Angular Transmission Error Research Articles

The Prediction of the Angular Transmission Error of a Harmonic Drive by Measuring Noncontact Tooth Profile and Considering Three-dimensional Tooth Engagement

The Prediction of the Angular Transmission Error of a Harmonic Drive by Measuring Noncontact Tooth Profile and Considering Three-dimensional Tooth Engagement

Design and implementation of a diagnostic system for measuring high-precision reducers

At present, the industry is in a phase where there is an effort to maximize the automation of production processes. In many places, human power is being replaced by automated machines and industrial robots. Automation makes it possible to increase work efficiency, significantly reduce production costs and also increase the quality of the final product. A precondition for increasing the quality of production is to achieve high accuracy of specialized machines and industrial robots, resp. the accuracy of positioning of individual parts. Due to the drive system and the achieved speed, the gear unit includes a gearbox. Reducers used in robotic joints are the most complex subsystems of robots. For very precise applications, the designers will reach for the so-called backlash-free reducers for their characteristic properties (minimum values of backlash in teeth, angular transmission errors, hysteresis and others). Despite many positive properties, high-precision reducers also show their characteristic nonlinearities, which influence the behavior of the whole system and it is so important to know their behavior. Given these facts, this article deals with the design and implementation of mechatronic diagnostic equipment for the identification of nonlinearities, static and dynamic parameters, vibrodiagnostic measurements and measurements of the efficiency of bearing reducers.

Backdrivability Improvement Method Based on Angular Transmission Error in a High Reduction Gear

The actuators in robot joints are often equipped with reduction gears for increasing the power output. However, a high reduction ratio is required to decrease the backdrivability. In this paper, the backdrivability is improved by installing motor- and load-side encoders in the reduction gear. The proposed method comprises a backdrive assist control, feedforward friction compensation, and estimation and feedback of the load-side disturbance by using a multi-encoder-based disturbance observer. The angular transmission error in the reduction gear is treated as a disturbance that affects the motor. This disturbance is estimated from the motor- and load-side angular accelerations, and provides feedback assistance to the backdrive. The effectiveness of the proposed method is verified through experiments.

Impacts of Misalignments on Mesh Behaviors of Face-Hobbed Hypoid Gear Considering System Deformation

Considering the system deformation, a procedure to predict the mesh behaviors for face-hobbed hypoid gear pair in car rear axle was proposed based on the tooth surface model and the finite element analysis (FEA) tooth contact model. The mathematical model of face-hobbed hypoid gear was derived based on the manufacturing process. The systematic model of the whole rear axle was developed in Masta, and the misalignments caused by system deformation of the hypoid gear pair was calculated. The impacts of the comprehensive misalignments and independent misalignments on mesh behaviors of hypoid gear were studied, respectively. Results show that the comprehensive misalignments under the rated load level have less influence on the contact characteristics. However, for the parametric studies of independent misalignment, the offset misalignment, and the gear axial misalignment have obvious influences on the contact pattern and transmission error. The peak-to-peak value for angular transmission error with the offset misalignment decreases significantly, when misalignment change from negative to positive. While that with the gear axial misalignment increases progressively. For shaft angle misalignment has an obvious impact on the location of the contact area and it causes a little increase of the peak-to-peak value for transmission error. Relatively, the pinion axial misalignment has diminutive impacts on the contact pattern and transmission error.

Manufacturing and contact characteristics analysis of internal straight beveloid gear pair

This paper presents a manufacturing method for straight internal beveloid gear pair by shaper cutter with parallel axes between the cutter and the gear blank. The cutting motions are represented using three degrees of freedom that are the rotation along its axes, translations along the axial and radial directions. With the proposed method, the beveloid gear with a linear or nonlinear variable profile shift coefficient along the tooth width direction can be generated and the tilt deviations by the inclined cutting tool shaft can be avoided. The mathematical description of shaper cutter and the coordinate systems for the cutting procedure were defined. And the mathematical model of external and internal beveloid gears were derived and the loaded tooth contact analysis were conducted. Results show that the teeth mesh in at the toe and mesh out at the heel. The length of the simultaneous contact line on tooth surface increases first and then decreases due to the cone angle. As the load increases, the mesh area, contact pressure, mean value of mesh stiffness and the peak-peak value of angular transmission error are increased due to the elastic deformation. However, the speeds of the increase tendency slow down.

Contribution of angular measurements to intelligent gear faults diagnosis

Currently, work on the automation of vibration diagnosis is mainly based on indicators extracted from Time sampled Acceleration signals. There are other attractive alternatives such as those based on Angle synchronized measurements, which can provide a considerable number of more relevant and diverse indicators and, thus, lead to better performance in gear fault classification. The diversity of angular measurements (Instantaneous Angular Speed, Transmission Error and Angular sampled Acceleration) represents potential sources of relevant information in fault detection and diagnosis systems. These complementary measurements of existing signals or new relevant signals allow the construction of Feature Vector (FV) offering robust and effective classification methods even for different or non-stationary running speed conditions. In this paper, we propose to build several FVs based on indicators derived from the angular techniques to compare them to the ones calculated from the time signals, proving their superior performance in detection and identification of gear faults. It will be a question to demonstrate the effectiveness of angular indicators in increasing classification performances, using a supervised classifier based on Artificial Neural Networks and thus determining the most suitable signals.

Measurement of Transmission Nonlinearities in Servodrives

Paper presents transmission nonlinearities of servodrives. These nonlinearities directly affect the performance and precision of industrial machines such as robots, manipulators, NC machine tools etc. For measuring purpose of these nonlinearities a measurement test bench was created. Presented measuring test bench is used for static and dynamic measurements of servodrives as well as for precision and gear error evaluation. Paper focuses on properties, analysis and experimental measurements of angular transmission error, torsional elasticity and repeated position accuracy.

Motion control of industrial robots by considering serial two-link robot arm model with joint nonlinearities

This paper presents a model based motion control approach for industrial robots by considering a serial two-link robot arm model with joint nonlinearities. In order to achieve the desired performance using the model based control approaches, it is important to obtain relevant models of both kinematics and dynamics including nonlinear characteristics. Main nonlinear components that lead to trajectory tracking errors of typical multi-axis industrial robot are joint nonlinearities in each axis and dynamic coupling effects between different axes. In this paper, a parametric modeling approach is introduced to reproduce behaviors of a serial two-link robot arm with joint nonlinearities. Nonlinear stiffness, angular transmission errors, and friction in these two links are directly identified as joint nonlinearities. This approach is applied for the serial two-link arm of a typical multi-axis industrial robot, which has low frequency vibration modes and significantly affects to the trajectory performance. Effectiveness of the modeling is verified by comparative studies with numerical simulations and experiments. Finally, a 2-DOF control scheme with the identified two-link dynamic model and a feedback loop-shaping with a variable notch filter are applied to improve the performance of trajectory tracking and residual vibration suppression.

Vibration Suppression Control Method using Extended State Observer for Angular Transmission Error in Cycloid Gear

This paper proposes a method for suppressing the speed vibration caused by the angular transmission error in cycloid gears used in industrial robots. It is important for industrial robots to have high accuracy. However, cycloid gears with an angular transmission error may cause vibration in the arms of a robot. The proposed method for compensating for the speed vibration uses a new extended state observer that is based on a model that considers a cycloid gear with an angular transmission error. A compensation current is generated by using the torque vibration which is converted from the estimated speed vibration. The speed vibration is suppressed using this compensation current. The experimental results show that the proposed system suppresses the vibration at the load speed.

Vibration Suppression for Angular Transmission Errors in Harmonic Drive Gearings and Application to Industrial Robots

This paper presents a vibration suppression approach for precision positioning mechanisms including harmonic drive gearings (HDGs), using a variable notch filter to suppress mechanical vibrations due to angular transmission errors (ATEs) in HDGs. Mechanisms with HDGs excite resonant vibrations, especially in the condition that the frequency of synchronous components of ATE correspond to the critical mechanical resonant frequency. In the proposed approach, therefore, a variable notch filter with free parameters of frequency and damping is designed to suppress the resonant vibrations during transient response, considering the sensitivity characteristics of the feedback system. The proposed approach has been applied to motion control of an actual industrial 6-axis robot and verified by numerical simulations and experiments.

波動歯車の角度伝達誤差に起因する共振振動の可変ノッチフィルタによる制振制御

This paper presents a vibration control using a variable notch filter to suppress mechanical vibrations due to angular transmission errors (ATEs) in harmonic drive gearings (HDGs). Mechanisms including HDGs excite resonant vibrations due to ATEs, especially in the condition that the frequency of synchronous components of ATE correspond to the ones of critical mechanical resonant vibration. In the proposed approach, therefore, a variable notch filter with free parameters of frequency and damping is designed to suppress the resonant vibrations during transient response, considering the sensitivity characteristics of the feedback system. The proposed control has been verified by numerical simulations and experiments for a uni-link robot arm.

S112012 焼入れ歯研削ホイールでの鼓形ウォームギヤの角度伝達誤差性能

The development of new hourglass worm gear set which wheel material was hardened steel and its surface was ground by CBN deposited grinding wheel was challenged. The result performance of load carrying capacity and efficiency were not so good as expected, but the performance of the angular transmission error was astonishingly well. And the reason was searched and reported here.

Modeling and Compensation for Angular Transmission Error in Harmonic Drive Gearings (1st Report)

The research deals with a novel modeling and compensation approach for the transmission error in harmonic drive gearings. This paper, as the first report, presents a mathematical modeling framework for nonlinear components in the gearing, where nonlinear friction, nonlinear elastic characteristic, and angular transmission errors are handled to provide a precise numerical simulator. In the modeling of transmission errors, physical phenomena due to nonlinear elastic deformations in micro-displacement region are especially dealt with, as well as the synchronous component which has been already discussed in a variety of conventional studies. Based on the analyses of the phenomena, the nonlinear elastic component can be mathematically formulated by applying a modeling approach for the rolling friction with hysteresis attributes. Numerical simulations and experimental results using a prototype show the effectiveness of the proposed modeling.

Modeling and compensation for angular transmission error in harmonic drive gearings

AbstractThis paper presents a novel modeling and compensation approach for the angular transmission error in harmonic drive gearings. In the modeling, physical phenomena of the transmission error due to nonlinear elastic deformations in micro‐displacement region are especially dealt with, as well as the synchronous component which has been discussed in a variety of conventional studies. On the basis of the analyses of the phenomena, the nonlinear elastic component is mathematically modeled by applying a modeling framework for the rolling friction with hysteresis attributes. The proposed transmission error model has been adopted to the positioning system as a model‐based feedforward compensation manner. Experimental results using a prototype show the effectiveness of the proposed modeling and compensation. Copyright © 2009 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

IND-01 M-MATE(MEASURING-MACHINE FOR THE ANGULAR TRANSMISSION ERROR)(INDUSTRIAL SESSION)

M-MATE (Measuring Machine for the Angular Transmission Error) is the systems which measure the performance of gears including the angular transmission error (ATE). The Performance of M-MATE is changed by the selection of parts. It is possible that the System accuracy of ATE is less than ±2arc-sec or the measuring rotational speed of the input shaft is more than 1000rpm. M-MATE can measure not only ATE but also the rotational fluctuation generated by gears, backlash and shaft torque simultaneously. *1 [arc-sec]=1/3600[deg]=4.85 [μrad]

ESTIMATING SIZE OF GEAR TOOTH ROOT CRACK USING EMBEDDED MODELLING

This paper describes an embedded modelling approach for identifying gear meshing stiffness from measured gear angular displacement or transmission error. An embedded model integrating a physical based model of the gearbox and a parametric representation, in the form of truncated Fourier series, of meshing stiffness is established. A solution method is then used to find the meshing stiffness that minimises the discrepancy between model output and measured output. Furthermore, an algorithm is also developed to estimate the size of tooth crack from identified meshing stiffness. Both simulation and experimental studies were conducted to evaluate if identified tooth meshing stiffness can reveal a tooth crack more effectively, and if the crack size can be estimated with an adequate level of accuracy.

Corrections to "robust speed control system considering vibration suppression caused by angular transmission error of planetary gear"

Corrections to "robust speed control system considering vibration suppression caused by angular transmission error of planetary gear"

Robust speed control system considering vibration suppression caused by angular transmission error of planetary gear

This paper proposes a new robust speed control to suppress vibration caused by angular transmission error of planetary gears. For this purpose, this paper first constructs a new numerical simulation model of angular transmission error of planetary gear, which is confirmed by experimental data from a robot arm. Next, in order to suppress the vibration caused by angular transmission error, we propose a robust speed control system based on disturbance observer and coprime factorization. Numerical simulation results show that the proposed system regulates the angular speed of motor satisfactorily, and it suppresses the vibration caused by angular transmission error.

328 はすば歯車の歯面精度と偏心による回転伝達誤差

328 はすば歯車の歯面精度と偏心による回転伝達誤差

Gear fatigue crack size estimation using embedded modeling

This paper describes an embedded modeling methodology for identifying gear meshing stiffness from measured gear angular displacement or transmission error. An embedded model integrating a physical based model of the gearbox and a parametric representation, in the form of truncated Fourier series, of meshing stiffness is established. A solution method is then used to find the meshing stiffness that minimizes the discrepancy between model output and the measured output. Furthermore, an algorithm is also developed to estimate the size of tooth crack from identified meshing stiffness. Both simulation and experimental studies were conducted to evaluate if identified tooth meshing stiffness can reveal a tooth crack more effectively, and if the crack size can be estimated with an adequate level of accuracy. [Work supported by ONR under the Multidisciplinary Research Program of the University Research Initiative.]