WO2020151683A1

WO2020151683A1 - Involute cylindrical gear envelope milling method taking precise characteristics of tooth surface into consideration

Info

Publication number: WO2020151683A1
Application number: PCT/CN2020/073343
Authority: WO
Inventors: 郭二廓; 任乃飞; 周长禄; 王杰; 张新洲
Original assignee: 江苏大学
Priority date: 2019-01-22
Filing date: 2020-01-21
Publication date: 2020-07-30
Also published as: CN109663991B; GB202009212D0; GB2585982B; CN109663991A; GB2585982A

Abstract

Provided is an involute cylindrical gear envelope milling method taking the precise characteristics of a tooth surface into consideration. The method comprises the following steps: S01, choosing a milling tool, and determining the diameter of the tool and the length of a cutting edge of the tool; S02, determining a dynamic eccentricity e_i of an axis of the tool relative to an axis of a gear; S03, constructing a step length formula of feeding in a tooth profile direction, constructing a curvilinear equation between an involute tooth profile extension angle and a tooth surface residual height difference, and calculating a cutter location point; and S04, planning a feeding path. According to the method, on the premise of ensuring the machining precision of a tooth surface of an involute cylindrical gear, the differential geometrical characteristics of an involute tooth surface are comprehensively taken into consideration to calculate a cutter location point and plan a tool path, such that a tool feeding trajectory is distributed as required, thereby reducing redundant feeding for the root and top of a tooth, and improving the machining efficiency of tooth envelope milling and the meshing performance of the tooth surface.

Description

An Envelope Milling Method for Involute Cylindrical Gear Considering the Accuracy of Tooth Surface

Technical field

The invention relates to the technical field of mechanical processing, in particular to an envelope milling processing method of an involute cylindrical gear considering the accuracy characteristics of the tooth surface.

Background technique

Gears are the key basic parts of machinery-related applications. In recent years, the traditional gear hobbing, gear shaping, gear shaving and other gear processing methods have problems such as the long processing cycle of single-piece, small-batch, large-modulus gear parts, and the high cost of special gear making equipment and special gear tools. A method for flexible envelope milling of cylindrical gears with universal tools on a universal multi-axis machining center is proposed, which can provide a low-cost, high-efficiency, and short-cycle for the processing of single-piece, small-batch and large-modulus gears for enterprises And fast response flexible tooth manufacturing method.

However, this advanced multi-axis turning-milling combined processing technology still has the problem of low processing efficiency in the processing of cylindrical gears. The reason is that the principle of turning-milling compound envelope milling is to fit the tooth surface into a free-form surface before planning the tool path, without considering the differential geometric characteristics of the tooth surface. Especially for involute cylindrical gears, the radius of curvature of each micro-segment on the tooth profile is different, which has a certain particularity. The second is that this free-form surface-based tool path planning method does not consider the requirement of meshing accuracy at the pitch circle of the tooth surface. In the meshing process of the involute cylindrical gear pair, the main meshing area is the tooth surface near the pitch circle, and the machining accuracy of this area should be given priority during the machining process. Although there are five-axis turning-milling composite machining centers in the prior art that can realize the milling of cylindrical gears, the milling form they adopt is to process the tooth surfaces as free-form surfaces, which leads to contradictions between machining efficiency and machining accuracy.

Therefore, if the differential geometric characteristics of the tooth surface and the precision characteristics of the tooth surface cannot be considered comprehensively, only processing the machining accuracy on the tooth surface according to the same residual height difference will inevitably cause a large number of redundant passes, leading to machining The efficiency is low, or the accuracy of the tooth surface meshing area is not high.

Summary of the invention

In view of the shortcomings in the prior art, the present invention provides an envelop milling method for involute cylindrical gears considering the characteristics of tooth surface accuracy, which is used to improve the processing of milling involute cylindrical gears with general tools on a general machining center. Efficiency and tooth surface meshing performance.

The present invention achieves the above technical objects through the following technical means.

An envelope milling method for involute cylindrical gears considering the accuracy characteristics of the tooth surface, including:

S01: Select the tool according to the parameters of the gear workpiece to be processed, and determine the tool diameter and the length of the cutting edge of the tool;

S02: Use eccentric milling to process to determine the dynamic eccentricity e _{i of the} tool axis relative to the gear axis;

S03: According to the accuracy requirements of the main meshing area of the tooth surface of the gear, by constructing the formula of the step length in the tooth profile direction, the maximum distance of the step length along the tooth profile direction Δl _max and the adjacent step length of the two tool position points are solved The distance Δl _i and the involute expansion angle u _i corresponding to each tool position point on the tooth surface are used to construct the curve equation Δt _i =f(Δu _i ) between the expansion angle of the involute tooth profile and the residual height difference of the tooth surface. Processing tool position points;

S04: Plan the tool path according to the tool location point.

Preferably, in the step S01, an end mill or a rod milling cutter is selected for the medium and small modulus involute cylindrical gears, and a conical disc milling cutter or a rod milling cutter is selected for the large modulus involute cylindrical gears.

Preferably, in the step S01, the tool diameter D _t ≥ 10 mm, and the blade length L _t ≥ 20 mm.

Preferably, the calculation formula of the eccentricity e _i is:

In the formula, r _b is the gear base circle radius; σ ₀ is the base circle tooth groove half angle; u _i is the involute expansion angle corresponding to each tool position on the tooth surface;

Is the rotation angle of the rotary table fixedly connected to the gear, and

D _t is the tool diameter.

Preferably, the step S03 is specifically:

S03.1 divides the tool position points of the tool along the gear tooth profile direction into n equal parts, and each tool position point on the tooth surface is distributed according to the parabolic equation. Set the maximum distance of the cutting step along the tooth profile direction as Δl _max and the minimum distance It is Δl _min = Δl _max /5, the distance between adjacent steps of two tool positions is Δl _i , and the step length of the tool along the tooth profile direction satisfies the following formula:

S03.2 According to the given gear workpiece, the height of the tooth surface involute along the radial direction is obtained as H, and the maximum distance Δl _{max of the} cutting step along the tooth profile direction can be solved by formula (3):

S03.3 Substituting the Δl _max obtained in step S03.2 into formula (2), the number of traversal passes i∈[0,n], the step distance corresponding to each tool position on the tooth surface is obtained in turn as Δl _i ；

S03.4 Given Δl _max and the current number of passes i, from formula (4), the involute expansion angle u _i on the tooth surface corresponding to each tool location point (x _p , y _p ) on the parabolic equation is obtained:

In the formula, r _f is the radius of the root circle; r _b is the radius of the base circle; σ ₀ is the half angle of the base circle tooth groove;

S03.5 Assuming that the coordinates of two adjacent tool position points A and B on the involute line are (x _A , y _A ) and (x _B , y _B ) respectively, and A and B intersect at point C, then point C Is the maximum residual height difference between adjacent tool location points, assuming that the coordinates of point C are (x _C ,y _C ), assuming that the slopes of two adjacent tool location points A and B on the involute line are k _A and k respectively _B , from the geometric relationship of A, B, and C, the following formula can be obtained:

According to the characteristics of involute, the slopes k _A and k _{B of} two adjacent tool positions A and B on the involute line are respectively:

In the formula, u _A and u _B are the involute expansion angles of two adjacent tool positions A and B respectively;

And the involute equations of two adjacent tool positions A and B are:

Substituting formula (6)(7)(8) into formula (5) can get the coordinates of point C (x _C ,y _C ),

Calculate the residual height difference of point C:

According to formula (9), the residual height difference Δt _i between adjacent tool positions can be obtained in turn. From the known involute tooth profile expansion angle Δu _i , the involute tooth profile expansion angle Δu _i and The curve equation between tooth surface residual height difference Δt _i is:

Δt _i =f(Δu _i ) Equation (10)

S03.6 Determine the machining tool position according to the curve equation between the involute tooth profile expansion angle Δu _i and the tooth surface residual height difference Δt _i .

Preferably, the specific method for determining the machining tool position point in step S03.6 is to make the tool path trajectory from the pitch circle of the tooth surface to the tooth profile of the upper and lower ends present a dense to sparse distribution, even if it is close to the pitch circle. the main engaging flank region residues minimum elevation Δt _i, Δt _i elevation residues flank pitch distance farther secondary engagement region is gradually increased, and the non-engagement region close to the tooth root and the tooth tip portion of the tooth surface height difference [Delta] t residues _{i is the} largest.

Preferably, the step S04 is specifically:

The tool starts from one end face of the tooth tip, and first moves the first tool along the tooth direction to complete the milling of the entire tooth width b;

Feed the length of Δu _i along the involute tooth profile in the tooth slot direction;

Then take the second cut along the tooth direction;

And so on, until the envelope milling of each tooth surface is completed.

The beneficial effects of the present invention:

1) When a general-purpose tool is used to process an involute cylindrical gear on a multi-axis machining center, the present invention comprehensively considers the differential geometric characteristics of the involute tooth surface on the premise of ensuring the accuracy of the involute cylindrical gear tooth surface processing, and calculates The tool location point is exited and the tool path is planned, so that the tool path is allocated on demand, reducing the redundant path of the tooth root and tooth tip, thereby improving the processing efficiency of envelope milling.

2) Under the premise of ensuring the efficiency of the tooth surface processing of the involute cylindrical gear, the present invention considers the accuracy characteristics of the involute tooth surface, so that the tool path from the pitch circle of the tooth surface to the tooth profile at both ends shows a dense to sparse Distribution to meet the machining requirements of high precision in the middle of the tooth surface and low precision at both ends, thereby improving the meshing performance of the tooth surface.

Description of the drawings

FIG. 1 is a plan view of the cutting step length and the cutting path of the involute tooth surface considering the accuracy characteristics of the tooth surface according to an embodiment of the present invention.

Figure 2 is a schematic diagram of each movement axis of a typical four-axis machining center.

Figure 3 is a schematic diagram of enveloping and milling involute gears with a flat end mill on a four-axis machining center.

Fig. 4 is a curve of the relationship between the expansion angle Δu _i of the involute tooth profile and the residual height difference Δt _{i of the} tooth surface according to an embodiment of the present invention.

Figure 5 shows the tool envelope tool location points of the involute tooth surface according to the embodiment of the present invention, where (a) corresponds to the finishing method considering the accuracy characteristics of the tooth surface, and (b) corresponds to the traditional based on equal residual height difference Method of finishing.

Fig. 6 shows the relationship between the radial length of the involute tooth surface and the residual height difference according to an embodiment of the present invention, where (a) corresponds to a finishing method considering the accuracy characteristics of the tooth surface, and (b) corresponds to a traditional Finishing method of equal residual height difference method.

1. Gear workpiece; 2. End mill.

detailed description

The present invention will be further described below in conjunction with the drawings and specific embodiments, but the protection scope of the present invention is not limited to this.

The present invention takes an involute cylindrical gear used in a certain transmission mechanism as an example to illustrate in detail an envelope milling method of an involute cylindrical gear in consideration of the accuracy characteristics of the tooth surface. The gear type is straight tooth, and the number of teeth z=44 , Modulus m _n ＝20mm, index circle pressure angle α _n ＝20, displacement coefficient x _n =0, tooth width b=160mm, accuracy requirement is ISO1328-2: 1997 level 6, among which, the pitch circle accuracy It is required to reach ISO level 3. For this gear, when the machining accuracy is ISO 6, the total tooth profile deviation is 27.42μm; when the machining accuracy is ISO 3, the total tooth profile deviation is 9.69μm. The existing processing equipment is a four-axis turning-milling composite machining center. As shown in Figure 2, the three linear axes are X-axis, Y-axis, and Z-axis, one rotary axis is C-axis, and the workpiece is installed on the C-axis to work. On the table, the tool is installed on the spindle SP, and the Z-axis and C-axis can realize two-axis linkage.

According to an embodiment of the present invention, an envelope milling method for an involute cylindrical gear considering the characteristics of tooth surface accuracy, specifically includes the following steps:

S01: Select tool

For the milling of involute cylindrical gears, a flat end mill 2 should be used. The tool parameters are as follows:

The tool diameter D _{t of the} flat end mill 2: According to the parameters of the gear workpiece 1, the smallest tooth groove width is calculated to be 21.9mm. In order to ensure that the tool has sufficient linear speed when cutting, the tool diameter D _{t is} selected as φ18mm;

The cutting edge length L _{t of the} flat end mill 2: According to the parameters of the gear workpiece 1, the cutting edge length L _{t is} selected as 38mm;

S02: Determine the tool eccentricity

When the processing equipment is a four-axis turning-milling composite machining center, it needs to be processed by eccentric milling, as shown in Figure 2. At this time, calculate the dynamic eccentricity e _{i of the} end mill 2 tool:

In the formula, r _b is the gear base circle radius; σ ₀ is the base circle tooth groove half angle; u _i is the involute expansion angle;

Is the rotation angle of the rotary table fixedly connected to the gear, that is, the rotation angle of the C axis, and

D _t is the diameter of the end mill 2.

S03: Calculate tool location points

According to the accuracy requirements of the main meshing area of the tooth surface of the gear, by constructing the formula of the cutting step length in the tooth profile direction, the maximum distance between the cutting step length along the tooth profile direction Δl _max and the adjacent step distance between two tool positions are solved Δl _i , solve the involute expansion angle u _i corresponding to each tool position point on the tooth surface, construct the curve equation Δt _i =f(Δu _i ) between the involute tooth profile expansion angle and the tooth surface residual height difference, and finally determine Machining tool position points. The S03 step is specifically:

S03.1 Constructs the formula for the step length of the tooth profile direction

Divide the tool position points of the end mill 2 along the gear tooth profile direction into n=20 equal parts. The tool position points on the tooth surface are distributed according to the parabolic equation. Assuming that the maximum distance of the cutting step along the tooth profile direction is Δl _max , The minimum distance is Δl _min = Δl _max /5, and the distance between adjacent steps of two tool position points is Δl _i , as shown in Figure 1. At this time, the cutting step length of the tool along the tooth profile direction satisfies the formula (2) :

S03.2 solves the maximum distance of the cutting step along the tooth profile direction as Δl _max

For a given gear workpiece 1, it can be seen that the height of the tooth surface involute along the radial direction is H=45mm, and the maximum distance of the cutting step along the tooth profile direction Δl _max =6.415mm can be solved by formula (3).

S03.3 Solve the step distance corresponding to each tool position point on the tooth surface of the gear as Δl _i

Substitute Δl _max obtained in step S03.2 into formula (2), traverse the number of passes i∈[0,20], and obtain the step distance of each point on the tooth surface as Δl _{i in turn} .

S03.4 Solve the involute expansion angle u _i corresponding to each tool position on the tooth surface

Given that Δl _max =6.415mm and the current total number of cutters n=20, from formula (4), the involute expansion angle on the tooth surface corresponding to each tool position point (x _p , y _p ) on the parabolic equation is obtained u _i :

In the formula, the tooth root circle radius r _f =415mm; the base circle radius is r _b =413.645mm; the base circle tooth groove half angle is σ ₀ =1.192°.

S03.5 Construct the curve equation between the involute tooth profile expansion angle Δu _i and the tooth surface residual height difference Δt _i

Assuming that the coordinates of two adjacent tool position points A and B on the involute line are (x _A ,y _A ) and (x _B ,y _B ), respectively, A and B intersect at point C, then point C is adjacent The maximum residual height difference between tool location points, assuming that the coordinates of point C is (x _C ,y _C ), assuming that the slopes of two adjacent tool location points A and B on the involute line are k _A and k _B , respectively, by The geometric relationship of the three points A, B, C can be obtained by the equation group (5):

According to the characteristics of the involute, the slopes k _A and k _{B of} two adjacent tool position points A and B on the involute are respectively:

In the formula, u _A and u _B are the involute expansion angles of two adjacent tool positions A and B respectively, which can be obtained by formula (4).

And the involute equations of two adjacent tool positions A and B are:

Substituting formula (6)(7)(8) into formula (5) can obtain the coordinates of point C (x _C , y _C ).

Calculate the residual height difference of point C:

According to formula (9), the residual height difference Δt _i between adjacent tool positions can be obtained sequentially, and the involute tooth profile expansion angle Δu _{i is known} , as shown in Figure 4, the involute tooth is constructed The curve equation between the profile expansion angle Δu _i and the tooth surface residual height difference Δt _i is:

Δt _i =f(Δu _i ) Equation (10)

S03.6 According to formula (10), the tool path path from the pitch circle of the tooth surface to the upper and lower ends of the tooth profile presents a dense to sparse distribution, that is, the residual height difference Δt of the tooth surface near the main meshing area near the pitch circle is realized. minimum _i, residues flank height difference Δt _i pitch distance farther secondary engagement region gradually increases, and close to the addendum and dedendum portions of the non-engaging region residues flank the maximum height difference Δt _i.

S04: Plan the tool path

During the machining process, the tool starts from one end face of the tooth tip, and first moves along the tooth direction to complete the milling of the entire tooth width b;

Then take the second cut along the tooth direction;

And so on, until the envelope milling of the tooth surface is completed.

In the whole milling process, the processing step and the tooth surface accuracy are controlled according to a specific algorithm to achieve high-precision and high-efficiency envelope milling processing of involute cylindrical gears.

As shown in Figure 5, it is the involute tooth enveloping tool position point simulated by the CAM software when the tool envelope cutter position points of the involute tooth surface are the same. Fig. 5(a) is a finishing method considering the accuracy characteristics of the tooth surface according to the present invention, and the tool position points of the tooth surface are mainly concentrated near the pitch circle with higher accuracy requirements. Figure 5(b) is a traditional finishing method based on the equal residual height method, and the tooth surface tool position points along the tooth root to the tooth tip show a trend from dense to sparse.

As shown in Figure 6, it is the relationship between the radial length of the involute tooth surface and the residual height difference. Figure 6 (a) is the use of the present invention to consider the precision characteristics of the tooth surface, the residual height difference of the tooth surface obtained along the pitch circle to the tooth tip and tooth root ends respectively show an increasing trend, near the pitch circle (435mm<r _v <445mm) the residual height difference Δt<2.5μm. Figure 6(b) is the traditional finishing method based on the equal residual height method, and the obtained tooth surface residual height difference is uniformly distributed along the tooth surface, that is, the residual height difference at the pitch circle and the residual height difference of the tooth tip and root part Δt= 6μm, and for involute gears, the tooth surface near the pitch circle is the main meshing area, and the part close to the tooth root and tooth tip hardly participates in the meshing. The involute tooth surface finishing based on the equal residual height difference method The method resulted in a large number of redundant passes in the tooth root and tooth tip, which not only reduced the machining efficiency, but also failed to consider the accuracy requirements of the meshing area at the pitch circle. Therefore, the envelope milling processing method of an involute cylindrical gear considering the accuracy characteristics of the tooth surface proposed by the present invention can not only improve the envelope milling processing efficiency of the gear, but also make the tooth surface have better meshing performance.

The embodiments are the preferred embodiments of the present invention, but the present invention is not limited to the above-mentioned embodiments. Without departing from the essence of the present invention, any obvious improvement, substitution, or replacement can be made by those skilled in the art. All variants belong to the protection scope of the present invention.

Claims

An envelope milling method for involute cylindrical gears considering the characteristics of tooth surface accuracy, which is characterized in that it comprises:

S01: Select the tool according to the parameters of the gear workpiece to be processed, and determine the tool diameter and the length of the cutting edge of the tool;

S02: Use eccentric milling to process to determine the dynamic eccentricity e i of the tool axis relative to the gear axis;

S03: According to the accuracy requirements of the main meshing area of the tooth surface of the gear, by constructing the formula of the step length in the tooth profile direction, the maximum distance of the step length along the tooth profile direction Δl max and the adjacent step length of the two tool position points are solved The distance Δl i and the involute expansion angle u i corresponding to each tool position point on the tooth surface are used to construct the curve equation Δt i =f(Δu i ) between the expansion angle of the involute tooth profile and the residual height difference of the tooth surface. Processing tool position points;

S04: Plan the tool path according to the tool location point.
The envelop milling method for involute cylindrical gears considering the characteristics of tooth surface accuracy according to claim 1, characterized in that, in the step S01, an end mill or rod milling cutter is selected for the medium and small modulus involute cylindrical gears For large-modulus involute cylindrical gears, use conical disk milling cutters or rod milling cutters.
The enveloping milling method of an involute cylindrical gear considering the accuracy characteristics of the tooth surface according to claim 2, wherein in the step S01, the tool diameter D t ≥ φ 10 mm, and the blade length L t ≥ 20 mm.
The enveloping milling method of an involute cylindrical gear considering the characteristics of tooth surface accuracy according to claim 1, wherein the calculation formula of the eccentricity e i is:

In the formula, r b is the gear base circle radius; σ 0 is the base circle tooth groove half angle; u i is the involute expansion angle corresponding to each tool position on the tooth surface;
Is the rotation angle of the rotary table fixedly connected to the gear, and
D t is the tool diameter.
The enveloping milling method of an involute cylindrical gear considering the characteristics of tooth surface accuracy according to claim 1, wherein the step S03 is specifically:

S03.1 divides the tool position points of the tool along the gear tooth profile direction into n equal parts, and each tool position point on the tooth surface is distributed according to the parabolic equation. Set the maximum distance of the cutting step along the tooth profile direction as Δl max and the minimum distance It is Δl min = Δl max /5, the distance between adjacent steps of two tool positions is Δl i , and the step length of the tool along the tooth profile direction satisfies the following formula:

S03.2 According to the given gear workpiece, the height of the tooth surface involute along the radial direction is obtained as H, and the maximum distance Δl max of the cutting step along the tooth profile direction can be solved by formula (3):

S03.3 Substitute the Δl max obtained in step S03.2 into formula (2), traverse the number of passes i∈[0,n], and get the step distance corresponding to each tool position on the tooth surface in turn as Δl i ;

S03.4 Given Δl max and the current number of passes i, from formula (4), the involute expansion angle u i on the tooth surface corresponding to each tool location point (x p , y p ) on the parabolic equation is obtained:

In the formula, r f is the radius of the root circle; r b is the radius of the base circle; σ 0 is the half angle of the base circle tooth groove;

S03.5 Assuming that the coordinates of two adjacent tool position points A and B on the involute line are (x A , y A ) and (x B , y B ) respectively, and A and B intersect at point C, then point C Is the maximum residual height difference between adjacent tool location points, assuming that the coordinates of point C are (x C ,y C ), assuming that the slopes of two adjacent tool location points A and B on the involute line are k A and k respectively B , from the geometric relationship of A, B, and C, the following formula can be obtained:

According to the characteristics of involute, the slopes k A and k B of two adjacent tool positions A and B on the involute line are respectively:

In the formula, u A and u B are the involute expansion angles of two adjacent tool positions A and B respectively;

And the involute equations of two adjacent tool positions A and B are:

Substituting formula (6)(7)(8) into formula (5) can get the coordinates of point C (x C ,y C ),

Calculate the residual height difference of point C:

According to formula (9), the residual height difference Δt i between adjacent tool positions can be obtained in turn. From the known involute tooth profile expansion angle Δu i , the involute tooth profile expansion angle Δu i and The curve equation between tooth surface residual height difference Δt i is:

Δt i =f(Δu i ) Equation (10)

S03.6 Determine the machining tool position according to the curve equation between the involute tooth profile expansion angle Δu i and the tooth surface residual height difference Δt i .
The envelop milling method of an involute cylindrical gear considering the accuracy characteristics of the tooth surface according to claim 5, wherein the specific method for determining the machining tool position in the step S03.6 is: making the tool path from The tooth profile from the pitch circle to the upper and lower ends respectively presents a dense to sparse distribution. Even if the tooth surface residual height difference Δt i is the smallest near the main meshing area near the pitch circle, the tooth surface of the secondary meshing area far away from the pitch circle The residual height difference Δt i gradually increases, and the tooth surface residual height difference Δt i is the largest in the non-meshing area near the tooth root and tooth tip.
The envelop milling method of an involute cylindrical gear considering the characteristics of tooth surface accuracy according to claim 1, wherein the step S04 is specifically:

The tool starts from one end face of the tooth tip, and first moves the first tool along the tooth direction to complete the milling of the entire tooth width b;

Feed the length of Δu i along the involute tooth profile in the tooth slot direction;

Then take the second cut along the tooth direction;

And so on, until the envelope milling of each tooth surface is completed.