Experiment statistical method and genetic algorithms based optimization method are used to obtain the optimum differential gear ratio for heavy truck that provides best fuel consumption when changing the working condi...Experiment statistical method and genetic algorithms based optimization method are used to obtain the optimum differential gear ratio for heavy truck that provides best fuel consumption when changing the working condition that affects its torque and speed range. The aim of the study is to obtain the optimum differential gear ratio with fast and accurate optimization calculation without affecting drivability characteristics of the vehicle according to certain driving cycles that represent the new working conditions of the truck. The study is carried on a mining dump truck YT3621 with 9 for- ward shift manual transmission. Two loading conditions, no load and 40 t, and four on road real driving cycles have been discussed. The truck powertrain is modeled using GT-drive, and DOE -post processing tool of the GT-suite is used for DOE analysis and genetic algorithm optimization.展开更多
Vehicles with variable steering characteristics have long been studied and compared with those having typical fixed gear ratio steering, and the variable gear ratio properties are reported to have improved maneuverabi...Vehicles with variable steering characteristics have long been studied and compared with those having typical fixed gear ratio steering, and the variable gear ratio properties are reported to have improved maneuverability and stability in high-speed lane changes and on slippery low-friction road surfaces. However, it is not clear how gear ratios should be set for individual vehicle characteristics. Therefore, the present study has investigated a variable steering gear system using body slip angle feedback for the purpose of improved maneuverability and stability in the critical cornering range and upwards, in excess of the critical limit, and into the countersteer range. The results of a driving simulator experiment show that the steering effect improves and maneuverability and stability increase in the critical cornering range and upwards, in excess of the critical limit, and into the countersteer range by applying linear-variable control to the steering ratio from a body slip angle of 5?. This result is seen both in double lane changes, such as in hazard avoidance, and in J-turns with long drifting. Moreover, it shows an improvement in drift controllability through prompt countersteering. Overall, the present system can enhance the driver’s hazard avoidance capability.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
Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profil...Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.展开更多
The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The gen...The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The general calculation formulas of sliding ratios are developed according to the conjugate curves. The applications to the circular arc gears based on conjugate curves and the novel involute-helix gears are studied. A comparison on the sliding coefficient with the conventional corresponding gear drive is also carried out. The influences of gear parameters such as spiral parameter, gear ratio and modulus on the sliding ratios of gear drive are discussed. Brief description of manufacturing method for conjugate-curve gear pair is given. The research results show that the sliding ratios of gear pair become smaller with the increase of spiral parameter and gear ratio, respectively. And it will be greater with the increase of modulus for the tooth profiles. The meshing characteristics of conjugate-curve gears are further reflected and the optimization design of tooth profiles with high performance may be obtained.展开更多
The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destro...The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.展开更多
Current research of automatic transmission(AT)mainly focuses on the improvement of driving performance,and configuration innovation is one of the main research directions.However,finding new configurations of ATs is o...Current research of automatic transmission(AT)mainly focuses on the improvement of driving performance,and configuration innovation is one of the main research directions.However,finding new configurations of ATs is one of the main limitations of configuration innovation.In the present study,epicyclic gear trains(EGTs)are applied to investigate mechanisms of 9-speed ATs.Then four kinematic configurations are proposed for automatic transitions.In order to evaluate the performance of proposed mechanisms,the lever analogy method is applied to conduct kinematic and mechanical analyses.The power flow analysis is conducted,and then transmission efficiencies are calculated based on the torque method.The comparative analysis between the proposed and existing mechanisms is carried out where obtained results show that proposed mechanisms have reasonable performance and can be used in ATs.The prototype of an AT is manufactured and the speed test is conducted,which proves the accuracy of analysis and the feasibility of proposed mechanisms.展开更多
The latching control represents an attractive alternative to increase the power absorption of wave energy converters(WECs)by tuning the phase of oscillator velocity to the wave excitation phase.However,increasing the ...The latching control represents an attractive alternative to increase the power absorption of wave energy converters(WECs)by tuning the phase of oscillator velocity to the wave excitation phase.However,increasing the amplitude of motion of the floating body is not the only challenge to obtain a good performance of the WEC.It also depends on the efficiency of the power take-off system(PTO).This study aims to address the actual power performance and operation of a heaving point absorber with a direct mechanical drive PTO system controlled by latching.The PTO characteristics,such as the gear ratio,the flywheel inertia,and the electric generator,are analyzed in the WEC performance.Three cylindrical point absorbers are also considered in the present study.A wave-to-wire model is developed to simulate the coupled hydro-electro-mechanical system in regular waves.The wave energy converter(WEC)performance is analyzed using the potential linear theory but considering the viscous damping effect according to the Morison equation to avoid the overestimated responses of the linear theory near resonance when the latching control system is applied.The latching control system increases the mean power.However,the increase is not significant if the parameters that characterize the WEC provide a considerable mean power.The performance of the proposed mechanical power take-off depends on the gear ratio and flywheel.However,the gear ratio shows a more significant influence than the flywheel inertia.The operating range of the generator and the diameter/draft ratio of the buoy also influence the PTO performance.展开更多
The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do th...The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do this,the method known as Taguchi and GRA(Grey Relation Analysis)were used in two stages to address the problem.The single-objective optimization problem was addressed first to close the gap between variable levels,and then the multi-objective optimization problem was solved to determine the best primary design variables.The first and second stage CWFWs(Coefficients of Wheel Face Width),ACS(Permissible Contact Stresses),and first stage gear ratio were also calculated.The study’s findings were utilized to identify the best values for five critical design aspects of a two-stage helical gearbox.展开更多
Based on the mathematical model of a novel cosine gear drive, a few characteristics, such as the contact ratio, the sliding coefficient, and the contact and bending stresses, of this drive are analyzed. A comparison s...Based on the mathematical model of a novel cosine gear drive, a few characteristics, such as the contact ratio, the sliding coefficient, and the contact and bending stresses, of this drive are analyzed. A comparison study of these characteristics with the involute gear drive is also carried out. The influences of design parameters including the number of teeth and the pressure angle on the contact and bending stresses are studied. The following conclusions are achieved: the contact ratio of the cosine gear drive is about 1.2 to 1.3, which is reduced by about 20% in comparison with that of the involute gear drive. The sliding coefficient of the cosine gear drive is smaller than that of the involute gear drive. The contact and bending stresses of the cosine gear drive are lower than those of the involute gear drive. The contact and bending stresses decrease with the growth of the number of teeth and the pressure angle.展开更多
Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-sp...Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-speed gearbox is studied. For this aim contact ratio effect on tooth bending stress by the changing of contact ratio with respect to pressure angle is analysed. Additionally, profile modification effects on tooth bending stress are presented. During the optimisation, the tooth bending stress is considered as the objective function, and all the geometric design parameters such as module, teeth number etc. are optimised under two different constraints, including tooth contact stress and constant gear centre distance. It can be concluded that higher the contact ratio results in a reduced tooth bending stress, while higher the pressure angle caused an increase in tooth bending stress and contact stress, since decreases in the contact ratio. In addition, application of positive profile modification on tooth reduces tooth bending stress. All of the obtained optimum solutions satisfy all constraints.展开更多
In recent years, a new type of gear named Logix gea r was developed. Actually, the tooth profile of this new type of gear is composed of lots of micro-segment involute curves, and on the profile, there exist lots of p...In recent years, a new type of gear named Logix gea r was developed. Actually, the tooth profile of this new type of gear is composed of lots of micro-segment involute curves, and on the profile, there exist lots of points, which their relative curvatures are equal to zero. This can result in the sliding coefficient smaller between two meshed Logix gears, and the mesh ch aracteristic becomes almost rolling transmission from sliding transmission accor dingly. So, this new type of gear has lots of advantages such as higher contact intensity, longer useful life and can easily realize power transfer of bigger tr ansmission ratio than standard involute gear. Study results showed that the cont act fatigue strength is 3 times larger, the bend fatigue strength is 2.5 times l arger, and the minimum tooth number can be decreased to 3, much smaller than tha t of standard involute gear. In this paper, following studies had been done: 1) The formation principle of Logix gear tooth profile was studied. The theoreti cal models describing the geometrical formations of this type of gear and its re lative Logix rack had been deduced. 2) While cutting a Logix gear, its tooth profile is decided by its normal tooth profile of Logix rack. Besides the basic parameters of standard involute gear, L ogix rack has its own specific parameters such as preliminary pressure angle, re lative pressure angle, and preliminary referential circle radius etc. So, the in fluence of connatural parameters of Logix rack on the tooth profile of Logix gea r had been farther studied. Reasonable selection for these parameters had been d iscussed. 3) Several kinds of transition curves for gear’s tooth profile had been introdu ced, its selection used by Logix gear had been described, and also its mathemati cal description model had been deduced. 4) The mesh theories of Logix gears had been developed. It had been proved that the transmission performance between Logix gears coincides with E-W theorem as that of ordinary standard involute gears. The formula calculating superposition coefficient was deduced according to its definition. Different from standard inv olute gears, the parameter of gear number has no effect on the superposition coe fficient of the Logix gears. Accordingly, bigger ratio transmission can be acqui red by means of decreasing the gear number, and its minimum gear number can be r eached to 3, much smaller than the minimum gear number of ordinary standard invo lute gear: 14~17. This is very important to realize the miniaturization of prod uction design. 5) The CAD special software was developed to design all kinds of Logix gears, an d a solid design example was offered. To sum up, by means of above study, the system info about Logix gear had been de veloped and enriched. This has most significant impact on its widely promotion a nd practical application, on the improvement of carrying capacity, miniaturizati on, and life of kinetic transmission products.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 aim of this study is to investigate the helix angle effect on the helical gear load carrying capacity, including the bending and contact load carrying capacity. During the simulation, the transverse contact ratio ...The aim of this study is to investigate the helix angle effect on the helical gear load carrying capacity, including the bending and contact load carrying capacity. During the simulation, the transverse contact ratio is calculated with respect to the constant pressure angle. By changing the helix angle, both the overlap contact ratio and total contact ratio are calculated and simulated. The bending stress and contact stress of a helical gear are calculated and simulated with respect to the helix angle. Solid (CAD) modelling of a pinion gear was obtained using SOLIDWORKS software. The analytically obtained results and finite elements method results are compared. It is observed that increasing the helix angle causes an increase of the contact ratio of the helical gear. Furthermore, increasing the contact ratio reduces the bending stress and contact stress of the helical gear. However, with a constant transverse contact ratio, it is possible to improve the total contact ratio depending on the helix angle. It is concluded that a higher helix angle increases the helical gear bending and contact load carrying capacity.展开更多
文摘Experiment statistical method and genetic algorithms based optimization method are used to obtain the optimum differential gear ratio for heavy truck that provides best fuel consumption when changing the working condition that affects its torque and speed range. The aim of the study is to obtain the optimum differential gear ratio with fast and accurate optimization calculation without affecting drivability characteristics of the vehicle according to certain driving cycles that represent the new working conditions of the truck. The study is carried on a mining dump truck YT3621 with 9 for- ward shift manual transmission. Two loading conditions, no load and 40 t, and four on road real driving cycles have been discussed. The truck powertrain is modeled using GT-drive, and DOE -post processing tool of the GT-suite is used for DOE analysis and genetic algorithm optimization.
文摘Vehicles with variable steering characteristics have long been studied and compared with those having typical fixed gear ratio steering, and the variable gear ratio properties are reported to have improved maneuverability and stability in high-speed lane changes and on slippery low-friction road surfaces. However, it is not clear how gear ratios should be set for individual vehicle characteristics. Therefore, the present study has investigated a variable steering gear system using body slip angle feedback for the purpose of improved maneuverability and stability in the critical cornering range and upwards, in excess of the critical limit, and into the countersteer range. The results of a driving simulator experiment show that the steering effect improves and maneuverability and stability increase in the critical cornering range and upwards, in excess of the critical limit, and into the countersteer range by applying linear-variable control to the steering ratio from a body slip angle of 5?. This result is seen both in double lane changes, such as in hazard avoidance, and in J-turns with long drifting. Moreover, it shows an improvement in drift controllability through prompt countersteering. Overall, the present system can enhance the driver’s hazard avoidance capability.
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.
文摘Common definition and calculating expressions of end-surface contact ratiofor all type of gears are put forward, and with calculation expressions for involute gears,micro-segments profile gears, and sine-curved profile gears being discussed. The end-surface contactratio of gears is defined as the ratio of the action angle (the rotation angle of gear from gear-into gear-out for one pair of teeth) to the rotation angle per pitch (or central angle per tooth).According to the theory of gearing, equation of the meshing line can be deduced from the toothprofiles of basic rack. Having obtained the equation of the meshing line, and being given theaddendum outline of the gears, the contact ratio can be calculated with the calculation expressions.For the involute gears, this definition has same effect as the well-known definition: ratio of thecontact line to the base pitch. This definition of contact ratio is also suitable to othernon-involute gears, such as micro-segments profile gears, sine-curved profile gears, and can givemore reliable results.
基金Project(2013BAF01B04) supported by the National Key Technology R&D Program during the Twelfth Five-year Plan of ChinaProject(51205425) supported by the National Natural Science Foundation of China
文摘The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The general calculation formulas of sliding ratios are developed according to the conjugate curves. The applications to the circular arc gears based on conjugate curves and the novel involute-helix gears are studied. A comparison on the sliding coefficient with the conventional corresponding gear drive is also carried out. The influences of gear parameters such as spiral parameter, gear ratio and modulus on the sliding ratios of gear drive are discussed. Brief description of manufacturing method for conjugate-curve gear pair is given. The research results show that the sliding ratios of gear pair become smaller with the increase of spiral parameter and gear ratio, respectively. And it will be greater with the increase of modulus for the tooth profiles. The meshing characteristics of conjugate-curve gears are further reflected and the optimization design of tooth profiles with high performance may be obtained.
文摘The paper considers the modification or the manufacture error of cycloidal gear, then analyzes the relationship of pin circle meshed with the modified cycloidal gear, discuases the amount of error that leads to destroying conjugate action and results in the changes of tbe instantaneous velocity ratio and so as to affect the smooth operation of cycloidal pin gearing. The idea of the relationship between amount of modification aud manufacture error and the smooth operation can be gotten from the curve diagrams of the instantaneous velocity ratio. Therefore, the directions for improving the reature of the cycloidal pin gear transmission are clear.
基金Supported by National Natural Science Foundation of China(Grant Nos.51975544,51675495).
文摘Current research of automatic transmission(AT)mainly focuses on the improvement of driving performance,and configuration innovation is one of the main research directions.However,finding new configurations of ATs is one of the main limitations of configuration innovation.In the present study,epicyclic gear trains(EGTs)are applied to investigate mechanisms of 9-speed ATs.Then four kinematic configurations are proposed for automatic transitions.In order to evaluate the performance of proposed mechanisms,the lever analogy method is applied to conduct kinematic and mechanical analyses.The power flow analysis is conducted,and then transmission efficiencies are calculated based on the torque method.The comparative analysis between the proposed and existing mechanisms is carried out where obtained results show that proposed mechanisms have reasonable performance and can be used in ATs.The prototype of an AT is manufactured and the speed test is conducted,which proves the accuracy of analysis and the feasibility of proposed mechanisms.
基金The authors acknowledge the support from the Brazilian Research Council(CNPq),contract numbers 380950/2018-9(INEOF-National Institute for Ocean and River Energy)and 305657/2017-8,respectivelySpecial thanks to FAPERJ for the support of the wave energy research at the Subsea Technology Lab(COPPE),contract number E-26/202.600/2019。
文摘The latching control represents an attractive alternative to increase the power absorption of wave energy converters(WECs)by tuning the phase of oscillator velocity to the wave excitation phase.However,increasing the amplitude of motion of the floating body is not the only challenge to obtain a good performance of the WEC.It also depends on the efficiency of the power take-off system(PTO).This study aims to address the actual power performance and operation of a heaving point absorber with a direct mechanical drive PTO system controlled by latching.The PTO characteristics,such as the gear ratio,the flywheel inertia,and the electric generator,are analyzed in the WEC performance.Three cylindrical point absorbers are also considered in the present study.A wave-to-wire model is developed to simulate the coupled hydro-electro-mechanical system in regular waves.The wave energy converter(WEC)performance is analyzed using the potential linear theory but considering the viscous damping effect according to the Morison equation to avoid the overestimated responses of the linear theory near resonance when the latching control system is applied.The latching control system increases the mean power.However,the increase is not significant if the parameters that characterize the WEC provide a considerable mean power.The performance of the proposed mechanical power take-off depends on the gear ratio and flywheel.However,the gear ratio shows a more significant influence than the flywheel inertia.The operating range of the generator and the diameter/draft ratio of the buoy also influence the PTO performance.
文摘The goal of this research is to look at multi-target optimization of a two-stage helical gearbox in order to determine the best key design elements for reducing gearbox height and enhancing gearbox efficiency.To do this,the method known as Taguchi and GRA(Grey Relation Analysis)were used in two stages to address the problem.The single-objective optimization problem was addressed first to close the gap between variable levels,and then the multi-objective optimization problem was solved to determine the best primary design variables.The first and second stage CWFWs(Coefficients of Wheel Face Width),ACS(Permissible Contact Stresses),and first stage gear ratio were also calculated.The study’s findings were utilized to identify the best values for five critical design aspects of a two-stage helical gearbox.
基金National Natural Science Foundation of China(No.50575071)Natural Science Foundation of Hunan Province,China(No.06JJl0008)+1 种基金S&T Programs of Hunan Province,China(No.2007FJ4047)Program for New Century Excellent Talents in University,China.
文摘Based on the mathematical model of a novel cosine gear drive, a few characteristics, such as the contact ratio, the sliding coefficient, and the contact and bending stresses, of this drive are analyzed. A comparison study of these characteristics with the involute gear drive is also carried out. The influences of design parameters including the number of teeth and the pressure angle on the contact and bending stresses are studied. The following conclusions are achieved: the contact ratio of the cosine gear drive is about 1.2 to 1.3, which is reduced by about 20% in comparison with that of the involute gear drive. The sliding coefficient of the cosine gear drive is smaller than that of the involute gear drive. The contact and bending stresses of the cosine gear drive are lower than those of the involute gear drive. The contact and bending stresses decrease with the growth of the number of teeth and the pressure angle.
文摘Optimisation of effective design parameters to reduce tooth bending stress for an automotive transmission gearbox is presented. A systematic investigation of effective design parameters for optimum design of a five-speed gearbox is studied. For this aim contact ratio effect on tooth bending stress by the changing of contact ratio with respect to pressure angle is analysed. Additionally, profile modification effects on tooth bending stress are presented. During the optimisation, the tooth bending stress is considered as the objective function, and all the geometric design parameters such as module, teeth number etc. are optimised under two different constraints, including tooth contact stress and constant gear centre distance. It can be concluded that higher the contact ratio results in a reduced tooth bending stress, while higher the pressure angle caused an increase in tooth bending stress and contact stress, since decreases in the contact ratio. In addition, application of positive profile modification on tooth reduces tooth bending stress. All of the obtained optimum solutions satisfy all constraints.
文摘In recent years, a new type of gear named Logix gea r was developed. Actually, the tooth profile of this new type of gear is composed of lots of micro-segment involute curves, and on the profile, there exist lots of points, which their relative curvatures are equal to zero. This can result in the sliding coefficient smaller between two meshed Logix gears, and the mesh ch aracteristic becomes almost rolling transmission from sliding transmission accor dingly. So, this new type of gear has lots of advantages such as higher contact intensity, longer useful life and can easily realize power transfer of bigger tr ansmission ratio than standard involute gear. Study results showed that the cont act fatigue strength is 3 times larger, the bend fatigue strength is 2.5 times l arger, and the minimum tooth number can be decreased to 3, much smaller than tha t of standard involute gear. In this paper, following studies had been done: 1) The formation principle of Logix gear tooth profile was studied. The theoreti cal models describing the geometrical formations of this type of gear and its re lative Logix rack had been deduced. 2) While cutting a Logix gear, its tooth profile is decided by its normal tooth profile of Logix rack. Besides the basic parameters of standard involute gear, L ogix rack has its own specific parameters such as preliminary pressure angle, re lative pressure angle, and preliminary referential circle radius etc. So, the in fluence of connatural parameters of Logix rack on the tooth profile of Logix gea r had been farther studied. Reasonable selection for these parameters had been d iscussed. 3) Several kinds of transition curves for gear’s tooth profile had been introdu ced, its selection used by Logix gear had been described, and also its mathemati cal description model had been deduced. 4) The mesh theories of Logix gears had been developed. It had been proved that the transmission performance between Logix gears coincides with E-W theorem as that of ordinary standard involute gears. The formula calculating superposition coefficient was deduced according to its definition. Different from standard inv olute gears, the parameter of gear number has no effect on the superposition coe fficient of the Logix gears. Accordingly, bigger ratio transmission can be acqui red by means of decreasing the gear number, and its minimum gear number can be r eached to 3, much smaller than the minimum gear number of ordinary standard invo lute gear: 14~17. This is very important to realize the miniaturization of prod uction design. 5) The CAD special software was developed to design all kinds of Logix gears, an d a solid design example was offered. To sum up, by means of above study, the system info about Logix gear had been de veloped and enriched. This has most significant impact on its widely promotion a nd practical application, on the improvement of carrying capacity, miniaturizati on, and life of kinetic transmission products.
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 aim of this study is to investigate the helix angle effect on the helical gear load carrying capacity, including the bending and contact load carrying capacity. During the simulation, the transverse contact ratio is calculated with respect to the constant pressure angle. By changing the helix angle, both the overlap contact ratio and total contact ratio are calculated and simulated. The bending stress and contact stress of a helical gear are calculated and simulated with respect to the helix angle. Solid (CAD) modelling of a pinion gear was obtained using SOLIDWORKS software. The analytically obtained results and finite elements method results are compared. It is observed that increasing the helix angle causes an increase of the contact ratio of the helical gear. Furthermore, increasing the contact ratio reduces the bending stress and contact stress of the helical gear. However, with a constant transverse contact ratio, it is possible to improve the total contact ratio depending on the helix angle. It is concluded that a higher helix angle increases the helical gear bending and contact load carrying capacity.