The equations determining a resultant screw of two given screws are applied to the studies on gearing and meshing theories. A kinematical classification is proposed and meanwhile proof is given to the First Theorem of...The equations determining a resultant screw of two given screws are applied to the studies on gearing and meshing theories. A kinematical classification is proposed and meanwhile proof is given to the First Theorem of Gearing and Willis Theorem.展开更多
Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regardin...Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.展开更多
Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-...Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.展开更多
Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state ...Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.展开更多
Sheet-bulk metal forming(SBMF)is a promising process for manufacturing complex sheet components with functional elements.In this study,the entire forming process for a typical thin-walled component with external geari...Sheet-bulk metal forming(SBMF)is a promising process for manufacturing complex sheet components with functional elements.In this study,the entire forming process for a typical thin-walled component with external gearing is investigated,including sheet forming and bulk forming processes.Deep drawn cups are prepared during sheet forming;subsequently,upsetting is performed on the sidewall to form external gearing.The upsetting method performed is known as upsetting with a controllable deformation zone(U-CDZ).Compared with the conventional upsetting method,a floating counter punch with a counter force is used in the U-CDZ method such that the forming mechanism is changed into the accumulation of the deformation zone instead of deformation throughout the entire sidewall.The effects of the counter force and material flow are investigated to understand the mechanism.The forming quality,i.e.,the formfilling and effective strain distribution,improved,whereas a high forming load is avoided.In addition,a punch with a lock bead is used to prevent folding at the inner corner during the experiment.展开更多
Pennate muscle is characterized by muscle fibers that are oriented at a certain angle(pennation angle)relative to the muscle’s line of action and rotation during contraction.This fiber rotation amplifies the shorteni...Pennate muscle is characterized by muscle fibers that are oriented at a certain angle(pennation angle)relative to the muscle’s line of action and rotation during contraction.This fiber rotation amplifies the shortening velocity of muscle,to match loading conditions without any control system.This unique variable gearing mechanism,which characterized by Architecture Gear Ratio(AGR),is involves complex interaction among three key elements:muscle fibers,connective tissue,and the pennation angle.However,how three elements determine the AGR of muscle-like actuator is still unknown.This study introduces a Himisk actuator that arranges five contractile units at a certain pennation angle in a flexible matrix,the experiment and simulation results demonstrated that the proposed actuator could vary AGR automatically in response to variable loading conditions.Based on this actuator,we present a series of actuators by simulations with the varying pennation angle(P),elastic modulus of the flexible matrix(E),and number of contractile units(N)to analyze their effects on AGR,and their interaction by three-factor analysis of variance.The results demonstrated that P and N effect on the AGR significantly,while E effects on AGR slightly,which supported the idea that the P is the essential factor for the AGR,and N is also an important factor due to the capability of force generation.This provides a better understanding of mechanical behavior and an effective optimizing strategy to muscle-like soft actuator.展开更多
Background:During human locomotion,a sufficiently stiff foot allows the ankle plantar flexors to generate large propulsive powers.Increasing foot stiffness(e.g.,via a carbon plate)increases the ankle’s external momen...Background:During human locomotion,a sufficiently stiff foot allows the ankle plantar flexors to generate large propulsive powers.Increasing foot stiffness(e.g.,via a carbon plate)increases the ankle’s external moment arm in relation to the internal moment arm(i.e.,increasing gear ratio),reduces plantar flexor muscles’shortening velocity,and enhances muscle force production.In contrast,when activation of the foot’s intrinsic muscles is impaired,there is a reduction in foot and ankle work and metatarsophalangeal joint stiffness.We speculated that the reduced capacity to actively control metatarsophalangeal joint stiffness may impair the gearing function of the foot at the ankle.Methods:We used a tibial nerve block to examine the direct effects of the intrinsic foot muscles on ankle joint kinetics,in vivo medial gastrocnemius’musculotendinous dynamics,and ankle gear ratio on 14 participants during maximal vertical jumping.Results:Under the nerve block,the internal ankle plantar flexion moment decreased(p=0.004)alongside a reduction in external moment arm length(p=0.021)and ankle joint gear ratio(p=0.049)when compared to the non-blocked condition.Although medial gastrocnemius muscle-tendon unit and fascicle velocity were not different between conditions,the Achilles tendon was shorter during propulsion in the nerve block condition(p<0.001).Conclusion:In addition to their known role of regulating the energetic function of the foot,our data indicate that the intrinsic foot muscles also act to optimize ankle joint torque production and leverage during the propulsion phase of vertical jumping.展开更多
An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influen...An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.展开更多
The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In conside...The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In consideration of the parts manufacturing errors, assembly errors, bearing stiffness and float, the power splitting rate of each star gear and the system were calculated by using the theory of equivalent mesh error. The effects of the errors, float and the bearing stiffness on power splitting were studied. The study provides a useful theoretical guideline for the design of star gearing.展开更多
Controllable modification of cone-generated cylindric worm gearing has been carriedout. The tooth contact state of modified gearing can be controlled by selecting the positions of con-tact points of worm surfaee and t...Controllable modification of cone-generated cylindric worm gearing has been carriedout. The tooth contact state of modified gearing can be controlled by selecting the positions of con-tact points of worm surfaee and the correction amount of curvature. The modification machiningcan be conveniently implemented by changing the geometrical sizes and setting parameters of grind-ing wheel. Therefore the research has better scientific basis and practical value.展开更多
Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teet...Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teeth are calculated, the contact zones and the distribution of the contact pressure are investigated. The variation of the contact states with the load is investigated by comparision of its contact patterns under different loads.展开更多
The lubrication behavior of double enveloping hourglass worm gearing is studied experimently. The effects of rotational speed of the worm and load on the formation of the fluid film between engagement tooth ...The lubrication behavior of double enveloping hourglass worm gearing is studied experimently. The effects of rotational speed of the worm and load on the formation of the fluid film between engagement tooth surfaces are investigated in detail. and working angle of this worm gearing is also analyzed. Some beneficial results are 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
A novel CAD method for tooth profile based on the gearing feature has been proposed in this paper, and this method could be applied to the variable transmission ratio and three-dimension situation. The two pitch curve...A novel CAD method for tooth profile based on the gearing feature has been proposed in this paper, and this method could be applied to the variable transmission ratio and three-dimension situation. The two pitch curves of the two gears can be generated due to the given transmission ratio. The tooth profile curves are formed in each coordinate system of its pitch curve by the gearing process. Finally, the tooth profile could be extracted and translated into a real dimension by CAD method. It is provided a simply thought for tooth profile design to avoid so much complicated mathematical reasoning.展开更多
The engaged feature of a pair of gears was determined by the geometrical characteristics of their tooth surfaces. Through an analysis of gearing theory on epi-cycloidal bevel gears, the method to examine if there exis...The engaged feature of a pair of gears was determined by the geometrical characteristics of their tooth surfaces. Through an analysis of gearing theory on epi-cycloidal bevel gears, the method to examine if there exists undercut during manufacturing of epicycloidal bevel gears, the approximate formulae to calculate the gap between the convex and concave tooth surfaces in meshing so as to guarantee against the occurrence of point-contact for tooth surfaces even in maximum angle of inclination are derived in this paper. Those formula derived are simple, compact and have practical value to the design and production of epicycloidal bevel gears.展开更多
The forms of the vibration disturbances inside the epicyclic gear train are analyzed. Thefrequency equations for the inner disturbances of the epicyclic gearing with one or two degrees offreedom have been built. The l...The forms of the vibration disturbances inside the epicyclic gear train are analyzed. Thefrequency equations for the inner disturbances of the epicyclic gearing with one or two degrees offreedom have been built. The latter of them is a 3-dimension problem and the range of the disturbance frequencies covers a series of planes inside the 3-dimension coordinates. As a result, thechances to lead to the system resonance are developed. The calculating results indicate that in thedesign process of the shaft system, the chances of resonance can be reduced by tunning the dynamicparameters and the structure of the system.展开更多
The model for computing frictional coefficient between two teeth faces at the state of mixed elastohydrodynamic lubrication is established. And then more than 80 sets of numerical calculations and six sets of disc fat...The model for computing frictional coefficient between two teeth faces at the state of mixed elastohydrodynamic lubrication is established. And then more than 80 sets of numerical calculations and six sets of disc fatigue tests are completed. The results show that when the film thickness ratio λ 〈1.6, frictional coefficient μ is drastically decreased as λ. rises; Thereafter it decreases smoothly until λ=4.5. When λ〉4.5, however, it goes up again with λ, which indicates that the excessive film thickness ratio will deteriorate gearing contact fatigue strength. At the end, the formulae for determining the frictional coefficients are formed.展开更多
文摘The equations determining a resultant screw of two given screws are applied to the studies on gearing and meshing theories. A kinematical classification is proposed and meanwhile proof is given to the First Theorem of Gearing and Willis Theorem.
基金Supported by National Key Technology R&D Program(No.2014BAF08B01)Natural Science Foundation of Tianjin(Grant No.17JCQNJC04300)
文摘Load sharing behavior is very important for power-split gearing system, star gearing reducer as a new type and special transmission system can be used in many industry fields. However, there is few literature regarding the key multiple-split load sharing issue in main gearbox used in new type geared turbofan engine. Further mechanism anal- ysis are made on load sharing behavior among star gears of star gearing reducer for geared turbofan engine. Compre- hensive meshing error analysis are conducted on eccentricity error, gear thickness error, base pitch error, assembly error, and bearing error of star gearing reducer respectively. Floating meshing error resulting from meshing clearance variation caused by the simultaneous floating of sun gear and annular gear are taken into account. A refined mathematical model for load sharing coefficient calculation is established in consideration of different meshing stiffness and support- ing stiffness for components. The regular curves of load sharing coefficient under the influence of interactions, single action and single variation of various component errors are obtained. The accurate sensitivity of load sharing coefficienttoward different errors is mastered. The load sharing coef- ficient of star gearing reducer is 1.033 and the maximum meshing force in gear tooth is about 3010 N. This paper provides scientific theory evidences for optimal parameter design and proper tolerance distribution in advanced devel- opment and manufacturing process, so as to achieve optimal effects in economy and technology.
基金Funded by Key Technology R&D Program of Chongqing(No. 2008AC3087)Science & Technology Project of Chongqing Education Committee(No. KJ091414)
文摘Due to low carrying capacity and short life of current ring reducer,we proposed a new planetary gearing with internal gear ring,which consisted of two stages.One was an involute planetary drive and the other was an N-type planetary drive with small teeth difference.The kinematic calculation was conducted based on the analysis of structural composition and working principle.Formulas of backlash calculation for the new planetary gearing were derived by using probabilistic theory and the analytical model was created at the same time.Then,main factors that affect the systematic backlash were introduced and the effects of manufacture error,misaligments and roller bearing parameters on the distribution of backlash were presented.The influence of gear backlash on systematic return difference was performed based on the backlash mathematic model proposed.The results show that the backlash is a little large,of which the backlash of bearing takes a greater part than two gearing stages.So we presented some practical methods to reduce the systematic backlash.
基金This project is supported by Science and Technology Developing Foundation of Tianjin Higher Education (No.20030703).
文摘Based on theory of mechanical dynamics, meshing characteristic as well as thedynamic model of double circular arc helical gearing, an analysis approach and a computer programhave been developed for studying the state of dynamic load and factor of dynamic load of thegearing, the changing situation of dynamic load and dynamic load factor vs some affecting factorssuch as gear width, helix angle and accuracy grade etc are investigated. A series of conclusions areobtained: ①With the increasing in the values of gear width, the dynamic load factor appears slowdecreasing tendency in most region of gear width. ②When the accuracy grades of the gearing areimproved, the values of dynamic load factor decrease. ③The value of dynamic load factor appears adecreasing tendency with the increasing of value of helix angle at the same ratio of criticalrotational speed.
基金Supported by National Natural Science Foundation of China(Grant Nos.51875351,51475296).
文摘Sheet-bulk metal forming(SBMF)is a promising process for manufacturing complex sheet components with functional elements.In this study,the entire forming process for a typical thin-walled component with external gearing is investigated,including sheet forming and bulk forming processes.Deep drawn cups are prepared during sheet forming;subsequently,upsetting is performed on the sidewall to form external gearing.The upsetting method performed is known as upsetting with a controllable deformation zone(U-CDZ).Compared with the conventional upsetting method,a floating counter punch with a counter force is used in the U-CDZ method such that the forming mechanism is changed into the accumulation of the deformation zone instead of deformation throughout the entire sidewall.The effects of the counter force and material flow are investigated to understand the mechanism.The forming quality,i.e.,the formfilling and effective strain distribution,improved,whereas a high forming load is avoided.In addition,a punch with a lock bead is used to prevent folding at the inner corner during the experiment.
基金supported by the projects of National Natural Science Foundation of China(No.52075216,No.91948302 and No.91848204).
文摘Pennate muscle is characterized by muscle fibers that are oriented at a certain angle(pennation angle)relative to the muscle’s line of action and rotation during contraction.This fiber rotation amplifies the shortening velocity of muscle,to match loading conditions without any control system.This unique variable gearing mechanism,which characterized by Architecture Gear Ratio(AGR),is involves complex interaction among three key elements:muscle fibers,connective tissue,and the pennation angle.However,how three elements determine the AGR of muscle-like actuator is still unknown.This study introduces a Himisk actuator that arranges five contractile units at a certain pennation angle in a flexible matrix,the experiment and simulation results demonstrated that the proposed actuator could vary AGR automatically in response to variable loading conditions.Based on this actuator,we present a series of actuators by simulations with the varying pennation angle(P),elastic modulus of the flexible matrix(E),and number of contractile units(N)to analyze their effects on AGR,and their interaction by three-factor analysis of variance.The results demonstrated that P and N effect on the AGR significantly,while E effects on AGR slightly,which supported the idea that the P is the essential factor for the AGR,and N is also an important factor due to the capability of force generation.This provides a better understanding of mechanical behavior and an effective optimizing strategy to muscle-like soft actuator.
基金funded by an Australian Research Council Linkage Grant(LP160101316),in collaboration with Asics Oceania and The Australian Sports Commission。
文摘Background:During human locomotion,a sufficiently stiff foot allows the ankle plantar flexors to generate large propulsive powers.Increasing foot stiffness(e.g.,via a carbon plate)increases the ankle’s external moment arm in relation to the internal moment arm(i.e.,increasing gear ratio),reduces plantar flexor muscles’shortening velocity,and enhances muscle force production.In contrast,when activation of the foot’s intrinsic muscles is impaired,there is a reduction in foot and ankle work and metatarsophalangeal joint stiffness.We speculated that the reduced capacity to actively control metatarsophalangeal joint stiffness may impair the gearing function of the foot at the ankle.Methods:We used a tibial nerve block to examine the direct effects of the intrinsic foot muscles on ankle joint kinetics,in vivo medial gastrocnemius’musculotendinous dynamics,and ankle gear ratio on 14 participants during maximal vertical jumping.Results:Under the nerve block,the internal ankle plantar flexion moment decreased(p=0.004)alongside a reduction in external moment arm length(p=0.021)and ankle joint gear ratio(p=0.049)when compared to the non-blocked condition.Although medial gastrocnemius muscle-tendon unit and fascicle velocity were not different between conditions,the Achilles tendon was shorter during propulsion in the nerve block condition(p<0.001).Conclusion:In addition to their known role of regulating the energetic function of the foot,our data indicate that the intrinsic foot muscles also act to optimize ankle joint torque production and leverage during the propulsion phase of vertical jumping.
基金the Doctorate Degree Program Foundation of the Ministry of Education (No. 2000061120)
文摘An approach for the contact analysis and load distribution of double-envelop hourglass worm gearing is presented, which is based on a 3-D elastic contact finite element method (FEM) model that accommodates the influence of errors and load. As compared with existing tooth contact analysis model that assumes rigidity for the contacting surfaces, the proposed model provides a more realistic analysis on the contact patterns, the distribution of contact load and transmission errors. It is also capable of exploring the influence of different errors on meshing performances, the contact deformation, the shift of the contact zone and load share among the meshing tooth-pairs under different load.
基金supported by the Natural Science Foundation of China (51175423)
文摘The deformation compatibility equations and the torque balance equations of star gearing with three branches have been found based on the characteristic that the system composes a closed-loop of power flow. In consideration of the parts manufacturing errors, assembly errors, bearing stiffness and float, the power splitting rate of each star gear and the system were calculated by using the theory of equivalent mesh error. The effects of the errors, float and the bearing stiffness on power splitting were studied. The study provides a useful theoretical guideline for the design of star gearing.
文摘Controllable modification of cone-generated cylindric worm gearing has been carriedout. The tooth contact state of modified gearing can be controlled by selecting the positions of con-tact points of worm surfaee and the correction amount of curvature. The modification machiningcan be conveniently implemented by changing the geometrical sizes and setting parameters of grind-ing wheel. Therefore the research has better scientific basis and practical value.
文摘Based on solid modeling, the geometry and the FE model of the hourglass worm gearing are established. By the hybrid method of FEM and penalty function, the load sharing among tooth paris and the stress of contact teeth are calculated, the contact zones and the distribution of the contact pressure are investigated. The variation of the contact states with the load is investigated by comparision of its contact patterns under different loads.
文摘The lubrication behavior of double enveloping hourglass worm gearing is studied experimently. The effects of rotational speed of the worm and load on the formation of the fluid film between engagement tooth surfaces are investigated in detail. and working angle of this worm gearing is also analyzed. Some beneficial results are 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.
文摘A novel CAD method for tooth profile based on the gearing feature has been proposed in this paper, and this method could be applied to the variable transmission ratio and three-dimension situation. The two pitch curves of the two gears can be generated due to the given transmission ratio. The tooth profile curves are formed in each coordinate system of its pitch curve by the gearing process. Finally, the tooth profile could be extracted and translated into a real dimension by CAD method. It is provided a simply thought for tooth profile design to avoid so much complicated mathematical reasoning.
文摘The engaged feature of a pair of gears was determined by the geometrical characteristics of their tooth surfaces. Through an analysis of gearing theory on epi-cycloidal bevel gears, the method to examine if there exists undercut during manufacturing of epicycloidal bevel gears, the approximate formulae to calculate the gap between the convex and concave tooth surfaces in meshing so as to guarantee against the occurrence of point-contact for tooth surfaces even in maximum angle of inclination are derived in this paper. Those formula derived are simple, compact and have practical value to the design and production of epicycloidal bevel gears.
文摘The forms of the vibration disturbances inside the epicyclic gear train are analyzed. Thefrequency equations for the inner disturbances of the epicyclic gearing with one or two degrees offreedom have been built. The latter of them is a 3-dimension problem and the range of the disturbance frequencies covers a series of planes inside the 3-dimension coordinates. As a result, thechances to lead to the system resonance are developed. The calculating results indicate that in thedesign process of the shaft system, the chances of resonance can be reduced by tunning the dynamicparameters and the structure of the system.
基金This project is supported by Provincial Natural Science Foundation of Shanxi, China (No. 20041057)Scholarship Council of Shanxi, China (No. 2005-22)
文摘The model for computing frictional coefficient between two teeth faces at the state of mixed elastohydrodynamic lubrication is established. And then more than 80 sets of numerical calculations and six sets of disc fatigue tests are completed. The results show that when the film thickness ratio λ 〈1.6, frictional coefficient μ is drastically decreased as λ. rises; Thereafter it decreases smoothly until λ=4.5. When λ〉4.5, however, it goes up again with λ, which indicates that the excessive film thickness ratio will deteriorate gearing contact fatigue strength. At the end, the formulae for determining the frictional coefficients are formed.
