Robotics is undergoing dynamic progression with the spread of soft robots and compliant mechanisms. The mechanical models describing these systems are underactuated, having more degrees of freedom than inputs. The trajectory tracking control of underactuated systems is not straightforward. The solution of the inverse dynamics is not stable in all cases, as it only considers the actual state of the system. Therefore employing the advances of optimal control theory is a reasonable choice. However, the real-time application of these is challenging as the solution to the discretized optimization problems is numerically expensive. This paper presents a novel iterative approach to solving nonlinear optimal control problems. The authors first define the iteration formula after which the obtained equations are discretized to prepare the numerical solution, contrarily to the accessible works in the literature having reverse order. The main idea is to approximate the cost functional with a second-order expansion in each iteration step, which is then extremized to get the subsequent approximation of the optimum. In the case of nonlinear optimal control problems, the process leads to a sequence of time-variant LQR problems. The proposed technique was effectively applied to the trajectory tracking control of a flexible RR manipulator. The case study showed that the initialization of the iteration is simple, and the convergence is rapid.
{"title":"Variational Principles for the Trajectory Tracking Control of Underactuated Mechanical Systems","authors":"Bálint Bodor, L. Bencsik","doi":"10.1115/1.4056593","DOIUrl":"https://doi.org/10.1115/1.4056593","url":null,"abstract":"\u0000 Robotics is undergoing dynamic progression with the spread of soft robots and compliant mechanisms. The mechanical models describing these systems are underactuated, having more degrees of freedom than inputs. The trajectory tracking control of underactuated systems is not straightforward. The solution of the inverse dynamics is not stable in all cases, as it only considers the actual state of the system. Therefore employing the advances of optimal control theory is a reasonable choice. However, the real-time application of these is challenging as the solution to the discretized optimization problems is numerically expensive.\u0000 This paper presents a novel iterative approach to solving nonlinear optimal control problems. The authors first define the iteration formula after which the obtained equations are discretized to prepare the numerical solution, contrarily to the accessible works in the literature having reverse order. The main idea is to approximate the cost functional with a second-order expansion in each iteration step, which is then extremized to get the subsequent approximation of the optimum. In the case of nonlinear optimal control problems, the process leads to a sequence of time-variant LQR problems. The proposed technique was effectively applied to the trajectory tracking control of a flexible RR manipulator. The case study showed that the initialization of the iteration is simple, and the convergence is rapid.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"12 19 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78725127","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.
{"title":"Stability Analysis of Nonlinear Rotating Systems Using Lyapunov Characteristic Exponents Estimated From Multibody Dynamics","authors":"G. Cassoni, A. Zanoni, A. Tamer, P. Masarati","doi":"10.1115/1.4056591","DOIUrl":"https://doi.org/10.1115/1.4056591","url":null,"abstract":"\u0000 The use of Lyapunov Characteristic Exponents to assess the stability of nonlinear, time-dependent mechanical systems is discussed. Specific attention is dedicated to methods capable of estimating the largest exponent without requiring the Jacobian matrix of the problem, which can be applied to time histories resulting from simulations performed with existing multibody solvers. Helicopter ground resonance is analyzed as the reference application. Improvements over the available literature are: the problem is formulated in physical coordinates, without eliminating periodicity through multiblade coordinates; the rotation of the blades is not linearized; the problem is modeled considering absolute positions and orientations of parts. The dynamic instability that arises at some angular velocities when the isotropy of the rotor is broken (e.g., caused by the failure of one lead-lag damper, a design test condition) is observed to evolve into a large amplitude limit cycle, where the usual Floquet-Lyapunov analysis of the linearized time-periodic simply predicts instability.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"450 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77750658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However their range of motion is limited due to a stress limitation and a loss of support stiffness in deformed configurations. The support stiffness can be significantly increased by using leafsprings of which the width and thickness vary over the length of the leafspring. This paper presents formulations for two beam elements with a varying cross section that can be used for the efficient modelling of these types of leafsprings. One of these beam-formulations includes the modelling of the warping due to torsion, which is shown to be essential for accurate modelling. The 90% accuracy in stiffness results and 80% accuracy in stress results, in comparison with results of finite element analyses, are sufficient for the evaluation of concept-designs. Optimizations shows that the support stiffness of two typical flexure joints can be increased by a factor of up to 4.0 keeping the same range of motion, by allowing the cross section to vary over the length of the leafspring. In these two flexure joints, 98% of this improvement can already be obtained by only varying the thickness, keeping a constant width.
{"title":"Beams with A Varying Cross Section in the Generalized Strain Formulation for Flexure Modelling","authors":"K. Dwarshuis, R. Aarts, M. Ellenbroek, D. Brouwer","doi":"10.1115/1.4056482","DOIUrl":"https://doi.org/10.1115/1.4056482","url":null,"abstract":"\u0000 Flexure joints are rapidly gaining ground in precision engineering because of their predictable behavior. However their range of motion is limited due to a stress limitation and a loss of support stiffness in deformed configurations. The support stiffness can be significantly increased by using leafsprings of which the width and thickness vary over the length of the leafspring. This paper presents formulations for two beam elements with a varying cross section that can be used for the efficient modelling of these types of leafsprings. One of these beam-formulations includes the modelling of the warping due to torsion, which is shown to be essential for accurate modelling. The 90% accuracy in stiffness results and 80% accuracy in stress results, in comparison with results of finite element analyses, are sufficient for the evaluation of concept-designs. Optimizations shows that the support stiffness of two typical flexure joints can be increased by a factor of up to 4.0 keeping the same range of motion, by allowing the cross section to vary over the length of the leafspring. In these two flexure joints, 98% of this improvement can already be obtained by only varying the thickness, keeping a constant width.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"5 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82332394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article provides a stochastic agent-based model to exhibit the role of aggregation metrics in order to mitigate polarization in a complex society. Our sociophysics model is based on interacting and nonlinear Brownian agents, which allow us to study the emergence of collective opinions. The opinion of an agent, xi(t) is a continuous positive value in an interval [0,1]. We find (i) most agent-metrics display similar outcomes. (ii) The middle-metric and noisy-metric obtain new opinion dynamics either towards assimilation or fragmentation. (iii) We show that a developed 2-stage metric provide new insights about convergence and equilibria. In summary, our simulation demonstrates the power of institutions, which affect the emergence of collective behavior. Consequently, opinion formation in a decentralized complex society is reliant to the individual information processing and rules of collective behavior.
{"title":"Nonlinear Agent-Based Dynamics: Which Metric Mitigates Polarization?","authors":"Bodo Herzog","doi":"10.1115/1.4056481","DOIUrl":"https://doi.org/10.1115/1.4056481","url":null,"abstract":"\u0000 This article provides a stochastic agent-based model to exhibit the role of aggregation metrics in order to mitigate polarization in a complex society. Our sociophysics model is based on interacting and nonlinear Brownian agents, which allow us to study the emergence of collective opinions. The opinion of an agent, xi(t) is a continuous positive value in an interval [0,1]. We find (i) most agent-metrics display similar outcomes. (ii) The middle-metric and noisy-metric obtain new opinion dynamics either towards assimilation or fragmentation. (iii) We show that a developed 2-stage metric provide new insights about convergence and equilibria. In summary, our simulation demonstrates the power of institutions, which affect the emergence of collective behavior. Consequently, opinion formation in a decentralized complex society is reliant to the individual information processing and rules of collective behavior.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"50 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79968062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Soukkou, Y. Soukkou, S. Haddad, M. Benghanem, A. Rabhi
The concept of fractional-order control (F-oC) is exploited in this paper to synchronize fractional-order dynamical systems. The addressed systems in this paper reflect the real physical phenomena characterized by the complicated relationship between supply and demand for energy resources in the Shanghai area. Thus, we provide the developed fractional energy resource attractor and the simulation results regarding synchronization under the proposed control law of the same fractional energy resource attractor. Note that most of the synchronization methods achieved excellent performance when dealing with complex continuous systems; however, no method addressed the synchronization problem of fractional-order energy resource systems based on the F-oC and modern optimization techniques, to the best of our knowledge. By designing the finite-time control theory, the finite-time full synchronization of two identical fractional-order energy resources demand-supply hyperchaotic systems (F-oERDSHSs) is investigated due to its performance. The advanced prediction-based fractional-order control law (Pb-FoCL) is established for finite-time synchronization of F-oERDSHSs. The design procedure becomes a multiobjective optimization problem of the knowledge base of the developed controller while satisfying the desired performance requirements. The Finite-Time Stability (F-TS) of the control-loop system is proved by using the finite-time Lyapunov stability theory. Furthermore, the Improved Artificial Hummingbird Algorithm (I-AHA) is used to find an optimal knowledge base of Pb-FoCL while achieving the design constraints. Simulation results are provided to verify the efficiency of the proposed control strategy.
{"title":"Finite-time Synchronization of Fractional-order Energy Resources Demand-Supply Hyperchaotic Systems via Fractional-order Prediction-based Feedback Control Strategy with Bio-inspired Multiobjective Optimization","authors":"A. Soukkou, Y. Soukkou, S. Haddad, M. Benghanem, A. Rabhi","doi":"10.1115/1.4056462","DOIUrl":"https://doi.org/10.1115/1.4056462","url":null,"abstract":"\u0000 The concept of fractional-order control (F-oC) is exploited in this paper to synchronize fractional-order dynamical systems. The addressed systems in this paper reflect the real physical phenomena characterized by the complicated relationship between supply and demand for energy resources in the Shanghai area. Thus, we provide the developed fractional energy resource attractor and the simulation results regarding synchronization under the proposed control law of the same fractional energy resource attractor. Note that most of the synchronization methods achieved excellent performance when dealing with complex continuous systems; however, no method addressed the synchronization problem of fractional-order energy resource systems based on the F-oC and modern optimization techniques, to the best of our knowledge. By designing the finite-time control theory, the finite-time full synchronization of two identical fractional-order energy resources demand-supply hyperchaotic systems (F-oERDSHSs) is investigated due to its performance. The advanced prediction-based fractional-order control law (Pb-FoCL) is established for finite-time synchronization of F-oERDSHSs. The design procedure becomes a multiobjective optimization problem of the knowledge base of the developed controller while satisfying the desired performance requirements. The Finite-Time Stability (F-TS) of the control-loop system is proved by using the finite-time Lyapunov stability theory. Furthermore, the Improved Artificial Hummingbird Algorithm (I-AHA) is used to find an optimal knowledge base of Pb-FoCL while achieving the design constraints. Simulation results are provided to verify the efficiency of the proposed control strategy.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"22 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73211885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two different cases are encountered in the thermal analysis of solids. In the first case, continua are not subject to boundary and motion constraints and all material points experience same displacement-gradient changes as the result of application of thermal loads. In this case, referred to as unconstrained thermal expansion, the thermal load produces uniform stress-free motion within the continuum. In the second case, point displacements due to boundary and motion constraints are restricted, and therefore, continuum points do not move freely when thermal loads are applied. This second case, referred to as constrained thermal expansion, leads to thermal stresses and its study requires proper identification of the independent coordinates which represent expansion degrees-of-freedom. To have objective evaluation and comparison between the two cases of constrained and unconstrained thermal expansion, the reference-configuration geometry is accurately described using the absolute nodal coordinate formulation (ANCF) finite elements. ANCF position-gradient vectors have unique geometric meanings as tangent to coordinate lines, allowing systematic description of the two different cases of unconstrained and constrained thermal expansions using multiplicative decomposition of the matrix of position-gradient vectors. Furthermore, generality of the approach for large-displacement thermal analysis requires using the Lagrange–D'Alembert principle for proper treatment of algebraic constraint equations. Numerical results are presented to compare two different expansion cases, demonstrate use of the new approach, and verify its results by comparing with conventional finite element (FE) approaches.
{"title":"Constrained Large-Displacement Thermal Analysis","authors":"A. Shabana, Mahmoud Elbakly, Dayu Zhang","doi":"10.1115/1.4056182","DOIUrl":"https://doi.org/10.1115/1.4056182","url":null,"abstract":"\u0000 Two different cases are encountered in the thermal analysis of solids. In the first case, continua are not subject to boundary and motion constraints and all material points experience same displacement-gradient changes as the result of application of thermal loads. In this case, referred to as unconstrained thermal expansion, the thermal load produces uniform stress-free motion within the continuum. In the second case, point displacements due to boundary and motion constraints are restricted, and therefore, continuum points do not move freely when thermal loads are applied. This second case, referred to as constrained thermal expansion, leads to thermal stresses and its study requires proper identification of the independent coordinates which represent expansion degrees-of-freedom. To have objective evaluation and comparison between the two cases of constrained and unconstrained thermal expansion, the reference-configuration geometry is accurately described using the absolute nodal coordinate formulation (ANCF) finite elements. ANCF position-gradient vectors have unique geometric meanings as tangent to coordinate lines, allowing systematic description of the two different cases of unconstrained and constrained thermal expansions using multiplicative decomposition of the matrix of position-gradient vectors. Furthermore, generality of the approach for large-displacement thermal analysis requires using the Lagrange–D'Alembert principle for proper treatment of algebraic constraint equations. Numerical results are presented to compare two different expansion cases, demonstrate use of the new approach, and verify its results by comparing with conventional finite element (FE) approaches.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"64 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81090704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study expands and modifies the homotopy analysis method to handle differential equations with generalized Caputo-type fractional derivatives. Analytical approximate solutions for such models were successfully provided using the proposed modification. The determination of the valid region of convergence for the proposed method, with respect to the auxiliary control parameter, was discussed when using fractional operators. Then, mainly, the accuracy and effectiveness of the proposed method was verified through illustrative examples and comparisons with the predictor corrector method and RK4 method. Finally, it is expected that the studied generalized operators and the suggested method can be widely applied in the field of fractional calculus.
{"title":"The Homotopy Analysis Method for Solving Differential Equations with Generalized Caputo-Type Fractional Derivatives","authors":"Wafia Fafa, Z. Odibat, N. Shawagfeh","doi":"10.1115/1.4056392","DOIUrl":"https://doi.org/10.1115/1.4056392","url":null,"abstract":"\u0000 This study expands and modifies the homotopy analysis method to handle differential equations with generalized Caputo-type fractional derivatives. Analytical approximate solutions for such models were successfully provided using the proposed modification. The determination of the valid region of convergence for the proposed method, with respect to the auxiliary control parameter, was discussed when using fractional operators. Then, mainly, the accuracy and effectiveness of the proposed method was verified through illustrative examples and comparisons with the predictor corrector method and RK4 method. Finally, it is expected that the studied generalized operators and the suggested method can be widely applied in the field of fractional calculus.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"58 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77772314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the optimized decomposition method, which was developed to solve integer-order differential equations, will be modified and extended to handle nonlinear fractional differential equations. Fractional derivatives will be considered in terms of Caputo sense. The suggested modifications design new optimized decompositions for the series solutions depending on linear approximations of the nonlinear equations. Two optimized decomposition algorithms have been introduced to obtain approximate solutions of broad classes of IVPs consisting of nonlinear fractional ODEs and PDEs. A comparative study was conducted between the proposed algorithms and the Adomian decomposition method by means of some test illustration problems. The implemented numerical simulation results showed that the proposed algorithms give better accuracy and convergence, and reduce the complexity of computational work compared to the Adomian's approach. This confirms the belief that the optimized decomposition method will be used effectively and widely as a powerful tool in solving various fractional differential equations.
{"title":"Effective Optimized Decomposition Algorithms for Solving Nonlinear Fractional Differential Equations","authors":"Marwa Laoubi, Z. Odibat, B. Maayah","doi":"10.1115/1.4056254","DOIUrl":"https://doi.org/10.1115/1.4056254","url":null,"abstract":"\u0000 In this paper, the optimized decomposition method, which was developed to solve integer-order differential equations, will be modified and extended to handle nonlinear fractional differential equations. Fractional derivatives will be considered in terms of Caputo sense. The suggested modifications design new optimized decompositions for the series solutions depending on linear approximations of the nonlinear equations. Two optimized decomposition algorithms have been introduced to obtain approximate solutions of broad classes of IVPs consisting of nonlinear fractional ODEs and PDEs. A comparative study was conducted between the proposed algorithms and the Adomian decomposition method by means of some test illustration problems. The implemented numerical simulation results showed that the proposed algorithms give better accuracy and convergence, and reduce the complexity of computational work compared to the Adomian's approach. This confirms the belief that the optimized decomposition method will be used effectively and widely as a powerful tool in solving various fractional differential equations.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"240 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87607252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The universal behaviors of a rational dynamical system associated with the Vannimenus–Ising model having two coupling constants on a Cayley tree of order three are studied. Cobweb diagrams and related map iterates for some relevant parameters are investigated. The local stability of fixed points is discussed and illustrated through cobweb diagrams. We deal with quantitative universality, such as orbit diagrams and Lyapunov exponents for a class of rational maps. We show that our model is periodic using orbit diagrams and relevant Lyapunov exponents.
{"title":"On the Periodicity of the Rational Dynamical System Corresponding to the Vannimenus–Ising Model","authors":"H. Akın","doi":"10.1115/1.4056133","DOIUrl":"https://doi.org/10.1115/1.4056133","url":null,"abstract":"\u0000 The universal behaviors of a rational dynamical system associated with the Vannimenus–Ising model having two coupling constants on a Cayley tree of order three are studied. Cobweb diagrams and related map iterates for some relevant parameters are investigated. The local stability of fixed points is discussed and illustrated through cobweb diagrams. We deal with quantitative universality, such as orbit diagrams and Lyapunov exponents for a class of rational maps. We show that our model is periodic using orbit diagrams and relevant Lyapunov exponents.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"4 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72457286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The noise of disk brake pair has always been a difficult problem for enterprises and researchers. Many factors induce the noise of disk brake pair, among which the influence of the third body particle flow generated by the external gravel or its own abrasive debris has not been paid much attention. Three-body contact has different friction properties and requires a new friction model to describe it. This paper presents a friction model of disk brake pair on the basis of the predecessors. The new model further considers the influence of the third body on the nonlinear behavior of the brake system on the basis of the previous model of the brake pair. Through numerical simulation, it is concluded that the geometry size of the third body has great influence on the stability interval of the braking system. Finally, the influence of the third body particles on the motion stability of the braking system under different particle size ranges is studied. It is found that larger particle size can improve the motion stability of the system.
{"title":"Construction of Friction Model of the Third Body Layer and Its Effects on the Dynamic Characteristics in Brake System","authors":"Yuhang Zhang, Daogao Wei, Bofu Wu, Ping Jiang","doi":"10.1115/1.4056181","DOIUrl":"https://doi.org/10.1115/1.4056181","url":null,"abstract":"\u0000 The noise of disk brake pair has always been a difficult problem for enterprises and researchers. Many factors induce the noise of disk brake pair, among which the influence of the third body particle flow generated by the external gravel or its own abrasive debris has not been paid much attention. Three-body contact has different friction properties and requires a new friction model to describe it. This paper presents a friction model of disk brake pair on the basis of the predecessors. The new model further considers the influence of the third body on the nonlinear behavior of the brake system on the basis of the previous model of the brake pair. Through numerical simulation, it is concluded that the geometry size of the third body has great influence on the stability interval of the braking system. Finally, the influence of the third body particles on the motion stability of the braking system under different particle size ranges is studied. It is found that larger particle size can improve the motion stability of the system.","PeriodicalId":54858,"journal":{"name":"Journal of Computational and Nonlinear Dynamics","volume":"25 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85025685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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