Indexable gear hob peripheral grinder control method

Abstract

The application discloses a grinding method for a peripheral grinding machine of an indexable gear hob, and based on the forming principle of involute, a mathematical model for solving the base circle radius of involute of the indexable gear hob is provided, and in combination with the grinding principle of the peripheral blade grinding machine of the indexable cutter, a mathematical model for grinding the indexable gear hob is established, so that the problem that the machining precision is low due to the use of an arc to fit the involute surface during the machining of the indexable gear hob is solved. The application provides a new solution for the grinding machining of the indexable gear hob, and can effectively improve the machining efficiency and the machining precision.

Description

Technical Field

[0001] This invention belongs to the field of peripheral grinding machines for indexable cutting tools, and specifically relates to a control method for peripheral grinding machines for indexable gear hobs. Background Technology

[0002] Indexable cutting tools, as an advanced type of tool, possess advantages such as high hardness, high durability, quick tool change, long tool life, and low operating costs, and are widely used in machining. With the continuous development of industrial technology, the shapes of indexable cutting tools are also constantly evolving to adapt to various high-precision machining requirements, making the characteristics of indexable cutting tools increasingly complex.

[0003] Involute gears are widely used in gear pairs, and gear hobbing is a highly efficient and widely used method for machining the tooth profile of gears. However, most current domestic research on the hobbing of indexable gears uses a circular arc fitting method for grinding, which leads to certain tooth profile errors in the machined gears. In severe cases, it can cause obvious fitting marks on the hob surface, affecting the surface accuracy of the involute gear hob and thus significantly impacting the machining accuracy of the hobbed gears. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a peripheral grinding control method for indexable gear hobs, solving the problem that existing indexable gear hobs, manufactured using circular arc fitting grinding methods, suffer from low hob precision and poor surface quality, thus affecting the machining accuracy of involute gears.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A control method for a peripheral grinding machine of an indexable gear hob, comprising the following steps:

[0006] 1) Measure blade data using DWG files;

[0007] 2) Calculate the base circle radius r of the involute segment of the cutting tool. b ;

[0008] 3) Based on the base circle radius r b Establish a polar coordinate system based on the positional relationship between the involute segment of the tool and its corresponding position on the base circle, and determine the poles and polar axes of the involute base circle polar coordinate system and the tool polar coordinate system, respectively.

[0009] 4) Calculate the radius of curvature R at the starting point of the involute segment of the cutting tool. CS The distance between the center of the tool and the center of the involute base circle is O-O';

[0010] 5) Determine the division of the physical axis B-axis for each rotation, denoted as BFD. Rotate the physical axis B-axis according to BFD to obtain the current angle B of the physical axis B-axis.θ = B θ + BFD

[0011] 6) judge the current angle B of the physical axis B, and judge the size of the tangent angle θ3 at the start and end points of the tool involute segment, if B θ < θ3, jump to step 7); if θ3 < B θ < θ3 + BFD, let B θ = θ3, and jump to step 7); if B θ = θ3 + BFD, jump to step 9); θ

[0012] 7) when the B axis drives the tool to rotate an incremental angle Δθ, calculate the curvature radius R CΔθ of the tool involute under the division;

[0013] 8) in the polar coordinate system O'-x, calculate the feed amount of the physical axis X when the incremental angle Δθ, and get the absolute coordinate X corresponding to the physical axis X Δθ ;

[0014] 9) write the current angle B of the physical axis B θ and the absolute coordinate X corresponding to the physical axis X Δθ into the point file executable by the system, and jump to step 5);

[0015] 10) send the data stored in the executable point file to the CNC system, and the system executes the point file, so as to realize the grinding of the indexable gear hob.

[0016] Further, the tool data measured in the above step 1) specifically includes:

[0017] Take the curvature radii of any two points M1 and M2 on the tool involute as R C1 , R C2 , draw the tangent lines L1 and L2 of the two points M1 and M2 on the involute, and the included angle is θ2; draw the tangent line L3 and the normal line L5 at the starting point of the tool involute, and take the distances from the tool center O' to L3 and L5 as XS and YS respectively, and take the included angle between L3 and L2 as θ1; draw the tangent line L4 at the end point of the tool involute, and take the included angle between L4 and L3 as θ3.

[0018] Further, the calculation of the base circle radius r b of the tool involute segment in the above step 2) includes the following contents:

[0019] The curvature radii R C1 and R C2 at any two points M1 and M2 are:

[0020] ​

[0021] In the formula Let M1 and M2 be the base circle rotation angles corresponding to points M1 and M2, respectively. According to the properties of the involute, for... have:

[0022]

[0023] Therefore, the radius r of the base circle corresponding to the involute segment of the cutting tool b for:

[0024]

[0025] Where θ2 is the angle between the tangents L1 and L2 on the involute at points M1 and M2.

[0026] Furthermore, the calculation of the radius of curvature and the distance between the centers of the base circles in step 4) above includes the following:

[0027] The radius of curvature R at the starting point of the involute segment of the cutting tool CS for:

[0028] R CS =R C2 -r b *θ1

[0029] In the formula R C2 Let θ be the radius of curvature at any point M2 on the involute of the tool, and θ1 be the angle between the tangent L2 at point M2 and the tangent L3 at the starting point of the involute.

[0030] The distance O-O' between the center of the tool and the center of its involute base circle is:

[0031]

[0032] α=arctan((R CS -X s ) / (r b +Y S ))

[0033] In the formula, α is the angle between line O-O' and line OB, and X s Y is the distance from the geometric center of the tool to the tangent at the starting point of the involute segment of the tool. s This is the distance from the geometric center of the tool to the normal at the starting point of the involute segment of the tool. Further, in step 7) above, the radius of curvature R... CΔθ The calculations include the following:

[0034] When the tool rotates by an incremental angle Δθ, the radius of curvature R of the involute segment of the tool... CΔθ for:

[0035] R CΔθ = r b * Δθ + R CS

[0036] wherein R CS is the radius of curvature at the start of the tool involute segment,

[0037]

[0038] wherein is the angle of rotation of the base circle corresponding to the start of the tool involute segment, said angle of rotation being in radians. Further, when the current angle of the physical axis B is B θ , the absolute coordinate X Δθ corresponding to the physical axis X is calculated as follows:

[0039] When the current angle of the physical axis B is B θ , in the polar coordinate system O'-x, the X-axis point position X Δθ corresponding to the point M can be obtained by the length L C′O′ of the segment C'O' and the radius of curvature R CΔθ of the tool involute segment at the index angle as follows:

[0040]

[0041] wherein

[0042] L C′O′ = L OO′ * sin (α + Δ θ )

[0043] wherein α is the angle between the straight line O-O' and the straight line O-B, and Δ θ is the incremental angle Δ θ .

[0044] Compared with the prior art, the present application divides the involute curve into small curve segments through the indexing algorithm, and calculates the linkage point position of the X-axis and the B-axis of the indexable peripheral grinding machine through the positional relationship between the hob center and the center of the involute base circle, so that the machining efficiency of the machine tool can be fully utilized, the grinding precision of the indexable gear hob can be improved, and the surface quality of the gear tooth surface can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 A model diagram of the indexable peripheral grinding machine.

[0046] Figure 2 A flow chart of the control method of the indexable gear hob peripheral grinding machine.

[0047] Figure 3 A preferable data measurement diagram of the indexable gear hob.

[0048] Figure 4 It is a polar coordinate system based on the center of the base circle and the geometric center of the cutter.

[0049] Figure 5 It is a more optimal key data calculation schematic diagram.

[0050] Figure 6 It is a more optimal X-axis feed coordinate calculation schematic diagram. DETAILED DESCRIPTION

[0051] The application will be further described below in conjunction with the drawings and specific embodiments. It should be pointed out that only an optimal technical solution is used to elaborate the technical solution and design principle of the application below, but the protection scope of the application is not limited thereto.

[0052] The embodiments are preferred embodiments of the application, but the application is not limited to the above-mentioned embodiments. Any obvious improvement, replacement or modification made by those skilled in the art without departing from the essential content of the application shall fall within the protection scope of the application.

[0053] The main structure of the indexable cutter peripheral edge grinder is shown in Figure 1 The main structure of the indexable cutter peripheral edge grinder is shown in The main structure of the indexable cutter peripheral edge grinder is shown in

[0054] The main structure of the indexable cutter peripheral edge grinder is shown in Figure 2 The control method of the indexable gear hobbing cutter peripheral grinder provided by the application comprises the following steps:

[0055] 1) measuring cutter data through a DWG file;

[0056] As a preferred embodiment of the application, as shown in Figure 2As shown, in AutoCAD and other drawing software, the relevant data for measuring indexable cutting tools are as follows: Take the radius of curvature R at any two points M1 and M2 on the involute of the tool. C1 R C2 Draw tangents L1 and L2 to points M1 and M2 on the involute, and set the included angle as θ2. Draw tangent L3 and normal L5 at the starting point of the involute of the tool, and take the distances from the tool center O' to L3 and L5 as XS and YS respectively, and take the included angle between L3 and L2 as θ1. Draw tangent L4 at the ending point of the involute of the tool, and take the included angle between L4 and L3 as θ3.

[0057] As a preferred embodiment of the present invention, R C1 =65.6289, R C2 =101.2917, θ1=6.612, θ2=9.421, θ3=19.7962.

[0058] 2) Calculate the base circle radius r of the involute segment of the cutting tool. b ;

[0059] As a preferred embodiment of the present invention, based on the relevant properties of the involute, it is known that the radius of curvature R at any point on the involute is... c for:

[0060]

[0061] In the formula r b The radius of the base circle corresponding to the involute. Let M be the base circle rotation angle corresponding to any point M;

[0062] therefore, Figure 3 The radius of curvature R at any two points M1 and M2 in the equation C1 R C2 for:

[0063]

[0064] In the formula Let M1 and M2 be the base circle rotation angles corresponding to points M1 and M2, respectively. According to the properties of the involute, for... have:

[0065]

[0066] Therefore, the radius r of the base circle corresponding to the involute segment of the cutting tool b for:

[0067]

[0068] Where θ2 is the angle between the tangents L1 and L2 on the involute at points M1 and M2.

[0069] 3) according to the base circle radius r b The position relationship corresponding to the tool involute segment on the base circle is established, and the pole and the polar axis of the polar coordinate system of the involute base circle and the polar coordinate system of the tool are determined respectively;

[0070] As a preferred embodiment of the present application, according to the calculated position relationship corresponding to the base circle radius and the tool involute segment on the base circle, a polar coordinate system as shown in Figure 4 The polar coordinate system O-r is established with the center of the involute base circle as the pole and the line connecting the center and the starting point of the involute as the polar axis, and the polar coordinate system O'-x is established with the tool center as the pole and the normal direction of the starting point of the tool involute segment as the polar axis. The coordinate system is fixed to the machine tool, O' is the center of the workpiece clamping shaft B axis, that is, the physical B axis.

[0071] 4) Calculate the curvature radius R CS of the starting point of the tool involute segment, and the distance O-O' between the tool center and the center of the involute base circle;

[0072] As a preferred embodiment of the present application, as shown in Figure 5 , the straight line B-K and K-K' are the normal line and tangent line at the starting point of the tool involute segment respectively, and the perpendicular lines are drawn through O' point to B-K and K-K' respectively, and the foot points are K" and K' respectively. Then O'-K' and O'-K" are XS and YS respectively. As known from the foregoing, the curvature radius R CS of the starting point of the tool involute segment is:

[0073] R CS =R C2 -r b *θ1

[0074] In the formula, R C2 is the curvature radius of any point M2 on the tool involute, and θ1 is the included angle between the tangent line L2 at point M2 and the tangent line L3 at the starting point of the involute;

[0075] And through the related properties of the involute, BK=R CS , OB=r b Therefore, the distance between the tool center and the center of its involute base circle, that is, the distance O-O' between the centers of the polar coordinate systems O-r and O'-x, is:

[0076]

[0077] α=arctan((R CS -X s ) / (r b +Y S ))

[0078] wherein a is the angle between the straight line O-B and the polar line O-O' of the polar coordinate system, X s is the distance from the geometric center O' of the tool to the tangent at the starting point of the tool involute segment, and Y s is the distance from the geometric center O' of the tool to the normal at the starting point of the tool involute segment.

[0079] 5) Determine the index of each rotation of the physical shaft B shaft, denoted as BFD, and the physical shaft B shaft is rotated by BFD to obtain the current angle B θ of the physical shaft B shaft. θ

[0080] As a preferred embodiment of the present application, according to the involute geometric principle, the angle θ3 between the tangents L3 and L4 at the starting and ending points of the tool involute segment is equal to the corresponding base circle rotation angle θ at the starting and ending points of the involute segment. According to the working principle of the peripheral grinder and the differential geometry principle, the rotation angle θ is subdivided into n small increments Δθ, and the increment of the rotation angle is the same as the increment of the rotation of the grinder B shaft, that is, the corresponding increments of rotation in the polar coordinate systems O-r and O'-x are the same. A commonly used incremental calculation empirical formula is given, which can be adjusted according to the actual processing situation:

[0081] BFD = Δθ = int(θ * 20) / 10000

[0082] Initialize the parameter B θ = 0, which represents the rotation angle of the B shaft relative to the starting position under the current index.

[0083] 6) Judge the size of the current angle B θ of the physical shaft B shaft and the angle θ3 between the tangents, if B θ < θ3, then jump to step 7); if θ3 < B θ < θ3 + BFD, then let B θ = θ3, and jump to step 7); if B θ = θ3 + BFD, then jump to step 9);

[0084] 7) When the B shaft drives the tool to rotate an incremental angle Δθ, calculate the curvature radius R CΔθ of the tool involute under this index.

[0085] As a preferred embodiment of the present application, when the B shaft drives the tool to rotate an incremental angle Δθ, that is, when Δθ radians are rotated in the polar coordinate system O'-x, the corresponding curvature radius R CΔθ of the tool involute is:

[0086] R CΔθ = r b * Δθ + R CS ​

[0087] wherein is the rotation angle of the base circle at the starting point of the tool involute segment, and is in radian.

[0088] And the radius of curvature R CS at the starting point of the tool involute segment is:

[0089]

[0090] Therefore, in the polar coordinate system O'-x, the radius of curvature R CΔθ of the involute at each incremental angle Δθ is:

[0091] R CΔθ = r b * Δθ + R CS

[0092] 8) In the polar coordinate system O'-x, the feed amount of the physical axis X-axis when calculating the incremental angle Δθ is obtained, and the absolute coordinate X Δθ corresponding to the physical axis X-axis is obtained.

[0093] As a preferred embodiment of the present application, according to the related properties of the involute, Figure 6 wherein And ∠C'OO' = α + Δθ. A parallel vector of is drawn through the tool center point O', and intersects the tangent at point M of the involute segment at point M', so that ΔC'OO' is obtained:

[0094]

[0095] wherein α is the included angle between the straight line O-O' and the straight line O-B, and Δ θ is the incremental angle Δ θ .

[0096] In the polar coordinate system O'-x, the corresponding X-axis point position X CΔθ is obtained by the curvature radius R C′O′ and L Δθ under the division:

[0097]

[0098] Then, when the current angle of the physical axis B-axis is B θ , the absolute coordinate corresponding to the physical axis X-axis is X Δθ .

[0099] 9) The current angle B θ of the physical axis B-axis and the absolute coordinate X Δθ corresponding to the physical axis X-axis are written into a point position file executable by the system; and step 5) is performed.​

[0100] 10) The data stored in the executable point file, including the physical axis B axis incremental angle B θ , the physical axis X axis absolute coordinate X Δθ , is sent to the CNC system, and the system executes the point file, thereby realizing the grinding of the indexable gear hob.

Claims

1. A control method for a peripheral grinder of an indexable gear hob, characterized in that, The method comprises the following steps: 1) measuring tool data through a DWG file; 2) calculating the base circle radius r of the tool involute segment b ; 3) According to the base circle radius r b The position relationship corresponding to the tool involute segment on the base circle, the polar coordinate system is established, and the polar points and polar axes of the involute base circle polar coordinate system and the tool polar coordinate system are determined respectively; 4) Calculate the radius of curvature R at the start point of the tool involute segment CS The distance between the tool center and the center of the base circle of the involute, i.e. the distance between the poles of the polar coordinate system O-O'. 5) determine the index of each rotation of the physical axis B axis, denoted as BFD, the physical axis B axis rotates by BFD to obtain the current angle B of the physical axis B axis θ = B θ + BFD; 6) judge the current angle B of the physical axis B axis θ the size of the tangent angle θ3 at the start and end points of the tool involute segment, if B θ < θ3, jump to step 7); if θ3 < B θ < θ3 + BFD, let B θ = θ3, and jump to step 7); if B θ = θ3 + BFD, jump to step 9); 7) When the B-axis brings the tool to rotate an incremental angle Δθ, calculate the curvature radius R of the involute of the tool at this division CΔθ ; 8) In the polar coordinate system O'-x, the feed amount of the physical axis X axis is calculated when the increment angle Δθ, and the absolute coordinate X corresponding to the physical axis X axis is obtained Δθ ; 9) write the current angle B of the physical axis B into the system executable point file, go to step 5) θ , the absolute coordinate X corresponding to the physical axis X Δθ write the system executable point file, go to step 5) 10) sending the data stored in the executable point file to a CNC system, and executing the point file by the system, so as to realize the grinding of the indexable gear hob.

2. A control method for a peripheral grinder of an indexable gear hob as defined in claim 1, characterized in that, The tool data measured in the step 1) comprises: Take the curvature radius of any two points M1, M2 on the tool involute as R C1 , R C2 , draw the tangent lines L1, L2 of the two points M1, M2 on the involute, and the included angle is θ2; draw the tangent line L3 and the normal line L5 at the starting point of the tool involute, and take the distance from the tool center O' to L3 and L5 as XS and YS, respectively; take the included angle between L3 and L2 as θ1; draw the tangent line L4 at the end point of the tool involute, and take the included angle between L4 and L3 as θ3.

3. A control method for a peripheral grinder of an indexable gear hob as defined in claim 1, characterized in that, The base circle radius r of the involute segment of the tool in step 2) b The calculation includes the following: The radius of curvature R at any two points M1, M2 C1 , R C2 is: In the formula respectively, the corresponding base circle rotation angle at points M1, M2, and according to the involute property, there are: have: Thus, the radius r of the base circle corresponding to the tool involute segment is b r = 2R sin (a / 2) Wherein θ2 is the included angle of the tangent L1, L2 on the involute at the points M1, M2.

4. The control method for a peripheral grinder of an indexable gear hob as set forth in claim 1, characterized in that, The calculation of the curvature radius and the distance between the centers of the base circles in the step 4) comprises the following contents: The curvature radius R at the start of the tool involute segment CS Is: R CS = R C2 - r b * θ1 wherein R C2 is the radius of curvature at a point M2 on the tool involute, and θ1 is the angle between the tangent L2 at the point M2 and the tangent L3 at the starting point of the involute. The distance O-O' between the tool center and the center of the involute base circle, i.e. the distance between the poles of the polar coordinate system, is: a = arctan((R CS - X s ) / (r b + Y S )) where a is the angle between the straight line O-O' and the straight line O-B, X s is the distance from the tool geometric center to the tangent at the start point of the tool involute segment, Y s is the distance from the tool geometric center to the normal at the start point of the tool involute segment.

5. The control method for a peripheral grinder of an indexable gear hob as set forth in claim 1, characterized in that, The calculation of the radius of curvature R in said step 7) CΔθ includes the following: The radius of curvature R of the tool involute segment when the tool is rotated by an incremental angle Δθ CΔθ is: R CΔθ = r b * Δθ + R CS wherein R CS is the radius of curvature at the start of the tool involute segment, In the formula is the angle of the base circle corresponding to the start point of the tool involute segment, which is in radian.

6. A control method for a hob grinder for indexable gear hobs as claimed in claim 1, characterized in that The calculation of the absolute coordinate X corresponding to the physical axis X when the current angle of the physical axis B is B θ is as follows: Δθ The calculation of the absolute coordinate X corresponding to the physical axis X when the current angle of the physical axis B is B When the current angle of the physical axis B is B θ At that time, in the polar coordinate system O'-x, the radius of curvature R of the involute segment of the tool under this indexing is... CΔθ The length L of line segment C'O' C′O′ We can obtain the X-axis position X corresponding to point M. Δθ for: Wherein, L C′O′ = L OO′ *sin(α+Δ θ ) where a is the angle between the straight line O-O' and the straight line O-B, Δ θ is the incremental angle Δ θ .

Images