Transmission error (TE) is an important index affecting the positioning accuracy and dynamic performance of gear drive. An original discrete slice model for TE analysis of herringbone gear drive based on the measured manufacturing errors (ME) is proposed, involving tooth surface error, cumulative pitch error and alignment error of double helical surfaces. In the model, herringbone gears are discretized into a series of slices in order to deal with the 3D contact problem. The measured cumulative pitch error and alignment error are described as the position error of slices, while the measured tooth surface error is constructed as the real surface shape by B-spline method. Thus, the measured ME are converted into the contact gaps of slices. The compatibility and equilibrium equations under error and load conditions are derived from the kinematic geometry and elastic mechanics. Based on the discrete slice model, the relationship between measured ME and TE are established explicitly. The ME of herringbone gear drive is measured, the effects of measured ME on TE under no-load and load conditions were analyzed, and TE test of herringbone gears was carried out. The test results are consistent with the properties and values of simulations, which verifies the proposed model.
传动误差（TE）是影响齿轮传动装置定位精度和动态性能的重要指标。本文提出了一种基于测量制造误差（ME）的人字齿轮传动 TE 分析离散切片模型，涉及齿面误差、累积节距误差和双螺旋面的对准误差。在该模型中，人字齿轮被离散成一系列切片，以处理三维接触问题。测量到的累积节距误差和对中误差被描述为切片的位置误差，而测量到的齿面误差则通过 B-样条法构建为真实的表面形状。因此，测量的 ME 被转换为切片的接触间隙。根据运动几何和弹性力学推导出误差和载荷条件下的相容性和平衡方程。基于离散切片模型，明确建立了测量 ME 与 TE 之间的关系。测量了人字形齿轮传动的 ME，分析了空载和负载条件下测量 ME 对 TE 的影响，并对人字形齿轮进行了 TE 测试。测试结果与模拟的特性和数值一致，验证了所提出的模型。
{"title":"Transmission error modeling and analysis of herringbone gear drive based on the measured manufacturing errors","authors":"Chu Zhang, Yunbo Hu, Huimin Dong, Changqing Wang","doi":"10.1139/tcsme-2024-0038","DOIUrl":"https://doi.org/10.1139/tcsme-2024-0038","url":null,"abstract":"Transmission error (TE) is an important index affecting the positioning accuracy and dynamic performance of gear drive. An original discrete slice model for TE analysis of herringbone gear drive based on the measured manufacturing errors (ME) is proposed, involving tooth surface error, cumulative pitch error and alignment error of double helical surfaces. In the model, herringbone gears are discretized into a series of slices in order to deal with the 3D contact problem. The measured cumulative pitch error and alignment error are described as the position error of slices, while the measured tooth surface error is constructed as the real surface shape by B-spline method. Thus, the measured ME are converted into the contact gaps of slices. The compatibility and equilibrium equations under error and load conditions are derived from the kinematic geometry and elastic mechanics. Based on the discrete slice model, the relationship between measured ME and TE are established explicitly. The ME of herringbone gear drive is measured, the effects of measured ME on TE under no-load and load conditions were analyzed, and TE test of herringbone gears was carried out. The test results are consistent with the properties and values of simulations, which verifies the proposed model.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":"15 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cette étude numérique s'intéresse à l'écoulement de jeu dans la configuration de grille rectiligne d'aubes de compresseur du laboratoire de Virginia Tech (VT). L'objectif est de proposer un modèle pour quantifier les pertes visqueuses associées à l'écoulement de jeu sur cette configuration. Pour ce faire, des simulations incompressibles sont réalisées s'appuyant sur les équations aux moyennes de Reynolds (RANS) pour différents débits tout en conservant le nombre de Reynolds de 4×10 5. L'écoulement dans la grille au point optimal est validé avec les mesures expérimentales. Les pertes visqueuses dans les couches limites, le sillage et le jeu sont quantifiées pour les différents débits simulés. Les pertes associées à l'écoulement de jeu sont par la suite employées pour évaluer, dans cette configuration de grille rectiligne, le modèle empirique de pertes proposé par Deveaux et al (2020). Le changement de débit modifie l'état du tourbillon de jeu et les différents paramètres du modèle de pertes sont alors calibrés pour la grille VT en fonction du débit.
{"title":"Analyse et modélisation des pertes dans une grille rectiligne de compresseur avec jeu.","authors":"A. Drame, Marlène Sanjosé","doi":"10.1139/tcsme-2024-0008","DOIUrl":"https://doi.org/10.1139/tcsme-2024-0008","url":null,"abstract":"Cette étude numérique s'intéresse à l'écoulement de jeu dans la configuration de grille rectiligne d'aubes de compresseur du laboratoire de Virginia Tech (VT). L'objectif est de proposer un modèle pour quantifier les pertes visqueuses associées à l'écoulement de jeu sur cette configuration. Pour ce faire, des simulations incompressibles sont réalisées s'appuyant sur les équations aux moyennes de Reynolds (RANS) pour différents débits tout en conservant le nombre de Reynolds de 4×10 5. L'écoulement dans la grille au point optimal est validé avec les mesures expérimentales. Les pertes visqueuses dans les couches limites, le sillage et le jeu sont quantifiées pour les différents débits simulés. Les pertes associées à l'écoulement de jeu sont par la suite employées pour évaluer, dans cette configuration de grille rectiligne, le modèle empirique de pertes proposé par Deveaux et al (2020). Le changement de débit modifie l'état du tourbillon de jeu et les différents paramètres du modèle de pertes sont alors calibrés pour la grille VT en fonction du débit.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":"53 27","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141804850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Junying Wei, Xiang Li, Yu Liu, Haowei Zhang, Lei Yang, Xueyi Li
This paper addresses the control of a hexapod robot’s foot trajectory tracking using an adaptive sliding mode control (SMC) approach based on Udwadia–Kalaba theory. Unlike the traditional control approach, the Udwadia–Kalaba theory allows for the transformation of the hexapod robot foot trajectory tracking control problem into a system servo binding solution problem. This method eliminates the requirement to linearize the nonlinear system. The system may contain uncertainties, such as less-than-ideal initial circumstances and vibration disturbances during operation, which have an impact on the control precision due to mistakes in modeling, measurements, and changes in operational states. To deal with the uncertainty, the adaptive SMC controller was developed. The stability analysis is carried out using the second Lyapunov function method. By modeling the hexapod robot’s legs and running simulations to compare the simulated tracking route to the planned trajectory, the precision and stability of the control approach suggested in this study are finally demonstrated, and by comparing with the simulation results of adaptive robust control strategy, the advantages of RBF neural network adaptive SMC strategy are obtained.
{"title":"The adaptive sliding mode control based on U–K theory for foot trajectory following of hexapod robot","authors":"Junying Wei, Xiang Li, Yu Liu, Haowei Zhang, Lei Yang, Xueyi Li","doi":"10.1139/tcsme-2023-0198","DOIUrl":"https://doi.org/10.1139/tcsme-2023-0198","url":null,"abstract":"This paper addresses the control of a hexapod robot’s foot trajectory tracking using an adaptive sliding mode control (SMC) approach based on Udwadia–Kalaba theory. Unlike the traditional control approach, the Udwadia–Kalaba theory allows for the transformation of the hexapod robot foot trajectory tracking control problem into a system servo binding solution problem. This method eliminates the requirement to linearize the nonlinear system. The system may contain uncertainties, such as less-than-ideal initial circumstances and vibration disturbances during operation, which have an impact on the control precision due to mistakes in modeling, measurements, and changes in operational states. To deal with the uncertainty, the adaptive SMC controller was developed. The stability analysis is carried out using the second Lyapunov function method. By modeling the hexapod robot’s legs and running simulations to compare the simulated tracking route to the planned trajectory, the precision and stability of the control approach suggested in this study are finally demonstrated, and by comparing with the simulation results of adaptive robust control strategy, the advantages of RBF neural network adaptive SMC strategy are obtained.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
W. Gao, Yuang Liao, Zhao-wen Deng, Youqun Zhao, Baohua Wang
To improve the lateral stability of tractor-semitrailer under low adhesion road surface, a direct yaw torque control strategy considering longitudinal speed control was proposed based on distributed electric drive technology. A hierarchical control strategy was designed, with the upper layer using a linear quadratic regulator (LQR) controller to calculate the yaw moment. To distribute the longitudinal force and additional yaw moment, the torque distribution method was adopted based on quadratic programming in the lower controller. The co-simulation was conducted by Trucksim and Matlab/Simulink under the conditions of single lane change (SLC) of 110 km/h and double lane change (DLC) of 70 km/h. The results indicate that in comparison with the PID controller and the uncontrolled vehicle, the LQR controller improves the lateral stability of the vehicle on the low-adhesion road.
为了提高牵引车-半挂车在低附着力路面下的横向稳定性，基于分布式电驱动技术提出了一种考虑纵向速度控制的直接偏航力矩控制策略。设计了一种分层控制策略，上层使用线性二次调节器（LQR）控制器计算偏航力矩。为了分配纵向力和附加偏航力矩，下层控制器采用了基于二次编程的扭矩分配方法。通过 Trucksim 和 Matlab/Simulink，在单线变道（SLC）110 km/h 和双线变道（DLC）70 km/h 的条件下进行了联合仿真。结果表明，与 PID 控制器和不受控制的车辆相比，LQR 控制器提高了车辆在低附着力路面上的横向稳定性。
{"title":"Study on lateral stability of distributed drive electric tractor semi-trailers under low adhesion road conditions","authors":"W. Gao, Yuang Liao, Zhao-wen Deng, Youqun Zhao, Baohua Wang","doi":"10.1139/tcsme-2023-0220","DOIUrl":"https://doi.org/10.1139/tcsme-2023-0220","url":null,"abstract":"To improve the lateral stability of tractor-semitrailer under low adhesion road surface, a direct yaw torque control strategy considering longitudinal speed control was proposed based on distributed electric drive technology. A hierarchical control strategy was designed, with the upper layer using a linear quadratic regulator (LQR) controller to calculate the yaw moment. To distribute the longitudinal force and additional yaw moment, the torque distribution method was adopted based on quadratic programming in the lower controller. The co-simulation was conducted by Trucksim and Matlab/Simulink under the conditions of single lane change (SLC) of 110 km/h and double lane change (DLC) of 70 km/h. The results indicate that in comparison with the PID controller and the uncontrolled vehicle, the LQR controller improves the lateral stability of the vehicle on the low-adhesion road.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":" 958","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A centrifugal compressor is the core equipment of the chemical industry. To solve the problems of assembly difficulties and poor mechanical properties caused by the connection between impeller and shaft end in existing compressor, this paper takes a small geared air compressor designed by Shenyang Borui Turbine Technical Service Co., Ltd. as an example and designs its first-stage impeller and shaft end into three structural forms of tie rod–pin connection, tie rod–end key connection, and flange connection, respectively, to find an optimal connection mode between the centrifugal impeller and shaft end. Firstly, the calculation method is verified. Then, the stress, strain, deformation, and critical rotor speed of these three structures are compared and analyzed based on multi-parameter genetic optimization method. The results show that when the impeller and shaft end are connected by the tie rod–end key structure, compared to the tie rod–pin connection structure and flange connection structure, the maximum stress is reduced by 43.8% and 61.2%, the strain is reduced by 43.8% and 61.8%, the deformation is reduced by 3.64 times and 6.27 times, respectively, and the resonance margin will also be greatly improved. The research results in this paper provide a theoretical basis for the reliable design of the connection between the centrifugal impeller and shaft end.
{"title":"Structural optimization design of connection between centrifugal impeller and shaft end based on finite element method","authors":"Yanjun Li, Zhichao Ma","doi":"10.1139/tcsme-2023-0147","DOIUrl":"https://doi.org/10.1139/tcsme-2023-0147","url":null,"abstract":"A centrifugal compressor is the core equipment of the chemical industry. To solve the problems of assembly difficulties and poor mechanical properties caused by the connection between impeller and shaft end in existing compressor, this paper takes a small geared air compressor designed by Shenyang Borui Turbine Technical Service Co., Ltd. as an example and designs its first-stage impeller and shaft end into three structural forms of tie rod–pin connection, tie rod–end key connection, and flange connection, respectively, to find an optimal connection mode between the centrifugal impeller and shaft end. Firstly, the calculation method is verified. Then, the stress, strain, deformation, and critical rotor speed of these three structures are compared and analyzed based on multi-parameter genetic optimization method. The results show that when the impeller and shaft end are connected by the tie rod–end key structure, compared to the tie rod–pin connection structure and flange connection structure, the maximum stress is reduced by 43.8% and 61.2%, the strain is reduced by 43.8% and 61.8%, the deformation is reduced by 3.64 times and 6.27 times, respectively, and the resonance margin will also be greatly improved. The research results in this paper provide a theoretical basis for the reliable design of the connection between the centrifugal impeller and shaft end.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":" 767","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140382867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Considering multidisciplinary characteristics of thin plate vibration, fluid–solid coupling, and other aspects of a relief valve controlled by annular thin plates, a dynamic finite element (FE) model in view of fluid–solid coupling is firstly established for capturing relationships between dynamic characteristics of crucial indexes and partial working conditions. Secondly, the partial dataset of FE model under different conditions is statistically analyzed, and it will be utilized to train the feedforward neural network (FNN) model. The training process of FNN could be completed if results drawn from the FNN model are highly consistent with those of the FE model. Thirdly, dynamic characteristics under more conditions will be predicted through such a trained model, and dynamic behaviors from the FE model for same conditions of the FNN model are also obtained. Finally, comparing with results from the FE model, the maximum absolute error of steady-state displacement from the FNN is 0.0052 mm in an instance, thus verifying the rationality of this combined method. Consequently, such a combination of the FE model and the FNN model presents high accuracy and avoids repeated calculations of FE model with long times.
考虑到环形薄板控制溢流阀的薄板振动、流固耦合等多学科特性，首先建立了流固耦合的动态有限元（FE）模型，以捕捉关键指标的动态特性与部分工况之间的关系。其次，对不同工况下有限元模型的部分数据集进行统计分析，并利用这些数据集训练前馈神经网络（FNN）模型。如果 FNN 模型得出的结果与 FE 模型的结果高度一致，则 FNN 的训练过程即可完成。第三，通过这样一个训练有素的模型，可以预测更多条件下的动态特性，并从 FE 模型中获得 FNN 模型在相同条件下的动态行为。最后，与 FE 模型的结果相比，FNN 得出的稳态位移最大绝对误差为 0.0052 mm，从而验证了这种组合方法的合理性。因此，这种将 FE 模型和 FNN 模型相结合的方法具有较高的精度，避免了长时间重复计算 FE 模型。
{"title":"Dynamic characteristics of a relief valve captured by a combination of fluid–solid coupling and feedforward neural network (FNN)","authors":"Chuyan Wang, Xianju Yuan, Junjie Chen, Xiaobing Chen, Tianyu Qiu","doi":"10.1139/tcsme-2023-0116","DOIUrl":"https://doi.org/10.1139/tcsme-2023-0116","url":null,"abstract":"Considering multidisciplinary characteristics of thin plate vibration, fluid–solid coupling, and other aspects of a relief valve controlled by annular thin plates, a dynamic finite element (FE) model in view of fluid–solid coupling is firstly established for capturing relationships between dynamic characteristics of crucial indexes and partial working conditions. Secondly, the partial dataset of FE model under different conditions is statistically analyzed, and it will be utilized to train the feedforward neural network (FNN) model. The training process of FNN could be completed if results drawn from the FNN model are highly consistent with those of the FE model. Thirdly, dynamic characteristics under more conditions will be predicted through such a trained model, and dynamic behaviors from the FE model for same conditions of the FNN model are also obtained. Finally, comparing with results from the FE model, the maximum absolute error of steady-state displacement from the FNN is 0.0052 mm in an instance, thus verifying the rationality of this combined method. Consequently, such a combination of the FE model and the FNN model presents high accuracy and avoids repeated calculations of FE model with long times.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":"4 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140382095","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cameras are increasingly used in modern vehicles equipped with advanced driver assistance systems (ADAS) to collect environmental information. Cameras suffer performance degradation when driving in adverse weather conditions, such as rain, as precipitation droplets impact the camera lens and cause obstruction and blurring of the vision. The relationships between image quality, object detection accuracy, and surface wettability of camera lenses are investigated. This paper applies a previously developed evaluation procedure for wind tunnel testing with simulated adverse driving and rain conditions. Realistic rain characteristics perceived by a moving vehicle at different driving speeds are simulated using a novel rain simulation system implemented into a wind tunnel. Moreover, an emphasis is put on comparing the use of hydrophilic and hydrophobic surfaces to provide insights into material selection when designing camera lenses for ADAS. It is found that droplet dynamics, such as size, velocity, shape, and motion can impact the camera image quality and, subsequently, object detection accuracy. This paper demonstrates the use of various materials and evaluation metrics, and their implications from a practical perspective when subjected to realistic driving-in-rain scenarios. The results suggest that the use of hydrophobic lenses promotes better performance over hydrophilic lenses in most cases with exceptions.
{"title":"Perceived Rain Dynamics on Hydrophilic/Hydrophobic Lens Surfaces and Their Influences on Vehicle Camera Performance","authors":"W. Y. Pao, Long Li, Martin Agelin-Chaab","doi":"10.1139/tcsme-2023-0156","DOIUrl":"https://doi.org/10.1139/tcsme-2023-0156","url":null,"abstract":"Cameras are increasingly used in modern vehicles equipped with advanced driver assistance systems (ADAS) to collect environmental information. Cameras suffer performance degradation when driving in adverse weather conditions, such as rain, as precipitation droplets impact the camera lens and cause obstruction and blurring of the vision. The relationships between image quality, object detection accuracy, and surface wettability of camera lenses are investigated. This paper applies a previously developed evaluation procedure for wind tunnel testing with simulated adverse driving and rain conditions. Realistic rain characteristics perceived by a moving vehicle at different driving speeds are simulated using a novel rain simulation system implemented into a wind tunnel. Moreover, an emphasis is put on comparing the use of hydrophilic and hydrophobic surfaces to provide insights into material selection when designing camera lenses for ADAS. It is found that droplet dynamics, such as size, velocity, shape, and motion can impact the camera image quality and, subsequently, object detection accuracy. This paper demonstrates the use of various materials and evaluation metrics, and their implications from a practical perspective when subjected to realistic driving-in-rain scenarios. The results suggest that the use of hydrophobic lenses promotes better performance over hydrophilic lenses in most cases with exceptions.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":"43 22","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140086002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pengyuan Qiu, Linxiang Wang, Yanjun Peng, Hua Qiao, Yanhu Lin
An integrated model is proposed to evaluate the contact pattern and load distribution of helical gear with different combinations of high-order topological modification, which is established combining the finite element method (FEM), the analytical method (AM), and the nonlinear programming method. Based on the elastomer contact model of tooth surface, the FEM is used to separate the flexural-shear deformation of the teeth, while the contact AM is introduced to derive the local contact deformation. The contact characteristics of gears can be finally obtained by solving the nonlinear programming model with the constraints of deformation and load and finally verified by the finite element analysis. The results show that the longitudinal crowning can significantly improve the load distribution and the edge contact of the tooth. When the modified curve becomes a parabola of higher order, the contact characteristics change obviously. The pressure of double-crowned (4) gears was uniform and the amplitude decreased, but the amplitude of pressure of double-crowned (6) gears increases and the variance of load sharing ratio is more obvious at the beginning of the middle meshing period.
本文结合有限元法（FEM）、分析法（AM）和非线性编程法，提出了一个综合模型，用于评估具有不同高阶拓扑修正组合的斜齿轮的接触模式和载荷分布。在齿面弹性体接触模型的基础上，利用有限元法分离出齿面的挠剪变形，同时引入接触 AM 法推导出局部接触变形。通过对变形和载荷约束的非线性编程模型进行求解，最终得到齿轮的接触特性，并通过有限元分析进行验证。结果表明，纵向加冠能显著改善载荷分布和齿边接触。当修正曲线变为高阶抛物线时，接触特性发生了明显变化。双冠（4）齿轮的压力均匀且振幅减小，但双冠（6）齿轮的压力振幅增大，且在啮合中期的初期，载荷分担比的差异更为明显。
{"title":"Influence of different combinations of high-order topological modification on contact pattern and load distribution of helical gear","authors":"Pengyuan Qiu, Linxiang Wang, Yanjun Peng, Hua Qiao, Yanhu Lin","doi":"10.1139/tcsme-2023-0039","DOIUrl":"https://doi.org/10.1139/tcsme-2023-0039","url":null,"abstract":"An integrated model is proposed to evaluate the contact pattern and load distribution of helical gear with different combinations of high-order topological modification, which is established combining the finite element method (FEM), the analytical method (AM), and the nonlinear programming method. Based on the elastomer contact model of tooth surface, the FEM is used to separate the flexural-shear deformation of the teeth, while the contact AM is introduced to derive the local contact deformation. The contact characteristics of gears can be finally obtained by solving the nonlinear programming model with the constraints of deformation and load and finally verified by the finite element analysis. The results show that the longitudinal crowning can significantly improve the load distribution and the edge contact of the tooth. When the modified curve becomes a parabola of higher order, the contact characteristics change obviously. The pressure of double-crowned (4) gears was uniform and the amplitude decreased, but the amplitude of pressure of double-crowned (6) gears increases and the variance of load sharing ratio is more obvious at the beginning of the middle meshing period.","PeriodicalId":510721,"journal":{"name":"Transactions of the Canadian Society for Mechanical Engineering","volume":"66 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140486226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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