Rathindranath Maiti

A Novel Harmonic Drive With Pure Involute Tooth Gear Pair

Consider commercially available harmonic drives or strain wave gearings (all patented designs). The tooth profiles of the mating pairs of teeth of the noncircular (pitch curve) flex gear and circular (pitch circle) ring gears are nearly conjugate and noninvolute. Evidently none of them offers ideal gear kinematics. In this paper, we propose a new wave generator (or cam) to drive flex gears of harmonic drives with fully conjugate gear pairs of purely involute profiles. The cam profile is made of circular arcs at the two diametrically opposite contact zones and shifted elliptical curves for the other two zones. The geometric construction is done in such a way that tip interference is properly avoided for both engagement and disengagement with nominally stubbed or full depth tooth involute gears. We develop the theory of geometric and gearing conditions. We have also built a physical model in order to verify the geometry of tooth interference and other relevant gearing kinematics.

Minimum tooth difference in internal-external involute gear pair

Abstract The transmission ratio increases with the decrease in gear ratio of internal-external gear pair in ‘two-gear epicyclic drive’ such as plano-centric, harmonic drives, etc. For an involute tooth the gear ratio, or in other words, the difference between the gear teeth and pinion teeth numbers, cannot be lower than a certain limit because of the tooth tip interference. In the present work an attempt has been made to examine the possibility of lowering the difference as much as possible in the internal-external involute gear pair with the help of simple gear corrections. It is found that by addendum modification the tooth difference can be reduced, though not to unity, from their value with full depth gears. By introducing center distance modification, although this number cannot be reduced further for practical purposes (avoiding tip interference) the contact ratio improves. A mathematical relation has also been established to investigate the conditions of avoiding tip interference when the pinion rim is deflected as in the case of harmonic drives. These analyses enable one in selecting a suitable involute gear pair for its application in two gear epicyclic drive units.

Kinematics of active contact in modified epitrochoid generated rotary piston machines

Abstract Epitrochoids and their associated envelopes are used as rotor-stator (or secondary rotor) elements in rotary piston machines (ROPIMA). Very little published work is available on the analysis and design of such machines with modified epitrochoids. In the present work a kinematic analysis has been carried out to investigate the pattern of rolling and sliding at the load transmitting (active) contact regions. The generalized equations can be used to analyse various type of epitrochoid (unmodified and modified) generated ROPIMAs as well as epitrochoid generated gearing units.

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

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 generating’ oval-shaped cam. This is due to varying root deformations of teeth. In case of teeth with widely used involute profile, away from the contacts on line of action through pitch point, they definitely experience force closeness to or separation from the circular spline’s (CS) originally conjugate tooth. We have estimated the deformed pitch distances at no load considering that FS teeth remain rigid while the rim deforms. The geometry of the oval-shaped pitch curve which is parallel to the elliptical outer profile of the cam is also defined. Similarly to maintain an elliptical pitch curve of FS, the oval cam is also defined. Both cases of tooth mesh of undeformed FS with CS and tooth mesh of deformed FS with CS, 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 FS, whereas the base circle of the CS remained circular.

Static load sharing by tooth pairs in contact in internal involute spur gearing with thin rimmed pinion

Involute toothed internal−external standard gear sets are modeled for load-sharing by the teeth pairs in mesh along the line of contact. An analytical solution is proposed. Considering the rigid body in rotation, it is assumed that angular rotation of a gear with respect to the other gear due to deformation along the line of contact is equal. The sum of the normal loads in all tooth pairs in contacts, which equals to the total transmitted load, is considered constant. All possible deformations such as, tooth bending deflection, tooth compressive (contact) deformation, tooth foundation deflection and tooth shearing deflection are considered in analyses. Detailed tooth geometries are incorporated in modeling. Ultimately, the map of load sharing by tooth pairs in contacts, at different angular position, over a cycle of similar contact pattern, is established. Finally, considering thin rimmed gears, the effects of the rim thickness on load sharing, which is the aim of the present investigation are analyzed and the results are presented in terms of backup ratios.

Unification of epitrochoid origin profile design approaches for external lobed star member used in hydrostatic and gear units

We propose unification of various geometric design approaches, available in the open literatures and published research papers, for profile of star rotor used in rotary piston machines type hydrostatic units, namely pumps and motors. The star rotor profile has cycloidal root. We consider three basic approaches. These approaches are otherwise self-sufficient for profile selection purpose although the end formulae are different in relation to the common parametric terms. A closer scrutiny reveals that the initial selection of co-ordinate systems, profile generating centrode pairs and the location of the generating point lead to such differences. Our unification provides infusion and integration of three different paradigms that we have considered. This investigation is aimed at helping researchers develop a better understanding design approaches of such machines.

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

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 characteristics and capacities in comparison to the conventional one of same size with oval-shaped strain wave generating cam. The cam profile has circular arcs at two working zones at 180° phases. The proposed profile shape is identified as the cause of trouble in assembly if the cam is made single piece. The split cam is made of two identical pieces having circular arc edges. These pieces constitute the cam in assembly after putting it inside the inner race of the flex bearing and adjusted by an adjuster. The design, kinematics, and the assembly method of the proposed split cam are presented in this article. The split cam arrangement not only solves the assembly problem but also gives a scope of fine adjustment of center distance (eccentricity). Such an adjustment is not possible in conventional oval wave generating cam. Stresses in flex gear cups assembled with both type cams at load and no-load conditions are estimated using finite element method. Some results are verified experimentally. Although the flex gear cup with the proposed split cam experiences lower stresses at load transmitting active gear contact zones, it shows higher stresses at some non-active zones (where teeth are free of load). It is apparent from results that stresses at those non-active zones do not increase substantially with the increase in torque, as they are away from active zones.

Evidence of secondary tooth contact in harmonic drive, with involute toothed gear pair, through experimental and finite element analyses of stresses in flex-gear cup:

Stresses in flex spline/gear cup in harmonic drives with involute toothed gear pair and conventional strain wave generating cam are analyzed using finite element method in ANSYS® environment and experiments. The most innovative part of this investigation is establishing the evidence of secondary contacts and probable load shared by those contacts experimentally over the finite element analysis. Aiming at the performance improvement of gearing in harmonic drives, with involute toothed gear pair, the investigations are carried out through the following analyses. (a) Initial stresses in flex gear cup due to cam insertion only. (b) Stresses in flex gear cup at no load in fully assembled harmonic drive components i.e. flex gear, ring gear, and strain wave generating cam. (c) Stresses in flex gear cup at full load passing through the two pitch points, i.e. the intersection points of ring gear pitch circle, flex gear pitch curve, and major axis on both sides. Finally, (d) stresses in flex gear cup at full load distributed over all possible primary and secondary contacts, in proportion to their contact intensities. Recorded strains of the flex-gear cup while the cam being rotated showed very good agreement with the results obtained by finite element analysis with proper modeling of loading.

Aspects of lubrication at the wave generator - flexspline interface in strain wave gearing units

Lubrication aspects, at the Wave Generator (WG)-Flexspline (FS) interface of Strain Wave Gearing or Harmonic Drive (HD), are investigated. Geometries of ‘coning’ of FS and its variation with rotation are established to incorporate in hydrodynamic lubrication equation based on generalized Reynolds equation. Non-Newtonian fluid parameters are also incorporated to cover up analysis for odd lubrication conditions that HD faces in many applications. Effort has been given to develop the analytical expression for separation of lubrication film and other various lubrication conditions at WG/FS interface with respect to few general boundary conditions. Results of analytical solutions are also verified in Ansys-APDL environment.

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

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