This application is a national stage of International Application No. PCT/MD2020/000004, filed Nov. 19, 2020, which claims the benefit of Republic of Moldova Application No. a 20190101, filed Dec. 31, 2019, in the State Agency on Intellectual Property (AGEPI).
The present invention relates to mechanical engineering, namely, to precessional planetary transmissions.
A precessional gear transmission is known wherein a satellite wheel has teeth with a rectilinear profile, and a central wheel with a circular arc profile with the radius origin placed on a normal raised from the contact point of mating teeth passing through an intersection point of a tooth evolute slope line with a circular arc profile with a rectilinear profile equidistance.
A disadvantage of the studied transmission is in the execution of the tooth profiles with approximation, which leads to a diminution of kinematic precision of the transmission and the mating of teeth with a presence of frictional sliding between a flanks of the mating teeth, which implies an increase of energetic losses in the gear and a decrease in mechanical efficiency.
A precessional gear transmission of conical bolts is also known, including a body, a crankshaft and a coaxially driven shaft, a satellite wheel with two bevel gear rings installed on an inclined portion of the crankshaft between two central bevel wheels, one immobile fixed in the body and the other mobile mounted on the driven shaft, wherein the satellite wheel rings are made of conical bolts, assembled with springs between them, which provide axial and radial flotation to gear rings, and, consequently, diminish the impact of the execution and mounting errors on the load distribution in the bolt gear.
An embodiment of the precessional transmission with bolt gear has disadvantages which limit the extension of its use by the following:
The technical problems in creating a precessional gear transmission, produce an increase in the load-bearing capacity and mechanical efficiency, extension of kinematic and functional possibilities, as well as extension of the scope of transmission.
The present invention, according to a first embodiment, removes the aforesaid disadvantages by comprising a body, a crankshaft and a coaxially driven shaft, a satellite wheel with two bevel gear rings installed on an inclined portion of the crankshaft between two central bevel wheels, one immobile fixed in the body and the other mobile mounted on the driven shaft. The novelty here lies in that the teeth engage in contacts with convex-concave geometry, wherein the central bevel wheels are made with straight teeth and have curvilinear flank profiles with variable curvature with one tooth less than the satellite wheel rings made with circular arc flank profiles, the teeth flanks mate with frontal overlap εf within the limits 1.5 ≤εf≤4.0 simultaneously engaged pairs of teeth, at the same time the gearwheels are made with the conical axoid angle within the limits 0°≤δ≤30°, with the angle between the axes of the crank and the central bevel wheels within the limits 1.5°≤θ≤7° and an angle at a center of precession of a radius of curvature of the profile of the teeth in the circular arc of the wheel bevel gear rings of the satellite wheel being within limits of 2°≤β≤7° and the circular arc radius r of the flank profile of a Z-toothed satellite wheel gear ring is within the limits 1.0 D/Z [mm]≤r≤1.57D/Z [mm], where D is the mean diameter of the gear and Z is the number of teeth of the bevel gear ring, which generally provides a reduction of the difference in the curvatures (ρki−r) of the flank profiles in the section with diameter D within the limits 0.02D/Z [mm]≤(ρki−r)≤1.5D/Z [mm], of the pressure angle α between the flanks of up to 15° as well as a decrease in the relative friction velocity between the mating flanks.
Second, the wheel teeth are made inclined, which provides an increase in the total length of the contact lines with their gradual entry into the gear field and an increase in the share of pure rolling of the engaged teeth flanks with sphero-spatial interaction.
Third, one of the satellite wheel bevel rings with the conical axoid angle δ=0° is made of bolts with one less or more than the number of central bevel wheel teeth with which it engages, which provides a pressure angle between the mating flanks α≤45° and the extension of kinematic possibilities.
Fourth, one of the satellite wheel rings with the conical axoid angle δ>0° is made of conical bolts with one less than the number of central bevel wheel teeth and with a profile angle α>45°, which provides for the rolling of the conical bolts on the flank profile of the central wheel teeth with inclined slope effect and the operation of the transmission in a multiplier mode.
Fifth, the satellite wheel is installed on a spherical support placed on the driven shaft in its center of precession and coaxially with the mobile central bevel wheel, at the same time the satellite wheel is equipped with a semi-axle, at the end of which is mounted a bearing, kinematically coupled with the crankshaft.
The precessional gear transmission, according to a second embodiment, comprises a body, a coaxial crankshaft and driven shaft, a satellite wheel with two bevel gear rings, mobile and immobile central bevel wheels.
The transmission with precessional gear, according to the second embodiment, includes a housing, a crank shaft and a coaxial driven shaft, a satellite rate with two conical gear crowns, and movable and immobile center conical wheels.
The novelty here lies in that the transmission includes at least two satellite wheels kinematically interconnected in series by means of at least an intermediate crankshaft installed in cantilever on bearings in a body, which is laterally equipped with an offset seat at a nutation angle θ with the common axis of the central wheels, the first satellite wheel by means of a bearing mounted on an end of its semi-axle is kinematically coupled with the crankshaft, and the second satellite wheel by means of a bearing mounted on the end of its semi-axle is kinematically coupled with the offset seat of the intermediate crankshaft at the nutation angle θ with the common axis of the central wheels.
The technical result includes:
These and/or other aspects and advantages of the invention will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
A precessional gear transmission according to an embodiment includes a body, a satellite wheel with two bevel gear rings installed on the inclined portion of the crankshaft between two central bevel wheels, one immobile fixed in the body and the other mobile mounted on the driven shaft. The teeth gearing is performed in contact with convex-concave geometry. The central bevel wheels are made with curvilinear flank profiles with variable curvature with one tooth less than the satellite wheel gear rings made with circular arc flank profiles. The teeth flanks mate with frontal overlap εf within the limits 1.5≤εf≤4.0 simultaneously engaged pairs of teeth. At the same time the gearwheels are made with a conical axoid angle within the limits 0°≤δ≤30°, with the angle between the axes of the crank and the central bevel wheels within the limits 1.5°≤θ≤7°. The circular arc radius r of the flank profile of the Z-toothed satellite wheel gear rings is within the limits 1.0 D/Z [mm]≤r≤1.57D/Z [mm], which generally provides a reduction of the difference in the curvatures (ρki−r) of the flank profiles in the section with diameter D within the limits 0.02D/Z [mm]≤(ρki−r)≤1.5D/Z [mm] and a decrease in the pressure angle α between the flanks of up to 15°, as well as a decrease in the relative sliding velocity between the mating flanks.
The bevel gear rings 3 and 4 of the satellite wheel 2 have teeth with circular arc flank profiles, and the central bevel wheels 6 and 7—variable curvilinear, depending on the angles θ and δ, the circular arc radius r, the number and the ratio of the numbers of teeth of the gears (Z1-Z2) and (Z3-Z4), the configuration of the numerical values which influence the change of the teeth profile shape, determines their degree of frontal overlap, expressed by the number of simultaneously engaged pairs of teeth εf, the size of the pressure angle α between the mating flanks and the frictional sliding velocity between the flanks.
The following approaches to the creation of a precessional gear with gearwheels shown in
The precessional gear transmission according to the invention operates in the following way: upon rotation of the crankshaft 5, the satellite wheel (
The difference in the number of teeth of the engaged wheels is only one tooth, and the numerical ratio of teeth is:
Z1=Z2−1 and Z4=Z3−1 (1)
Due to the fact that the central bevel wheel 6 is fixed in the body 1, and the central bevel wheel 7 is mounted on the driven shaft 8, when rotating the crankshaft 5 with the electromotor rotational frequency, the driven shaft 8 will rotate with reduced rotational frequency with the transmission rat iHVb:
Generally, when transmitting the motion and load through the gears (Z1-Z2) and (Z3-Z4) with the ratio of the numbers of teeth Z1(4)=Z2(3)±1, the direction of rotation of the driven shaft 8 coincides or not with the direction of the input crankshaft 5.
If Z2>Z3, the crankshaft 5 and the driven shaft 8 rotate counterclockwise, and if Z2<Z3, rotate in the same direction.
Frontal multiplicity of the mating wheel teeth gearing in the precessional transmission is determined by three interdependent constructive-kinematic conditions:
It was found that the absolute multiplicity of gearing (100%) with the compliance of the three conditions can only occur when using the variable convex/concave profile of the teeth flanks, usually of the central wheels, depending on the values of the conical axoid δ and nutation θ angles of radius r of the curvature of the teeth profiles of the satellite wheel gear rings, as well as on the number of teeth of the wheels Z and their ratio ±1 (see
The load-bearing capacity and mechanical efficiency of the precessional gear transmission, according to the invention, are increased by achieving the following technical solutions:
The constructive-kinematic conditions and the distinctive technical solutions mentioned above, constitute the basis for the development of the precessional gear transmission, for both the power transmissions shown in
The elaboration of the precessional gear transmission in the embodiment according to the invention, cover the following approaches and technical solutions:
1. Creation of the Contact with Convex-Concave Geometry Between the Flanks of the Teeth with Small Difference of Curvatures.
For creating the convex-concave contact of the engaged teeth with sphero-spatial motion, the profile of the satellite wheel teeth 2 is described by an arbitrary curve LEM, for example, in circular arc of radius r with the origin in point G (
From the Euler equations, taking into account the kinematic relation between the angles σ and ψ expressed by σ=−Z1/Z2ψ, we obtain the coordinates of the origin G of the circular arc radius XG, YG, ZG depending on the rotation angle ψ of the crankshaft:
The origin G of the circular arc radius, with which the teeth of the satellite wheel 2 gear rings 3 and 4 are arbitrarily described (see
The path of motion G of the circular arc LEM on the sphere with radius R is projected on the plane P1 using the rules of spherical trigonometry. Thus, it is obtained the path TG of motion of the origin of the circular arc G radius on the plane P1, expressed by the dependence ζ=f(ξ1).
Knowing the path of motion of the origin of the circular arc G radius, expressed in the coordinates XG, YG, ZG (
The family of contact points E obtained in a precession cycle 0≤ψ≤2πZ3/Z4 represents the profile of the teeth of the immobile 6 or mobile 7 central wheels.
To describe the flank profiles of the teeth of the central wheels 6 and 7, the projections of the velocity vector VG on the coordinate axes of the mobile system OX1Y1Z1 are determined depending on the angular velocity of the crankshaft 5 (see
To determine the position of the contact point E of the teeth on the spherical surface, we identify the equation of a plane P2 drawn perpendicular to the velocity vector VG, passing through the center of precession O and the origin of the circular arc radius G. The equation of plane P2 can be written by the expression:
[OG×OC]×VG=0, (6)
where OG and OC are vectors that determine the position of the origin of the circular arc radius of curvature of the satellite tooth G and, respectively, of an arbitrary point C of plane P2 with respect to the origin of the immobile coordinate system OXYZ (
The vectorial product [OG×OC] (6) is expressed as a third-order determinant, and by opening it according to the elements of the first line, we obtain:
[OG×OC]=i(YGZ−ZGY)+j(ZGX−XGZ)+k(XGY−YGX), (7)
wherein XG,YG,ZG are the coordinates of the origin of the radius of curvature G of the circular arc profile of the satellite wheel teeth; X,Y,Z—the coordinates of the arbitrary point C on the plane P2.
If the contact point of the teeth E is placed on the sphere with the radius R, then its coordinates satisfy the equation:
XE2+YE2+ZE2−R2=0. (8)
From
OG·OE=R2 cos β (9)
or
XEZG+XEYG+ZEZG−R2 cos β=0. (10)
From the equation (12) we determine:
XE=(R2 cos β−YEYG−ZEZG)/XG. (11)
To determine the coordinate YE of the contact point of the teeth E, we substitute (11) in (8) and obtain:
YE=k1ZE−d1, (12)
and by substituting (12) into (11), we obtain the expression of the contact point coordinate XE:
XE=k2ZE+d2, (13)
where
k1=[XG(XG·{dot over (X)}G+YG{dot over (Y)}G )+ZG2{dot over (X)}G]/(XG{dot over (Y)}G−YG{dot over (X)}G)ZG
d1=R2 cos β{dot over (X)}g/(XG{dot over (X)}G−YG{dot over (X)}G)
k2=−(k1YG+ZG)/XG
d2=(R2 cos β+d1YG)/XG. (14)
Substituting (12) and (13) in (8) and, considering that the profile curve of the central wheel teeth is equidistant from the path of motion of the origin G of the circular arc radius, and for any rotation angle ψ of the crankshaft 5, the condition ZE<ZG must be met, the coordinate ZE can be determined by the relation:
Relationships (12), (13) and (15) determine the coordinates XE, YE and ZE of the contact point E of the teeth, the set of which in a precession cycle represents the flank profile of the central wheel teeth, placed on the sphere of radius R.
From the analysis of equations (12), (13) and (15), we state that the flank profile of the central wheel teeth is variable depending on the number of teeth Z2, the ratio of the numbers of teeth of the engaged wheels Z1=Z2−1 or Z1=Z2+1, the conical axoid δ, nutation θ and contact angles at the center of precession of the radius of curvature of the circular arc profile β of the satellite wheel teeth.
The precessional gear being bevel, with the extensions of the generators intersected in the center of precession, it is appropriate to render the teeth profile in normal section, for example, in the plane P1 drawn by the points E1 and E2 perpendicular to the plane OE1E2 (
The coordinates XE,YE and ZE of points E1 and E2 on the teeth profile on the sphere are determined from the relations (12), (13) and (15) for the angles of precession ψ=0 and ψ=2πZ2/Z1, corresponding to a precession cycle.
Using the rules of spherical trigonometry, we design the teeth profile on the sphere with the radius R on the plane P1.
To design the profile of the central wheel teeth in two coordinates ζ and ξ in the plane P1 we draw the coordinate system E1ξζ with the origin in point E1, whose axis E1ξ passes through point E2 (
The expressions (16) represent the coordinates of the curve points, whose family constitute the flank profile of the central wheel teeth, designed on the plane P1, expressed in parametric form with the variation of the precession angle from ψ=0 to ψ=360·Z2/Z12[°].
To design the path of motion of the origin of the circular arcs G in 2D, we pass from coordinates XN, YN and ZN to Cartesian coordinates ξ1, ζ1 using the relations:
Function ξ1 of ζ1 (17) represents the projection of the path of motion of the origin of the circular arcs G on the plane P1, and function ξ of ζ (16) represents the flank profile of the central wheel teeth projected on the plane P1.
The value configuration of parameters Z, r, δ and θ influences the shape of the flank profile of the central wheel teeth and provides for the teeth front reference gear of up to 100% simultaneously engaged pairs of teeth. In the precessional transmission shown in
2. Transformation of Teeth Contact Geometry into the Precessional Gear Depending on the Angle of Precession ψ and Distinctive Solutions for Creating the Convex-Concave Contact with Small Difference of Curvatures.
The profiles of the central wheel teeth are presented by the functions ζ=f(ξ) constructed according to the relations (17), and of the satellite teeth are prescribed in circular arc with radius r.
The generalizing shape parameters of the teeth contact in the gears of the mechanical transmissions are the radius of equivalent curvature of the teeth profiles and the difference parameters of the curvatures of the mating flanks.
In designing the teeth contact geometry in the precessional gear, it was admitted that LEM is a circular arc shaped-curve (
To address the degree of influence of the gear geometric and kinematic parameters on the teeth contact geometry and the kinematics of their contact analyses for gears with concrete parameters will be presented.
In the sphero-spatial movement of the satellite wheel, in the position of the crankshaft 5 with the precession angle ψ=0°, the satellite teeth circular arc profile LEM comes in contact with the active profile of the central wheel teeth E1EC in point E (
Geometrically, the location of the contact points E (
The positions of the origins of the circular arcs G placed on the curve ζ1=f(ξ1), denoted by p. 1, 2, 3 . . . i, correspond to the precession angles ψ of the crankshaft increasing from one pair of teeth to another with the angular pitch ψ=360·Z2/Z12[°].
Depending on the satellite precession phase, determined by the precession angle ψ of the crankshaft, each pair of satellite—central wheel teeth passes through three geometrical contact forms, namely from convex-concave in contacts k0, k1 and k2, located in the dedendum area of the central wheel teeth, to convex-rectilinear in contacts k3 and k4, located in the passage area of the central wheel teeth profile from concave curvature to convex and convex-convex curvature in contacts k5 . . . k14 (
According to the invention, for increasing the load-bearing capacity of the teeth contact, a convex-concave geometrical shape is proposed, and considering the classical theory of contact between deformable bodies, the difference of the radii of curvature of the conjugated tooth flank profiles should be minimal. This feature in precessional gear transmissions is achievable by two interdependent solutions: first—by varying, selecting the configuration of parameters Z1, Z2, δ, θ and r, which determines the shape of the central wheel tooth profile, and second—by excluding from the gear the pairs of teeth with convex-convex and/or convex-rectilinear geometrical contact, with extension of the teeth contact area with convex-concave geometry.
From the analysis of
Modifying the shape of the central wheel tooth by shortening its height (
Based on the computer simulations on virtual models, it was found that when varying the precession angle of the crankshaft 0≤ψ≤37°, the convex-concave contact is provided in the engaged pairs of teeth in the contacts k0, k1, k2 and k3, presented in the tooth profilogram evolute in
Thus, for example, for the gear with geometric parameters Z1=29, Z2=30, R=75 mm, r=5.0 mm, θ=2.5°, δ=30°, β=3.8°, the teeth contact has the following geometry (
By varying the parameters Z, β, δ, θ and the tooth ratio ±1 by changing the shape of the central wheel teeth, a single, two-pair, three-pair or four-pair precessional toothed gear is designed. In the three-pair gear shown in
When the crankshaft rotates, each pair of teeth in contacts ki performs an improvised motion along the same path, moving imaginary, for example, from contact k0 of the satellite tooth on the bottom of the central wheel tooth (
In classical mechanical transmissions, to provide the transformation of motion with constant transmission ratio, it is necessary that when one pair of teeth disengages, the preceding pair is already engaged, thus the degree of overlap ε>1 is provided.
In the precessional toothed gear shown in
According to
It is worth mentioning that analogously with the precessional toothed gear with four simultaneously engaged pairs of teeth shown in
3. Influence of the Ratio of the Numbers of Teeth of the Mating Wheels on the Linematics of the Contact Point and Shape of the Tooth Flank Profile.
In precessional toothed gears, unlike those with bolts, the transformation and transmission of motion and load occur with the presence of relative frictional sliding between the teeth flanks, depending on the kinematics of the teeth contact point, in particular on the ratio of the numbers of teeth of the mating gear rings Z1=Z2−1 or Z1=Z2+1 .
Therefore, the calculation and design of precessional toothed gears, unlike classical, including precessional toothed gears with bolts, include a separate algorithm for designing the teeth contact geometry, which generally defines the load-load-bearing capacity and mechanical efficiency of the transmission.
The design of the teeth contact geometry from the precessional toothed gear is limited to the identification of the contact form (see
4. Reduction of the Pressure Angle Between the Mating Flank Profiles.
From
Unlike the classical ones, in the precessional gear transmission, the profile of the central wheel teeth is variable, which leads to the variation of the teeth contact geometry in one and the same gear, passing from one form to another, namely from convex-concave at the dedendum of central wheel tooth to convex-rectilinear towards the middle of the tooth and convex-convex towards the tip of tooth.
5. Relative Sliding Between the Teeth Flanks in Gear.
The kinematics of the teeth contact point in precessional gears and the geometric shape of the mating flanks are two determining characteristics of the mechanical efficiency and the load-load-bearing capacity of the contact.
The mechanical efficiency of the gear is the expression of energy losses generated by the frictional sliding forces between the mating flanks, and the load-bearing capacity of the convex-concave contact results from the size of the difference in their radii of curvature.
For these reasons, the gear contact kinematics and geometry (
The analysis of kinematics in the contact points k0, k1, k2 . . . ki corresponding to the crankshaft positioning angles takes place by varying the linear velocities of the contact points E1 on the central wheel teeth profile and E2 on the satellite teeth profile and the relative sliding velocity between the flanks , and the teeth contact geometry is presented through the radii of curvature ρk
Thus, in the gear Z, δ, β, θ with the ratio of the numbers of teeth Z1=Z2−1 and the conical axoid angle δ=22.5°, shown in
As the angular coordinate increases from one mating pair to the other with the pitch ψ=360iZ2/Z1[°], for example, from the angular coordinate ψk
Table 1 presents the argumentation and justification of the limits of variation of the frontal overlap degree values εf of the pairs of teeth that are concomitantly in the gear field, of the conical axoid angle δ, of the nutation angle θ between the axes of the crank and central conical wheels, as well as of the circular arc radius r of the flank profile of Z teeth of the satellite wheel gear ring in the section with diameter D, which generally provides for the mating of teeth in convex-concave contact and the reduction in the difference of curvatures of the mating flanks and the relative sliding velocity in the teeth contacts.
Argumentation of the Limits of Variation of the Precessional Gear Parameters According to the Invention
Variation of the frontal overlap within the limits 1.5≤εf≤4.0 pairs of teeth that are concomitantly in the gear field, of the bevel axoid angle within the limits 0°≤δ≤30° and of the nutation angle within the limits 1.5°≤θ≤7°, as well as of the circular arc radius r of the tooth flank profiles of the satellite wheel gear rings within the limits 1.0 D/Z [mm]≤r≤1.57 D/Z [mm], provides for the existence of convex-concave geometry in the contacts of the pairs of teeth located in the gear area with the decrease in the difference of curvatures (ρki−r) of the flank profiles in the section with diameter D within the limits 0.02D/Z [mm]≤(ρki−r)≤1.5D/Z [mm] and of the pressure angle α between the flanks by up to 15°, as well as the decrease of the relative sliding velocity between the mating flanks.
These technical solutions favor the increase of the load-bearing capacity and mechanical efficiency of the transmission.
Another difference of the transmission, wherein the wheel teeth are made inclined, which provides an increase in the total length of the contact lines with their gradual entry into the gear field and an increase in the share of pure rolling of the engaged teeth flanks with sphero-spatial interaction is that the teeth of the fixed 6 and mobile 7 central wheels, as well as of the gear rings 3 and 4 of the satellite wheel 2, are inclined. This provides for the increase of the pure rolling share of the engaged teeth flanks with sphero-spatial interaction dependent on the nutation 9 and inclination β angles, and the increase of the total length of the contact lines, with their gradual entry into the gear field.
The total teeth contact line lΣ in the gear with inclined teeth is determined from the condition of frontal gear εf of a certain number of pairs of teeth (εf=1, 2, 3 . . . ), but not less than one pair (εf,min=1). In the case of εf,min=1, it turns out that a pair of teeth engages, while the previous pair disengages.
According to the condition of providing continuity of gear and the slow course of the transmission, it is necessary that the tooth overlap degree be εm>1. Thus, in the case of εf,min=1, it is proposed to incline the teeth at the angle βg, which would ensure a degree of longitudinal (axial) overlap.
From the analysis of the succession of the entry and exit of the tooth pairs from the gear area, we state that the degree of overlap of the engaging teeth and, respectively, the total length of the contact lines of the engaged teeth depend on the frontal overlap εfβ, determined by the frontal gear multiplicity εf and the longitudinal overlap εα dependent on the teeth inclination angle βg, including the configuration parameters Z, δ, θ and the ratio ± of the mating teeth, and on the modification of the teeth height. It is also observed that the contact lines between the inclined teeth are positioned in space so that their extensions are tangent to the cylinder with radius e.
It should be mentioned that the inclination of teeth leads to a diminution of the frictional sliding in the engaged teeth contact, because the teeth mating for the same parameters of the configuration Z, δ, β, θ and Z1=Z2∓1 takes place with an increased share of pure rolling of teeth depending on the angle θ.
Unlike straight teeth, the inclined ones do not engage concomitantly along the entire length, but gradually with a certain angle offset ψ depending on the inclination angle β and the tooth length bw.
The position of contact lines in the gear with concave-concave contact of the teeth inclined within the limits of the gear field is shown in
In
When the crankshaft positioning angle Δψ is increased (
In the case of gearing with two pairs of teeth in frontal gear εf=2 shown in
In the precessional gear, the inclined teeth are loaded gradually, as they enter the gear field, and in permanent gear there are at least two pairs of teeth:
εm=εfβ+εαβ. (19)
The precessional gear with inclined teeth can also work without frontal overlap, thus with εfβ>1, if the axial overlap εβ is ensured, i.e. bw>(2πZ2)/(Z1tgβ). In the precessional gear with inclined teeth, the load between simultaneously engaged teeth is distributed proportionally to the contact line lengths of the required teeth pairs with load.
Obviously, the specific teeth load q decreases with the increase of the total length of the contact lines lΣ=εmbw sin δ/cos β, and lΣ does not change over time, because decreasing the length of the teeth contact line 1-1′ in any position ψ of the crankshaft is compensated by an equal increase in the length of the contact line 3-3′ (
At the same time, we can state that in gear the convex-concave contact of the mating teeth in the frontal gear (
The maximum effect produced by the inclined teeth of the gear consists in the essential decrease of the relative sliding velocity Val between the flanks (
The optimal choice (see
From the analysis of
The third difference of the transmission (
According to an embodiment, one of the satellite wheel bevel gear rings with the conical axoid angle δ=0° is made of bolts with one less or more than the number of central bevel wheel teeth with which it engages, which provides the pressure angle between the mating flanks α≤45° and the extension of kinematic possibilities. In
Thus, the difference of the transmissions (
According to an aspect, one of the satellite wheel gear rings with the conical axoid angle δ>0° is made of conical bolts with one less than the number of central bevel wheel teeth and with a profile angle α>45°, which provides the transformation of motion and the transmission of load by rolling the conical bolts on the flank profile of the central wheel teeth with inclined slope effect and, respectively, the operation of the transmission in multiplier mode.
A fourth difference is that at least one of the bevel gear rings 3 or 4 of the satellite wheel 2 is made of bolts with one less than the number of teeth of the engaged bevel central wheel and has the conical axoid angle δ>0° (
It is worth mentioning that, according to
This configuration with δ>0° and Z4=Z3+1 provides for the increase of the pressure angle α between the flanks of the central wheel teeth 7 and the toothed crown 4 made in the form of bolts of the satellite wheel 2, which favors, from the point of view of energy losses, the transformation of the rotational motion of the driving shaft 5 (which replaces the function of the crankshaft) in sphero-spatial motion of the satellite wheel 2 by using the inclined slope effect.
Thus, the solution according to
According to an aspect, the satellite wheel is installed on a spherical support placed on the driven shaft in its center of precession and coaxially with the mobile central bevel wheel. At the same time the satellite wheel is equipped with a semi-axle, at the end of which is mounted a bearing, kinematically coupled with the crankshaft. A fifth difference of the claimed transmission is that the satellite wheel 2 (
The precessional gear reducer shown in
The rotational motion of the crankshaft 5 (or the electric motor) is transformed in sphero-spatial motion of the satellite wheel 2 by means of the bearing 11, mounted on the end of the semi-axle 10 of the satellite wheel 2, which, in turn, is mounted in the seat of the crankshaft 5. The satellite wheel 2 involved in the sphero-spatial motion with the frequency of precession cycles respectively with the teeth of the immobile 6 and mobile 7 central wheels. As a result, the driven shaft will rotate with reduced rotational frequency with the transmission ratio
Thus, the technical solutions as disclosed above and in the figures provide for the increase of the load-bearing capacity and mechanical efficiency, as well as the extension of the kinematic and functional possibilities.
The load-bearing capacity of the mechanical transmission gears depends on the degree of overlap and the contact geometry of the engaging teeth.
Based on these considerations, the analysis of the load-bearing capacity of the precessional gear transmission according to the invention, in comparison with the most efficient existing transmissions, for example Wildhaber-Novicov (W-N) shows the following:
It is also worth mentioning that in the gear (W-N), the frontal overlap of the teeth is εf=(0.85−0.95) pairs of teeth, and in the precessional gear transmission according to aspects of the present invention, the frontal overlap of the teeth is εf=(1.5−4.0) pairs of teeth concomitantly in the gear field.
Number | Date | Country | Kind |
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md a 2019 0101 | Dec 2019 | MD | national |
Filing Document | Filing Date | Country | Kind |
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PCT/MD2020/000004 | 11/19/2020 | WO |
Publishing Document | Publishing Date | Country | Kind |
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WO2021/137682 | 7/8/2021 | WO | A |
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Machine-generated English language translation of claims of JP S54120347 A (Sep. 18, 1979). |
English language Abstract of JP S6011749 A (Jan. 22, 1985). |
Machine-generated English language translation of Abstract of SU 1455094 A1 (Jan. 30, 1989). |
Machine-generated English language translation of Abstract of SU 1758322 A1 (Aug. 30, 1992). |
International Search Report in International Application No. PCT/MD2020/000004, dated Mar. 15, 2021. |
Written Opinion of the International Searching Authority in International Application No. PCT/MD2020/000004, dated Mar. 15, 2021. |
English language Abstract of CN 201672005 U (Dec. 15, 2010). |
English language Abstract of CN 201412479 Y (Feb. 24, 2010). |
English language Abstract of MD 471 B1 (Sep. 30, 1996). |
English language Abstract of MD 495 B1 (Oct. 31, 1996). |
English language Abstract of MD 2729 B1 (Mar. 31, 2005). |
English language Abstract of MD 4354 B1 (Jun. 30, 2015). |
English language Abstract of MD 2177 B1 (May 31, 2003). |
English language Abstract of MD 20010368 A (Jun. 30, 2004). |
English language Abstract of RO 116120 B1 (Oct. 30, 2000). |
English language machine translation of Abstract of RU 2054592 C1 (Feb. 20, 1996). |
Search Report in related Moldovan Application No. a 2019 0101, dated Sep. 29, 2021. |
Number | Date | Country | |
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20220412437 A1 | Dec 2022 | US |