is investigated using the newly provided friction model.
Firstly, the definition and history of friction is summarized. In terms of“static and dynamic”, the state-of-the-art of frictional characteristics is classified. In the light of this point, the static and dynamical friction models and their merits and drawbacks are introduced in this work. The current researching progress on nonlinear reponses of system with frictional parts such as stick-slip and limit cycling are also briefly presented.
Secondly, based on the pratical research target in mechanical engineering field, the lateral/vertical friction characteristics between rail and guide shoe/pad in an elevator system are investigated macroscopically. By designing different test rigs, choosing different friction materials and performing a large amount of tests, the property of friction with respect to the variation of normal loads, relative velocities and lubricational conditions is examined. The static and dynamical properties of friction in the stage of pre-sliding and gross sliding are also studied, which results in the finding of Friction Overshoot property in the transforming stage from pre-sliding to gross sliding. The experimentally obtained Stribeck curve for different normal loads and materials are parameterized. The effects of wear on the frictional properties of surface in contact are carried out and analysed by experiments macroscopically and microscopically. Some meaningful results are visualized which provide a experimental basis for future friction modelings.
Based on the linearly reciprocating friction tests, a new Bouc-Wen based single-state-variable friction model (termed as SSV) is presented. By introducing the normalized Bouc-Wen model, the new model is able to describe the behaviors of friction in the pre-sliding stage precisely. Meanwhile, a exponential function with respect to velocity and a linear function with respect to accerlation are added, which make it possible for the new model to describe the Stribeck effect and friction lag happened in gross sliding stage. According to the definition of average inflection in the bristle theory, the average effective mass of bristle is defined, which is capable to predict the experimentally found friction overshoot property smoothly during the transation from pre-sliding to gross sliding regime. The comparisons between simulation using SSV and LuGre model and the experiment results show that the proposed friction model gives better results than traditional model without losing the flexibility.
Relyed on a rotational tribometer, the friction hysteresis and friction lag are further verified, and the friction lag under the uni-directional velocity excitation in gross sliding regime is also investigated. The non-local memory effect in lubricated condition is evalued as well. The tests show that the frction force varies linearly with respect to displacment in the stage of pre-sliding which is different from the cases of dry frictions. The working range of the Stribeck curve is widened by measuring Stribeck curves under different normal loads. The improved Stribeck curve becomes the function of normal load besides the relative velocity. The coupling relations between tangential and normal motions are investigated, It is the first time to observe a cross hysteretic relations between normal and tangential displacements and a hysteretic relationship between normal displacement and tangential velocity. Based on these results, a theoretical model is proposed from the physically microscopic viewpoint, and is validated by comparing the simulations with the experimental results. The measuring precision of the rotational tribometer is upgraded from the millimeter level to the micrometer level compared with the linearly reciprocating friction test rig, which gives a more profund understanding of friction characteristics and is necessary for developing high precision frition models. Grounded on the linear reciprocating and rotational friction measurements, the generalized Bouc-Wen Maxwell-Slip model (named as the GBM model) is developed.
The GBM model uses a series of parallelly connected spring and friction elements to simulate properties in the pre-sliding stage; while in the gross sliding stage, the extended Stribeck curve and improved Bouc-Wen model is utilized. According to comparisons between four friction models, it is clear that the GBM model performs better on predicting friction hysteresis, friction lag, Stribeck effect, friction overshoot and normal variations than other models. At the same time, GBM model is able to describe the non-local memory and non-drifting property in the stage of pre-sliding because of the incorporation of Maxwell-Slip elements. The model equations used in pre-sliding stage is one signle-state-variable ordinary differential equation. While in the gross sliding stage, it relies on several multi-variable algebra equations which balanced the effieciency and performance of the GBM model. In addition, the GBM is able to boiled down to the Dahl, LuGre, SSV and GMS model by simplifying model parameters, making it quite suitable in the fileds where high precision and real time control abilities are extremely appreciated.
Taking the single degree of freedom train model as the research object, the stick-slip effect and its mechanism in structures with frictional parts are analysed in detail. Two types of vibrations induced by stick-slip motion are dicussed. One is the cycling of stick-slip-stick motion, running in different frequencies being excited by different pulling velocities, taking the form of reciprocating motion along the relative equilibrium position of the object M, and the frequency is irrelevant with the natural frequency. The other is the high frequency vibration in the stage of stick motion. The qualitative, quantitative analyses and experimental verication show that the high frequency of the vibration is not accumulated in single value frequency but a distributed frequency range, which come from the varying stiffness between surfaces in contact. When system is in stick-slip motion, the system response can be periodic, quasi-periodic and chaos with the change of pulling velocities, system stiffness and viscous. When these parameters are increasing, system motion tends to be stabilized periodic motion from chaos. Along with this trend, the stick-slip motion will decrease and vanish, and turns out to be quais-harmonic vibration, which could disappear under extreme theoretical conditions.
The results of this work may provide a scientific path through which one can obtain a better understanding on performing frictional experiments, friction characteristics, friction modeling and stick-slip effect, and then improve operational precison and service lifetime of structures.
引文
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