CN112123038B - A dual-parameter single-sided forming grinding method for the flank face of a gear shaper - Google Patents

Abstract

The invention discloses a double-parameter single-side forming grinding method for the flank of a gear-shaping cutter, which belongs to the field of gear-shaping cutter processing. The invention includes the steps: (1) determining the machining center distance of the gear shaper according to the parameters of the workpiece to be processed; (2) designing the theoretical side flank of the gear shaping cutter; (3) designing the flank surface of the gear shaping cutter based on the double-parameter cylindrical projection method Cutter face approximation; (4) double-parameter single-sided grinding sand profile design of side flank; (5) gear-shaping cutter split-tooth grinding. The invention adopts the double-parameter cylindrical projection to approximate the theoretical side flank of the gear shaper, and the obtained directrix approaching the cylindrical surface is an interpolation curve, which is not the cylindrical directrix preset by the traditional method; With additional relief grinding motion, the machine tool is easy to adjust and the processing efficiency is high; the cylindrical directrix is the interpolation curve of discrete projection points, which further expands the degree of freedom of the profile design of the gear shaper, making the tooth profile design of tooth parts more flexible and greatly improved. The processing range of the gear shaper has been broadened.

Description

A dual-parameter single-sided forming grinding method for the flank face of a gear shaper

technical field

The invention belongs to the field of gear-shaping tool processing, in particular to a dual-parameter single-side forming grinding method for the flank of a gear-shaping tool.

Background technique

Gears, sprockets, cams, splines, ratchets and other components with toothed structures have the advantages of constant transmission ratio, large transmission power, reliable operation and compact structure, and are widely used in modern industrial and mechanical products. There is a large part that requires or must rely on gear shaper cutters for machining.

In the field of mechanical processing, the process of processing the tooth surfaces of internal and external gears or racks with a gear shaping cutter according to the generating method or forming method is called gear shaping. In addition to processing ordinary cylindrical gears, gear shapers can do some work that other tools can't do or are not easy to do, such as internal gears, small teeth, herringbone gears, multiple gears, etc. Special-shaped gear shapers can also Machining workpieces of various other profiles, such as cams, internal splines, sprockets, etc. Although they are not gears, because of their toothed structure, they can also be processed by the generation method through the principle of gear meshing, so they can be processed by a gear shaper.

At the end of the 19th century, E.R. Fellowes in the United States created a method of grinding gear shaper cutters with a large flat grinding wheel, which is characterized by high precision, low efficiency and complex machine tool movements. In order to improve the machining efficiency of the gear shaper cutter, a method of machining the gear shaper cutter by forming method is proposed. With the continuous improvement of the performance of tool materials, the improvement of coating technology and equipment, and the development of numerical control technology, the use efficiency of gear shaper cutters has been greatly improved, and the gap between it and gear hobbing technology has been further narrowed.

In the process of gear shaping cutter, the regrinding error caused by its clearance angle is one of the main factors affecting the machining accuracy of gear shaping, and it is also the difficulty in designing gear shaping cutter. In the processing methods of gear shaper cutters, the commonly used methods are generating method and forming method, and the profile calculation of forming grinding wheel is an important technology, which can grind gear modification, tooth tip chamfering, full arc tooth tip at one time Tooth-shaped workpieces or tools with special requirements, such as tools, gear shapers with convex heads, etc.

According to the forming processing method of the gear shaper, it is mainly divided into two categories from the principle, one is the relief grinding manufacturing of the gear shaper, and the other is the forming grinding based on the approximation of the surface. The former uses a forming grinding wheel, and adds a radial shovel tooth movement to form a rear angle on the basis of the forming movement, so that the tooth shape of the new and sharpened tooth shaper is the same, and the actual tooth shape of the old knife is the same. It is inconsistent with the tooth shape of the old knife calculated according to the displacement principle, resulting in a tooth shape error. The latter is to use elliptical cylindrical surface, helical surface, conical surface or conical surface helical surface to approximate the flank surface of the gear shaper, replace the flank of the gear shaper with a machinable surface, and then use forming grinding. is an elliptical cylinder. The reason for this problem is that the flank on the side of the gear shaper is a non-analytical surface, which cannot be processed accurately by the existing technology. Surface approximation is to replace this difficult-to-machine non-analytical theoretical surface with a machinable surface that is close to the theoretical surface. However, how to determine this machinable and easy-to-machine surface becomes the core of efficient manufacturing of high-precision gear shapers. question.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the disadvantage that the flank face of the existing gear shaper cutter is a non-analytical curved surface and cannot be accurately machined, and to provide a dual-parameter single-sided forming grinding method for the flank face of a gear shaper cutter.

To achieve the above object, the present invention adopts the following technical solutions to realize:

A dual-parameter single-side forming grinding method for a flank face of a gear shaper cutter, comprising the following steps:

(1) Determine the machining center distance of each section of the gear shaper according to the basic parameters of the workpiece to be processed and the basic parameters of the gear shaper;

The cross section is perpendicular to the axis of the gear shaper;

(2) When ignoring the rake angle, for the j-th section of the shaper tooth, according to the meshing relationship between the shaper cutter and the processed tooth profile, the discrete points of the side edge in the section are obtained;

Introduce the grinding thickness in the axial direction of the gear shaper to obtain the discrete matrix of the side edge;

The thickness direction is corrected by introducing the rake angle, and the discrete matrix of the flank face on the theoretical side of the gear shaper is obtained;

(3) The right-handed orthogonal coordinate system S _xyz is established with the axis of the gear shaper as the z-axis, and the discrete matrix of the flank face on the theoretical side of the gear shaper obtained in step (2) is rotated around the x-axis by an angle θ ₁ , and then around the z-axis Rotate an angle θ ₂ ;

Then project the blade shapes of several regrind sections into the xoy plane to obtain a series of projection points, and use the curve to fit the projection points;

Adjust the rotation angle until the projection profile error in each sharpening section is the smallest, and obtain the optimal rotation angle and the optimal fitting curve;

Taking the optimal fitting curve as the guideline, and moving with the straight line in the same direction as the z-axis as the generatrix, the optimal fitting cylindrical surface is obtained, which is used as the flank on the side of the gear shaping cutter;

(4) According to the flank face of the gear shaper cutter, design the profile of single-sided grinding sand;

(5) To carry out gear-shaping cutter grinding.

Further, the basic parameters in step 1) include:

The number of teeth z of the workpiece to be processed, the pressure angle α _n0 , the gear ratio i _n0 between the gear shaper and the workpiece, and the tooth profile of the workpiece to be processed.

Further, in step (3), the specific operation of fitting the projection point by curve is:

Let the interpolation curve of the jth regrind section be l _j , and the interpolation function be f _j (x);

Take the j _0th section as the reference section, and the i-th point of its projection curve on the projection plane is M _ij (x _iM , y _iM ), and the normal equation of this point and the interpolation function f ₁ (x), f ₂ (x), ..., f _n (x), and the slope of its normal line is assumed to be k _iM , the equation for solving the intersection of the normal line and the interpolation curve l _j is:

f _j (x)-k _iM (xx _iM )-y _iM =0

For the projected series points of the blade truncation in the reference section, find the distances e _ij from them to the interpolation curve respectively, denote e _ij as the two-parameter cylindrical fitting error of each projected point, and obtain the error matrix E:

Let the maximum value of the elements in the array E be e _max , then e _max is the maximum tooth profile error under the rotation angle θ=[θ ₁ , θ ₂ ];

Taking the minimum e _max as the goal, obtain the optimal value θ ^* = [θ ₁ ^* , θ ₂ ^* ] and the corresponding interpolation curve, that is, the optimal rotation angle and the optimal fitting curve.

Further, in step (4), the profile shape of the single-sided grinding sand is the directrix of the projected cylindrical surface.

Further, in step (5), the gear shaper is divided into teeth for 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.

Further, the cross-tooth indexed grinding is adopted, and the number of cross-tooth is prime and has no common divisor with the number of teeth of the gear-shaping cutter.

Compared with the prior art, the present invention has the following beneficial effects:

The dual-parameter single-side forming grinding method for the flank of the gear shaper of the present invention, for the non-analytical curved surface that is difficult to machine on the flank of the gear shaper, firstly, the theoretical flank of the gear shaper is carried out according to the tooth shape of the workpiece to be processed. From the perspective of high-precision and high-efficiency machining of the tool, a dual-parameter cylindrical projection approximation method is proposed based on the surface approximation principle and the cylindrical projection principle, and a cylindrical flank that is easy to grind is obtained. profile shape, so as to realize dual-parameter single-sided grinding of the flank on the side of the gear shaper; the present invention adopts the dual-parameter cylindrical projection to approximate the flank on the theoretical side of the gear shaper, and the fitting accuracy is high, and theoretically it can reach AA level According to the requirements, double-parameter single-sided grinding is adopted, no additional relief grinding motion is required, the machine tool is easy to adjust, and the processing efficiency is high; the method of the invention has broad application prospects and great benefit space.

Further, the obtained directrix line approximating the cylinder is an interpolation curve, not the cylinder generatrix preset by the traditional method, which further expands the degree of freedom of the profile design of the gear shaper, making the tooth profile design of tooth parts more flexible and greatly broadening the The machining range of the gear shaper cutter has been expanded.

Description of drawings

1 is a schematic diagram of the relative position of the flank grinding of the gear shaper cutter of the present invention;

Fig. 2 is the dual-parameter cylindrical projection principle diagram of the present invention;

FIG. 3 is a schematic diagram of the approximation principle of the flank face by the cylindrical projection method of the present invention;

FIG. 4 is a relative relationship diagram of a grinding wheel and a gear shaper for dual-parameter single-side grinding according to the present invention.

Among them, 1 is the grinding wheel, and 2 is the gear shaper.

Detailed ways

In order to make those skilled in the art better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only Embodiments are part of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts 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 the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific sequence or sequence. It is to be understood that the data so used may be interchanged under appropriate circumstances such that the embodiments of the invention described herein can be practiced in sequences other than those illustrated or described herein. Furthermore, the terms "comprising" and "having", and any variations thereof, are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those expressly listed Rather, those steps or units may include other steps or units not expressly listed or inherent to these processes, methods, products or devices.

Below in conjunction with accompanying drawing, the present invention is described in further detail:

The relative position of the grinding wheel and the tool in the flank forming grinding of the gear shaper is shown in Figure 1. The grinding wheel moves along the axis of the shaper to form a grinding motion, and moves along the radial direction of the shaper to realize the grinding feed; The cogging completes one or more reciprocating grinding movements to perform rotary indexing of the gear shaper.

On this basis, a dual-parameter single-side forming grinding method for the flank face of a gear shaper cutter includes the following steps:

The parameters of the workpiece to be processed and the shaper cutter: the number of teeth z of the workpiece to be machined, the tooth profile angle of the workpiece to be machined α _n0 , the transmission ratio of the shaper cutter to the workpiece i _n0 , the maximum allowable grinding thickness h of the shaper cutter, the top edge clearance angle α _a , grinding rake angle γ;

(1) According to the basic parameters of the workpiece to be processed and the gear shaper: the number of teeth z of the workpiece to be processed, the pressure angle α _n0 , the gear ratio i _n0 between the gear shaper and the workpiece, and the tooth shape of the workpiece, determine the gear shaper machining center distance a. The specific process is as follows :

First, determine the minimum pitch circle diameter d _pmin of the workpiece to be machined, and then determine the center distance of different sections of the gear shaper according to the allowable maximum grinding thickness h and top edge clearance angle α _e of the gear shaper. The specific process is as follows:

101) According to the principle that there is no meshing limit point for the tooth profile to be processed, the minimum pitch circle diameter d _pmin of the workpiece to be processed is not less than the minimum value of the diameter of the concentric circles tangent to the normal of each point of the tooth profile D _amin , usually d _pmin = D _amin ;

102) Let n be the calculation times of the axial tooth profile of the gear shaper within the allowable regrinding thickness, then the center distance of the j-th section is:

When j=1, corresponding to the new knife, the center distance is the largest;

(2) The design and calculation process of the flank face on the theoretical side of the gear shaper cutter is as follows:

201) Establish a right-handed orthogonal coordinate system S _XYZ with the axis of the workpiece to be processed as the z-axis, and establish a right-handed orthogonal coordinate system S _xyz with the axis of the gear shaper as the z-axis. In the j-th interface of the gear shaper without rake angle, The tool edge point (x _ij , y _ij ) meshing with any point (X, Y) of the tooth profile to be machined satisfies:

为被加工工件转角，

为插齿刀转角，且满足

Among them, i represents the serial number of the tooth profile discrete points (1≤i≤N, N is the number of tooth profile discrete points),

For the corner of the workpiece to be processed,

is the angle of the gear shaper, and it satisfies

Considering the sharpening thickness in the axial direction of the gear shaper, the calculation equation of the flank matrix on the side of the gear shaper is:

202) Tooth surface correction of the rake angle of the gear shaper introduced: after the introduction of the rake angle γ, the blade should be on the conical surface. Since the gear shaping movement is along the axis direction, the x _ij and y _ij of the blade remain unchanged, and only z _ij needs to be corrected. ;

Assuming that the outer diameter of the gear shaper in the j-th interface of the gear shaper is r _gj , and the radius of any edge point is s _rj , the rake face section equation in the shaft section of the gear shaper is:

The amount of movement of the axis in the z direction caused by the rake angle:

203) The discrete matrix calculation formula of the flank face on the theoretical side of the gear shaping cutter:

(3) Approximation of flank face of gear shaper based on double-parameter cylindrical projection method

Rotate the theoretical side flank obtained in step (2) by an angle θ _{1 around the x-axis, and then rotate an angle θ 2 around} the axis of the gear shaper itself, as shown in Figure 2, discrete the flank along the regrinding direction of the gear shaper. By projecting each section along the direction of the tool axis before rotation, the projection curve of the blade shape of each section can be obtained. Taking the minimum profile error in each sharpening section as the goal, the rotation angle is optimized to obtain the optimal fitting cylinder, The specific process is as follows:

301) For the j-th section of the gear shaper, the tool edge point equation of the section after two rotations:

302) Project it into the horizontal xoy plane, then the equation is:

303) Perform parameter curve fitting on the shape of the shaper blade in each regrind section, set the interpolation curve of the jth regrind section to be l _j , and the interpolation function to be f _j (x); take the j _0th section as the benchmark Section, the i-th point of its projection curve on the projection plane is M _ij (x _iM , y _iM ), as shown in Figure 3, the point normal equation and the interpolation functions f ₁ (x), f ₂ ( x), ..., f _n (x), set the normal slope to be k _iM , then the equation for solving the intersection of the normal and the interpolation curve l _j is:

f _j (x)-k _iM (xx _iM )-y _iM =0

304) For the projected series points of the blade truncation in the reference section, calculate the distances e _ij from them to the interpolation curve respectively, and denote e _ij as the two-parameter cylindrical fitting error of each projection point, and the error matrix E can be obtained:

Let the maximum value of the elements in the array E be e _max , then e _max is the maximum tooth profile error under the rotation angle θ=[θ ₁ , θ ₂ ];

Taking the maximum tooth profile error as the minimum, the optimal value θ ^* = [θ ₁ ^* , θ ₂ ^* ] can be obtained, then the adjustment parameter in the grinding process is θ ^* ;

Taking the fitting curve as the guideline, and moving with the axis direction of the gear shaping cutter as the generatrix, the optimal fitting cylindrical surface is obtained, which is used as the flank on the side of the gear shaping cutter.

(4) Two-parameter single-sided grinding sand profile design of side flank

The profile shape (axis truncation) of the double-parameter single-sided grinding sand is the projection directrix determined in step (3). At this time, the cross-section of the middle axis of the grinding wheel is the symmetric plane of the tooth groove of the gear shaper; let the nominal radius of the grinding wheel be r _C , taking the axis of the grinding wheel as the x _C axis, the profile of the grinding wheel in the x _C oy _C section can be expressed as:

(5) The single-parameter double-sided grinding adjustment of the gear shaper is shown in Figure 4. The grinding motion is the 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; For high-speed grinding, the number of cross teeth is generally a prime number, and there is no common divisor with the number of teeth of the gear shaper.

Example:

According to the above method, the single-parameter double-sided grinding processing calculation of the flank of the gear shaper cutter is carried out for a rectangular spline.

Rectangular spline parameters: number of teeth z = 8, key width B = 8mm, top circle diameter da = 45.5mm, root circle diameter d _{f =} 38.5mm;

Gear shaper parameters: number of teeth z ₀ =12, nominal pitch circle radius r ₀ =33.302mm, rake angle γ = 5°, radial relief angle α _e = 6°, allowable regrind thickness h = 5mm;

Grinding wheel parameters: radius r _C = 100mm, center distance P = 133.54mm

The specific implementation is as follows:

Calculate the machining center distance of rectangular spline gear shaping:

Rectangular spline pitch circle diameter d _p = 44.3mm

The tooth shaper center distance a ₀ =55.9mm

The jth interface center distance

Theoretical flank design calculation of gear shaper cutter:

1) Rectangular spline tooth profile (tooth right side) equation:

2) The discrete matrix equation of the flank face (right side of the groove) in the theory of gear shaper:

Among them, ε _i is the corner of the rectangular spline profile when meshing at point i;

Two-parameter cylindrical projection approximation of the flank face of the gear shaper: taking the middle section of the gear shaper as the reference section, the two-parameter cylindrical projection optimization is carried out, and the adjustment parameters θ ^* = [3.918°, 0.625°] are obtained. , the maximum tooth profile error is 0.0057mm, and the tooth profile design accuracy reaches AA level. The cylinder equation of the side flank is:

Two-parameter single-sided grinding sand profile design: take the tooth shaper tooth groove symmetry plane as the grinding wheel intermediate shaft section, and the grinding wheel axis as the x _C axis, the profile of the grinding wheel in the x _C -oy _C section can be expressed as:

Among them, Δr _C is the radius reduction caused by grinding wheel dressing;

Gear shaper double-parameter single-sided grinding: first grind the flank on one side of the tooth shaper, and then grind the other side; adopt cross-tooth indexing grinding, the number of cross-tooth 5, grinding order: 1, 6 , 11, 4, 9, 2, 7, 12, 5, 10, 3, 8. The above content is only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any modification made on the basis of the technical solution proposed in accordance with the technical idea of the present invention falls within the scope of the claims of the present invention. within the scope of protection.

Claims (6)

1. a double-parameter single-sided forming grinding method for the flank of a gear shaper cutter, is characterized in that, comprises the following steps: (1) Determine the machining center distance of each section of the gear shaper according to the basic parameters of the workpiece to be processed and the basic parameters of the gear shaper; The cross section is perpendicular to the axis of the gear shaper; (2) When ignoring the rake angle, for the j-th section of the shaper tooth, according to the meshing relationship between the shaper cutter and the processed tooth profile, the discrete points of the side edge in the section are obtained; Introduce the grinding thickness in the axial direction of the gear shaper to obtain the discrete matrix of the side edge; The thickness direction is corrected by introducing the rake angle, and the discrete matrix of the flank face on the theoretical side of the gear shaper is obtained; (3) The right-handed orthogonal coordinate system S _xyz is established with the axis of the gear shaper as the z-axis, and the discrete matrix of the flank face on the theoretical side of the gear shaper obtained in step (2) is rotated around the x-axis by an angle θ ₁ , and then around the z-axis Rotate an angle θ ₂ ; Then project the blade shapes of several regrind sections into the xoy plane to obtain a series of projection points, and use the curve to fit the projection points; Adjust the rotation angle until the projection profile error in each sharpening section is the smallest, and obtain the optimal rotation angle and the optimal fitting curve; Taking the optimal fitting curve as the guideline, and moving with the straight line in the same direction as the z-axis as the generatrix, the optimal fitting cylindrical surface is obtained, which is used as the flank on the side of the gear shaping cutter; (4) According to the flank face of the gear shaper cutter, design the profile of single-sided grinding sand; (5) To carry out gear-shaping cutter grinding. 2. a kind of gear shaping cutter flank dual-parameter single-sided forming grinding method according to claim 1, is characterized in that, the basic parameter in step (1) comprises: The number of teeth z of the workpiece to be processed, the pressure angle α _n0 , the gear ratio i _n0 between the gear shaper and the workpiece, and the tooth profile of the workpiece to be processed. 3. a kind of gear shaping cutter flank dual-parameter single-sided forming grinding method according to claim 1, is characterized in that, in step (3), utilize the concrete operation of curve fitting described projection point to be: Let the interpolation curve of the jth regrind section be l _j , and the interpolation function be f _j (x); Take the j _0th section as the reference section, and the i-th point of its projection curve on the projection plane is M _ij (x _iM , y _iM ), and the normal equation of this point and the interpolation function f ₁ (x), f ₂ (x), ..., f _n (x), and the slope of its normal line is assumed to be k _iM , the equation for solving the intersection of the normal line and the interpolation curve l _j is: f _j (x)-k _iM (xx _iM )-y _iM =0 For the projected series points of the blade truncation in the reference section, find the distances e _ij from them to the interpolation curve respectively, denote e _ij as the two-parameter cylindrical fitting error of each projected point, and obtain the error matrix E:

Let the maximum value of the elements in the array E be e _max , then e _max is the maximum tooth profile error under the rotation angle θ=[θ ₁ , θ ₂ ]; Taking the minimum e _max as the goal, obtain the optimal value θ ^* = [θ ₁ ^* , θ ₂ ^* ] and the corresponding interpolation curve, that is, the optimal rotation angle and the optimal fitting curve. 4. a kind of gear shaping cutter flank dual-parameter single-sided forming grinding method according to claim 1, is characterized in that, in step (4), described single-sided grinding sand profile is projected cylindrical surface line of sight. 5. a kind of gear shaping cutter flank dual-parameter single-sided forming grinding method according to claim 4, is characterized in that, in step (5), gear shaping cutter is divided into teeth for grinding, and the grinding motion is a grinding wheel The reciprocating motion along the projection direction of the cylinder, the feed motion is the vertical direction of the grinding motion. 6. a kind of gear shaper flank dual-parameter single-sided forming grinding method according to claim 5, is characterized in that, adopts cross-tooth indexing grinding, the number of cross-tooth is prime and has no common divisor with the number of teeth of the gear-shaping cutter .

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