A harmonic drive is a two gear epicyclic drive with a gear set of circular ring gear (RG), a flex rimmed external toothed gear (FG) and an oval cam. FG, with oval cam inside, takes non-circular gear shape encounters improper teeth mating with RG, having only two teeth difference. Consequently, interferences occur at several tooth pairs even at no load. These are inherent and obvious. Overcoming such interferences and further with applied load estimation of load sharing by tooth pairs poses a complex problem. In solving it, first, tooth stiffness of internal gear and external gear are derived in the present investigation. A method of estimating the load shared by the multiple tooth pairs in contact is proposed. The load distribution pattern in proportion to the tooth deformation is considered. Load shared by contacting tooth pairs is estimated and stresses in FG cup are found out using FEM. Finally, such results are compared with experimental results, which have good agreement.

Load sharing by tooth pairs in involute toothed harmonic drive with conventional wave generator cam

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

Modeling and analysis of pure kinematic error in 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

Originally fixed and uniform circular pitches of flex spline (FS) teeth of a ‘Strain Wave Gearing’ or ‘Harmonic Drive’ (HD) experience variations in pitch lengths when teeth move on ‘strain wave ge...

An investigation on secondary force contacts of tooth pairs in conventional harmonic drives with involute toothed gear set

The present paper aims at review on different aspects of harmonic drive gear to identify literature gap for future research. The present article is started first making the comparative study of harmonic drive gear over conventional gear, highlighting its historical background, its application, limitation etc. and then describing working principle of each and every components of it with detail dimensioning and modelling. The present article is further extended to study the different design aspects i.e. synthesis of tooth profiles, lubrication, stress, strain, torque, load sharing, kinematics error and vibration in details etc., identifying problems and then suggesting future perspective for the performance improvement of harmonic drive gear.

Design aspects of harmonic drive gear and performance improvement of its by problems identification: A review

Purpose




In a harmonic drive during assembly of its components like strain wave generating (SWG) cam, flexspline (FS) and circular spline, a gap is formed between the cam’s outer surface and the FS cup inner surface due to mismatching. This gap, which is known as “Coning”, plays a vital role in the flow of lubricant at that interface. This paper aims to analyse the coning phenomenon and the lubrication mechanism.




Design/methodology/approach




In the present investigation, the geometry of the coning gap and its variation with the SWG cam rotation are established. Essentially, the deflection of FS cup and deformation of SWG cam (bearing outer race) are derived to find the gap due to coning. Next, the hydrodynamic lubrication equation is solved to get pressure profiles for this gap under suitable boundary conditions assuming non-Newtonian lubrication.




Findings




Methods of estimating the coning gap and lubrication pressure profiles are established. Effects of non-Newtonian terms (coupling number and non-dimentionalized characteristic length) and SWG length (finite, long and short) on pressure profiles are also shown. All analyses are done in non-dimensionalized form.




Originality/value




Establishing the geometry of coning and non-Newtonian hydrodynamic lubrication aspects in the coning in the FS cup and SWG cam interface are the originality of the present investigation.

Analysis of coning and lubrication at flexspline cup and cam interface in conventional harmonic drives

A split cam design is proposed to solve the problem of assembly of the single piece cam in the flexible raced bearing of an earlier proposed novel harmonic drive system, which shows better torque c...

Design and development of strain wave generating cam for a new concept ‘harmonic drive’

Circular pitches of flex spline teeth of a ‘Strain Wave Gearing’, also known as a ‘Harmonic Drive’, are deformed when the Strain Wave Generating Cam is inserted into the flex spline cup. In the present work the deformed pitch distances considering that flex spline teeth remain rigid while the rim deforms, are estimated. No applied load is considered. It is also shown that if the cam is elliptical then the pitch curve is not an ellipse and vice versa. Geometries of such curves can be defined following the analysis presented in this paper. Cases of both undeformed flex spline with circular spline and deformed flex spline with circular spline, with involute teeth, are considered to find out tooth positions. Geometries of involute teeth profiles in mesh are examined and compared considering oval shaped (on deformation) base drum of flex spline where as base circle of circular spline remained circular.© 2011 ASME

Bikash Routh

Papers

An investigation on secondary force contacts of tooth pairs in conventional harmonic drives with involute toothed gear set

Design aspects of harmonic drive gear and performance improvement of its by problems identification: A review

Analysis of coning and lubrication at flexspline cup and cam interface in conventional harmonic drives

Design and development of strain wave generating cam for a new concept ‘harmonic drive’

On a Gearing Problem in Conventional Harmonic Drives With Involute Toothed Gear Set