CN112987648B - Method for controlling grinding error and contact characteristic of cycloidal-tooth bevel gear pair - Google Patents

Method for controlling grinding error and contact characteristic of cycloidal-tooth bevel gear pair Download PDF

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CN112987648B
CN112987648B CN202110180705.6A CN202110180705A CN112987648B CN 112987648 B CN112987648 B CN 112987648B CN 202110180705 A CN202110180705 A CN 202110180705A CN 112987648 B CN112987648 B CN 112987648B
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gear
tooth
grinding
sand rod
tooth surface
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CN112987648A (en
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张卫青
魏新琪
郭晓东
谭儒龙
张明德
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Chongqing University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23F—MAKING GEARS OR TOOTHED RACKS
    • B23F5/00—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made
    • B23F5/02—Making straight gear teeth involving moving a tool relatively to a workpiece with a rolling-off or an enveloping motion with respect to the gear teeth to be made by grinding
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/31—From computer integrated manufacturing till monitoring
    • G05B2219/31434—Zone supervisor, collects error signals from, and diagnoses different zone

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Abstract

The invention discloses a method for controlling a gear grinding error and contact characteristics of a cycloidal-tooth bevel gear pair, which comprises the following steps of: the method comprises the following steps: carrying out continuous indexing gear grinding processing on the bull wheel by utilizing a generatrix of the conical sand rod, wherein the motion track of the conical sand rod is a quasi-extension epicycloid; step two, solving the normal vector, radial vector and curvature parameter of the middle point of the gear surface contact zone of the large gear grinding wheel; step three, obtaining a theoretical normal vector, a theoretical radial vector and a theoretical curvature parameter of the middle point of the small wheel tooth grinding tooth surface contact area meeting the conjugate contact condition by using a conjugate meshing principle; step four, tool parameters are introduced for iterative solution, so that the normal vector, the radial vector and the curvature parameter in the tooth surface contact area of the small gear grinding are equal to theoretical values respectively, and the continuous indexing gear grinding processing parameters of the small gear are obtained; and step five, continuously indexing and grinding the small wheel according to the machining parameters obtained in the step four. The state of the tooth surface contact area after continuous indexing gear grinding can be ensured to be consistent with the state of the contact area after end face gear hobbing.

Description

Method for controlling grinding error and contact characteristic of cycloidal-tooth bevel gear pair
Technical Field
The invention relates to machining and manufacturing of a cycloid tooth bevel gear, in particular to a method for controlling a tooth grinding error and contact characteristics of a cycloid tooth bevel gear pair.
Background
The end face hobbing method can perform continuous indexing processing, while the end face milling method can only perform single indexing processing, namely after one tooth surface is processed, a cutter head is separated from a tooth blank, the tooth blank rotates for an angle, and then tooth cutting processing is performed. Therefore, compared with an end face gear milling method, the end face hobbing method has higher processing efficiency and is widely applied to the gear industry. However, due to the forming principle of the face hobbing method, the longitudinal tooth profile curve of the tooth surface of the forming wheel is an extended epicycloid generated by continuous indexing motion, and the face hobbing gear is difficult to grind by using a grinding wheel.
The cycloidal-tooth bevel gear can be subjected to continuous indexing cutting by adopting an end face hobbing method, and has high production efficiency. Meanwhile, the gear is widely applied to mechanical equipment such as automobiles, aerospace, large ships, heavy engineering machinery and the like due to high bearing capacity and high transmission stability. The generating gear tooth surface of the cycloidal-tooth bevel gear is a swept curved surface with a cutting edge extending along an epicycloid in theory, but not a revolution curved surface, and the gear grinding processing is difficult in theory. At present, some enterprises improve the tooth surface precision of the gear by adopting a lapping process, although the lapping process can eliminate the tooth error of the tooth surface to a certain extent, and improve the roughness of the tooth surface and reduce the noise. However, for gear pairs with large deformation after heat treatment, the gear grinding process cannot change the position of the contact region, so the gear grinding process has certain application conditions, cannot be adopted under the condition of large deformation in the heat treatment process, and gears after being ground can only be used in pairs, and have no good interchangeability. Or using carbide inserts to scrape off a very thin hardened surface, but in machining using carbide scraping tools, higher demands are made on the strength of the tool and the rigidity of the machine tool to avoid the tool from being damaged due to the periodic fluctuation of the cutting force, thereby causing large cost loss, and such a way is difficult to adapt to the trend of modern manufacturing industry. Compared with the end face hobbing method, the shaping principle of the gear grinding method is changed, and the shape of the tooth surface of the gear grinding method is also changed, so that the shape and the position of a large wheel contact area and a small wheel contact area of the gear pair are also changed, and the contact transmission performance of the gear pair is influenced.
Disclosure of Invention
The invention aims to provide a method for controlling the tooth grinding error and the contact characteristic of a cycloidal-tooth bevel gear pair, which can ensure that the state of a tooth surface contact zone after continuous indexing and tooth grinding is consistent with the state of a contact zone after end face hobbing, so that the cycloidal-tooth bevel gear pair has good contact transmission performance after tooth grinding, and the influence of the tooth grinding tooth profile error on the contact performance of the gear pair after tooth grinding, which is caused by the fact that a conical sand rod replaces a milling cutter bar for processing, is reduced.
The invention relates to a method for controlling the grinding error of a cycloidal-tooth bevel gear, which comprises the following steps:
the method comprises the following steps: processing a large wheel and a small wheel of a cycloidal-tooth bevel gear pair by an end face hobbing method, replacing a cutter bar used for end face hobbing on a cutter disc with a conical sand rod, and performing continuous indexing gear grinding processing on the large wheel by using a bus of the conical sand rod by adopting the same technological parameters as those of end face hobbing, wherein the motion track of the conical sand rod is a quasi-extension epicycloid;
step two, solving the normal vector of the midpoint of the tooth surface contact area of the bull wheel grinding tooth according to the equation of the tooth surface of the shape-producing gear of the continuous indexing grinding tooth
Figure BDA0002942145840000021
Sagittal vector
Figure BDA0002942145840000022
And a curvature parameter;
step three, the theoretical normal vector of the midpoint of the tooth surface contact area of the small gear grinding tooth meeting the conjugate contact condition is obtained by utilizing the conjugate meshing principle
Figure BDA0002942145840000023
Radius of theory
Figure BDA0002942145840000024
And a theoretical curvature parameter;
step four, according to a generated gear tooth surface equation of continuous indexing gear grinding, tool parameters are introduced for iterative solution, and normal vectors, radial vectors and curvature parameters in a tooth surface contact area of the small gear grinding are guaranteed to be respectively equal to theoretical normal vectors
Figure BDA0002942145840000025
Radius of theory
Figure BDA0002942145840000026
The parameters are equal to the theoretical curvature parameters, and the continuous indexing gear grinding processing parameters of the small wheel are obtained;
and step five, continuously indexing and grinding the small wheel according to the machining parameters obtained in the step four.
Furthermore, according to the movement of the conical sand rod in the cutter head relative to the cradle, the track of the generatrix of the conical sand rod in the coordinate system of the cradle is deduced, namely the generatrix gear tooth surface equation is obtained.
Further, by a system of equations
Figure BDA0002942145840000027
Determining the radial vector and the normal vector of the whole tooth surface, wherein v is the movement speed of a node on the conical sand rod, nlIs the normal vector, v, of the conical sand rod in the cradle coordinate system after the conical sand rod moveswlFor the relative movement speed of the profile surface relative to the gear blank in the machining meshing, n is the normal vector of a node on the conical sand rod in a machine tool coordinate system, VwIs the radial vector, V, of the upper node of the conical sand rod in the gear blank coordinate systempAnd L is the projection distance of any point on the tooth surface on the projection point of the shaft section on the tooth blank axis, and R is the distance from any point on the tooth surface on the projection point of the shaft section to the tooth blank axis.
Further, the cutter parameters in the fourth step comprise a cutter position angle, a radial cutter position and a pressure angle of the sand rod.
Furthermore, the generatrix of the conical sand rod is superposed with the edge line of the knife strip, and the generatrix of the conical sand rod is the same as the normal vector on the edge line of the knife strip.
Compared with the prior art, the invention has the following beneficial effects.
1. According to the invention, the cutter bars used for end face hobbing on the cutter head are replaced by the conical sand rods, the tooth surfaces of the cycloidal-tooth bevel gears are subjected to continuous indexing grinding processing by utilizing the generatrices of the conical sand rods, and any instantaneous curved surface envelope of the conical sand rods in the tooth length direction forms a tooth trace shape of a kind of extension epicycloid through space motion, so that the tooth surfaces of the cycloidal-tooth bevel gears can be subjected to efficient and accurate grinding processing. Through the coincidence of the generatrix of the sand rod and the edge line of the knife strip and the same normal vector of the generatrix of the sand rod and the edge line of the knife strip, the form parameters and the installation parameters of the conical sand rod can be determined, and the normal operation of continuous indexing gear grinding is further ensured.
2. The invention adopts the same processing parameters as the face hobbing to continuously scale and grind the gear of the large gear of the cycloidal bevel gear pair, obtains the normal vector, the radial vector and the curvature parameter of the midpoint of the tooth surface contact zone of the large gear grinding according to the equation of the generating gear tooth surface of the continuous scale and grinding, can obtain the theoretical normal vector, the theoretical radial vector and the theoretical curvature parameter of the midpoint of the tooth surface contact zone of the small gear grinding which meet the conjugate contact condition by the gear conjugate meshing principle, introduces the cutter parameters for processing the small gear, is used for correcting the tooth surface of the small gear to meet the meshing requirement, thereby obtaining the continuous scale and grinding processing parameters of the small gear, further realizing the control of the large and small gear contact zones of the gear pair, ensuring that the state of the tooth surface contact zone after continuous scale and grinding is consistent with the state of the contact zone after the face hobbing, thereby ensuring that the cycloidal bevel gear pair has good contact transmission performance after grinding, the influence of the grinding tooth profile error caused by the conical sand rod replacing the milling cutter bar for processing on the contact performance of the gear pair after grinding is reduced, and the meshing transmission quality, the service life and the reliability of the cycloidal tooth bevel gear pair are improved.
Drawings
FIG. 1 is a schematic flow diagram of the present invention;
FIG. 2 is a schematic view of the normal vector of the tooth surface of the bull wheel of the present invention at the contact reference point;
FIG. 3 is a schematic view of the normal vector of the tooth surface of the small wheel of the present invention at the contact reference point;
FIG. 4 is a schematic view of a grinding motion model of a cycloidal-tooth bevel gear of the present invention;
FIG. 5 is an axial cross-sectional view of the impeller of the present invention;
FIG. 6 is a schematic view of tooth surface meshing in accordance with the present invention;
FIG. 7 is a schematic representation of tooth flank deviation of the crowning of a large wheel prior to tooth grinding;
FIG. 8 is a schematic illustration of tooth flank deviation of the concave surface of the bull wheel before tooth grinding;
FIG. 9 is a schematic illustration of tooth flank deviation of the crowning of the bull wheel after tooth grinding;
FIG. 10 is a schematic illustration of the tooth flank deviation of the concave surface of the bull wheel after tooth grinding.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
Referring to fig. 1, the method for controlling a grinding error and a contact characteristic of a cycloidal-tooth bevel gear includes the steps of:
the method comprises the following steps: the method comprises the steps of processing a large wheel and a small wheel of a cycloidal-tooth bevel gear pair by an end face hobbing method, replacing a cutter bar used for end face hobbing on a cutter disc with a conical sand rod, enabling a generatrix of the conical sand rod to coincide with a blade line of the cutter bar, and enabling the generatrix of the conical sand rod to be the same as a normal vector on the blade line of the cutter bar. The large wheel is subjected to continuous indexing gear grinding by using the same technological parameters as those of end face gear hobbing, and the generatrix of a conical sand rod is a quasi-extension epicycloid;
step two, solving the normal vector of the midpoint of the tooth surface contact area of the bull wheel grinding tooth according to the equation of the tooth surface of the shape-producing gear of the continuous indexing grinding tooth
Figure BDA0002942145840000031
Sagittal vector
Figure BDA0002942145840000032
And a curvature parameter; referring to fig. 2, in the method for controlling the contact characteristics of the cycloidal-tooth continuous indexing gear grinding, the large gear is calculated by using the same adjustment parameters as those of the face hobbing, and the normal vector of the tooth surface of the large gear at the contact reference point is different from the normal vector in the continuous indexing gear grinding process due to the different forming principles of the continuous indexing gear grinding and the face hobbing methods.
Step three, the theoretical normal vector of the midpoint of the tooth surface contact area of the small gear grinding tooth meeting the conjugate contact condition is obtained by utilizing the conjugate meshing principle
Figure BDA0002942145840000041
Radius of theory
Figure BDA0002942145840000042
And a theoretical curvature parameter; referring to fig. 3, the normal vector, the radial vector and the curvature parameter of the large wheel calculated by the continuous indexing gear grinding are used for obtaining the radial vector, the normal vector and the curvature parameter of the small wheel which meets the conjugate meshing relationship with the large wheel according to the gear meshing principle. Thereby obtaining new adjustment parameters of the grinding teeth of the small wheel and ensuring the contact area of the small wheelThe position and the form parameters of the gear hobbing machine are consistent with those of gear hobbing, and the gear hobbing machine has good contact transmission performance.
Step four, according to a generated gear tooth surface equation of continuous indexing gear grinding, introducing a cutter position angle, a radial cutter position and a pressure angle of the sand rod for iterative solution, and ensuring that the normal vector, the radial vector and the curvature parameter in the gear tooth surface contact area of the small gear grinding are respectively equal to the theoretical normal vector
Figure BDA0002942145840000043
Radius of theory
Figure BDA0002942145840000044
The parameters are equal to the theoretical curvature parameters, and the continuous indexing gear grinding processing parameters of the small wheel are obtained;
and step five, continuously indexing and grinding the small wheel according to the machining parameters obtained in the step four.
Tooth surface deviation analysis is respectively carried out on the convex surface of the big wheel and the concave surface of the big wheel before and after gear grinding, and the results are shown in fig. 7 to fig. 10, so that control over the contact areas of the big wheel and the small wheel of the gear pair is realized, and the state of the contact area of the tooth surface after continuous indexing gear grinding is consistent with the state of the contact area after end face gear hobbing is ensured, so that the cycloidal-gear bevel gear pair has good contact transmission performance after gear grinding, the influence of the tooth grinding tooth shape error caused by the conical sand rod replacing the milling cutter bar for processing on the contact performance of the gear pair after gear grinding is reduced, and the meshing transmission quality, the service life and the reliability of the cycloidal-gear bevel gear pair are improved.
The equation of the generating gear tooth surface of the continuous indexing grinding gear is as follows: the method is characterized in that the method is used for analyzing the relative motion relation between a cutter head and a workpiece in the continuous indexing gear grinding process by taking the generation method for processing a left-handed cycloid tooth bevel gear as an example, and the track of a generatrix of a sand rod in a cradle coordinate system is deduced according to the motion of the sand rod in the cutter head relative to a cradle, namely the tooth surface equation of the forming wheel. Before calculating the tooth surface equation of the generating wheel, a mathematical model is established for the structure of the machine tool and the structure of the cutter head, and the mathematical model is shown in figure 4. In the analysis and calculation, the calculation process can be clearer by using the operation method of vector algebra, and the operations of addition and subtraction, dot multiplication, cross multiplication and the like in the operation method of vector algebra can be written conveniently in a program; meanwhile, in order to facilitate understanding of calculation, translation conversion is expressed in a homogeneous coordinate conversion matrix mode.
Let Σl＝{Ol,il,jl,klIs a static coordinate system, i.e. a machine coordinate system, wherein OlIs the cradle center, ilOljlForming a cradle plane and coinciding with the cradle axis, ilHorizontal axis, k, directed in the plane of the cradlelIs the cradle axis and points outside the machine tool.
Let Σ ═ { O, i, j, k } be the motion coordinate system of the cradle during the gear cutting process and rotate along with the cradle, the origin O and O of the coordinate systemlAnd (4) overlapping.
Let Σc＝{Oc,ic,jc,kcIs a coordinate system describing the position of the cutter head, OcIs the center of the cutter head, icThe direction is from the center of the cradle to the center of the cutter head.
Let Σ'c＝{O′c,i′c,j′c,k′cIs a rotating coordinate system describing the cutterhead, where i'cO′cj′cIs the plane of the tooth node in the cutter head, k'cIs directed away from the tool tip plane as a vector of the tool holder axis.
Let Σp＝{Op,ip,jp,kpIs a coordinate system describing the gear, OpThe origin of the coordinate system of the gear is also the shaft staggered point, omega, of the large wheel and the small wheelpThe angular velocity of the relative linkage of the gears in the machining process, and p is the position of the cutter tooth node.
The generating gear tooth surface equation is the track of the sand rod in the cutter head in the space of the relative cradle, so that firstly, a coordinate system sigma of the sand rod needs to be establisheds＝{Os,is,js,ksK, see FIG. 5sIs the axis of the sand stick and is directed towards the bottom of the sand stick, jsJ in the coordinate system of the cutter headcThe directions are the same and are the directions of radial vectors from the center of the cutter head to the nodes of the cutter teeth.
Sand rod coordinate system sigmasUnit normal vector sum on axial section generatrix of middle inner cutterThe unit tangent vectors are respectively:
ns＝[0,sinα,cosα,0]，ts＝[0,cosα,-sinα,0](ii) a In the formula, alpha is a bus pressure angle of the sand rod;
in the same way, the unit normal vector and the unit tangent vector on the outer cutter section bus are respectively as follows:
ns＝[0,-sinα,cosα,0]，ts＝[0,-cosα,-sinα,0](ii) a In the formula, alpha is the generatrix pressure angle of the sand rod.
According to the structural definition of a cutter head of the cycloidal-tooth bevel gear, the distance from an upper node of the sand rod to the top end of the sand rod, namely the height of a cutter node is set to be HeWhen the width of the top of the sand rod is w, the origin of coordinates O of the sand rod of the inner cuttersSagittal V to the sand stick node pspCan be represented by the following formula: vsp＝[0,Rs,0,0]In the formula: rs＝w/2+Hetan α. The radial vector from the origin of coordinates of the outer cutter sand rod to the node of the sand rod on the section of the same axial line can be expressed as: vsp＝[0,-Rs,0,0]。
In the gear grinding process, the sand rod needs high-speed autorotation to effectively grind the tooth surface, so that the origin of coordinates of the sand rod is converted into a radial vector V in a cutter head coordinate systemcsAnd vector ncsAnd tangent tcsCan be represented by the following:
Figure BDA0002942145840000051
in the formula, delta is an offset angle of the sand rod, phi is a self-rotation angle of the sand rod, a coordinate transformation matrix M (k, t) represents a rotation angle t around a coordinate axis k, and the expansion formula is as follows:
Figure BDA0002942145840000052
wherein M (k)sδ) not only the coordinate system direction conversion of the radial vector of the sand rod node is consistent with the cutterhead coordinate system, but also translation transformation is needed for converting the radial vector into the cutterhead coordinate system, and the conversion of the inner cutter sand rod is expressed as:
Figure BDA0002942145840000061
similarly, conversion table of outer knife sand rodShown as follows:
Figure BDA0002942145840000062
in the formula RcThe distance from the axis of the cutter head to the node of the sand rod.
In actual processing, a cutter tilting and rotating mechanism is generally used for controlling relative curvature parameters of a tooth surface and morphological parameters such as diagonal directions of a contact area, an included angle I between the axis of a cutter disc and the axis of a cradle is set as a cutter inclination angle, and the section of a shape-generating wheel shaft where a cutter tooth node p is located and a coordinate plane j are setcOckcThe included angle J is called the knife angle. After the tool is tilted, the radial vector, the normal vector and the tangent vector on the tool tooth node at the moment after the tool rotates are expressed in a cradle coordinate system as follows:
Figure BDA0002942145840000063
the axis of the cutter head passes through the cutter inclination, and the cutter rotation coordinate is transformed to be expressed as: k'c＝M(kc,-J)M(ic,I)ksAnd the tool corner rotation matrix is the same as the coordinate matrix rotating around the k, and the tool inclination angle coordinate transformation matrix around the i axis is expressed as follows:
Figure BDA0002942145840000064
after the cutter inclination and the cutter rotation coordinate transformation are carried out, the cutter head rotates around the cutter head, the self-rotation angle of the cutter head is set to be theta, and the radial vector of the upper node of the sand rod in the cradle coordinate system is expressed as follows: vlc＝M(k′c,θ)Vcs(ii) a Where M (a, θ) is a rotation matrix that rotates θ about an arbitrary vector axis a, represented as:
Figure BDA0002942145840000065
in a similar way, after the cutter head rotates by the angle theta, the normal vector and the tangent vector of the sand rod are expressed as follows:
nlc＝M(k′c,θ)ncs，tlc＝M(k′c,θ)tcs。
according to the principle of continuous indexing gear grinding, when the cutter head rotates by an angle theta, the cradle can drive the cutter head to rotate in the same direction to be thetasThen, the radial vector on the edge of the rotated sand bar is expressed as:
Figure BDA0002942145840000071
and the distance from the center of the cutter head to the center of the cradle is SrThen, the radial vector from the center of the cutter head to the center of the cradle in the machining process is expressed as: vs＝Sr·[cosθs,-sinθs,0,0]。
The nodes on the sand bar can therefore be represented in the cradle coordinate system as: v'l＝Vs+Vl。
As the sand rod is a revolving body cutter, the envelope surface of the tooth surface of the generating wheel is formed by the generatrix of the sand rod relative to the track surface of the cradle according to the envelope theory of the single-parameter surface family. That is, if the velocity of a point on the sand bar is perpendicular to the normal vector of the surface of the point, then the point lies on the envelope.
From the above calculation, the normal vector n in the cradle coordinate system obtained after the sand rod moveslAnd the radial vector V of the upper node of the sand rod in the cutter head coordinate system under the cradle coordinate systemlAnd sagittal V 'of the sand rod upper node in the cradle coordinate system'lTherefore, the movement speed of the node on the sand rod can be obtained as follows:
Figure BDA0002942145840000072
then the essential condition that one point on the tooth surface of the shaping wheel is the tangent point of the envelope surface is expressed as: v.nlBy solving this equation at 0, the relationship between the sand bar phase angle and the cutter head rotation angle can be obtained under given conditions if there is a solution. The equation typically has two solutions, one for the cutting face and one for the non-cutting face. The angle phi of the processing generatrix of the sand rod relative to the knife edge line of the knife strip is constantly changed when the sand rod envelopes the gear tooth surface of the generating shape, although the pressure angle alpha of the sand rod is not changed,but the pressure angle of the profile surface with respect to the tooth flank of the profile wheel machined by the bar changes because its instantaneous contact trace with the profile surface changes constantly.
According to the machining principle of the face hobbing method, in the generating method, the machining tooth face cradle also has an angle q which drives the forming wheel to mesh with the tooth blank, so that a real tooth face is generated on the tooth blank. Therefore, when the cradle rotates around the self-rotation angle q, the radial vector, the normal vector and the tangent vector of the nodes on the sand rod are expressed in a machine tool coordinate system as follows:
Figure BDA0002942145840000073
when machining is performed by a forming method, the angle of rotation q of the cradle is a constant value q0But only the position of the cutter head when feeding along its own axis. Since the tooth surface of the processed gear consists of conjugate meshing points between the generating surface and the processed tooth surface, the meshing condition of the processed gear is conveniently calculated and converted into a gear coordinate system to be shown as follows: vw＝V+Dl(ii) a In the formula:
Dl＝XpVp-Xbkl+Xejlwherein D islRadial vector, X, from the origin of the cradle coordinate system to the point of axial staggeringp,Xb,XeThe adjustment amounts of the machine tool are respectively the horizontal wheel position, the bed position and the vertical wheel position of the machine tool.
Vp＝[-cosγ,0,sinγ,0]In which V ispWhen the cradle drives the shape-generating wheel to rotate by an angle q, the gear correspondingly rotates by an angle q around the gearwExpressed as: q. q.sw＝q·Ra，RaFor the roll ratio, the transmission ratio of the cradle and the gear, therefore, the radial vector coordinate system needs to be converted into the tooth blank coordinate system and also needs to be rotated in a reverse direction, and finally, the radial vector and the normal vector of a point on the tooth surface under the tooth blank coordinate system are represented as follows:
Figure BDA0002942145840000081
when using generating method to process gear, cradleThe driven shaping wheel and the gear blank do conjugate meshing motion, so the meshing equation is required to be satisfied: v. ofwl·n＝0，vwlThe relative motion speed of the forming surface relative to the gear blank in the machining meshing is expressed as follows:
Figure BDA0002942145840000082
solving to obtain:
Figure BDA0002942145840000083
wherein b istThe distance from the instantaneous contact point on the sand rod to the node along the tangential direction.
The calculation of the tooth surface equation of the cycloidal-tooth bevel gear grinding is completed through the calculation, and the boundary range of the tooth surface needs to be determined for the subsequent analysis of the tooth surface, so that q, theta and b contained in the equation need to be determinedtAnd phi four unknowns are solved, so that specific tooth surface point data can be determined. In order to determine the boundary conditions of the tooth surface, the tooth surface of the tooth blank model is subjected to grid division and discretization by using the axial section of the tooth blank model and is projected in a gear coordinate system, so that the projection coordinate axis of any point on the tooth surface on the axial section can be obtained, and the tooth surface is divided into m × n tooth surface grid points, referring to fig. 6. The radial vector of the grid point in the gear blank coordinate system is set as VwThe distance from the tooth blank axis is R, and the projected distance on the tooth blank axis is L.
The radial and normal vectors of the entire tooth flank can be determined by solving the following equations:
Figure BDA0002942145840000084
the first formula is an envelope equation of the generating wheel, the second formula is a meshing equation of the gear, and four unknown parameters q, theta and b can be iteratively solved through the four formulastPhi thus determines the radial and normal vectors of the entire tooth surface.
The tooth surface radial vector, the normal vector and the curvature parameter of the middle point of the contact area after the large gear is ground can be obtained through a continuous indexing gear grinding tooth surface equation, the theoretical normal vector, the theoretical radial vector and the theoretical curvature parameter of the middle point of the contact area corresponding to the small gear grinding tooth surface and the large gear which meet the conjugate contact condition can be obtained through a gear conjugate meshing principle, the cutter parameter for processing the small gear is introduced to correct the tooth surface of the small gear to meet the meshing requirement, so that the continuous indexing gear grinding processing parameter of the small gear is obtained, the control on the contact area of the large gear and the small gear of the gear pair is further realized, the state of the tooth surface contact area after the continuous indexing gear grinding is ensured to be consistent with the state of the contact area after the end face hobbing, the cycloidal bevel gear pair has good contact transmission performance after the gear grinding, and the influence of the gear grinding tooth profile error caused by the conical sand rod replacing the milling cutter bar processing on the contact performance of the gear pair after the gear grinding is reduced, the meshing transmission quality, the service life and the reliability of the cycloid tooth bevel gear pair are improved.
The above description is only exemplary of the present application and should not be taken as limiting the present application, as any modification, equivalent replacement, or improvement made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims (4)

1. A method for controlling a gear grinding error and a contact characteristic of a cycloidal-tooth bevel gear pair is characterized by comprising the following steps of:
the method comprises the following steps: processing a large wheel and a small wheel of a cycloidal-tooth bevel gear pair by an end face hobbing method, replacing a cutter bar used for end face hobbing on a cutter disc with a conical sand rod, and performing continuous indexing gear grinding processing on the large wheel by using a bus of the conical sand rod by adopting the same technological parameters as those of end face hobbing, wherein the motion track of the conical sand rod is a quasi-extension epicycloid;
step two, solving the normal vector of the midpoint of the tooth surface contact area of the bull wheel grinding tooth according to the equation of the tooth surface of the shape-producing gear of the continuous indexing grinding tooth
Figure FDA0003401005040000011
Sagittal vector
Figure FDA0003401005040000012
And a curvature parameter;
step three, utilizing conjugate engagementTheoretical normal vector for calculating midpoint of small wheel gear grinding tooth surface contact area meeting conjugate contact condition according to principle
Figure FDA0003401005040000013
Radius of theory
Figure FDA0003401005040000014
And a theoretical curvature parameter;
step four, according to a generated gear tooth surface equation of continuous indexing gear grinding, tool parameters are introduced for iterative solution, and it is ensured that normal vectors, radial vectors and curvature parameters in a gear tooth surface contact area of the small gear grinding are respectively equal to theoretical normal vectors
Figure FDA0003401005040000015
Radius of theory
Figure FDA0003401005040000016
The parameters are equal to the theoretical curvature parameters, and the continuous indexing gear grinding processing parameters of the small wheel are obtained; the cutter parameters are a cutter position angle, a radial cutter position and a pressure angle of the sand rod;
and step five, continuously indexing and grinding the small wheel according to the machining parameters obtained in the step four.
2. The method for controlling a tooth grinding error and a contact characteristic of a cycloid tooth bevel gear pair according to claim 1, characterized in that: and deducing the track of the generatrix of the conical sand rod in a cradle coordinate system according to the movement of the conical sand rod in the cutter head relative to the cradle, namely the generating gear tooth surface equation.
3. The method for controlling a grinding error and a contact characteristic of a cycloid tooth bevel gear pair according to claim 2, characterized in that: by a system of equations
Figure FDA0003401005040000017
Determining the radial vector and the normal vector of the whole tooth surface, wherein v is the movement speed of a node on the conical sand rod, nlIs obtained after the conical sand rod is movedNormal vector in the cradle coordinate system, vwlFor the relative movement speed of the profile surface relative to the gear blank in the machining meshing, n is the normal vector of a node on the conical sand rod in a machine tool coordinate system, VwIs the radial vector, V, of the upper node of the conical sand rod in the gear blank coordinate systempAnd L is the projection distance of any point on the tooth surface on the projection point of the shaft section on the tooth blank axis, and R is the distance from any point on the tooth surface on the projection point of the shaft section to the tooth blank axis.
4. The method for controlling a grinding error and a contact characteristic of a cycloid tooth bevel gear pair according to claim 1 or 2, characterized in that: the generatrix of the conical sand rod is superposed with the edge line of the knife strip, and the generatrix of the conical sand rod is the same as the normal vector on the edge line of the knife strip.
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