A method for grinding processing of involute cylindrical gear parabolic modification

Abstract

The application discloses a grinding machining method for involute cylindrical gear parabolic modification, selects multiple position points on the parabolic modification tooth profile, fits into an approximate circular arc, calculates the circular arc drum-shaped amount and the fitting circular arc error value, and solves the forming grinding machine tool machining problem of the involute cylindrical gear parabolic modification. The application has the advantages of simple operation.

Description

Technical Field

[0001] This invention relates to the field of gear grinding, and more particularly to a gear grinding method for parabolic shaping of involute cylindrical gears. Background Technology

[0002] When machining tooth profiles without a specified crowning amount (such as parabolic profiles) on similar machine tools, both domestically and internationally, a gradual adjustment method is generally used. This involves first setting initial values ​​based on experience, then comparing measurement data with drawings, and finally adjusting the relevant points using the point correctors interface in the machine tool program. This process is repeated until the requirements are met. This method requires adjusting the correction values ​​of multiple points (up to 50 points) for any single defect in the tooth profile, and these points must be adjusted proportionally. This method is difficult to master and inefficient. In some aerospace products, the tooth profile of involute cylindrical gears requires parabolic (consisting of 5 points) modification. Although the GP500H equipment has a point programming program, its programming is complex, with many parameters and complicated parameter settings, requiring high operator skill and technical expertise. It is generally used for non-involute gears. Furthermore, in forming gear grinding machines such as the GP500H, the tooth profile can be programmed in up to three segments, each segment being either a straight line or an arc. Each segment program needs to define the starting diameter, ending diameter, taper (i.e., the ending modification amount), and arc camber amount (the straight camber amount is 0). However, these parameters are not present in the parabolic modification parameters for involute cylindrical gears, and the gear grinding machine cannot process parabolic modified involute cylindrical gears. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a simple grinding method for parabolic shaping of involute cylindrical gears.

[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0005] A grinding method for parabolic profile modification of involute cylindrical gears includes the following steps:

[0006] Step S1: Based on the involute principle, basic gear parameters, and parabolic profile modification requirements, determine the tooth profile drawing parameters and draw the parabolic modified tooth profile;

[0007] Step S2: Select at least five points on the parabolic tooth profile, establish a coordinate system, and obtain the coordinate values ​​of the points.

[0008] Step S3: Select three of the at least five position points in step S2 to fit an approximate arc, and calculate the coordinates of the center point C of the approximate arc, the radius r of the approximate arc, and the arc bulge δ.

[0009] Step S4: Calculate the error value ΔP of the fitted arc based on the coordinates of the remaining position point P that was not selected in step S3, the coordinates of the reference point P' on the approximate arc with the same diameter as point P, the coordinates of the center point C of the approximate arc, and the radius r. If the error value ΔP is less than the standard error value, proceed to step S5; otherwise, reselect the position point and proceed to step S2.

[0010] Step S5: Grind the parabolic profile of the involute cylindrical gear using a gear grinding machine according to the arc drum shape δ.

[0011] As a further improvement to the above technical solution:

[0012] In step S3, the coordinates of the three positions are set as M1(x1, y1), M2(x2, y2), and M3(x3, y3). The coordinates of the center C of the approximate arc are obtained according to formulas (I) and (II), the parabola shaping radius r is obtained according to formula (III), and the arc bulging amount δ is obtained according to formula (V).

[0013]

[0014]

[0015]

[0016]

[0017] In step S4, let the coordinates of point P be P(x, y) and the coordinates of P' be P′(x', y), and calculate the error value ΔP of the fitted arc according to formulas (VI) and (VII).

[0018]

[0019]

[0020] The upper limit of the standard error value is 0.006 mm.

[0021] As a general inventive concept, the present invention also provides a gear grinding system for parabolic profile modification of involute cylindrical gears, comprising:

[0022] The first acquisition module is used to determine the tooth profile drawing parameters and draw the parabolic modified tooth profile based on the involute principle, basic gear parameters and parabolic modification requirements.

[0023] The second selection module is used to select at least five position points on the parabolic tooth profile, establish a coordinate system and obtain the coordinate values ​​of the position points.

[0024] The third fitting module is used to select three of the at least five location points to fit an approximate arc, and calculate the coordinates of the center point C of the approximate arc, the radius r of the approximate arc, and the arc bulge δ.

[0025] The fourth judgment module is used to calculate the error value ΔP of the fitted arc based on the coordinate value of the remaining position point P that was not selected in step S3, the coordinate value of the reference point P' on the approximate arc with the same diameter as point P, the coordinate value of the center position C of the approximate arc, and the radius r. When the error value ΔP is less than the standard error value, it jumps to the fifth processing module; otherwise, it reselects the position point and jumps to the second selection module.

[0026] The fifth processing module is used to grind the parabolic profile of the involute cylindrical gear using a gear grinding machine according to the arc drum shape δ.

[0027] As a general inventive concept, the present invention also provides a computer-readable storage medium storing a computer program programmed or configured to perform the aforementioned grinding process for parabolic shaping of involute cylindrical gears.

[0028] Compared with the prior art, the advantages of the present invention are as follows:

[0029] This invention provides a grinding method for parabolic shaping of involute cylindrical gears. By selecting multiple points on the parabolic tooth profile and fitting them into an approximate circular arc, the amount of the circular arc bulge and the error value of the fitted circular arc are calculated. This method solves the problem of parabolic shaping of involute cylindrical gears in the machining of forming grinding machines and is simple to operate. Attached Figure Description

[0030] Figure 1 This is a flowchart of the present invention.

[0031] Figure 2 It is a geometric coordinate diagram of a three-point circular arc.

[0032] Figure 3 It is a fitted circular arc coordinate graph.

[0033] Figure 4 This is the tooth-shaped metering sheet of Example 1. Detailed Implementation

[0034] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Unless otherwise specified, the instruments or materials used in the present invention are commercially available.

[0035] Example 1:

[0036] like Figure 1As shown, this invention discloses a grinding method for parabolic shaping of involute cylindrical gears. The gear blank has been finished, including the machining of reference datums such as supports, fixation, and positioning for grinding. The tooth profile has been rough-machined, with a certain grinding allowance. The grinding equipment is a forming grinding machine, and the grinding process card provides parabolic shaping parameters (shaping diagram or 5-point diagram).

[0037] Where r refers to the radius of the shaping circle, δ refers to the amount of bulging, and ΔP refers to the error at point P. The grinding method for parabolic shaping of involute cylindrical gears according to the present invention includes the following steps:

[0038] Step S1: Based on the involute principle, basic gear parameters, and parabolic profile modification requirements, determine the tooth profile drawing parameters and draw the parabolic modified tooth profile;

[0039] Step S2: Select at least five points on the parabolic tooth profile, establish a coordinate system, and obtain the coordinate values ​​of the points.

[0040] Step S3: Select three of the at least five position points in step S2 to fit an approximate arc, and calculate the coordinates of the center point C of the approximate arc, the radius r of the approximate arc, and the arc bulge δ.

[0041] Step S4: Calculate the error value ΔP of the fitted arc based on the coordinates of the remaining position point P that was not selected in step S3, the coordinates of the reference point P' on the approximate arc with the same diameter as point P, the coordinates of the center point C of the approximate arc, and the radius r. If the error value ΔP is less than the standard error value, proceed to step S5; otherwise, reselect the position point and proceed to step S2.

[0042] Step S5: Based on the arc drum shape amount δ, the position of the selected point on the approximate arc, and the modification amount, use a gear grinding machine to grind the parabolic modified tooth profile of the involute cylindrical gear.

[0043] This invention relates to the following principles:

[0044] 1) Geometric coordinate diagram of a three-point circular arc.

[0045] Given three points M1(x1, y1), M2(x2, y2), and M3(x3, y3), see the rectangular coordinate diagram below. Figure 2 (The X-axis of the rectangular coordinate graph represents the shaping amount, and the Y-axis represents the radius value). C(x0, y0) is the center of the approximate arc determined by the three points M1, M2, and M3, and the radius of the approximate arc is r. Points A, B, and D are the midpoints of line segments M1M2, M2M3, and M1M3, respectively.

[0046] According to geometry, the intersection point C of the perpendicular bisectors of any two chords is the center of the circle;

[0047] The coordinates of point A are:

[0048] The coordinates of point B are:

[0049] The coordinates of point D are:

[0050] Point E is the intersection of the extension of CD and the arc, and DE is the drum-shaped quantity δ of the sector M1M2M3.

[0051] 2) Calculation of the amount of circular arc bulge

[0052] Since the slope of M1M2 is:

[0053] Therefore, the slope of AC is:

[0054] Again ∵

[0055] From (1) = (2), we get:

[0056]

[0057]

[0058] Similarly, according to line BC, we can obtain:

[0059]

[0060]

[0061] From (4) = (6) and (3) = (5), we can obtain:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] 3) Calculation of circular arc error for parabolic fitting

[0068] The fitted circular arc of the parabola (composed of points M1, M2, and M3) is shown below. Figure 3 Let P(x, y) be a point on the parabola, and P′(x′, y) be a point on the fitted circular arc with the same diameter as point P.

[0069] but,

[0070] Error at point P

[0071] If the calculated error is large and exceeds the standard error value of the tooth shape (0.006 mm in this invention), the coordinates of the three points of the fitted arc should be adjusted within the tolerance range according to the specific situation, and the calculation should be repeated.

[0072] Example 1

[0073] Taking the parabolic profile modification of aerospace gear parts as an example, the basic parameters of the gear are known as follows: number of teeth Z = 48, module m = 3.90291, pressure angle α = 25.90507°, helix angle B = 0, and addendum circle diameter d. a =196, tooth root circle diameter d i =178, the diameter of the starting circle of the involute, dq, is Φ181.0095.

[0074] Given the parabola shaping requirements: the diameter / shaping amount at 5 points (P1~P5) of the parabola are as follows: d1=Φ190.676 / 0, d2=Φ191.842 / -0.002375, d3=Φ193.008 / -0.0095, d4=Φ194.174 / -0.021375, d5=Φ195.34 / -0.038. The shaping amount / radius coordinates of each point are P1(0,95.338), P2(0.002375,95.921), P3(0.0095,96.504), P4(0.021375,97.087), and P5(0.038,97.67). The parabolic profile modification amount is given by the design, which specifies the modification amount at the corresponding diameter of the tooth surface. A coordinate system is established with the center of the circle as the origin.

[0075] 1) Calculation of the amount of circular arc bulge

[0076] Taking the first, middle, and last three points, namely P1, P3, and P5, as the fitted arc for calculation, and substituting the coordinates of the three points P1, P3, and P5 into formulas (7) to (11), we can obtain:

[0077] x0 = 71.58882895;

[0078] y0 = 95.3377678;

[0079] r = 71.58882895;

[0080] δ=0.00949874≈0.0095.

[0081] 2) Calculation of the error of the circular arc fitted to the parabola

[0082] Points P2 and P4 were not involved in the calculation of the fitted circular arc, so their error values ​​need to be calculated.

[0083] Substituting the coordinates of points P2 and P4, and the calculated x0, y0, and r into formulas (12) and (13), we can obtain:

[0084] have to:

[0085]

[0086] The error at point P2 is ΔP2 = x'2 - x2 = 8 × 10 -7 .

[0087] The error at point P4 is ΔP4 = x'4 - x4 = 1 × 10 -6 .

[0088] Therefore, the error is extremely small and can be ignored.

[0089] 3) Grinding parameter settings

[0090] Involute starting circle: Φ181.0095mm

[0091] End point of segment 1: Φ190.676mm

[0092] Segment 1 shaping amount: 0

[0093] First segment drum shape: 0

[0094] End point of segment 2: Φ190.676mm

[0095] Second trimming amount: -0.038mm

[0096] Second stage drum shape measurement: 0.0095mm

[0097] Paragraph 3 is for other needs (omitted here).

[0098] 4) Tooth profile inspection

[0099] Tooth profile measurement sheet Figure 4 As shown. By Figure 4 As can be seen, the tooth profile is qualified and within the K-shape diagram. The actual effect is as follows (taking the working surface parameters as an example, with the unit of measurement being mm by default):

[0100] The tooth profile pressure angle deviation requirement is ±0.004, but the actual deviation is -0.003.

[0101] The tooth profile deviation requirement is 0.006, but the actual deviation is 0.0008.

[0102] The total tooth profile deviation requirement is 0.0075, but the actual deviation is 0.0032.

[0103] The parabola shaping requirement is -0.038max, but the actual value is -0.0356.

[0104] Other items such as cumulative pitch, gear runout, and tooth direction are all 100% qualified.

[0105] A gear grinding system for parabolic profile modification of involute cylindrical gears, comprising:

[0106] The first acquisition module is used to determine the tooth profile drawing parameters and draw the parabolic modified tooth profile based on the involute principle, basic gear parameters and parabolic modification requirements.

[0107] The second selection module is used to select at least five position points on the parabolic tooth profile, establish a coordinate system and obtain the coordinate values ​​of the position points.

[0108] The third fitting module is used to select three of the at least five location points to fit an approximate arc, and calculate the coordinates of the center point C of the approximate arc, the radius r of the approximate arc, and the arc bulge δ.

[0109] The fourth judgment module is used to calculate the error value ΔP of the fitted arc based on the coordinate value of the remaining position point P that was not selected in step S3, the coordinate value of the reference point P' on the approximate arc with the same diameter as point P, the coordinate value of the center position C of the approximate arc, and the radius r. When the error value ΔP is less than the standard error value, it jumps to the fifth processing module; otherwise, it reselects the position point and jumps to the second selection module.

[0110] The fifth processing module is used to grind the parabolic modified tooth profile of the involute cylindrical gear using a gear grinding machine, based on the arc drum shape δ, the position of the selected point on the approximate arc, and the modification amount.

[0111] A computer-readable storage medium storing a computer program programmed or configured to perform the aforementioned grinding process for parabolic shaping of involute cylindrical gears.

[0112] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0113] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] While the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the invention. Any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the scope of the present invention, should fall within the protection scope of the present invention.

Claims

1. A method of generating involute cylindrical gear parabolic modification by gear grinding, characterized in that: The method comprises the following steps: Step S1, determining tooth profile drawing parameters and drawing parabolic modification tooth profile according to the involute principle, basic parameters of the gear and parabolic modification requirements; Step S2, selecting at least five position points on the parabolic modification tooth profile, establishing a coordinate system and obtaining coordinate values of the position points; Step S3, selecting three position points from the at least five position points in step S2 to fit an approximate circular arc, and calculating the center position of the approximate circular arc Point coordinate value, radius r of the approximate circular arc, and circular arc drum amount ; The step S3, set three position point coordinate values are , , , according to formula (I) and (II) get the approximate circular arc center position Point coordinate values are ( ), according to formula (III) get parabolic modification radius r, according to formula (V) get circular arc drum amount ; (Ⅰ) (Ⅱ) （Ⅲ） （Ⅴ） Step S4, according to the coordinate values of the remaining position points P not selected in step S3, the coordinate values of the reference points P' on the approximate circular arc with the same diameter as the P points, the center position of the approximate circular arc the point coordinate values and the radius r to calculate the error value Δ of the fitted circular arc When the error value Δ is less than the standard error value, step S5 is performed, otherwise, the position points are reselected and step S2 is performed; Step S5, calculating the drum amount according to the circular arc The parabolic modification profile of the involute cylindrical gear is ground by a gear grinding machine.

2. The gear grinding method according to claim 1, characterized in that: The step S4, set P point coordinate value is , , P' coordinate value is , , according to formula (VI) and (VII) calculation fitting circle error value Δ ; （Ⅵ） （Ⅶ）。 3. A gear grinding method according to claim 2, characterized in that: The upper limit of the standard error value is 0.006 mm.

4. A gear lapping system for involute cylindrical gear parabolic modification for performing the gear lapping method of any one of claims 1 to 3, characterized in that: The method comprises the following steps: A first acquisition module is configured to determine tooth profile drawing parameters and draw parabolic modification tooth profile according to the involute principle, basic parameters of the gear and parabolic modification requirements; A second selection module is configured to select at least five position points on the parabolic modification tooth profile, establish a coordinate system and obtain coordinate values of the position points; The third fitting module is configured to select three position points from the at least five position points to fit an approximate circular arc, and calculate a center position of the approximate circular arc The point coordinate value, the radius r of the approximate circular arc, and the circular arc drum amount ; The fourth judgment module is used to approximate the center position of the arc based on the coordinates of the remaining position point P that was not selected in step S3, the coordinates of the reference point P' on the arc that has the same diameter as point P, and the approximate coordinates of the arc. The error value Δ of the fitted circular arc is calculated using the point coordinates and radius r. When the error value Δ If the value is less than the standard error, proceed to the fifth processing module; otherwise, reselect the position point and proceed to the second selection module. A fifth processing module is configured to process the circular-arc drum-shaped quantity according to a fifth processing formula The parabolic modification profile of the involute cylindrical gear is ground by a gear grinding machine.

5. A computer readable storage medium, characterized in that, The computer readable storage medium stores a computer program programmed or configured to perform the gear grinding method for parabolic modification of an involute cylindrical gear according to any one of claims 1-3.

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