The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the ...The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.展开更多
Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynami...Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.展开更多
Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-a...Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.展开更多
With an advanced foreign hydraulic automatic transmission as the objective,an analytical method for the gear-shifting schedule is proposed.First the demanded maximum gradient of test is estimated.Then a test scheme an...With an advanced foreign hydraulic automatic transmission as the objective,an analytical method for the gear-shifting schedule is proposed.First the demanded maximum gradient of test is estimated.Then a test scheme and analytical procedure is formulated by initial test and hypothetical shift parameters.Finally through gear-shifting tests under different road conditions,load,accelerator pedal position limitation,throttle opening and output shaft speed are found to be the gear-shifting parameters.Under a common road condition,the gear-shifting schedule is a double-parameter schedule.Based on the driver's demands on braking and dynamic performance,different shift schedules are made under downhill,uphill and quick releasing acceleration pedal conditions.The operation criteria of down-shift schedule on abrupt grade are proposed.展开更多
With a transmission system suitable for a medium or large self-propelled cotton picker as the object of the study,the following work focuses on the influence law of an independently designed hydro-mechanical continuou...With a transmission system suitable for a medium or large self-propelled cotton picker as the object of the study,the following work focuses on the influence law of an independently designed hydro-mechanical continuously variable transmission(HMCVT)in the process of changing sections.An HMCVT simulation model was established using the multibody dynamics Simulation X software.The accuracy of the simulation model was verified by comparing the numerical values of the output speed of the HMCVT with model predictions.The HMCVT test bench was built independently using a John Deere 4045HYC11 diesel engine as power input.The engine speed,load torque,oil pressure,and flow of speed regulating valve were considered the influencing factors.The sliding friction power was the response index for the segment change process test.We analysed the reasons for the decrease in output speed during the shifting process,and proposed to effectively reduce the stable speed difference before and after the output shaft shifting by shifting the stage ahead(with displacement ratio of-0.96).This study provides a reference value for the smoothness of the HMCVT of the self-propelled cotton picker,and is relevant in promoting the use of the cotton picker.展开更多
The kinetic precision of transmission chain is a key problem in the research of gear cutting machine transmission system.The traditional point of view is to consider the transmission chain as a geometrical meshing sys...The kinetic precision of transmission chain is a key problem in the research of gear cutting machine transmission system.The traditional point of view is to consider the transmission chain as a geometrical meshing system,thus it is deemed that the kinetic precision of the transmission chain only depends on the manufacturing and assembly errors of its transmission parts.But further research reveals that the kinetic precision of transmission system is closely related with the system dynamic effects.Therefore,from the dynamic point of view,it is discerned that not only deems the transmission chain as a geometrical meshing system but also considers it as a dynamic system performing with torsional vibration.On the basis of analyses and processes of measuring data of samples from tests of cutting machine's kinetic precision of transmission chain,the results represent that the influences of dynamic characteristics of the transmission system on its kinetic precision is non negligible.Experimental methods for discerning the transfer function of torsional vibration of gear transmission system and experimental results have been given.展开更多
Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification...Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.展开更多
A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, appli...A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.展开更多
In order to diagnose gear shifting process in automated manual transmission(AMT),a semi-quantitative signed directed graph(SDG)model is applied.Mathematical models are built by analysis of the power train dynamic ...In order to diagnose gear shifting process in automated manual transmission(AMT),a semi-quantitative signed directed graph(SDG)model is applied.Mathematical models are built by analysis of the power train dynamic and the gear shifting control process.The SDG model is built based on related priori knowledge.By calculating the fuzzy membership degree of each compatible passway and its possible fault source,we get the possibilities of failure for each possible fault source.We begin with the nodes with the maximum possibility of failure in order to find the failed part.The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.展开更多
A method, which compares the angular acceleration and vibration spectrums of shafts and gears with physical characteristics of gearbox as tooth numbers and speed ratios, is proposed to find the source of gear rattle v...A method, which compares the angular acceleration and vibration spectrums of shafts and gears with physical characteristics of gearbox as tooth numbers and speed ratios, is proposed to find the source of gear rattle vibration. A mathematical and multi-body dynamics co-simulation model is built to reproduce the gear rattle phenomenon of one typical type of manual transmission. In the model, multi-body dynamics part is used for rotational motion and engagement simulation of gearbox shafts and gears, while mathematical part for control and data processing. The simulation results show that the sound source of the gear rattle from the first gear to the third gear is similar to the experimental results;different parameters like rotating damping, contact stiffness,contact damping, inertia moment and torque fluctuation making effects on gear rattle vibration strength are researched and simulated. The comparison of the simulation and experimental results shows that this method can provide recommendations for solving practical gear rattle problems.展开更多
Multispeed transmissions can enhance the dynamics and economic performance of electric vehicles(EVs),but the coordinated control of the drive motor and gear shift mechanism during gear shifting is still a difficult ch...Multispeed transmissions can enhance the dynamics and economic performance of electric vehicles(EVs),but the coordinated control of the drive motor and gear shift mechanism during gear shifting is still a difficult challenge because gear shifting may cause discomfort to the occupants.To improve the swiftness of gear shifting,this paper proposes a coordinated shift control method based on the dynamic tooth alignment(DTA)algorithm for nonsynchronizer automated mechanical transmissions(NSAMTs)of EVs.After the speed difference between the sleeve(SL)and target dog gear is reduced to a certain value by speed synchronization,angle synchronization is adopted to synchronize the SL quickly to the target tooth slofs angular position predicted by the DTA.A two-speed planetary NS AMT is taken as an example to carry out comparative simulations and bench experiments.Results show that gear shifting duration and maximum jerk are reduced under the shift control with the proposed method,which proves the effectiveness of the proposed coordinated shift control method with DTA.展开更多
In order to improve the driving dynamics and riding comfort of pure electric vehicles,taking a two-speed I-AMT(Inverse-Automatic Mechanical Transmission)with rear friction clutch as the research object,a gear shift st...In order to improve the driving dynamics and riding comfort of pure electric vehicles,taking a two-speed I-AMT(Inverse-Automatic Mechanical Transmission)with rear friction clutch as the research object,a gear shift strategy,which consists of the open-loop control of the clutch position control and the closed-loop control of the drive motor speed control,is proposed.Considering the inherent time-delay and external disturbances within the motor speed adjustment system,a two DOF(degree-of-freedom)Smith predictor with feedforward input is designed to track the target speed of the drive motor.The feedforward input is used to eliminate the influence of clutch sliding friction on the motor speed control,while the feedback speed tracking controller is applied to realize the speed tracking performance with the existence of time-delay and the external disturbance.In order to verify the effectiveness of the gear shift control strategy and the accuracy of the two DOF Smith controller with feedforward control,simulation results comparison is firstly carried out to illustrate the effectiveness of the control scheme.Then,a light pure electric vehicle equipped with I-AMT was used for downshift experiments under large throttle,which is the most difficult working scenario to control the transmission.The experimental results show that the two DOF Smith controller can eliminate the influence of time-delay on the closed-loop control,and the proposed whole gear shift control strategy can limit the clutch slippage time within 1.5 s,resulting in a smaller shift jerk,thus guarantee the driving dynamics and riding comfort simultaneously.展开更多
A dynamic model of gear transmission system which includes time-varying meshing stiffness,meshing damp and transmission error is established.Next,the analytical solution of the vibration response would be obtained by ...A dynamic model of gear transmission system which includes time-varying meshing stiffness,meshing damp and transmission error is established.Next,the analytical solution of the vibration response would be obtained by solving the dynamic model based on the harmonic balance method.And on this basis,a dynamic performance discrete optimization model of transmission sub-system would be constructed,which sets objective function up from vibration acceleration and the total mass of transmission sub-system,treats the module,number of teeth and helix angle as design variables,and takes gear strength and assembly relationship as constraints.Last,the optimal solution of design variables could be obtained through the multivariable mixed discrete optimization program which based on the branch-bound algorithm.The results show that the vibration acceleration and the total mass of transmission sub-system reduce by 34.6%and 6.8%,respectively.展开更多
基金Project(2011CB706800) supported by the National Basic Research Program of ChinaProject(51275530) supported by the National Natural Science Foundation of China
文摘The effect of static transmission error on nonlinear dynamic response of the spiral bevel gear system combining with time-varying stiffness and backlash was investigated.Firstly,two different control equations of the spiral bevel gear model were adopted,where the static transmission error was expressed in two patterns as predesigned parabolic function and sine function of transmission errors.The dynamic response,bifurcation map,time domain response,phase curve and Poincare map were obtained by applying the explicit Runge-Kutta integration routine with variable-step.A comparative study was carried out and some profound phenomena were detected.The results show that there are many different kinds of tooth rattling phenomena at low speed.With the increase of speed,the system enters into stable motion without any rattling in the region(0.72,1.64),which indicates that the system with predesigned parabolic function of transmission error has preferable capability at high speed.
基金the National Natural Science Foundation of China under Contract No.51875073the Scientific Research Project of Education Department of Liaoning Province under Contract No.JDL2019005+1 种基金the Dalian Science and Technology Innovation Fund Plan under Contract No.2019J11CY017the Innovation Team Support Plan of Liaoning Higher Education under Contract No.LT2016010.
文摘Multiple failuremodes and strength degradation are usually inherent in the gear transmission system,which brings new challenges for conducting fatigue reliability analysis and design.This paper proposes a novel dynamic fatigue reliability analysis method for failure dependence and strength degradation based on the combination of theCopula function and Gamma process.Firstly,the dynamic simulation model of the gear transmission system is established to obtain the dynamic stress-time history.The Gamma process is then used to describe the strength degradation to establish the dynamic stress-strength interference model.The marginal distribution functions of tooth contact fatigue and dedendumbending fatigue are calculated respectively based on the dynamic interferencemodel.Finally,the joint distribution of the two failure modes can be obtained by the t-Copula function to characterize the failure dependence,and so the dynamic fatigue reliability considering failure dependence can be estimated.The effectiveness of the proposed method is illustrated with examples.The results reveal the temporal law of reliability and the effects of failure dependence on dynamic fatigue reliability.
基金Supported by National Basic Research Program of China("973"Program,No.2013CB632305)
文摘Monte Carlo method was adopted to calculate the meshing error considering the manufacture error and assembly error of the meshing point along the time-varying contact line for helical gear pair. The flexural-torsion-axis dynamic model coupled was established under the tooth friction force and solved by the perturbation method to compute real dynamic tooth load. The change laws of the friction force and friction torque were obtained in a meshing period. The transmission error formulation was analyzed to introduce meshing excitations. The maximum dynamic transmission error, the maximum meshing force and the maximum dynamic factor were calculated under different speeds, external loads and damping factors. The conclusions can provide theoretical basis for the gear design especially in tooth profile correction.
基金Supported by the National High Technology Research and Development Program of China(863 Program)(2012AA112101)
文摘With an advanced foreign hydraulic automatic transmission as the objective,an analytical method for the gear-shifting schedule is proposed.First the demanded maximum gradient of test is estimated.Then a test scheme and analytical procedure is formulated by initial test and hypothetical shift parameters.Finally through gear-shifting tests under different road conditions,load,accelerator pedal position limitation,throttle opening and output shaft speed are found to be the gear-shifting parameters.Under a common road condition,the gear-shifting schedule is a double-parameter schedule.Based on the driver's demands on braking and dynamic performance,different shift schedules are made under downhill,uphill and quick releasing acceleration pedal conditions.The operation criteria of down-shift schedule on abrupt grade are proposed.
基金Supported by the National Natural Science Foundation of China(51665051)the Autonomous Region Graduate Innovation Project of China(XJ2019G112)。
文摘With a transmission system suitable for a medium or large self-propelled cotton picker as the object of the study,the following work focuses on the influence law of an independently designed hydro-mechanical continuously variable transmission(HMCVT)in the process of changing sections.An HMCVT simulation model was established using the multibody dynamics Simulation X software.The accuracy of the simulation model was verified by comparing the numerical values of the output speed of the HMCVT with model predictions.The HMCVT test bench was built independently using a John Deere 4045HYC11 diesel engine as power input.The engine speed,load torque,oil pressure,and flow of speed regulating valve were considered the influencing factors.The sliding friction power was the response index for the segment change process test.We analysed the reasons for the decrease in output speed during the shifting process,and proposed to effectively reduce the stable speed difference before and after the output shaft shifting by shifting the stage ahead(with displacement ratio of-0.96).This study provides a reference value for the smoothness of the HMCVT of the self-propelled cotton picker,and is relevant in promoting the use of the cotton picker.
文摘The kinetic precision of transmission chain is a key problem in the research of gear cutting machine transmission system.The traditional point of view is to consider the transmission chain as a geometrical meshing system,thus it is deemed that the kinetic precision of the transmission chain only depends on the manufacturing and assembly errors of its transmission parts.But further research reveals that the kinetic precision of transmission system is closely related with the system dynamic effects.Therefore,from the dynamic point of view,it is discerned that not only deems the transmission chain as a geometrical meshing system but also considers it as a dynamic system performing with torsional vibration.On the basis of analyses and processes of measuring data of samples from tests of cutting machine's kinetic precision of transmission chain,the results represent that the influences of dynamic characteristics of the transmission system on its kinetic precision is non negligible.Experimental methods for discerning the transfer function of torsional vibration of gear transmission system and experimental results have been given.
基金Sponsored by the National Natural Science Foundation of China(Grant No.2009AA04Z404)
文摘Based on Newton ' s second law,the bend-torsion-shaft coupling nonlinear dynamic model and equations of power split gear transmission system are established.According to the principle of tooth profile modification,the tooth profile modification is considered as time-varying gear backlash function acting along the line of action.Then the dynamic functions are solved by using Runge-Kutta numerical method.After analyzing the effect of tooth profile modification quantity( TPMQ) and relative tooth profile modification length( TPML) to the nonlinear dynamic characteristics of power split gear transmission,the following conclusions are drawn:1 The TPMQ of a certain stage transmission affects the vibration of its own stage more significantly than the other stage,and the coupling effect between two stages can be ignored usually in the modification design;2 If the first stage TPMLs are less than 0.3,the influence of the first stage TPMLs to the first stage transmission vibration is much more greatly than the influence of the second stage TPMLs to the first stage transmission vibration,or else both the first and second stage TPMLs affect the first stage transmission vibration largely.The same is true for the second stage TPMLs,and the cutoff value is 0.2;3 The TPMQ affects the vibration of power split gear transmission system more principally than the TPML,and should be top-priority in the modification design.
基金Project(51175505)supported by the National Natural Science Foundation of China
文摘A nonlinear model of anti-backlash gear with time-varying friction and mesh stiffness was proposed for the further study on dynamic characteristics of anti-backlash gear. In order to improve the model precision, applied force analysis was completed in detail, and single or double tooth meshing states of two gear pairs at any timing were determined according to the meshing characteristic of anti-backlash gear. The influences of friction and variations of damping ratio on dynamic transmission error were analyzed finally by numerical calculation and the results show that anti-backlash gear can increase the composite mesh stiffness comparing with the mesh stiffness of the normal gear pair. At the pitch points where the frictions change their signs, additional impulsive effects are observed. The width of impulsive in the same value of center frequency is wider than that without friction, and the amplitude is lower. When gear pairs mesh in and out, damping can reduce the vibration and impact.
基金Supported by the Basic Research Foundation of Beijing Institute of Technology(20130342035)
文摘In order to diagnose gear shifting process in automated manual transmission(AMT),a semi-quantitative signed directed graph(SDG)model is applied.Mathematical models are built by analysis of the power train dynamic and the gear shifting control process.The SDG model is built based on related priori knowledge.By calculating the fuzzy membership degree of each compatible passway and its possible fault source,we get the possibilities of failure for each possible fault source.We begin with the nodes with the maximum possibility of failure in order to find the failed part.The diagnosis example shows that it is feasible to use the semi-quantitative SDG model for fault diagnosis of the gear shifting process in AMT.
文摘A method, which compares the angular acceleration and vibration spectrums of shafts and gears with physical characteristics of gearbox as tooth numbers and speed ratios, is proposed to find the source of gear rattle vibration. A mathematical and multi-body dynamics co-simulation model is built to reproduce the gear rattle phenomenon of one typical type of manual transmission. In the model, multi-body dynamics part is used for rotational motion and engagement simulation of gearbox shafts and gears, while mathematical part for control and data processing. The simulation results show that the sound source of the gear rattle from the first gear to the third gear is similar to the experimental results;different parameters like rotating damping, contact stiffness,contact damping, inertia moment and torque fluctuation making effects on gear rattle vibration strength are researched and simulated. The comparison of the simulation and experimental results shows that this method can provide recommendations for solving practical gear rattle problems.
基金This work was supported by the Science and Technology Planning Project of Guangdong Province,China(Grant Nos.2015B010119002 and 2016B010132001).
文摘Multispeed transmissions can enhance the dynamics and economic performance of electric vehicles(EVs),but the coordinated control of the drive motor and gear shift mechanism during gear shifting is still a difficult challenge because gear shifting may cause discomfort to the occupants.To improve the swiftness of gear shifting,this paper proposes a coordinated shift control method based on the dynamic tooth alignment(DTA)algorithm for nonsynchronizer automated mechanical transmissions(NSAMTs)of EVs.After the speed difference between the sleeve(SL)and target dog gear is reduced to a certain value by speed synchronization,angle synchronization is adopted to synchronize the SL quickly to the target tooth slofs angular position predicted by the DTA.A two-speed planetary NS AMT is taken as an example to carry out comparative simulations and bench experiments.Results show that gear shifting duration and maximum jerk are reduced under the shift control with the proposed method,which proves the effectiveness of the proposed coordinated shift control method with DTA.
基金the National Natural Science Foundation of China under Grant 62003244the Perspective Study Funding of Nanchang Automotive Institute of Intelligence and New Energy+1 种基金Tongji University under Grant TPD-TC202110-10,in part by the Jilin Provincial Science&Technology Department under Grant 20200301011RQthe Fundamental Research Funds for the Central Universities under Grant 22120210160.
文摘In order to improve the driving dynamics and riding comfort of pure electric vehicles,taking a two-speed I-AMT(Inverse-Automatic Mechanical Transmission)with rear friction clutch as the research object,a gear shift strategy,which consists of the open-loop control of the clutch position control and the closed-loop control of the drive motor speed control,is proposed.Considering the inherent time-delay and external disturbances within the motor speed adjustment system,a two DOF(degree-of-freedom)Smith predictor with feedforward input is designed to track the target speed of the drive motor.The feedforward input is used to eliminate the influence of clutch sliding friction on the motor speed control,while the feedback speed tracking controller is applied to realize the speed tracking performance with the existence of time-delay and the external disturbance.In order to verify the effectiveness of the gear shift control strategy and the accuracy of the two DOF Smith controller with feedforward control,simulation results comparison is firstly carried out to illustrate the effectiveness of the control scheme.Then,a light pure electric vehicle equipped with I-AMT was used for downshift experiments under large throttle,which is the most difficult working scenario to control the transmission.The experimental results show that the two DOF Smith controller can eliminate the influence of time-delay on the closed-loop control,and the proposed whole gear shift control strategy can limit the clutch slippage time within 1.5 s,resulting in a smaller shift jerk,thus guarantee the driving dynamics and riding comfort simultaneously.
基金the Chongqing Research Program of Basic Research and Frontier technology No.cstc2016jcyjA0514 and No.cstc2015jcyjA70012Scientific and Technological Research Program of Chongqing Municipal Education Commission No.KJ1600503National Natural Science Foundation of P.R.China under Contract No.51375519 and No.51405048.
文摘A dynamic model of gear transmission system which includes time-varying meshing stiffness,meshing damp and transmission error is established.Next,the analytical solution of the vibration response would be obtained by solving the dynamic model based on the harmonic balance method.And on this basis,a dynamic performance discrete optimization model of transmission sub-system would be constructed,which sets objective function up from vibration acceleration and the total mass of transmission sub-system,treats the module,number of teeth and helix angle as design variables,and takes gear strength and assembly relationship as constraints.Last,the optimal solution of design variables could be obtained through the multivariable mixed discrete optimization program which based on the branch-bound algorithm.The results show that the vibration acceleration and the total mass of transmission sub-system reduce by 34.6%and 6.8%,respectively.