The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold r...The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold roll-beating,etc.However,the research on law of metal flow in the forming process of involute spline cold roll-beating is rare.According to the principle of involute spline cold roll-beating,the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established,and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded.A finite element model of the spline cold roll-beating process is established,the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied,and the node flow tracks of the deformation area are analyzed.The experimental research on the metal flow of cold roll-beating spline is conducted,and the metallographic structure variation,grain characteristics and metal flow line of the different tooth profile area are analyzed.The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance.There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming.The characteristics of involute spline cold roll-beating forming are given,and the forming mechanism of involute spline cold roll-beating is revealed.This paper researches the law of metal flow in the forming process of involute spline cold roll-beating,which provides theoretical supports for solving the tooth profile forming quality problem.展开更多
The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many pri...The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.展开更多
The manufacturing accuracy of ultra-precision master gears signifies the technological capability of the ultra-precision gear.Currently,there is little report about the manufacturing technologies of ultra-precision ma...The manufacturing accuracy of ultra-precision master gears signifies the technological capability of the ultra-precision gear.Currently,there is little report about the manufacturing technologies of ultra-precision master gears at home and aboard.In order to meet the requirement of grinding ultra precision master gear,the gear grinder with flat-faced wheel Y7125 is chosen as the object machine tool and the geometric model of its precision generating part,the involute cam,is established.According to the structure of the involute cam,the effective working section and its adjustable range of the cam are determined,and the mathematical expressions of the effects of comprehensive eccentricity of the involute cam on gear profile deviations are derived.According to the primary harmonic trends of the deviation curve,it is shown that gear profile form and slope deviations in different work generating sections of the involute cam are different which the latter changes with the cam eccentricity obviously.Then,the issues of extreme values and methods of error compensation are studied and the conclusion that large adjustable range is benefit to search the optimal involute-cam section which is responding to the minimum gear profile deviations is obtained.A group of examples are calculated by choosing master gears with d=120 mm and m=2-6 mm and an involute cam with base diameter djcam =117 mm.And it is found that the maximum gear profile deviation counts for no more than 5% of the cam eccentricity after error compensation.A gear-grinding experiment on the master gear with m=2 mm is conducted by choosing different sections of the involute cam and the differences of gear profile deviations then the existence of the cam eccentricity are verified.The research discloses the rule of gear profile deviations caused by the comprehensive eccentricity of the involute cam and provides the theoretical guidance and the processing methods for grinding profile of the ultra precision master gear.展开更多
Design of forming dies and whole process of simulation of cold rolling involutes spline can be realized by using of CAD software of PRO-E and CAE software of DEFORM-3D. Software DEFORM-3D provides an automatic and opt...Design of forming dies and whole process of simulation of cold rolling involutes spline can be realized by using of CAD software of PRO-E and CAE software of DEFORM-3D. Software DEFORM-3D provides an automatic and optimized remeshing function, especially for the large deformation. In order to use this function sufficiently, simulation of cold rolling involutes spline can be implemented indirectly. The relationship between die and workpiece, forming force and characteristic of deformation in the forming process of cold rolling involutes spline are analyzed and researched. Meanwhile, reliable proofs for the design of dies and deforming equipment are provided.展开更多
The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points o...The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained.Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters.The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore,the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.展开更多
Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short...Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short) is investigated. The results suggest that gearlubrication effects bear close relations to a dimensionless parameter D which is syntheticallydetermined by gearing rotational speed, load, material, dimension and lubricant viscosity. When D<=8, the gear fatigue life increases as the lubricant viscosity is increased; When D>8, however, thelife decreases with the viscosity addition, which is in marked contrast to the lubrication factorZ_L recommended by the International Standard for Computing Cylindrical Gear Strength. At the end, aset of formulae for calculating gear lubrication factors suitable for different working conditionsare advanced.展开更多
Lubrication failure is one of the main failure forms of gear failure.Time varying meshing stiffness is an important factor affecting the dynamic behavior of gears.However,the influence of oil film stiffness is usually...Lubrication failure is one of the main failure forms of gear failure.Time varying meshing stiffness is an important factor affecting the dynamic behavior of gears.However,the influence of oil film stiffness is usually ignored in the research process.In this paper,according to the meshing characteristics of double involute gears,based on the non-Newtonian thermal EHL theory,a new calculation method of normal and tangential oil film stiffness for double involute gears is established by the idea of subsection method.The oil film stiffness difference between double involute gears and common involute gears is analyzed,and the influence of tooth waist order parameters,working conditions,and thermal effect on the oil film stiffness are studied.The results reveal that there are some differences between normal and tangential oil film stiffness between double involute gears and common involute gears,but there is little difference.Compared with the torque,rotation speed and initial viscosity of the lubricating oil,the tooth waist order parameters have less influence on the oil film stiffness.Thermal effect has a certain influence on normal and tangential oil film stiffness,which indicates that the influence of thermal effect on the oil film can not be ignored.This research proposes a calculation method of normal and tangential oil film stiffness suitable for double involute gears,which provides a theoretical basis for improving the stability of the transmission.展开更多
Because of good quality of compressive resistance, the hyperbolic arch dam is being increasingly applied to engineering projects. In order to satisfy the needs of compressive resistance under the conditions of high wa...Because of good quality of compressive resistance, the hyperbolic arch dam is being increasingly applied to engineering projects. In order to satisfy the needs of compressive resistance under the conditions of high water pressure, a stress analysis is required for the dam. During the stress analysis process however, due to the complexity of the three-dimensional modeling, it is very hard to form a model. Therefore, the stress analysis process is a barrier for the arch dam. In this article, based on the research of the new line-type arch dam, a mathematical model in different degree of convexity conditions of the dam is established; using the C ＋ ＋ language program, a computer three-dimensional model simulation is realized on AutoCAD. The accurate three-dimensional model is providing a finite element optimization design of the involute hyperbolic arch dam for the next step.展开更多
In wrist watches gear drives with undercut pinions are used. Those pinions have got a tooth number as few as 5—7. The efficiency of such gear drives is important because of the limited energy supply. The mean efficie...In wrist watches gear drives with undercut pinions are used. Those pinions have got a tooth number as few as 5—7. The efficiency of such gear drives is important because of the limited energy supply. The mean efficiency of gear drives can be expressed as E<sub>m</sub>=1/（φ<sub>2</sub>-φ<sub>1</sub>）（integral from φ<sub>1</sub> to φ<sub>2</sub>（E（φ）dφ）） in which <sup>0</sup><sub>1</sub>, <sup><</sup>sub>2</sub> are the approach angle and the recess angle respectively. In the discussion we assume that the friction coefficient between the two tooth flanks is constant because the sliding speed is relatively low in wrist watches and the main purpose is to find out the relation between gear parameters and its efficiency rather than to calculate the exact value of the efficiency. In normal conditions <sup>o</sup><sub>1</sub> and <sup>o</sup><sub>2</sub> can be found from the gear geometry without much difficulty. However when the pinion is an undercut one we have to first find the forming diameter where the involute profile starts. In this paper equations for the computation of the efficiency and the contact ratio of those gear drives are discussed.展开更多
The D'Alembert-Lagrange equation is introduced and used to derive theformulas of momentary efficiency for external gearing of standard involutes spur gears. The gearingswith correct and increased center distance a...The D'Alembert-Lagrange equation is introduced and used to derive theformulas of momentary efficiency for external gearing of standard involutes spur gears. The gearingswith correct and increased center distance are discussed. The momentary efficiency formula iscalculated and analyzed using software Matlab. The derived formula of momentary efficiency is alsocompared with the traditional formula.展开更多
Base on the theory of energy minimization, a numerical algorithm is established to calculate load distribution, and the relationship curve of spur gear load distribution is obtained, and the load distribution ratio ch...Base on the theory of energy minimization, a numerical algorithm is established to calculate load distribution, and the relationship curve of spur gear load distribution is obtained, and the load distribution ratio changes from 033 to 067 in double contact zone. This theory is adopted to compute the load distribution of helical gear along time-varying contact line, and the load distribution varies with the instantaneous position of the meshing point and the length of contact line, and the maximum value of load appears at the pitch point. Compared with the load distribution results, the helical gear changes more smoothly than spur gear. The load distribution provides a basis for calculate tooth bending deformation and critical stress.展开更多
The deformation principles of the steady- state and the unsteady一state of open- die cold extrusion for involute spline shafts are analyzed by means of experiments. On one hand,based on the deformation princ...The deformation principles of the steady- state and the unsteady一state of open- die cold extrusion for involute spline shafts are analyzed by means of experiments. On one hand,based on the deformation principles of the steady- state, data for determining structural parameters of the die, the size of the billet and the constraint condition of this technique are given. On the other hand, according to the principles of the unsteady- state, data for modifying the shapes and sizes of the bil- lets are provided.展开更多
The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role i...The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role in determining the output performance of the scroll expander.In this study,in order to investigate the output characteristics of a variable cross-section scroll expander,numerical simulation and experimental studies were con-ducted by using Computational Fluid Dynamics(CFD)methods and dynamic mesh techniques.The impact of critical parameters on the output performance of the scroll expander was analyzed through the utilization of the control variable method.It is found that increasing the inlet pressure and temperature within a certain range can improve the output power of the scroll expander.However,the increase in temperature and meshing clearance leads to a decline in the overall output performance of the scroll expander,leading to a decrease in volumetric efficiency by 8.43%and 12.79%,respectively.The experiments demonstrate that under equal inlet pressure conditions,increasing the inlet temperature elevates both the rotational speed and torque output of the scroll expander.Specifically,compared to operating at normal temperatures,the output torque increases by 21.8%under high-temperature conditions.However,the rate of speed and torque variation decreases as a consequence of enlarged meshing clearance,resulting in increased internal leakage and reduction in isentropic efficiency.展开更多
Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a thre...Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.展开更多
We construct an involution over Dyck paths,which implies the distribution of statistics“the number of peak”,“the number of returns”and“the height of the last peak”.As an application,equidistributions of several ...We construct an involution over Dyck paths,which implies the distribution of statistics“the number of peak”,“the number of returns”and“the height of the last peak”.As an application,equidistributions of several Stirling statistics over 132-avoiding and 321-avoiding permutations are presented.展开更多
This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two...This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,showing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(i)the explicit symmetrization of the system,which can be achieved by adding terms that contain linear combinations of the curl involution,similar to the Godunov-Powell terms in the MHD equations;(ii)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illustrate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.5107512450975229)Doctoral Foundation of Henan University of Science and Technology of China(Grant No.09001331)
文摘The present research on involute spline cold roll-beating forming is mainly about the principles and motion relations of cold roll-beating,the theory of roller design,and the stress and strain field analysis of cold roll-beating,etc.However,the research on law of metal flow in the forming process of involute spline cold roll-beating is rare.According to the principle of involute spline cold roll-beating,the contact model between the rollers and the spline shaft blank in the process of cold roll-beating forming is established,and the theoretical analysis of metal flow in the cold roll-beating deforming region is proceeded.A finite element model of the spline cold roll-beating process is established,the formation mechanism of the involute spline tooth profile in cold roll-beating forming process is studied,and the node flow tracks of the deformation area are analyzed.The experimental research on the metal flow of cold roll-beating spline is conducted,and the metallographic structure variation,grain characteristics and metal flow line of the different tooth profile area are analyzed.The experimental results show that the particle flow directions of the deformable bodies in cold roll-beating deformation area are determined by the minimum moving resistance.There are five types of metal flow rules of the deforming region in the process of cold roll-beating forming.The characteristics of involute spline cold roll-beating forming are given,and the forming mechanism of involute spline cold roll-beating is revealed.This paper researches the law of metal flow in the forming process of involute spline cold roll-beating,which provides theoretical supports for solving the tooth profile forming quality problem.
文摘The effect of involute contact ratio on the torsional vibration behavior ofspur gear-pair is studied analytically through a mass-spring model. The tooth stiffness in model notonly has a relation with time, as many prior studies presented, but, more important, with involutecontact ratio (ICR) as well. The ICR embodies its impact on the spur gear's dynamic performancethrough changing the proportion of tooth stiffness when there are n+1 teeth in contact to toothstiffness when there are n teeth in contact. A couple of curves about impact of ICR on the gear'sdynamic performance are presented, and they clearly demonstrate that the model can accuratelydescribe the effects of ICR on dynamic transmission error. Finally, some conclusions useful toreduce vibration and noise of gear-pair are proposed.
基金supported by National Hi-tech Research and Development Program of China (863 Program,Grant No.2008AA042506)
文摘The manufacturing accuracy of ultra-precision master gears signifies the technological capability of the ultra-precision gear.Currently,there is little report about the manufacturing technologies of ultra-precision master gears at home and aboard.In order to meet the requirement of grinding ultra precision master gear,the gear grinder with flat-faced wheel Y7125 is chosen as the object machine tool and the geometric model of its precision generating part,the involute cam,is established.According to the structure of the involute cam,the effective working section and its adjustable range of the cam are determined,and the mathematical expressions of the effects of comprehensive eccentricity of the involute cam on gear profile deviations are derived.According to the primary harmonic trends of the deviation curve,it is shown that gear profile form and slope deviations in different work generating sections of the involute cam are different which the latter changes with the cam eccentricity obviously.Then,the issues of extreme values and methods of error compensation are studied and the conclusion that large adjustable range is benefit to search the optimal involute-cam section which is responding to the minimum gear profile deviations is obtained.A group of examples are calculated by choosing master gears with d=120 mm and m=2-6 mm and an involute cam with base diameter djcam =117 mm.And it is found that the maximum gear profile deviation counts for no more than 5% of the cam eccentricity after error compensation.A gear-grinding experiment on the master gear with m=2 mm is conducted by choosing different sections of the involute cam and the differences of gear profile deviations then the existence of the cam eccentricity are verified.The research discloses the rule of gear profile deviations caused by the comprehensive eccentricity of the involute cam and provides the theoretical guidance and the processing methods for grinding profile of the ultra precision master gear.
文摘Design of forming dies and whole process of simulation of cold rolling involutes spline can be realized by using of CAD software of PRO-E and CAE software of DEFORM-3D. Software DEFORM-3D provides an automatic and optimized remeshing function, especially for the large deformation. In order to use this function sufficiently, simulation of cold rolling involutes spline can be implemented indirectly. The relationship between die and workpiece, forming force and characteristic of deformation in the forming process of cold rolling involutes spline are analyzed and researched. Meanwhile, reliable proofs for the design of dies and deforming equipment are provided.
基金Project(51105287)supported by the National Natural Science Foundation of ChinaProject(2012BAA08003)supported by the Key Research and Development Project of New Product and New Technology of Hubei Province,ChinaProject(IRT13087)supported by the Progress for Innovative Research Team in University of Ministry of Education of China
文摘The meshing characteristic of asymmetric involute spur gear was studied, the equations of the geometric shape of the asymmetric gear for both sides were deduced, and the equations of contact ratio and the key points of contact were also obtained.Meanwhile, an involute slope modification method considering the effects of static transmission errors was proposed based on the meshing properties. The characteristic of the involute slope modification was analyzed by changing different modification parameters.The mesh stiffness and synthetic mesh stiffness of unmodified and modified asymmetric spur gears were investigated. Furthermore,the spectrums of synthetic mesh stiffness under different modification parameters were compared. Research results showed that the modification parameters influence the meshing performance of gear pairs, and the proposed modification method was feasible to improve the transmission performance of gear pairs with appropriate modification parameters.
基金This project is supported by Provincial Natural Science Foundation of shanxi,China(No.20001047)
文摘Based on a lot of numerical solutions to the problems of the thermalnon-Newtonian elastohydrodynamic lubrication and some fatigue tests with rollers, the lubricationfactor of involute spur gears (called gear for short) is investigated. The results suggest that gearlubrication effects bear close relations to a dimensionless parameter D which is syntheticallydetermined by gearing rotational speed, load, material, dimension and lubricant viscosity. When D<=8, the gear fatigue life increases as the lubricant viscosity is increased; When D>8, however, thelife decreases with the viscosity addition, which is in marked contrast to the lubrication factorZ_L recommended by the International Standard for Computing Cylindrical Gear Strength. At the end, aset of formulae for calculating gear lubrication factors suitable for different working conditionsare advanced.
基金Supported by National Natural Science Foundation of China(Grant No.52075279)。
文摘Lubrication failure is one of the main failure forms of gear failure.Time varying meshing stiffness is an important factor affecting the dynamic behavior of gears.However,the influence of oil film stiffness is usually ignored in the research process.In this paper,according to the meshing characteristics of double involute gears,based on the non-Newtonian thermal EHL theory,a new calculation method of normal and tangential oil film stiffness for double involute gears is established by the idea of subsection method.The oil film stiffness difference between double involute gears and common involute gears is analyzed,and the influence of tooth waist order parameters,working conditions,and thermal effect on the oil film stiffness are studied.The results reveal that there are some differences between normal and tangential oil film stiffness between double involute gears and common involute gears,but there is little difference.Compared with the torque,rotation speed and initial viscosity of the lubricating oil,the tooth waist order parameters have less influence on the oil film stiffness.Thermal effect has a certain influence on normal and tangential oil film stiffness,which indicates that the influence of thermal effect on the oil film can not be ignored.This research proposes a calculation method of normal and tangential oil film stiffness suitable for double involute gears,which provides a theoretical basis for improving the stability of the transmission.
基金Supported by Postgraduate Education Innovation Fund of Chongqing Jiaotong University
文摘Because of good quality of compressive resistance, the hyperbolic arch dam is being increasingly applied to engineering projects. In order to satisfy the needs of compressive resistance under the conditions of high water pressure, a stress analysis is required for the dam. During the stress analysis process however, due to the complexity of the three-dimensional modeling, it is very hard to form a model. Therefore, the stress analysis process is a barrier for the arch dam. In this article, based on the research of the new line-type arch dam, a mathematical model in different degree of convexity conditions of the dam is established; using the C ＋ ＋ language program, a computer three-dimensional model simulation is realized on AutoCAD. The accurate three-dimensional model is providing a finite element optimization design of the involute hyperbolic arch dam for the next step.
文摘In wrist watches gear drives with undercut pinions are used. Those pinions have got a tooth number as few as 5—7. The efficiency of such gear drives is important because of the limited energy supply. The mean efficiency of gear drives can be expressed as E<sub>m</sub>=1/（φ<sub>2</sub>-φ<sub>1</sub>）（integral from φ<sub>1</sub> to φ<sub>2</sub>（E（φ）dφ）） in which <sup>0</sup><sub>1</sub>, <sup><</sup>sub>2</sub> are the approach angle and the recess angle respectively. In the discussion we assume that the friction coefficient between the two tooth flanks is constant because the sliding speed is relatively low in wrist watches and the main purpose is to find out the relation between gear parameters and its efficiency rather than to calculate the exact value of the efficiency. In normal conditions <sup>o</sup><sub>1</sub> and <sup>o</sup><sub>2</sub> can be found from the gear geometry without much difficulty. However when the pinion is an undercut one we have to first find the forming diameter where the involute profile starts. In this paper equations for the computation of the efficiency and the contact ratio of those gear drives are discussed.
文摘The D'Alembert-Lagrange equation is introduced and used to derive theformulas of momentary efficiency for external gearing of standard involutes spur gears. The gearingswith correct and increased center distance are discussed. The momentary efficiency formula iscalculated and analyzed using software Matlab. The derived formula of momentary efficiency is alsocompared with the traditional formula.
基金Sponsored by the Eleventh Five-years Drive for Basic Research Project
文摘Base on the theory of energy minimization, a numerical algorithm is established to calculate load distribution, and the relationship curve of spur gear load distribution is obtained, and the load distribution ratio changes from 033 to 067 in double contact zone. This theory is adopted to compute the load distribution of helical gear along time-varying contact line, and the load distribution varies with the instantaneous position of the meshing point and the length of contact line, and the maximum value of load appears at the pitch point. Compared with the load distribution results, the helical gear changes more smoothly than spur gear. The load distribution provides a basis for calculate tooth bending deformation and critical stress.
文摘The deformation principles of the steady- state and the unsteady一state of open- die cold extrusion for involute spline shafts are analyzed by means of experiments. On one hand,based on the deformation principles of the steady- state, data for determining structural parameters of the die, the size of the billet and the constraint condition of this technique are given. On the other hand, according to the principles of the unsteady- state, data for modifying the shapes and sizes of the bil- lets are provided.
基金funded by the National Key Research and Development Program of China(No.2024YFE0208100).
文摘The scroll expander,as the core component of the micro-compressed air energy storage and power generation system,directly affects the output efficiency of the system.Meanwhile,the scroll profile plays a central role in determining the output performance of the scroll expander.In this study,in order to investigate the output characteristics of a variable cross-section scroll expander,numerical simulation and experimental studies were con-ducted by using Computational Fluid Dynamics(CFD)methods and dynamic mesh techniques.The impact of critical parameters on the output performance of the scroll expander was analyzed through the utilization of the control variable method.It is found that increasing the inlet pressure and temperature within a certain range can improve the output power of the scroll expander.However,the increase in temperature and meshing clearance leads to a decline in the overall output performance of the scroll expander,leading to a decrease in volumetric efficiency by 8.43%and 12.79%,respectively.The experiments demonstrate that under equal inlet pressure conditions,increasing the inlet temperature elevates both the rotational speed and torque output of the scroll expander.Specifically,compared to operating at normal temperatures,the output torque increases by 21.8%under high-temperature conditions.However,the rate of speed and torque variation decreases as a consequence of enlarged meshing clearance,resulting in increased internal leakage and reduction in isentropic efficiency.
基金support provided by the National Nature Science Foundation of China (Grant Nos.52075340,51875360)Project of Science and Technology Commission of Shanghai Municipality (No.19060502300).
文摘Gears are pivotal in mechanical drives,and gear contact analysis is a typically difficult problem to solve.Emerging isogeometric analysis(IGA)methods have developed new ideas to solve this problem.In this paper,a threedimensional body parametric gear model of IGA is established,and a theoretical formula is derived to realize single-tooth contact analysis.Results were benchmarked against those obtained from commercial software utilizing the finite element analysis(FEA)method to validate the accuracy of our approach.Our findings indicate that the IGA-based contact algorithmsuccessfullymet theHertz contact test.When juxtaposed with the FEA approach,the IGAmethod demonstrated fewer node degrees of freedomand reduced computational units,all whilemaintaining comparable accuracy.Notably,the IGA method appeared to exhibit consistency in analysis accuracy irrespective of computational unit density,and also significantlymitigated non-physical oscillations in contact stress across the tooth width.This underscores the prowess of IGA in contact analysis.In conclusion,IGA emerges as a potent tool for addressing contact analysis challenges and holds significant promise for 3D gear modeling,simulation,and optimization of various mechanical components.
基金National Natural Science Foundation of China(Grant No.11701420)。
文摘We construct an involution over Dyck paths,which implies the distribution of statistics“the number of peak”,“the number of returns”and“the height of the last peak”.As an application,equidistributions of several Stirling statistics over 132-avoiding and 321-avoiding permutations are presented.
基金Initiative 2018–2027 attributed to DICAM of the University of Trento(grant L.232/2016)the PRIN 2022 project High-order structure-preserving semi-implicit schemes for hyperbolic equations and by the European Union-Next GenerationEU(PNRR,Spoke 7 CN HPC).
文摘This paper presents a high-order discontinuous Galerkin(DG)finite-element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible(SHTC)model of compressible two-phase flow,introduced by Romenski et al.in[59,62],in multiple space dimensions.In the absence of algebraic source terms,the model is endowed with a curl constraint on the relative velocity field.In this paper,the hyperbolicity of the system is studied for the first time in the multidimensional case,showing that the original model is only weakly hyperbolic in multiple space dimensions.To restore the strong hyperbolicity,two different methodologies are used:(i)the explicit symmetrization of the system,which can be achieved by adding terms that contain linear combinations of the curl involution,similar to the Godunov-Powell terms in the MHD equations;(ii)the use of the hyperbolic generalized Lagrangian multiplier(GLM)curl-cleaning approach forwarded.The PDE system is solved using a high-order ADER-DG method with a posteriori subcell finite-volume limiter to deal with shock waves and the steep gradients in the volume fraction commonly appearing in the solutions of this type of model.To illustrate the performance of the method,several different test cases and benchmark problems have been run,showing the high order of the scheme and the good agreement when compared to reference solutions computed with other well-known methods.
