Ein erster und ein zweiter ausen verzahnter Verzahnungsbereich (7, 9) eines Verformungswellgetriebes (1) werden durch einen Wellgenerator (10) in eine elliptische Form verbogen, um in ein erstes bzw. in ein zweites innen verzahntes Zahnrad (2, 4) einzugreifen. Der erste und der zweite ausen verzahnte Verzahnungsbereich (7, 9) werden so verbogen, dass sie elliptische Formen haben, deren Phasen um eine Rotationszentralachse (1a) um 90° gegeneinander verdreht sind. Zwischen dem ersten und dem zweiten ausen verzahnten Verzahnungsbereich (7, 9) ist ein ausen verzahntes Kopplungsverzahnungsbereich (8) ausgebildet, der eine kreisformige Querschnittsform behalt, die sich nicht verbiegt. Der ausen verzahnte Kopplungsverzahnungsbereich (8) wird so auf eingreifende Art und Weise mit einem innen verzahnten Kopplungszahnrad (3) gekoppelt gehalten. Das Verformungswellgetriebe (1) hat eine hohe Eingriffssteifigkeit und ist in der Lage, ein groses Drehmoment zu ubertragen.

The strain wave gearing

Accurate description of the elastic deformation of the flexspline is the foundation for optimization design of the structure and conjugate profiles of the harmonic drive gear. This paper proposed an experimental method to investigate the effect of the driving speed on the deformation characteristics of the flexspline. First, an experimental apparatus that integrates a special-fabricated micro-displacement platform and a pair of laser displacement sensors is developed, and the radial displacement of the flexspline is measured in vertical and horizontal directions. Next, the deformation analyses of the flexspline at different driving speeds are performed with our method and the conventional method, and the comparison results reveal that the radial displacement of the flexspline is actually composed of both harmonic and random components, and the amplitude decreases and tends to zero with the increase of the driving speed, especially near the closed end of the flexspline. Last, the mechanisms of the inherent multi-frequency and amplitude attenuation characteristics of the radial displacement of the flexspline are discussed. It is indicated that the impact and friction existing in the flexible bearing of the wave generator is likely responsible for the existence of the random component, and the assumption of linear distribution of the flexspline deformation along the rotating axis is invalid under high speed condition. Our research promotes the further study on the contact-impact problem of the flexible bearing of the wave generator and the transfer characteristic of the elastic deformation of the flexspline.

Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors

Optimal design of wave generator profile for harmonic gear drive using support function

This article studies the causes of the time-varying stiffness of harmonic drive gear and the number of meshing teeth and the meshing length under different torques. Multi-pair tooth meshing charact...

https://journals.sagepub.com/doi/pdf/10.1177/1687814018767494

Simulation of meshing characteristics of harmonic reducer and experimental verification

Harmonic drives are the core components to enable movement in industrial robots. Unfortunately, the deformation of flexspline causes obvious partial axial load on gear engagement. This synthetic error leads to a series of additional problems, such as the deterioration of transmission quality, and the reduction of both precision and fatigue life. This study focuses on a harmonic drive with a double circular-arc tooth profile. A coordinate transformation is carried out based on the kinematics of harmonic drives. On this basis, the conjugate tooth profile of a circular spline is derived. A simulation model is developed based on the motion relationship for harmonic transmission. The effect of inhomogeneity of the load distribution on the surface of the gear teeth was investigated using the partial axial-load index. The effect of different factors on the partial axial load is analyzed. To reduce the effect of partial axial load of flexspline, we select a suitable material and wall thickness. For a certain practical range, both tooth width and chamfering of the flexspline teeth help reduce the partial axial load and increase the flexspline length. These conclusions enable improvements of future designs of reliable flexspline.

Analysis of the Partial Axial Load of a Very Thin-Walled Spur-Gear (Flexspline) of a Harmonic Drive

A lack of accurate description of the meshing characteristics and the corresponding frictional mechanism of the harmonic drive gear has limited progress toward modeling the hysteresis stiffness. This paper presents a method for detection and quantification of the meshing characteristics of the harmonic drive gear based on computer vision. First, an experimental set-up that integrates a high speed camera system with a lighting system is developed, and the image processing is adopted to extract and polish the tooth profiles of the meshed teeth pairs in each acquired video sequence. Next, a physical-mathematical model is established to determine the relative positions of the selected tooth pair in the process of the gear engagement, and the combined standard uncertainty is utilized to evaluate the accuracy of the calculated kinematics parameters. Last, the kinematics analysis of the gear engagement under the ultra-low speed condition is performed with our method and previous method, and the influence of the input rotational speed on the results is examined. The results validate the effectiveness of our method, and indicate that the conventional method is not available in the future friction analysis. It is also shown that the engaging-in phase is approximately a uniform motion process, the engaging-out phase is a variable motion process, and these characteristics remain unchanged with the variation of the input rotational speed. Our method affords the ability to understand the frictional mechanism on the meshed contact surfaces of the harmonic drive gear, and also allows for the dynamic monitoring of the meshing properties.

A method for detection and quantification of meshing characteristics of harmonic drive gears using computer vision

Accurate and efficient analysis of the meshing performance of harmonic drives (HDs) is the core and challenging problem for the improvement of the positioning accuracy of robots. This paper presents an integrated hardware and software system for an automated analysis of the meshing performance of the HD under various operating conditions. First, an optical measurement method based on the principle of periscope is proposed to capture the meshing images at a different driving speed and load torque. Next, a position tracking algorithm based on image processing and pattern recognition is designed to obtain the positions of the flexspline and circular spline teeth in the meshing process. Furthermore, a mathematical model based on the geometric relationship between the flexspline and the circular spline teeth is established to calculate the meshing backlash and depth. Last, the performance and advantages of the proposed method are demonstrated through uncertainty analysis and comparing with the conventional method. The results show that the error of the calculated meshing parameters is close to 0, and 1.59 s are required to track the FS teeth in each video frame with a laptop of 2.6-GHz CPU and 12-GB RAM. Moreover, the total rotation angle of the wave generator and the backlash and depth in the meshing process are seriously affected by the driving speed and load torque. Our method offers an effective tool for the HD manufacturers to examine the quality of products, and the obtained results can help to optimize the tooth profile of the HD.

Automated Analysis of Meshing Performance of Harmonic Drive Gears Under Various Operating Conditions

The invention belongs to the technical field of harmonic drive, and particularly relates to a harmonic drive gear mesh and flexible gear deformation dynamic characteristic testing system which mainly comprises a base, a harmonic wave support, a motor support, a sliding frame and two laser displacement sensor horizontally-moving systems. A servo motor and a harmonic wave sensor are fixed on the motor support and the harmonic wave support respectively, and a high-sped camera is used for recording rotation of a wave generator. Two laser displacement sensors with the horizontal position and the vertical position adjustable are arranged on the sliding frame and used for detecting deformation of a flexible gear. The harmonic drive gear mesh and flexible gear deformation dynamic characteristic testing system is simple in structure and convenient to assemble and disassemble, different sensors and servo motors are selected to test various dynamic characteristics of harmonic wave reducers of different sizes, and a fine adjustment device of a pure mechanical structure is adopted to achieve precise adjustment.

Harmonic drive gear mesh and flexible gear deformation dynamic characteristic testing system

The friction behavior of the harmonic drive (HD) at low speed is investigated in this paper. First, a dedicated experimental setup that integrates a pair of torque sensors is developed, and the friction torque of the HD is measured based on a torque transmission model. The results show that the friction torque of the HD has Stribeck effect at low speed. Further, a Coulomb-viscous-Stribeck friction model is established to replicate the friction behavior of the HD at low speed, and an exact match between the simulation and experimental results proves the validity of the model. Last, a parametric analysis is performed to investigate the dependence of the friction behavior of the HD on different model parameters. It is indicated that the Coulomb friction torque, the maximum static friction torque and the viscous friction coefficient affect the whole, ultra-low and high speed regions of the friction torque-rotating speed curve of the HD, respectively. Our research suggests that the friction loss of the HD can be reduced by applying surface coating and improving lubrication condition in teeth meshing and flexible bearing regions, and it also promotes further studies on friction mechanisms in these regions of the HD.

Donghui Ma

Papers

Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors

A method for detection and quantification of meshing characteristics of harmonic drive gears using computer vision

Automated Analysis of Meshing Performance of Harmonic Drive Gears Under Various Operating Conditions

Harmonic drive gear mesh and flexible gear deformation dynamic characteristic testing system

Investigation of the friction behavior of harmonic drive gears at low speed operation