# Gear mechanism

FIELD: mechanical engineering.

SUBSTANCE: rotor axis of gear mechanism, performing a planetary movement, is displaced relatively to stator axis for distance of engagement eccentricity. As source auxiliary contour ellipse is used, while proportional coefficient k, determining radius of guiding circle, is taken equal to half necessary number of teeth z of wheel (k = z/2), optimal shape of its teeth is provided by rational combination of ellipse shape coefficient λ, equal to relation of lengths of its semi-axes and eccentricity coefficient of auxiliary contour, in form of relation of length of greater ellipse semi-axis to rolling circle radius, while inner and outer profiles are made in form of elliptic profiles from common ellipse contour.

EFFECT: simplified manufacture.

3 cl, 11 dwg

The invention relates to toothed gerotor mechanisms (GM) internal engagement with difference in numbers of teeth of the rotor and stator is equal to the unit. The axis of the rotor GM, performing a planetary motion that is offset from the axis of the stator at a distance of eccentricity of the gear.

GM can be used in various branches of mining as working bodies of pumps, hydraulic motors, compressors, internal combustion engines and reduction gears with straight and helical teeth.

Famous traditional GM with internal vnetsentrenno cycloidal gearing, mechanical profiles which are formed in the General case as envelopes of the equidistant shortened cycloidal Reiki when it is run along the guide circumference [Gyratory mechanism. Asssss 803572 from 08.10.1979] [1].

Known for classic GM limit type with anosovym rotor of circular cross section centroid cycloidal gearing, mechanical profile of the stator which is formed as equidistant trajectory point of a circle rolling on the last rail of the double circle of radius [Screw pumps, Meters, machinery, 1983].

The disadvantage of the traditional GM is the complexity of its original profile, the form of which is given contour diameter in the General case is determined by a combination of five dimensionless geometric parameters the ditch (kinematic relations, factors type of engagement (EPI or Hypo), netsentralnoe, tooth shape and displacement of the slats), which complicates the manufacturing technology (the need for procedures, bias and equidistantly path of Reiki, the acquisition of specialized machines and create special cutters) and the choice of the optimal shape of the profiles described by complex mathematical expressions (combinations of values of the four dimensionless parameters).

The lack of classic GM, the shape of the profiles which depends on a single dimensionless parameter (coefficient form of the tooth), is limited in its applications because of the increased pressure differential between the working chambers due to the smaller number of contact lines between the input and output hydraulic machines, which requires the creation of a high-pressure pump of a significant increase in axial dimension of the working bodies and, as a consequence, additional technological and material costs.

Known GM closest to the proposed is a special case of traditional cycloidal GM with the kinematic ratio of 2:3 (with oval two-pronged rotor)that is used as the working bodies of the single-screw pumps instead of the classic pairs with the kinematic ratio of 1:2 to increase the pressure [2]. The drawback of such GM are also difficulties t is hnologie their manufacture and selection of the optimal form of profiles.

The objective of the invention is to increase the effectiveness of the design and simplification of manufacturing technology working bodies of GM.

The problem is solved by the fact that as the initial contour in the formation GM used the ellipse, and the profile of the working body GM is formed as the outer envelope of the family of ellipses in the initial running-in circles (centroid) of a certain radius depending on the desired kinematic relations.

The invention is further explained in the description and accompanied drawings, in which figure 1 shows the initial position of the starting circle and the auxiliary circuit in the formation of ellipsoidal profile; figure 2-5 shows a schematic education profiles ellipsoidal GM with a different number of teeth (respectively z=3; 4; 5; 6) method of the running of the ellipse; figure 6-8 - profiles chetyrehuhogo working body GM for various values of the coefficient of netsentralnoe (respectively With=1; 2; 3) and the same aspect ratio of the ellipse (λor=1.5); Fig.9-11 - paired profiles GM with the ellipsoidal engagement with the kinematic ratio of 2:3 with different aspect ratio of the ellipse (respectively λ=1,1; 1,5; 2).

Ellipsoidal GM is a notched a pair of internal gears, consisting of paired z_{1}-Tobago outer wheel (the stator is) and z_{
2}-Tobago inner wheel (rotor), the difference in numbers of teeth which is equal to (z_{1}=z_{2}+1), the profiles are formed from the right of the ellipse.

Ellipsoidal profile gears is formed according to the method of test initial circles (figure 1), one of which (of radius r)associated with the source of the auxiliary circuit is located inside the guide (larger radius R=kr, where k is the number varying from 1.5 to 0.5: k=1,5; 2; 2,5; 3; 3,5; 4...) and rolls without slipping, making planetary motion.

Profile gear is an external envelope of the auxiliary circuit.

When profiling ellipsoidal wheels as a source of auxiliary circuit adopted the correct ellipse major and minor axis which are respectively a and b, and the axis of the ellipse coincide with the axes of the rolling circle.

The ellipsoidal shape of the profile hmm given its contour diameter (maximum outer diameter) is completely determined by three dimensionless geometric parameters:

the number of teeth of the wheel equal to twice the ratio of the radii of the initial circles

the aspect ratio of the ellipse is equal to the ratio of the lengths of its semiaxes:

the ratio unicentro the activity of the source circuit, equal to the ratio of the length of the major axis of the ellipse to the radius of the rolling circle of radius one:

Examples of profiles of elliptical gears with different numbers of teeth, obtained by rolling are shown in Fig 2-5. By varying the values of the coefficients λ and (c_{about}you can widely change the shape of the profile. Impact factor netsentralnoe on the form chetyrehuhogo profile shown in Fig.6-8.

Parametric equations of the original auxiliary contour (right ellipse) relative to the moving axes have the basic form:

,

where τ - angular parameter varying in the interval from 0 to 2π.

Family profile of the ellipse during rolling is described by the following coordinates relative to the Central axis associated with the guiding circumference:

X=x_{1}cosϕ-y_{1}sinϕ+H cosϕ_{p},

where N - pupillary distance, H=R-r=(k-1)r;

ϕ_{p}- the angle of rotation axis of the rolling circle figurative movement,

ϕ - the angle of rotation of the rolling circle in absolute motion.

Parametric equation of the ellipsoidal profile (envelope of the family of ellipses) floor is evidence of the substitution in (2) equation of the relationship between ϕ and τto be installed using the main theorem of the engagement.

The diameters of the elliptical wheels on the tops of the projections and depressions of his teeth respectively

The height of the teeth

On the basis of the wheels with the ellipsoidal mesh you can create a GM with different kinematic relation.

In General, when the selected z-tooth ellipsoidal profile, taken as a source, coupled his profile is formed as an external (epithalamia) or internal (Hipotecaria) envelope of the original profile when running the centroid of the wheels, the ratio of the radii of which is selected depending on the kinematic relations GM.

In practice, GM, the teeth of the wheels of the outer element are elastic, it is advisable to use a simplified method of education paired profile, proven in the manufacture of the working bodies of screw machines with a cycloidal rack and pinion gearing, when mated profile is similar to the original method of running from a shared source auxiliary circuit.

In the General case, the condition for conjugacy profiles (condition engage the tops of the projections and depressions) has the following form:

where there is further the index 1 refers to the outer element (stator), 2 - internal (rotor).

In an ideal cycloidal engagement condition (5) is observed only for the centroidal profile (c_{about}=1), i.e. can be implemented in the mechanisms of 1:2.

The rack and pinion gearing for compliance with the conditions (5) take some combination between the displacements contours of Reiki in the education profile of the stator and rotor.

In ellipsoidal engaged with the numbers of teeth of the wheels that differ by one (k_{2}=k_{1}-1), the conjugacy condition (5) in contrast to a cycloidal mechanism can be implemented for GM with any kinematic relationship, if the relationship between the shape factor of the ellipse and netsentralnoe expressed by the formula:

Thus, for education vzaimozavisimikh profiles GM from the General contour of the ellipse coefficients λ and (c_{about}are dependent parameters in the form of an ellipse (with given values of a and λ) radius rolling circumference should be

and the radii of the guides of the circumferences of the stator and rotor, depending on the kinematic relations of the mechanism chosen as follows:

R_{1}=kr; R_{2}=(k-0.5)r.

The numbers of teeth of the wheels of the stator and rotor respectively

z_{1}=2k; z_{2}=2k-1,

and contour diameter (mA is the maximum diameter of the stator) according to (3) and (6) is expressed by dependence

The eccentricity of the gear GM for a given contour of the ellipse does not depend on the kinematic relations:

In the particular case trekhzubogo original path (k=1.5; z_{1}=3) paired profile is the outline of the ellipse.

The greatest practical interest from the point of view of the efficiency of production is ellipsoidal GM with the kinematic ratio of 2:3 (with multiplicity mechanism equal to 2), the cross section of the rotor which is the correct ellipse that can be used in the creation of high-pressure pumps instead of working bodies with kinematic ratio of 1:2.

Used in pump engineering turn out like GM made on the basis of traditional hypocycloidal gearing has the original profile (in this case, the outer profile element)described by the parametric equations:

where c_{about}cΔ, c_{e}- the dimensionless coefficients netsentralnoe, displacement and shape of a tooth.

As you can see, traditional parametric equations of the original profile (7) is much more complicated equations of the ellipse (1), which provides an advantage when designing and manufacturing ellipticus is x working bodies, profiling which does not provide procedures for mixing and equidistantly the auxiliary circuit.

Figure 9-11 presents different versions of the profiles ellipsoidal mechanism 2:3, formed from a common auxiliary circuit and wherein the aspect ratio of the ellipse.

The invention will simplify the process of designing and manufacturing of the working bodies of machines and mechanisms using in their construction of GM, which will create prerequisites for further increasing the efficiency of the use of rotary machines with planar and spatial engaged in various branches of engineering.

Sources of information

1. USSR author's certificate No. 803572, 1979.

2. Balenko J.F. ñ and other downhole drilling motors, Handbook, Moscow, Nedra, 1999, p.20-22.

1. Gyratory mechanism containing the inner rotor and the outer stator in the form of wheels, the teeth of which are in continuous contact with each other and have the difference in numbers of teeth equal to one, and the axis shifted by the distance of eccentricity, wherein the ellipsoidal profile gears of the mechanism formed by the method of test initial circles, one of radius r, concentric associated with the source of the auxiliary circuit is placed inside another district fixed the tee with radius R=kr with the possibility of running it without slipping, at the same time as the original auxiliary circuit used the ellipse, and the proportionality coefficient k, which determines the radius of the guiding circle is equal to half of the required number of teeth z of the wheel, k = z / 2.

2. Gyratory mechanism according to claim 1, characterized in that the shape of its teeth provided by the combination of the aspect ratio of the ellipse λequal to the ratio of the lengths of its axes and the ratio netsentralnoe auxiliary circuit c_{about}representing the ratio of the length of the major axis of the ellipse to the radius of the rolling circle.

3. Gyratory mechanism according to any one of paragraphs. 1 and 2, characterized in that the inner and outer profiles are made in the form of ellipsoidal profiles from the General contour of the ellipse, the shape factor of the ellipse λ and the coefficient of netsentralnoe c_{about}to ensure mating conditions profiles connected by the relation:

and the radii of the guides of the outer circumferences of the stator R_{1}and the inner rotor R_{2}equal to

where r is the radius of the starting circle.

z_{1}; z_{2}respectively the number of teeth of the outer stator and the inner rotor.

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