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Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to correctly understand the output characteristics of gear-motors with different types of backlash sizes/offset unloading slots, a unified simplified formula for output characteristics such as speed/torque is constructed based on the different meshing line intervals of meshing tooth profiles/output characteristics, using the type value that measures the backlash size and the offset value between the symmetrical line of the double unloading slots and the centerline of the gear pair as variables. The results show that through the interval of the output characteristic meshing-line, the output speed and torque curve can be directly obtained from the speed and torque curve of meshing tooth-profile; under the symmetrical relief-groove type, the average output speed is the smallest, the average torque is the biggest, and the ripple coefficients of the output speed and torque are the smallest; the offset range of the relief-groove and the range of the output speed and torque regulating are larger under small backlash type than large backlash type; with small backlash and symmetrical relief-groove type, the average output speed is smaller, the average output torque is larger, and the ripple coefficient of the output speed and torque is smaller; the torque-ripple coefficient of the gear-motor is completely consistent with the flow-ripple coefficient of the gear-pump; the torque-ripple coefficient is slightly less than the speed-ripple coefficient, and can be approximately equal under the condition of large tooth-number; when high-speed is pursued, the type combination of large backlash and relief groove limit-offset shall be selected; with the pursuit of large torque or high output ripple-quality, the type combination of small backlash and symmetrical relief-groove shall be selected, etc. It is concluded that the obtaining method of output characteristics is simpler, the principle is clearer, the form is more concise, and the results are more reliable.

A steering control system is one of the key steps in the tractor's automatic navigation. Many nonlinear factors (such as hydraulic dead zone, saturation zone, and mechanical backlash) can dominate the performance of steering control, even the accuracy and stability of tractor navigation. In this study, the Lovol Europa M704-2H tractor was taken as the test platform with the electric steering wheel instead of the onboard steering wheel as the actuator, where the angle sensor on the steering wheel axle of the tractor to measure the size of the wheel turning angle. The steering control system included the steering angle calibration and the steering control. The steering angle calibration aimed to obtain the limit angle and median AD value size of the tractor, and then the steering wheel angle size at any angle by linear fitting. The limit steering angle calibration was required for the tractor steering wheel close to the limit through a circle, the satellite positioning of the trajectory point, and the least squares, in order to obtain the minimum turning radius of the tractor. The two-wheel model of the tractor was then utilized to calculate the maximum steering angle. The median steering angle calibration was required for the tractor to drive a section of an approximate straight-line trajectory. The least squares method (LSM) was also used to identify the correction of the zero position for the accurate median AD value. The TZ-QX2A6/5T front wheel angle meter was selected to compare the front wheel angle with the sensor measurement. The results show that the maximum error of calibrated angle measurement was 1.3°, and the average error was 0.11°, fully meeting the demand of steering control. At the same time, the mechanical backlash of the steering system was firstly quantified, in terms of the angular size of steering wheel reversal across the free travel. The accurate size of mechanical backlash was obtained through experimental identification. Then, the fuzzy PD steering control with backlash compensation was designed at the same time. When the electric steering wheel was out of the free travel, the fuzzy PD control was adopted; when the electric steering wheel was in free travel, the steering control was compensated to add the backlash P control into the output of the fuzzy PD control. Simulation results in Simulink show that better performance was achieved in the tracking of the steering angle signals of square wave and sinusoidal wave, fully meeting the requirements. The fuzzy PD steering control with/without the backlash compensation was also used to compare the tracking performance of square wave and sinusoidal steering angle signals. The experimental results show that the response time of the square wave angle signal tracking without backlash compensation was 1.3 s, where the maximum and average steady-state errors were 0.672°, and 0.244°, respectively. The average delay time of the sine wave angle signal tracking without backlash compensation was 0.5 s, where the maximum and average errors were 2.59° and 1.32°, respectively. Compared to the algorithm without backlash compensation, the time of steering angle error within ±0.2° was improved by 71%, the maximum steady state error was reduced by 0.022°, and the average steady state absolute error was reduced by 0.112°. Once the backlash compensation was performed, the response time of the square wave angle signal tracking was 1.1 s, where the maximum and average steadystate errors were 0.65°, and 0.132°, respectively. The average delay time of the sine wave angle signal tracking was 0.5 s, the maximum and average errors were 1.91° and 1.09°, respectively. Compared to the algorithm without backlash compensation, the maximum error was reduced by 0.68°, and the average error was reduced by 0.23°. The experimental results show that the backlash compensation outstandingly improved the stability of steering control for the less control error. The linear navigation test on the leveled field showed that the maximum and absolute average errors of angle tracking were 2.82° and 0.61°, respectively, when the system was in a steady state. Therefore, better performance was achieved with the high accuracy of the steering control system. [ABSTRACT FROM AUTHOR]

Taking cylindrical spur gear as study object，a nonlinear dynamics model of planetary gear transmission system is established by using mass concentration method. Four influences factors，namely backlash，time-varying meshing stiffness，meshing damping and comprehensive meshing error，are considered in the model，the dynamics equations corresponding to the model are listed and solved by the fourth-order Runge Kutta method. By changing the size of the backlash，the response states of the system under different backlash sizes are obtained. Finally，the time displacement image of relative position error，phase plane diagram and FFT spectrum are used to reflect the effect of specific backlash size on gear vibration response.

The torsional dynamics model of herringbone gear pair considering time-varying meshing stiffness， constant backlash， dynamic backlash， static transmission error and external dynamic excitation is established. The frequency response characteristics of the system under constant and dynamic backlashes are solved by incremental harmonic balance method， and the results are further verified by Runge-Kutta numerical integration method. The influence of time-varying meshing stiffness， damping， static transmission error and external load excitation on the amplitude frequency characteristics of the system is analyzed. The results show that， there is not only main harmonic response， but also super-harmonic response in the system. The time-varying meshing stiffness and static transmission error can stimulate the amplitude frequency response of the system， while the damping can restrain the amplitude frequency response of the system. Changing the external load excitation has little effect on the amplitude frequency response state change of the system. Compared with the constant backlash， increasing the dynamic backlash amplitude can further control the nonlinear vibration of the gear system.

Copyright of Systems Engineering & Electronics is the property of Journal of Systems Engineering & Electronics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The backlash of the planetary reducer was an important index that affected the transmission accuracy and smoothness of the reducer, and it was also the main parameter for dividing the accuracy grade. Aiming at the problems of inaccurate torque loading, poor compatibility, and low measurement efficiency that were common in backlash detection equipment, an automatic detection device for the backlash of the reducer was developed. First, a mechanical structure with a simple structure and suitable for operation of multiple models was designed to improve the compatibility of the device;then combining the precision servo system with the high-precision torque sensor, the torque loading closed-loop feedback system was constructed to realize the precise and dynamic torque loading, and the PLC control system was developed to realize the automation of the work process and improve the detection efficiency. Finally, a comparative measurement experiment was designed, and the device was analyzed for the measurement system. The test results show that the repeatability and reproducibility of the measurement device is 0. 218, the total variation TV is 1. 219, and the measurement variation accounts for the percentage of the total variation in the process. The GRR value is 17. 9%, indicating that the device has good detection performance and can be used to detect the backlash of a medium-precision reducer. [ABSTRACT FROM AUTHOR]

Aiming at the problem of the helical gears meshing which lead to the fatigue damage and shock of the gear surface， the dynamic performance and modification are analyzed and studied. The dynamics model of helical gears meshing is built based on the impact is affected by the backlash. The coupled model of rigid and flexible is built by Adams， and the angular velocity and load torque of the gear are obtained. Then， the finite element model of helical gear is established， the position and the curve of the maximum contact stress of are obtained. Finally， the angular acceleration， load torque and stress variation curve of the driven gear after modification are obtained by using the arc modification method. The research results indicate that the contact strength is improved based on the short-modification， which can provide the basis for gears analysis， such as， the fatigue life and the transmission efficiency.

Based on the large size and high precision worm gear pair after the temperature rise of deformation as the research object,analyses the deformation characteristics of the deformation of parts,combined with the calculation of the different parts of the deformation,the main factors affecting backlash is determined. On the other hand to explore the influence of temperature rise on the indexing accuracy principle and level. For this kind of turntable under different temperature conditions at the time of assembly back gap value provides a calculation method,as well as provides a quantitative reference for practical use and maintenance.

Taking spur gear pair as the research object, a 6-DOF coupled bending-torsion nonlinear vibration model including time-varying meshing stiffness, comprehensive error, backlash and input torque is established. Based on the bifurcation diagram and Poincare map, the influence of backlash, input torque, their coupling effect and the support stiffness of the main and follower gear bearings on the vibration characteristics of the system is studied. The results show that under a certain input torque, the system transits from single-period response to chaos through bifurcation and catastrophe with the increase of backlash. Under a certain backlash, the system transits from chaos to one-period response through inverted bifurcation and catastrophe with the increase of input torque. When the input torque is large, the backlash has little effect on the system response. The stiffness of the follower gear bearing has a great influence on the vibration characteristics of the system.

For the improvements of dynamical load stability of split torque-combine gear transmission， dynamical models of the system consisting of spur gears and herringbone gears is set up including excitations of multiple backlashes. The Gaussian elimination technique is introduced to deal with the elimination of extra rigid body displacements， ultimately， the dynamics equations are reduced to be 9 degrees of freedom. By applying the fourth order Runge-Kutta algorithm to solve the system dimensionless dynamical equations， dynamic load characteristic is analyzed under the excitations of backlash， general transmission error and time-varying mesh stiffness. The results show that dynamic load factor happens to jump to 2.705 under the backlash excitation， load sharing characteristic keeps very similar on the same stage when general transmission error varies， the dynamic characteristic vibrates severely on split torque gears while the perturbation factor of time-varying mesh stiffness is larger than 0.25， the investigation will provide a guidance for dynamic load design of this typical gear system.

Based on the NGW planetary gear transmission system,a gear transmission of parallel uniform planetary gear is proposed to reduce the transmission error of asteroid transmission system and improve its transmission accuracy. The backlash formula is obtained by considering the influence of gear eccentricity error and working load on the backlash of planetary transmission system. The influence of load and gear eccentricity error on the transmission system is analyzed. The results show that,as the working load increasing,the backlash of gear transmission of parallel Uniform Planetary gear and NGW planetary gear transmission system are all increased. But the backlash of NGW planetary gear transmission system is slightly larger. Under the condition of same gear eccentricity error,the backlash of gear transmission of parallel uniform planetary gear is less than the backlash of NGW planetary gear transmission system. In the gear transmission of parallel uniform planetary gear,the eccentricity error of the solar wheel has a great impact on the transmission system,but the eccentricity error of the outer ring has less influence on the transmission system. The influence of planetary wheel eccentricity error on the transmission system is between sun wheel and planet gear.

Based on higher order contact meshing theory of conjugate curvature,a three-dimensional model of the new type double helical tooth synchronous belt and the belt drive are established. The nonlinear finite element analysis software is used to analyze the stress and deformation of the new type double helical tooth synchronous belt and the pulley. Through the analysis,the change law of the helix angle,backlash,and pulley structural parameters on the stress and deformation of belt tooth and strength layers is studied,and the structural parameters of the new type double helical tooth synchronous belt with high integrated load carrying capacity are optimized. During laboratory bench fatigue life test,the new type double helical tooth synchronous belt has longer fatigue life than the same tooth profile with straight tooth synchronous belt.

The lightly loaded or unloaded gears rattle in vehicle transmission systems is an unsolved issue for vehicle manufacturers. Rattle noises affect customer perception of vehicle quality. Rattle is an unwanted byproduct of clearances and is affected by design of the torsional system,including clutch spring,hysteresis and flywheel inertias and so on. By using a generic torsional drivetrain model for loaded gear rattle analysis,then,the nonlinear responses of the rattling gear is examined. The rattle of the 1 st gear set and 5 th gear set are considered while 2 nd gear is meshed and driven. The accelerations of the 5 th gear set are shown to be more severe under the same excitation condition and thus found to be a larger contributor to the rattle noise. The system is simulated by using a frequency sweep with engine excitation derived from measured data and then peak responses is examined.

In harmonic gear drive,backlash has a significant effect on transmission performance. Based on the exact conjugate method of harmonic drive,the changes of conjugate zone,circular spline conjugate tooth profile and backlash of harmonic drive with the variation of flexspline tooth profile parameters are studied. The results show that flexspline profile parameters play a decisive role in conjugate section,circular spline conjugate tooth profile and backlash. Reducing the circular arc radius of convex tooth profile is helpful to increase the meshing conjugate zone,but not conducive to reducing the backlash. The circular arc radius of concave tooth profile has no obvious effect on the conjugate zone,but has a significant effect on the backlash. Reducing the common tangent angle is helps to increase the conjugate zone,reduce the backlash and improve the backlash distribution. The circular arc radius of convex and concave tooth profile of flexspline have obvious influence on the circular spline tooth profile parameters,but the common tangent angle have little effect on it. A reasonable choice of flexspline tooth profile parameters may bring a bigger conjugate zone and more well-distributed backlash,the carrying capacity and transmission performance can then be improved.

The backlash and stiffness are important parameters of vector rotate（ RV） reducer,a backlash and stiffness measurement system is designed. The measuring method of the fixed output,loaded input and angle tested input is put forward. The relation between input and output torque and angle of the RV reducer is used to process the data. The RV-40 E-121 reducer is tested and the model of RV reducer stiffness curve fitting is proposed,the stiffness curve of RV-40 E reducer is obtained. The backlash and stiffness of the RV-40 E reducer meet the performance requirements,which indicated that the measurement system is reasonable.

A test rig for RV reducers is developed,which can measure the mechanical transmission property of the RV reducer,fault monitoring and fatigue life test. The RV reducer test rig mainly consists of mechanical system,measurement and control system and software system,which can acquire the mechanical parameters of the RV reducers and the signal of fault quickly and automatically. The transmission efficiency,transmission error and backlash of domestic SHPR-20 E RV reducer are investigated with the test rig,and the measurement efficiency is high and the results are accurate. It is verified that the RV reducer test rig can measure the performance of RV reducers quickly and accurately,and can be used to investigate,optimize and enhance the performance of RV reducer.

Taking the homemade high precision RV reducer as study object,According to the characteristics of the transmission principle and structure,by using the sensitivity index analysis,the parameter optimization design of the RV reducer is carried out,the theoretical value of geometry backlash of theory reducer is obtained,the effectiveness of the proposed method is verified by experiment. The study results show that,the calculated value of theoretical geometric backlash is 0. 397’ 0. 859’,and the backlash of experiment test is0. 93’. The test results are verified through the experiment and theory calculation results contrast analysis,the homemade RV reducer can meet the using requirement of the reducer. A theoretical basis for the research and development of RV reducer is provided by this study.

A comprehensive parameter measuring machine for precise RV reducer is developed,which can measure the parameters of transmission error,backlash,stiffness and friction moment and so on. This machine mainly consists of mechanical structure design,measuring & control system and measuring software,which can acquire the parameters of RV reducer rapidly and accurately by a simply one-time clamping. The mechanical structure includes base,input & output components and mounting support. By using the FEA software Hypermesh 12. 0,the output shaft strength is analyzed,it is meeting the strength condition under the condition of output maximum torque of 2 000 N·m when measuring the backlash.

The gear backlash is in the process of gear and rack transmission,the gear backlash needed to be eliminated to ensure the bidirectional transmission precision of the transmission mechanism. In the designed mechanical mechanism,two racks meshing gears is driven through the axial relative displacement of the mechanism of sliding lead screw nut,and an axial relative displacement between the two racks（ gear rack staggered teeth） appeared,and the equivalent tooth thickness increased,and one mechanism is designed to eliminate gears backlash automatically. The mechanism is used in rotary table of NC machine driving by gear- rack successfully,it can obtain simple structure and high transmission precision.

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A six degrees non-linear dynamics model of a gear system with meshing beyond pitch point is established considering the time-varying meshing stiffness, time-varying friction, load distribution among teeth and backlash. Time-varying meshing stiffness is calculated by material mechanics method, and time-varying friction coefficient is calculated by elasto-hydrodynamic lubrication (EHL) theory and compared with that of the Coulomb friction model. Moreover, the system differential equation is obtained and solved by Runge-Kutta numerical integration method. At last, dynamic response and phase diagram are obtained, and dynamics characteristics of the system are analyzed. [ABSTRACT FROM AUTHOR]

A novel structure of differential A/B bi-rotary head was designed， which can be used for five-axis machine centers. The heads were driven by four servo motors. Pitching and tilting motions were achieved through controlling angle and velocity of the motors. The motors and reducers were fixed on the machine body. The structure of motion parts was more simplified than that of the typical A/B bi-rotary head. The backlash of the head was eliminated owing to the dual-motor master-slave control method being used， and the motion accuracy of the head was improved. Transmission characters， backlash eliminating method and structural characters of the head were analyzed， and the results provide an important theoretical basis for the design of A/B bi-rotary head. [ABSTRACT FROM AUTHOR]

Copyright of Electric Machines & Control / Dianji Yu Kongzhi Xuebao is the property of Electric Machines & Control and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To provide accurate numerical basis for the forecast of lifetime and analysis of fretting wear of the spline couplings, the nonlinear dynamic characteristics of involute splines was studied. Four degrees of freedom nonlinear dynamic equations of the spline couplings using the lumped mass model was established, the number of actual meshing teeth and the time-varying mesh stiffness of the systems were calculated, and the nonlinear dynamic equations adopting the fourth order Runge-Kutta method was solved. The results show that; the time-varying mesh stiffness changes periodically with time and is a piecewise linear distribution with torque changing; when n = 300 r/min, the system presents harmonic response; when n = 348 r/min, the system presents double-cycle response; when n = 360 r/min, the system presents 5-cycle response; and when n = 1 080 r/min, the system gets into chaos response. The dynamic load coefficient of the spline couplings changes periodically and increases with torque and backlash. It is concluded that reducing the clearance of the spline couplings is beneficial to lowering the dynamic load and improving the stability of involute splines. [ABSTRACT FROM AUTHOR]