CN112123038A - Double-parameter single-side forming grinding method for rear cutter face of slotting cutter - Google Patents
Double-parameter single-side forming grinding method for rear cutter face of slotting cutter Download PDFInfo
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Abstract
The invention discloses a double-parameter single-side forming and grinding method for a rear cutter face of a gear shaping cutter, and belongs to the field of gear shaping cutter machining. The invention comprises the following steps: (1) determining the gear shaping machining center distance according to the parameters of the machined workpiece; (2) designing a theoretical side rear cutter face of the slotting cutter; (3) approaching a rear cutter face at the side of the slotting cutter based on a two-parameter cylindrical projection method; (4) designing the profile of the double-parameter single-side grinding wheel of the side rear cutter face; (5) and (5) grinding the gear shaping cutter in a tooth dividing manner. The method adopts the bi-parameter cylindrical projection to approach the rear cutter face of the theoretical side of the slotting cutter, and the obtained cylindrical alignment is an interpolation curve which is not a cylindrical alignment preset by the traditional method; double-parameter single-side grinding is adopted, additional relief grinding movement is not needed, the machine tool is simple to adjust, and the machining efficiency is high; the cylindrical surface alignment is an interpolation curve of discrete projection points, the design freedom degree of the profile of the gear shaper cutter is further expanded, the tooth shape design of the gear parts is more flexible, and the processing range of the gear shaper cutter is greatly expanded.
Description
Technical Field
The invention belongs to the field of processing of gear shaping cutters, and particularly relates to a two-parameter single-side forming and grinding method for a rear cutter face of a gear shaping cutter.
Background
The gear, the chain wheel, the cam, the spline, the ratchet wheel and other parts with tooth-shaped structures have the advantages of constant transmission ratio, large transmission power, reliable work, compact structure and the like, are widely applied to modern industrial and mechanical products, and a large part of the products need to be processed or must be processed by a slotting cutter.
In the field of machining, a process of machining the tooth surfaces of internal and external gears, racks, or the like by a generating method or a forming method using a pinion cutter is called gear shaping. Besides the processing of the common cylindrical gear, the gear shaper cutter can be used for processing other cutters which cannot be manufactured or are not easy to manufacture, such as an internal gear, a small number of teeth, a herringbone gear, a multi-gang gear and the like, and the special gear shaper cutter can also be used for processing workpieces with various other profiles, such as a cam, an internal spline, a chain wheel and the like. Although they are not gears, they can be processed by a slotting cutter because they have a tooth-shaped structure and can also be processed by a generating method based on the principle of gear engagement.
At the end of the 19 th century, fischer in the united states created a method for generating grinding pinion cutters with large-plane grinding wheels, which was characterized by high precision, low efficiency and complex machine tool motion. In order to improve the processing efficiency of the pinion cutter, a method for processing the pinion cutter by a forming method is provided. With the continuous improvement of the material performance of the cutter, the improvement of the coating technology and equipment and the development of the numerical control technology, the use efficiency of the slotting cutter is greatly improved, and the technical difference between the slotting cutter and the hobbing cutter is further reduced.
In the process of processing the gear shaping of the gear shaping cutter, the regrinding error brought by the back angle of the gear shaping cutter is one of the main factors influencing the processing precision of the gear shaping and is the difficult point of designing the gear shaping cutter. In the machining method of the gear shaper cutter, a generating method and a forming method are commonly used, and the calculation of the profile of the formed grinding wheel is an important technology, and can grind tooth-shaped workpieces or cutters with special requirements, such as gear shaping, tooth top chamfer, full-arc tooth top cutters, gear shaper cutters with raised heads and the like at one time.
The forming and processing method for the pinion cutter is mainly divided into two types in principle, namely relief grinding manufacturing of the pinion cutter and forming grinding based on curved surface approximation. The former adopts a forming grinding wheel, and adds a radial relieving motion for forming a back angle on the basis of the forming motion, so that the tooth profile of a new ground slotting cutter is the same as that of a slotting cutter after sharpening, and the actual tooth profile of an old cutter is not consistent with the due tooth profile of the old cutter calculated according to the displacement principle, thereby causing tooth profile error. The latter adopts an elliptic cylindrical surface, a spiral surface, a conical surface or a conical surface spiral surface and the like to carry out the approach design of the rear cutter surface at the side of the slotting cutter, replaces the rear cutter surface of the slotting cutter with a machinable curved surface and adopts the forming grinding machining, and the common elliptic cylindrical surface is adopted. The reason for this problem is that the flank of the slotting cutter is a non-analytic curved surface, and the existing process method cannot accurately process. The curved surface approximation is to replace the non-analytic theoretical curved surface which is difficult to machine by a machinable curved surface which is close to the theoretical curved surface, however, how to determine the machinable and easy-to-machine curved surface becomes the core problem of manufacturing the high-precision slotting cutter with high efficiency.
Disclosure of Invention
The invention aims to overcome the defect that the side rear cutter face of the existing slotting cutter is a non-analytic curved surface and cannot be accurately machined, and provides a double-parameter single-face forming and grinding method for the rear cutter face of the slotting cutter.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a two-parameter single-side forming grinding method for a rear cutter face of a slotting cutter comprises the following steps:
(1) determining the machining center distance of each section of the pinion cutter according to the basic parameters of the machined workpiece and the basic parameters of the pinion cutter;
the section is vertical to the axis of the pinion cutter;
(2) when the rake angle is ignored, for the jth section of the cutter tooth of the gear shaping, obtaining a side edge discrete point in the section according to the meshing relationship between the gear shaping cutter and the processed tooth profile;
introducing the sharpening thickness of the slotting cutter in the axial direction to obtain a side edge discrete matrix;
leading in a rake angle to correct the thickness direction to obtain a discrete matrix of a theoretical side rear cutter face of the slotting cutter;
(3) establishing a right-hand orthogonal coordinate system S by taking the axis of the pinion cutter as a z-axisxyzRotating the discrete matrix of the theoretical side rear cutter surface of the slotting cutter obtained in the step (2) by an angle theta around the x axis1Then rotated by an angle theta around the z-axis2；
Then projecting the edge shapes of the plurality of reground sections into an xoy plane to obtain a series of projection points, and fitting the projection points by using a curve;
adjusting the rotation angle until the projection profile error in each sharpening section is minimum, and obtaining the optimal rotation angle and the optimal fitting curve;
moving by taking the optimal fitting curve as a directrix and taking a straight line in the same direction as the z axis as a bus to obtain an optimal fitting cylindrical surface serving as a rear cutter face on the side of the slotting cutter;
(4) designing a profile of a single-side grinding wheel according to a rear cutter face on the side of the pinion cutter;
(5) and carrying out tooth dividing and grinding on the gear shaper cutter.
Further, the basic parameters in step 1) include:
number of teeth z and pressure angle alpha of workpiece to be machinedn0Gear shaper cutter to workpiece transmission ratio in0And the tooth form of the processed workpiece.
Further, the specific operation of fitting the projection curve with a curve in the step 3) is as follows:
let the interpolation curve of the jth regrinding cross section be ljThe interpolation function is fj(x)；
Get j (th)0The cross section is a reference cross section, and the ith point of a projection curve on a projection plane is Mij(xiM，yiM) The normal equation of the point and the interpolation function f are combined1(x)、f2(x)、…、fn(x) Let the normal slope be kiMThen solve for the normal and interpolation curve ljThe equation for the intersection is:
fj(x)-kiM(x-xiM)-yiM＝0
the distances e from the projected points of the blade section in the reference section to the interpolation curve are calculatedijRecord eijObtaining an error matrix E for the fitting error of the two-parameter cylindrical surface of each projection point:
setting the maximum value of the elements in the array E as EmaxThen emaxIs angle of rotation theta ═ theta1，θ2]The lower maximum tooth profile error;
with emaxMinimum target, find the optimum value theta*＝[θ1 *，θ2 *]And corresponding interpolated curves, i.e., the optimal rotation angle and the best-fit curve.
Further, in the step (4), the profile of the single-side grinding wheel is a directrix of a projection cylinder.
Further, in the step (5), the gear shaping cutter performs tooth division grinding, the grinding motion is the reciprocating motion of the grinding wheel along the projection direction of the cylindrical surface, and the feeding motion is the vertical direction of the grinding motion.
Furthermore, the step-tooth indexing grinding is adopted, and the step-tooth number is prime and has no common divisor with the tooth number of the slotting cutter.
Compared with the prior art, the invention has the following beneficial effects:
according to the two-parameter single-side forming grinding method for the rear cutter face of the slotting cutter, for the rear cutter face on the side of the slotting cutter which is a non-analytic curved surface difficult to machine, firstly, the theoretical rear cutter face on the side of the slotting cutter is designed according to the tooth form of a machined workpiece, and from the high-precision and high-efficiency machining angle of the cutter, a two-parameter cylindrical projection approximation method is provided based on the curved surface approximation principle and the cylindrical projection principle, so that the cylindrical rear cutter face easy to grind is obtained, and the grinding wheel profile is further obtained by combining with the basic parameters of a grinding wheel, so that the two-parameter single-side grinding of the rear cutter face; the invention adopts the bi-parameter cylindrical projection to approach the theoretical side rear cutter face of the slotting cutter, the fitting precision is high, the AA-level requirement can be theoretically met, the bi-parameter single-side grinding is adopted, no additional relief grinding motion is needed, the machine tool is simple to adjust, and the processing efficiency is high; the method has wide popularization and application prospect and great benefit space.
Furthermore, the obtained quasi line approaching to the cylindrical surface is an interpolation curve, and is not a cylindrical surface bus preset by a traditional method, so that the design freedom degree of the profile of the gear shaper cutter is further expanded, the tooth shape design of the gear parts is more flexible, and the processing range of the gear shaper cutter is greatly expanded.
Drawings
FIG. 1 is a schematic diagram of the relative position of the flank grinding of the slotting cutter of the present invention;
FIG. 2 is a schematic diagram of a bi-parametric cylindrical projection of the present invention;
FIG. 3 is a schematic diagram of the flank approximation principle of the cylindrical projection method of the present invention;
FIG. 4 is a diagram showing the relationship between a grinding wheel and a pinion cutter for two-parameter single-side grinding according to the present invention.
Wherein, 1 is a grinding wheel, and 2 is a pinion cutter.
Detailed Description
In order to make the technical solutions of the present invention better understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that the terms "first," "second," and the like in the description and claims of the present invention and in the drawings described above are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments of the invention described herein are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
The invention is described in further detail below with reference to the accompanying drawings:
the relative positions of the grinding wheel and the cutter for forming and grinding the rear cutter surface of the pinion cutter are shown in figure 1, the grinding wheel moves along the axial direction of the pinion cutter to form grinding motion, and moves along the radial direction of the pinion cutter to realize grinding feeding; the grinding wheel performs one or more reciprocating grinding motions in one tooth slot to rotationally index the pinion cutter.
On the basis, the double-parameter single-face forming and grinding method for the rear cutter face of the slotting cutter comprises the following steps:
the parameters of the processed workpiece and the gear shaper cutter are as follows: number of teeth z of workpiece to be machined, and tooth profile angle α of workpiece to be machinedn0Gear shaper cutter to workpiece transmission ratio in0Maximum sharpening thickness h allowed by gear shaper cutter and top edge back angle alphaaGrinding a rake angle gamma;
(1) according to basic parameters of a workpiece to be processed and the gear shaping cutter: number of teeth z and pressure angle alpha of workpiece to be machinedn0Gear shaper cutter to workpiece transmission ratio in0And determining the tooth profile of the workpiece, and determining the machining center distance a of the gear shaping, wherein the specific process is as follows:
firstly, the minimum pitch circle diameter d of the processed workpiece is determinedpminAccording to the maximum sharpening thickness h and the top edge relief angle alpha allowed by the pinion cuttereDetermining the center distance of the different cross sections of the slotting cutter, and the specific process is as follows:
101) according to the principle that the tooth profile to be machined can not have a meshing limit point, the minimum pitch circle diameter d of the workpiece to be machinedpminNot less than the minimum D of diameters of concentric circles tangent to the normal of each point of the tooth profileaminIn general dpmin＝Damin；
102) And if n is the number of times of calculating the axial tooth profile of the pinion cutter within the allowable regrinding thickness, the center distance of the jth section is as follows:
when j is 1, corresponding to a new knife, and the center distance is the largest;
(2) the design and calculation process of the theoretical side rear cutter face of the slotting cutter is as follows:
201) establishing a right-handed orthogonal coordinate system S by taking the axis of the processed workpiece as a z-axisXYZEstablishing a right-hand orthogonal coordinate system S by taking the axis of the pinion cutter as a z-axisxyzIn the jth interface of the non-forward-angle pinion, the tool edge point (X) meshing with any point (X, Y) of the profile being machinedij，yij) Satisfies the following conditions:
wherein i represents the serial number of the tooth profile discrete points (i is more than or equal to 1 and less than or equal to N, N is the number of the tooth profile discrete points),
in order to obtain the corner of the workpiece to be processed,
is the corner of the gear shaper cutter and meets the requirements
Considering the sharpening thickness of the slotting cutter in the axial direction, the calculation equation of the matrix of the rear cutter face at the side of the slotting cutter is as follows:
202) introducing the tooth surface correction of the front angle of the pinion cutter: after the rake angle gamma is introduced, the cutting edge should be on the conical surface, and since the gear shaping movement is along the axial direction, the x of the cutting edgeij、yijUnchanged, only needing to correct zij；
The outer diameter of an inserted gear cutter arranged at the jth interface of the gear cutter is rgjAny point of the blade has a radius of srjThe section line equation of the front tool face in the section plane of the pinion cutter shaft is
Axial z-direction movement amount by rake angle:
203) the discrete matrix calculation formula of the side rear cutter face of the slotting cutter theory is as follows:
(3) gear slotting cutter side rear cutter face approximation method based on double-parameter cylindrical projection method
Rotating the theoretical side flank face obtained in the step (2) by an angle theta around the x axis1Then rotated by an angle theta around the axis of the slotting cutter2As shown in fig. 2, the flank face is dispersed along the regrinding direction of the slotting cutter, each section is projected along the axial direction of the cutter before rotation, a projection curve of the edge shape of each section can be obtained, and the rotation angle is optimized by taking the minimum profile error in each sharpening section as a target to obtain the optimal fitting cylindrical surface, and the specific process is as follows:
301) for the jth section of the slotting cutter, the cutter edge shape point equation of the section after two rotations:
302) projecting it into the horizontal xoy plane, the equation is:
303) performing parameter curve fitting on the edge shape of the gear shaping cutter in each regrinding section, and setting the interpolation curve of the jth regrinding section as ljThe interpolation function is fj(x) (ii) a Get j (th)0The cross section is a reference cross section, and the ith point of a projection curve on a projection plane is Mij(xiM，yiM) The point normal equation and the interpolation function f are combined as shown in FIG. 31(x)、f2(x)、…、fn(x) Let the normal slope be kiMThen solve for the normal and interpolation curve ljThe equation for the intersection is:
fj(x)-kiM(x-xiM)-yiM＝0
304) the distances e from the projected points of the blade section in the reference section to the interpolation curve are calculatedijRecord eijFor the bi-parametric cylinder fitting error of each projection point, an error matrix E can be obtained:
setting the maximum value of the elements in the array E as EmaxThen emaxIs angle of rotation theta ═ theta1，θ2]The lower maximum tooth profile error;
optimum value theta obtained by taking maximum tooth profile error as minimum*＝[θ1 *，θ2 *]The adjustment parameter in the gear grinding process is theta*；
And moving by taking the fitting curve as a reference line and taking the axis direction of the slotting cutter as a bus to obtain an optimal fitting cylindrical surface as a rear cutter surface on the side of the slotting cutter.
(4) Double-parameter profile design of single-side grinding wheel with side rear cutter face
Grinding the profile (shaft section shape) of the grinding wheel on the single side by using double parameters, namely the projection alignment line determined in the step (3), wherein the section of the grinding wheel intermediate shaft is a tooth socket symmetrical surface of the slotting cutter; let the nominal radius of the grinding wheel be rCWith the grinding wheel axis as xCAxis, grinding wheel in xCoyCThe profile in cross-section can be expressed as:
(5) single-parameter double-sided grinding adjustment of the pinion cutter is shown in fig. 4, wherein the grinding motion is reciprocating motion (left and right) of the grinding wheel along the projection direction of the cylindrical surface, and the feeding motion is the vertical direction of the grinding motion; and (3) adopting the step-tooth indexing grinding, wherein the step-tooth number is generally prime and has no common divisor with the tooth number of the slotting cutter.
Example (b):
and carrying out single-parameter double-sided grinding processing calculation on the rear cutter face of the slotting cutter for a rectangular spline according to the method.
Parameters of the rectangular spline: number of teeth z is 8, bond width B is 8mm, diameter of tip circle daRoot diameter d of 45.5mmf＝38.5mm；
Slotting cutter parameters: number of teeth z0Nominal pitch radius r of the slotting cutter, 12033.302mm, the rake angle gamma is 5 deg. and the radial relief angle alpha iseThe thickness h of the mill is 5mm after the grinding process is carried out for 6 degrees;
grinding wheel parameters: radius rC100mm, 133.54mm center distance P
The specific implementation is as follows:
calculating the machining center distance of the rectangular spline gear shaping:
pitch diameter d of rectangular splinep＝44.3mm
Gear shaping center distance a of gear shaping cutter0＝55.9mm
Center distance of j interface
Designing and calculating a theoretical rear cutter face of the slotting cutter:
1) rectangular spline tooth profile (tooth right side) equation:
2) the theoretical flank face (groove right side) discrete matrix equation of the slotting cutter:
wherein,iis the corner of the rectangular spline tooth profile at the point i engagement;
the two-parameter cylindrical projection of the rear cutter face on the side of the slotting cutter approaches: using the middle section of the gear shaper cutter during regrinding as a reference section, and performing double-parameter cylindrical projection optimization to obtain an adjustment parameter theta*＝[3.918°，0.625°]The maximum tooth profile error is 0.0057mm, the tooth profile design precision reaches the AA level, the cylindrical equation of the side rear cutter face is that a bus is parallel to the z axis:
designing the profile of the double-parameter single-side grinding wheel: taking the tooth space symmetrical surface of the gear shaper cutter as the cross section of the grinding wheel intermediate shaft, and taking the axis of the grinding wheel as xCAxis, grinding wheel in xC-o-yCThe profile in cross-section can be expressed as:
wherein, Δ rCThe reduction in radius caused for wheel dressing;
double-parameter single-side grinding of the pinion cutter: firstly, grinding the rear cutter face on one side of the cutter tooth of the gear shaper cutter, and then grinding the other side of the cutter tooth; adopting the step-tooth indexing grinding, step-tooth number 5, gear grinding sequence: 1. 6, 11, 4, 9, 2, 7, 12, 5, 10, 3, 8. The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (6)
1. A two-parameter single-side forming and grinding method for a rear cutter face of a slotting cutter is characterized by comprising the following steps:
(1) determining the machining center distance of each section of the pinion cutter according to the basic parameters of the machined workpiece and the basic parameters of the pinion cutter;
the section is vertical to the axis of the pinion cutter;
(2) when the rake angle is ignored, for the jth section of the cutter tooth of the gear shaping, obtaining a side edge discrete point in the section according to the meshing relationship between the gear shaping cutter and the processed tooth profile;
introducing the sharpening thickness of the slotting cutter in the axial direction to obtain a side edge discrete matrix;
leading in a rake angle to correct the thickness direction to obtain a discrete matrix of a theoretical side rear cutter face of the slotting cutter;
(3) to insertEstablishing right-hand orthogonal coordinate system S with tooth cutter axis as z-axisxyzRotating the discrete matrix of the theoretical side rear cutter surface of the slotting cutter obtained in the step (2) by an angle theta around the x axis1Then rotated by an angle theta around the z-axis2；
Then projecting the edge shapes of the plurality of reground sections into an xoy plane to obtain a series of projection points, and fitting the projection points by using a curve;
adjusting the rotation angle until the projection profile error in each sharpening section is minimum, and obtaining the optimal rotation angle and the optimal fitting curve;
moving by taking the optimal fitting curve as a directrix and taking a straight line in the same direction as the z axis as a bus to obtain an optimal fitting cylindrical surface serving as a rear cutter face on the side of the slotting cutter;
(4) designing a profile of a single-side grinding wheel according to a rear cutter face on the side of the pinion cutter;
(5) and carrying out tooth dividing and grinding on the gear shaper cutter.
2. The two-parameter single-sided forming grinding method for the back face of the slotting cutter according to claim 1, wherein the basic parameters in the step 1) comprise:
number of teeth z and pressure angle alpha of workpiece to be machinedn0Gear shaper cutter to workpiece transmission ratio in0And the tooth form of the processed workpiece.
3. The two-parameter single-sided forming and grinding method for the back surface of the slotting cutter according to claim 1, wherein the specific operation of fitting the projection curve by using the curve in the step 3) is as follows:
let the interpolation curve of the jth regrinding cross section be ljThe interpolation function is fj(x)；
Get j (th)0The cross section is a reference cross section, and the ith point of a projection curve on a projection plane is Mij(xiM，yiM) The normal equation of the point and the interpolation function f are combined1(x)、f2(x)、…、fn(x) Let the normal slope be kiMThen solve for the normal and interpolation curve ljThe equation for the intersection is:
fj(x)-kiM(x-xiM)-yiM＝0
the distances e from the projected points of the blade section in the reference section to the interpolation curve are calculatedijRecord eijObtaining an error matrix E for the fitting error of the two-parameter cylindrical surface of each projection point:
setting the maximum value of the elements in the array E as EmaxThen emaxIs angle of rotation theta ═ theta1，θ2]The lower maximum tooth profile error;
with emaxMinimum target, find the optimum value theta*＝[θ1 *，θ2 *]And corresponding interpolated curves, i.e., the optimal rotation angle and the best-fit curve.
4. The dual-parameter single-side forming grinding method for the back face of the slotting cutter according to claim 1, wherein in the step (4), the profile of the single-side grinding wheel is a directrix of a projection cylindrical surface.
5. The two-parameter single-sided forming and grinding method for the rear face of the pinion cutter as claimed in claim 4, wherein in the step (5), the pinion cutter performs split grinding, the grinding motion is a reciprocating motion of the grinding wheel along the projection direction of the cylindrical surface, and the feeding motion is a vertical direction of the grinding motion.
6. The two-parameter single-sided forming and grinding method for the rear tool surface of the slotting cutter according to claim 5, wherein cross-tooth indexing grinding is adopted, and the number of the cross-tooth is prime and has no common divisor with the number of teeth of the slotting cutter.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN113319656A (en) * | 2021-06-25 | 2021-08-31 | 泉州华中科技大学智能制造研究院 | Grinding method for special-shaped workpiece |
| CN114101807A (en) * | 2021-10-28 | 2022-03-01 | 西安交通大学 | Edge shape design method of gear workpiece end face continuous equidistant chamfering cutting tool |
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| CN114101807B (en) * | 2021-10-28 | 2022-12-09 | 西安交通大学 | Edge shape design method of gear workpiece end face continuous equidistant chamfering cutting tool |
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