Pub Date : 2023-04-25DOI: 10.1177/14644193231169325
Ekansh Chaturvedi, J. Mukherjee, C. Sandu
This work presents a novel continuously differentiable, dynamic dry friction model, with dependence on normal contact force, slip velocity, and static and dynamic coefficients of friction. The state-of-the-art, Brown and McPhee friction model depends on transitional velocity, which is an empirical parameter. A limitation with this model is that there is no generic approach to select the optimal value for the transitional velocity for a certain application. The simulation results presented in this work highlight the sensitivity of friction force with transitional velocity in Brown and McPhee’s model to obtain smooth solutions, which are supportive in control system applications. It is because control systems require jitter-free signals in order to save costs on low-pass filters. The proposed model overcomes such empirical dependence on transition velocity through a combination of an iterative methodology and an empirical parameterization. In this article, a comprehensive analysis of the proposed friction model and the contributing parameters is carried out. The algorithm to implement the proposed friction model is elaborated. The proposed friction model is then simulated and compared against Brown and McPhee’s model. using a stick-slip benchmark problem. Furthermore, the proposed force model is applied to two spatial multibody systems formulated using index 0 tangent space differential-algebraic equations. The results demonstrate how the proposed friction model can be employed in dynamical mechanical systems. The independence on transitional velocity in the proposed friction model is observed to be effective for obtaining smooth solutions that make it suitable for control system applications.
{"title":"A novel dynamic dry friction model for applications in mechanical dynamical systems","authors":"Ekansh Chaturvedi, J. Mukherjee, C. Sandu","doi":"10.1177/14644193231169325","DOIUrl":"https://doi.org/10.1177/14644193231169325","url":null,"abstract":"This work presents a novel continuously differentiable, dynamic dry friction model, with dependence on normal contact force, slip velocity, and static and dynamic coefficients of friction. The state-of-the-art, Brown and McPhee friction model depends on transitional velocity, which is an empirical parameter. A limitation with this model is that there is no generic approach to select the optimal value for the transitional velocity for a certain application. The simulation results presented in this work highlight the sensitivity of friction force with transitional velocity in Brown and McPhee’s model to obtain smooth solutions, which are supportive in control system applications. It is because control systems require jitter-free signals in order to save costs on low-pass filters. The proposed model overcomes such empirical dependence on transition velocity through a combination of an iterative methodology and an empirical parameterization. In this article, a comprehensive analysis of the proposed friction model and the contributing parameters is carried out. The algorithm to implement the proposed friction model is elaborated. The proposed friction model is then simulated and compared against Brown and McPhee’s model. using a stick-slip benchmark problem. Furthermore, the proposed force model is applied to two spatial multibody systems formulated using index 0 tangent space differential-algebraic equations. The results demonstrate how the proposed friction model can be employed in dynamical mechanical systems. The independence on transitional velocity in the proposed friction model is observed to be effective for obtaining smooth solutions that make it suitable for control system applications.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78240020","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}
Pub Date : 2023-04-19DOI: 10.1177/14644193231168675
Yachao Sun, Jianghai Shi, Yang Yang, M. Du, Hongrui Cao
The gear–spline system consisting of the internal spline of gears and the external spline of shafts is widely used in mechanical transmission systems. However, considering the nonuniform spline clearance caused by the assembly and manufacturing errors, the vibration characteristics of the system and the spline wear mechanism are still unclear. This article proposed a dynamic model of the gear–spline system with nonuniform spline clearance and wear evolution of spline. Compared with the existing models, the new contribution of this article is to reveal the coupling vibration mechanism of the gear–spline system under the condition of nonuniform spline clearance through the dynamic model. On this basis, the support stiffness characteristics and wear evolution law of the spline pair under the dynamic gear meshing force are studied. The results show that under the condition of nonuniform clearance, the displacement response of the system is modulated by the rotation frequency, and the motion trajectory tends to be chaotic. The load distribution of spline teeth and the equivalent stiffness of the spline depends on the number of loaded spline teeth, which in turn depends on the input torque and clearance distribution. In addition, the spline teeth with smaller clearance bear more loads and wear faster, and the wear causes the nonuniform clearance to gradually increase and become uniform. This study can provide theoretical guidance for revealing the vibration mechanism of the gear–spline system and calculating the support stiffness of the spline shaft.
{"title":"Dynamic modelling of gear–spline system with nonuniform spline clearance and wear evolution of spline","authors":"Yachao Sun, Jianghai Shi, Yang Yang, M. Du, Hongrui Cao","doi":"10.1177/14644193231168675","DOIUrl":"https://doi.org/10.1177/14644193231168675","url":null,"abstract":"The gear–spline system consisting of the internal spline of gears and the external spline of shafts is widely used in mechanical transmission systems. However, considering the nonuniform spline clearance caused by the assembly and manufacturing errors, the vibration characteristics of the system and the spline wear mechanism are still unclear. This article proposed a dynamic model of the gear–spline system with nonuniform spline clearance and wear evolution of spline. Compared with the existing models, the new contribution of this article is to reveal the coupling vibration mechanism of the gear–spline system under the condition of nonuniform spline clearance through the dynamic model. On this basis, the support stiffness characteristics and wear evolution law of the spline pair under the dynamic gear meshing force are studied. The results show that under the condition of nonuniform clearance, the displacement response of the system is modulated by the rotation frequency, and the motion trajectory tends to be chaotic. The load distribution of spline teeth and the equivalent stiffness of the spline depends on the number of loaded spline teeth, which in turn depends on the input torque and clearance distribution. In addition, the spline teeth with smaller clearance bear more loads and wear faster, and the wear causes the nonuniform clearance to gradually increase and become uniform. This study can provide theoretical guidance for revealing the vibration mechanism of the gear–spline system and calculating the support stiffness of the spline shaft.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79525992","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 view of the lack of ready formulae for modification calculation of non-standard planetary spur gear trains, the paper is focused on new modification methods of non-standard planetary spur gear trains with X-gears. Firstly, a novelty transform method from the parameters on the pitch circle to the parameters on the reference circle for a non-standard planetary spur gear train with X-gears is proposed in order to study the modification method. Secondly, a scheme of teeth surface modification for non-standard planetary spur gear train with X-gears is put forward. Thirdly, the calculation method of loaded transmission error and flash temperature on the tooth surface under mixed elastohydrodynamic lubrication for external meshing spur gear pairs is proposed using tooth contact analysis as well as loaded tooth contact analysis. Then, a new modification optimization method for non-standard planetary spur gear train with X-gears is proposed, and formulae of the maximal modification length along the tooth height are derived. Finally, the effectiveness of the modification optimization method is confirmed by an example, and the transform formulae of the optimized modification parameters for sun gear are derived.
{"title":"Transform of parameter and teeth surface modification for non-standard planetary spur gear train with X-gears","authors":"Xijin Zhang, Z. Fang, Xunmin Yin, Haitao Jia, Yaoguo Ma, Yingqiang Xu, Huan Zhao","doi":"10.1177/14644193231169321","DOIUrl":"https://doi.org/10.1177/14644193231169321","url":null,"abstract":"In view of the lack of ready formulae for modification calculation of non-standard planetary spur gear trains, the paper is focused on new modification methods of non-standard planetary spur gear trains with X-gears. Firstly, a novelty transform method from the parameters on the pitch circle to the parameters on the reference circle for a non-standard planetary spur gear train with X-gears is proposed in order to study the modification method. Secondly, a scheme of teeth surface modification for non-standard planetary spur gear train with X-gears is put forward. Thirdly, the calculation method of loaded transmission error and flash temperature on the tooth surface under mixed elastohydrodynamic lubrication for external meshing spur gear pairs is proposed using tooth contact analysis as well as loaded tooth contact analysis. Then, a new modification optimization method for non-standard planetary spur gear train with X-gears is proposed, and formulae of the maximal modification length along the tooth height are derived. Finally, the effectiveness of the modification optimization method is confirmed by an example, and the transform formulae of the optimized modification parameters for sun gear are derived.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75059684","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}
Pub Date : 2023-04-12DOI: 10.1177/14644193231169057
Long Yang, Bing Yuan, Jingyi Gong, Mingjian Qin, Geng Liu
The vibration level is the key index to measure the performance of marine gear transmission device. The compound gear transmission system, which is composed of a helical gear pair and a spur star gear train, is widely used in marine gear transmission device. This paper presents a multi-node dynamic model for a marine compound gear transmission system, investigating the modal properties and dynamic responses of the system. The mesh stiffness and transmission error for each gear pair are determined using the loaded tooth contact analysis (LTCA) model. The theoretical and experimental vibration acceleration responses of the gearbox housing are contrastively analysed. The results show that some vibration modes are very similar to those of a single planetary gear train, but other modes are multi-node and multi-degree of freedom coupling modes. The vibration coupling and transferring phenomenon between two stages can be observed remarkably, but those show obvious differences under different working conditions. The torsional stiffness of the elastic connecting shaft has significant influence on the vibration coupling and transferring phenomenon. The results can provide useful guidance for the low vibration and noise design of the marine compound gear transmission system.
{"title":"Dynamic modelling and vibration characteristics of a marine compound gear transmission system","authors":"Long Yang, Bing Yuan, Jingyi Gong, Mingjian Qin, Geng Liu","doi":"10.1177/14644193231169057","DOIUrl":"https://doi.org/10.1177/14644193231169057","url":null,"abstract":"The vibration level is the key index to measure the performance of marine gear transmission device. The compound gear transmission system, which is composed of a helical gear pair and a spur star gear train, is widely used in marine gear transmission device. This paper presents a multi-node dynamic model for a marine compound gear transmission system, investigating the modal properties and dynamic responses of the system. The mesh stiffness and transmission error for each gear pair are determined using the loaded tooth contact analysis (LTCA) model. The theoretical and experimental vibration acceleration responses of the gearbox housing are contrastively analysed. The results show that some vibration modes are very similar to those of a single planetary gear train, but other modes are multi-node and multi-degree of freedom coupling modes. The vibration coupling and transferring phenomenon between two stages can be observed remarkably, but those show obvious differences under different working conditions. The torsional stiffness of the elastic connecting shaft has significant influence on the vibration coupling and transferring phenomenon. The results can provide useful guidance for the low vibration and noise design of the marine compound gear transmission system.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91205718","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}
Pub Date : 2023-03-20DOI: 10.1177/14644193231163631
Ankitkumar Dandiwala, Jigneshsinh Sindha, Basab Chakraborty, D. Chakravarty
The issues like traffic congestion, parking space and vehicular emission can be reduced by adopting electric narrow tilting three-wheelers, which can also provide a cost-effective and safe mode of transport for low-income people. According to energy technology perspectives 2017, well-to-wheel global greenhouse gas emissions can be reduced up to 1.3 GtCO2-eq by 2060 by adopting electric mobility. This study presents a new and modified SDTC strategy and performance parameters that takes Road Bank Angle (RBA) into account so as to exhibit the adverse effects on rollover safety, ride comfort in terms of the perceived lateral acceleration and desired trajectory. Besides, this study identifies the importance of the RBA consideration in active tilt controlled vehicle for the scenario of parking on sloped surface. Simple electronic control architecture of the SDTC approach with real-time RBA consideration is proposed to address the limitations of SDTC and its supplementary advantages. This study evaluates the scenario of constant turn manoeuvre and vehicle parking on the banked roads. A multi-body model is used to capture the dynamic characteristics of the vehicle, whereas a characteristic of the Tilt Actuation System (TAS) and Active Steering (AS) system is incorporated in the form of a Transfer Function (TF) estimated using a system identification approach. The results indicate that the inclusion of a real-time RBA in the SDTC enables it to maintain steady-state torque and perceived lateral acceleration close to zero with the proposed controlled strategy, and it also keeps the vehicle upright on the sloped surface. It may be concluded that RBA compensation improves the ease of handling the vehicle while parking or riding on a sloped surface without significant control system alterations, which also makes it a viable alternative for physically disabled people.
{"title":"Simulation-based study on active tilt controlled narrow tilting three-wheeler considering road bank angle","authors":"Ankitkumar Dandiwala, Jigneshsinh Sindha, Basab Chakraborty, D. Chakravarty","doi":"10.1177/14644193231163631","DOIUrl":"https://doi.org/10.1177/14644193231163631","url":null,"abstract":"The issues like traffic congestion, parking space and vehicular emission can be reduced by adopting electric narrow tilting three-wheelers, which can also provide a cost-effective and safe mode of transport for low-income people. According to energy technology perspectives 2017, well-to-wheel global greenhouse gas emissions can be reduced up to 1.3 GtCO2-eq by 2060 by adopting electric mobility. This study presents a new and modified SDTC strategy and performance parameters that takes Road Bank Angle (RBA) into account so as to exhibit the adverse effects on rollover safety, ride comfort in terms of the perceived lateral acceleration and desired trajectory. Besides, this study identifies the importance of the RBA consideration in active tilt controlled vehicle for the scenario of parking on sloped surface. Simple electronic control architecture of the SDTC approach with real-time RBA consideration is proposed to address the limitations of SDTC and its supplementary advantages. This study evaluates the scenario of constant turn manoeuvre and vehicle parking on the banked roads. A multi-body model is used to capture the dynamic characteristics of the vehicle, whereas a characteristic of the Tilt Actuation System (TAS) and Active Steering (AS) system is incorporated in the form of a Transfer Function (TF) estimated using a system identification approach. The results indicate that the inclusion of a real-time RBA in the SDTC enables it to maintain steady-state torque and perceived lateral acceleration close to zero with the proposed controlled strategy, and it also keeps the vehicle upright on the sloped surface. It may be concluded that RBA compensation improves the ease of handling the vehicle while parking or riding on a sloped surface without significant control system alterations, which also makes it a viable alternative for physically disabled people.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85609031","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}
Pub Date : 2023-03-20DOI: 10.1177/14644193231164214
JH Tian, XL Dong
The polygon effect seriously affects the running stability and safety of the vehicle. In order to suppress the wheel polygon, a dynamic model is established that can calculate the force on the resilient wheel's rim and core. With straight lines, curves, and vertical curves as input excitation, combined with wheel–rail force and acceleration, the suppression effect of the resilient wheel on the polygon is analyzed from the perspective of the time domain, frequency domain, and polygon order. The results show that the resilient wheel can effectively reduce the vertical wheel–rail force and restrain the wheel polygon. After 30 Hz, with the increase in frequency, the suppression effect of the resilient wheel on the polygon becomes increasingly significant. The resilient wheel can sufficiently suppress the polygons generated by 50–150 Hz carriage vibration without affecting the dominant frequency of carriage vibration. This study can provide a new idea for the suppression of wheel polygon.
{"title":"Research on polygon suppression of resilient wheels under multiple operating conditions","authors":"JH Tian, XL Dong","doi":"10.1177/14644193231164214","DOIUrl":"https://doi.org/10.1177/14644193231164214","url":null,"abstract":"The polygon effect seriously affects the running stability and safety of the vehicle. In order to suppress the wheel polygon, a dynamic model is established that can calculate the force on the resilient wheel's rim and core. With straight lines, curves, and vertical curves as input excitation, combined with wheel–rail force and acceleration, the suppression effect of the resilient wheel on the polygon is analyzed from the perspective of the time domain, frequency domain, and polygon order. The results show that the resilient wheel can effectively reduce the vertical wheel–rail force and restrain the wheel polygon. After 30 Hz, with the increase in frequency, the suppression effect of the resilient wheel on the polygon becomes increasingly significant. The resilient wheel can sufficiently suppress the polygons generated by 50–150 Hz carriage vibration without affecting the dominant frequency of carriage vibration. This study can provide a new idea for the suppression of wheel polygon.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76096847","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}
Pub Date : 2023-03-14DOI: 10.1177/14644193231161136
R. Turnbull, N. Dolatabadi, R. Rahmani, H. Rahnejat
In this paper, a mathematical model of a rotor-bearing system is presented. The model includes modal elastodynamics of a flexible rotor as well as the in-plane radial dynamics of the bearing with a flexible outer race. Elastodynamics of the flexible shaft utilises a solution based on Green's function to provide a computationally efficient approach. The flexible bearing outer race is modelled using Timoshenko beam theory. The system model also includes detailed lubricated contact mechanics of balls-to-races contacts with viscous friction. Therefore, the rotor-bearing analysis represents a detailed multi-physics tribodynamics and modal elastodynamic responses of the system which closely represents broad-band vibration response of such systems in practice, an approach not hitherto reported in the literature. It is also demonstrated that the outer race flexibility changes the location of the stability orbital centres, as well as the spread of limit cycle vibrations. Furthermore, it accentuates the occurrence of multiples of ball pass frequency. The importance of integrated system dynamics and lubricated contact mechanics is highlighted, showing that although the elastodynamic response of the rotor's flexible elements may not be clear in the acquired vibration signal, its effect on energy efficiency of the system can be quite important.
{"title":"Nonlinear tribodynamics of an elastic shaft with a flexible bearing outer race","authors":"R. Turnbull, N. Dolatabadi, R. Rahmani, H. Rahnejat","doi":"10.1177/14644193231161136","DOIUrl":"https://doi.org/10.1177/14644193231161136","url":null,"abstract":"In this paper, a mathematical model of a rotor-bearing system is presented. The model includes modal elastodynamics of a flexible rotor as well as the in-plane radial dynamics of the bearing with a flexible outer race. Elastodynamics of the flexible shaft utilises a solution based on Green's function to provide a computationally efficient approach. The flexible bearing outer race is modelled using Timoshenko beam theory. The system model also includes detailed lubricated contact mechanics of balls-to-races contacts with viscous friction. Therefore, the rotor-bearing analysis represents a detailed multi-physics tribodynamics and modal elastodynamic responses of the system which closely represents broad-band vibration response of such systems in practice, an approach not hitherto reported in the literature. It is also demonstrated that the outer race flexibility changes the location of the stability orbital centres, as well as the spread of limit cycle vibrations. Furthermore, it accentuates the occurrence of multiples of ball pass frequency. The importance of integrated system dynamics and lubricated contact mechanics is highlighted, showing that although the elastodynamic response of the rotor's flexible elements may not be clear in the acquired vibration signal, its effect on energy efficiency of the system can be quite important.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87555952","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}
Pub Date : 2023-03-06DOI: 10.1177/14644193231160841
Jin Gao, Xiaoping Qi
As an important component of the steering system, steering trapezoids should be designed to satisfy multiple performances of the vehicle. In this study, theoretical and simulation analysis has been conducted focusing on the influence of the steering tie rod on the Ackermann error, bump steer, forces at the tie rod joints, and frequency characteristics of the whole vehicle. The results show that the Ackermann error is mainly influenced by the position of the outer point of the steering tie rod. The bump steer is mainly influenced by the Z coordinate of the outer point. The impact force at the joint and the frequency characteristics are mainly influenced by the X and Z coordinates of the outer point of the tie rod. The trends of the evaluation indexes for each performance to the hard point coordinates are not completely consistent and some are conflicting. To integrate the vehicle performance, multi-objective optimization is carried out with Archival Micro Genetic Algorithm, Neighborhood Cultivation Genetic Algorithm, and Non-Dominated Sorting Genetic Algorithm-II algorithms considering the hard point coordinates as variables and the evaluation indexes as optimization objectives. The optimization results show that the relative optimal solutions obtained by the three optimization algorithms provide a significant improvement to the Ackermann error, while other performance indexes have differences. In the practical application of steering trapezoid optimization, it is possible to choose the appropriate optimization algorithm based on the focus of the vehicle performance requirements.
{"title":"Optimal design of steering trapezoid considering multiple performances of the whole vehicle","authors":"Jin Gao, Xiaoping Qi","doi":"10.1177/14644193231160841","DOIUrl":"https://doi.org/10.1177/14644193231160841","url":null,"abstract":"As an important component of the steering system, steering trapezoids should be designed to satisfy multiple performances of the vehicle. In this study, theoretical and simulation analysis has been conducted focusing on the influence of the steering tie rod on the Ackermann error, bump steer, forces at the tie rod joints, and frequency characteristics of the whole vehicle. The results show that the Ackermann error is mainly influenced by the position of the outer point of the steering tie rod. The bump steer is mainly influenced by the Z coordinate of the outer point. The impact force at the joint and the frequency characteristics are mainly influenced by the X and Z coordinates of the outer point of the tie rod. The trends of the evaluation indexes for each performance to the hard point coordinates are not completely consistent and some are conflicting. To integrate the vehicle performance, multi-objective optimization is carried out with Archival Micro Genetic Algorithm, Neighborhood Cultivation Genetic Algorithm, and Non-Dominated Sorting Genetic Algorithm-II algorithms considering the hard point coordinates as variables and the evaluation indexes as optimization objectives. The optimization results show that the relative optimal solutions obtained by the three optimization algorithms provide a significant improvement to the Ackermann error, while other performance indexes have differences. In the practical application of steering trapezoid optimization, it is possible to choose the appropriate optimization algorithm based on the focus of the vehicle performance requirements.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89915757","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}
Pub Date : 2023-02-22DOI: 10.1177/14644193231154159
Zhibin Li, S. Wang
The power six-branch herringbone gear transmission system has the advantages of large power transmission and transmission ratio. Because of its multi-way transmission and over-constraint structure, to prevent loaded tooth interference, there are large backlashes between teeth. The system shows complex nonlinear dynamic characteristics under the influence of backlashes, which seriously affects meshing performance. The modification technology can effectively improve gear meshing performance. Hence, on the basis of optimizing meshing performance of the active pair of the six-branch herringbone gear transmission system, this article will combine 3D modification with system nonlinear vibration characteristics and propose an analysis method of the system nonlinear vibration characteristics under 3D modification to reduce vibration and noise. First, the 3D modified tooth surface equation is determined by forming grinding, the loaded transmission error (LTE) of the system's active pair is obtained by tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) technology, and the optimal modification parameters are obtained by Ant Lion Optimizer (ALO) with the minimum error amplitude as optimization objective. Then, the time-varying meshing stiffness of system under the optimal modification is calculated, and the pure torsional nonlinear dynamic model with backlashes, meshing stiffness, and static transmission error (STE) is established. Finally, the global vibration characteristics in parameter field are studied through time domain and bifurcation diagram of system. Results show that the 3D modification can eliminate edge contact of tooth and improve tooth contact performance. With the increase of input power, the root mean square (RMS) values of acceleration increase and the RMS values and jump decrease after 3D modification. With the increase of input speed, the RMS curves appear multiple resonance peaks and jumps at low input speed. After 3D modification, the RMS, jump, and resonance peak values decrease. Compared with level І, the backlashes and STEs of level II and phase difference ϛsII have great influence on system dynamic characteristics and easily make system in chaotic motion, while the 3D modification reduces their influence and makes system motion periodic.
{"title":"Study on nonlinear dynamic characteristics of power six-branch herringbone gear transmission system with 3D modification","authors":"Zhibin Li, S. Wang","doi":"10.1177/14644193231154159","DOIUrl":"https://doi.org/10.1177/14644193231154159","url":null,"abstract":"The power six-branch herringbone gear transmission system has the advantages of large power transmission and transmission ratio. Because of its multi-way transmission and over-constraint structure, to prevent loaded tooth interference, there are large backlashes between teeth. The system shows complex nonlinear dynamic characteristics under the influence of backlashes, which seriously affects meshing performance. The modification technology can effectively improve gear meshing performance. Hence, on the basis of optimizing meshing performance of the active pair of the six-branch herringbone gear transmission system, this article will combine 3D modification with system nonlinear vibration characteristics and propose an analysis method of the system nonlinear vibration characteristics under 3D modification to reduce vibration and noise. First, the 3D modified tooth surface equation is determined by forming grinding, the loaded transmission error (LTE) of the system's active pair is obtained by tooth contact analysis (TCA) and loaded tooth contact analysis (LTCA) technology, and the optimal modification parameters are obtained by Ant Lion Optimizer (ALO) with the minimum error amplitude as optimization objective. Then, the time-varying meshing stiffness of system under the optimal modification is calculated, and the pure torsional nonlinear dynamic model with backlashes, meshing stiffness, and static transmission error (STE) is established. Finally, the global vibration characteristics in parameter field are studied through time domain and bifurcation diagram of system. Results show that the 3D modification can eliminate edge contact of tooth and improve tooth contact performance. With the increase of input power, the root mean square (RMS) values of acceleration increase and the RMS values and jump decrease after 3D modification. With the increase of input speed, the RMS curves appear multiple resonance peaks and jumps at low input speed. After 3D modification, the RMS, jump, and resonance peak values decrease. Compared with level І, the backlashes and STEs of level II and phase difference ϛsII have great influence on system dynamic characteristics and easily make system in chaotic motion, while the 3D modification reduces their influence and makes system motion periodic.","PeriodicalId":54565,"journal":{"name":"Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76392618","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}
Pub Date : 2023-02-16DOI: 10.1177/14644193231157176
S. Kaloni, P. Tiwari, Ghanapriya Singh
In the past few decades, time–frequency (TF) methods have become increasingly popular in the field of modal identification and structural health monitoring. The general and significant shortfalls of the TF models are the distributed and vague frequency components as an output. To overcome the cons of the initial TF technique, segregation of the modes incorporated within the affected vibration signatures evolved eventually. The most utilized and preferred technique can be named empirical mode decomposition (EMD) and its variants. However, these variants, along with the basic framework, possess the multi-mode tendency, which further compels the extension of the whole damage identification procedure. This work presents the development of a temporally evolved, generalized and high impulsive frequency acquisition model for structural damage identification. To meet the said outcome, variational mode decomposition (VMD) is considered an optimization-based signal decomposition tool that utilizes the contents of the generated modal responses. This work also aims to investigate the applicability of VMD for the purpose of structural damage identification for the following situations: the old ADA steel bridge under vehicle-induced vibration for various damage scenarios; a three-story shear frame building model. Along with the said validation of the proposed condition monitoring model, this paper addresses the need of stable and reliable novel damage indicator (DI) as a statistical alteration of the extracted instantaneous outputs. The proposed DI as the mean of the ratio of the instantaneous outputs collectively indicates the relative capacity of the structure to produce a stable response. The selected outputs are instantaneous frequency, phase and energy, taken into consideration to depict the physical alterations in the measured response. The proposed DI evidently explains the physical relation of the involved factors with the degradation causes in the considered structure. The DI also reflects the remaining usefulness of the system and provides the measurements in safety aspects to the operators. The results so obtained are well competent for real bridge structures under the influence of dynamic loading conditions induced by vehicle movements.
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