Tooth surface error correction method of spiral bevel gears using double spiral machining method

Abstract

The present invention relates to the automotive field and provides a method for correcting tooth surface errors of spiral bevel gears using a double helical machining method. The method obtains basic design parameters of the tooth surface of the spiral bevel gear, calculates measured point data of the tooth surface and tooth surface errors, defines differential surface features as tooth length features and tooth height features, obtains sensitive differential surfaces, and calculates sensitivity, thereby achieving separate corrections for tooth length inclination and tooth height inclination of the measured tooth surface. The beneficial effects of the present invention are that the present invention can input the errors between the actual tooth surface and the theoretical tooth surface into a computer, extract the shape features of the sensitive differential surfaces based on the actual differential surfaces, perform permutations and combinations, and separate the changes in the differential surfaces caused by parameter changes into changes in the tooth length direction and tooth height direction, thereby achieving separate corrections for the tooth length direction and tooth height direction of the measured tooth surface and simplifying the difficulty of reverse adjustment.

Description

Technical Field

[0001] The present invention relates to the automotive field, and in particular to a tooth surface error correction method for a spiral bevel gear using a double helical machining method. Background Art

[0002] Spiral bevel gears, also known as spiral bevel gears, are transmission components that provide stable transmission ratios with smooth, low-noise transmission. They offer advantages such as a large overlap factor, smooth transmission, low impact and noise, high load capacity, and long life. They are increasingly used in aerospace, construction machinery, automotive, and other fields.

[0003] The double helix method is a cutting principle for spiral bevel gears. It's highly efficient and allows for dry cutting. It's an advanced machining method for Gleason spiral bevel gears. Based on the principles of meshing and differential geometry, it uses the vector method to establish a mathematical model for cutting based on three reference points on the tooth surface, according to the kinematic positional relationship between the cutterhead, machine tool, and workpiece. This model then derives the calculation process for machine tool adjustment parameters.

[0004] Compared to the traditional "five-cut method," the double-helix method for machining spiral bevel gears offers advantages such as high efficiency, low production costs, high gear strength, and high-speed dry cutting. The double-helix method uses a single cutter head for both the large and small gears, simultaneously cutting both sides of the tooth groove. This method, also known as the "two-cut method or full-process method," is used. The large gear can be machined using the forming or generating method, while the small gear is machined using the spiral method.

[0005] The parameter error of the mathematical model directly affects the tooth surface error. The double-helix method uses a set of machine tool adjustment parameters to simultaneously process concave and convex tooth surfaces. Changing one machine tool adjustment parameter will simultaneously change the tooth surfaces on both sides, and the degree of influence and the influence rules on the two sides are different, making tooth surface design and correction more difficult.

[0006] The patent with application number 202110769068.6 provides a method for modifying line-contact arc bevel gears, and proposes a conjugate difference surface solution method based on fitting and interpolation algorithms, which can effectively improve computational efficiency, effectively alleviate the gear edge effect under error, and reduce the sensitivity of installation errors. However, it does not further refine the corrections in all directions of the gear teeth, and does not reduce the difficulty of counter-adjustment. Summary of the Invention

[0007] Aiming at the shortcomings of existing technologies, it is very difficult to solve the problem of the modification and reverse adjustment of spiral bevel gears.

[0008] The present invention provides a double helical spiral bevel gear tooth surface error correction method, comprising the following steps:

[0009] Step (1): Obtain the basic design parameters of the tooth surface of the spiral bevel gear;

[0010] Step (2): Based on the basic design parameters of the tooth surface obtained in step (1), the theoretical tooth surface is obtained by tooth surface modeling, and then discretized to obtain the preset tooth surface grid for CMM measurement. The CMM is used to measure the spiral bevel gear to obtain the actual measured point data of the tooth surface and the tooth surface error;

[0011] Step (3): Calculate the difference surface based on the theoretical tooth surface obtained in step (2) and the measured points on the tooth surface, and define the difference surface features as tooth length features and tooth height features. The tooth length feature refers to the row-direction feature of the gear tooth surface, and the tooth height feature refers to the column-direction feature of the gear tooth surface. The shape feature of the corresponding row or column is set as tilted or curved.

[0012] Step (4): Perform sensitivity analysis on the difference surface obtained based on step (3) to obtain the change trend of the tooth surface error after the adjustment parameters of each machine tool and the cutter head parameters change, that is, the sensitive difference surface, and decompose this change trend into the tooth length direction and the tooth height direction;

[0013] Step (5): Based on the sensitivity difference curve of each parameter obtained in step (4), which has features in the tooth length direction and tooth height direction, these features are extracted and divided by the parameter change to obtain the sensitivity. In other words, each parameter has sensitivity in the tooth length direction and tooth height direction. By selecting parameters with low sensitivity and performing proportional calculation and combination, the tooth length and tooth height direction features are eliminated, thereby achieving separate correction of the measured tooth surface tooth length inclination and tooth height inclination.

[0014] Preferably, in step (3), the specific steps are:

[0015] 3.1) The difference surface is the surface formed by the distance from the measured point on the tooth surface to the theoretical tooth surface. For each discrete point Pt(xt,yt,zt), its R and L values ​​can be calculated (R refers to the middle value in the tooth height direction, and L refers to the middle value in the tooth length direction). If the rotation axis is the z-axis, the R and L calculation formulas are:

[0016]

[0017] If there are i rows and j columns of tooth surface measurement points Pt(i, j), the corresponding tooth surface points Rt(i, j) and Lt(i, j) can be obtained by substituting them into formula (1). By inputting the basic tooth surface design parameters, machine tool processing parameters and cutter head parameters obtained in step (1) through CAGE software, the tooth surface point R(i, j) corresponding to the theoretical tooth surface direction and its normal vector N(i, j) can be obtained. The distance d′(i, j) between Pt and R is calculated, and the normal error can be approximately calculated as:

[0018] d(i,j)=d'(i,j)·N(i,j) (2)

[0019] i is the x-axis variable, j is the y-axis variable, and d is the z-axis variable, and the difference surface can be obtained.

[0020] 3.2) Define the difference surface features as tooth length features and tooth height features, i.e., row-wise features and column-wise features. Extract the endpoints P1, Pj and the middle point Pj / 2 of each row or column. If the extreme values ​​of the three data appear at the endpoints, then:

[0021] P1≥P i / 2 ≥P i ∨P1≤P i / 2 ≤P i (3)

[0022] The shape feature of the corresponding row or column is recorded as the tilt, and the difference between the extreme values ​​is the tilt; if an extreme point appears in the middle of the three data, that is:

[0023] P1≥P i / 2 ∧P i / 2 ≤P i ∨P1≤P i / 2 ∧P i / 2 ≥P i (4)

[0024] The shape feature of the corresponding row or column is recorded as curvature, and the difference between the extreme values ​​is recorded as curvature.

[0025] Preferably, in step (4), the specific steps of calculating the sensitivity difference surface are:

[0026] Because the tooth surface equations of spiral bevel gears are highly nonlinear, while sensitivity is inherently linear, changes in machine tool parameters should be kept as small as possible or as close to the linear region as possible when calculating sensitivity. This paper proposes that when the tooth surface error is minimized, changes in machine tool parameters are approximately linear. Therefore, during sensitivity analysis, the tooth surface error should not exceed the actual tooth surface error.

[0027] The specific procedure for calculating the sensitivity difference surface is as follows: Input the maximum error e of the tooth surface measured max , machine tool adjustment parameter X, parameter change Δ=0.05X; change the machine tool adjustment parameter to X=X+Δ; calculate the difference surface and maximum error e max' ; if e max' <e max , record the data; otherwise, change the machine tool adjustment parameters to Δ=-0.5Δ; calculate the difference surface and the maximum error e max' ;Record data.

[0028] In step (4), the shape features of the calculated sensitive difference surfaces are all tilted, with no curved features. This is because the curved features can be understood as secondary features, while the tilt is a primary feature, and it is difficult to obtain secondary features by adding primary features (the effect of multiple parameter corrections is considered to be additive). Therefore, it can be seen that the measured difference surfaces with curved features will not appear.

[0029] Preferably, in step (5), the specific steps are:

[0030] The sensitivity difference curve of each parameter has characteristics in the tooth length and tooth height directions. These characteristics are extracted and divided by the parameter change to obtain the sensitivity. The tooth length and tooth height directions of the measured results are adjusted separately.

[0031] The sensitivity of a parameter in the tooth length direction and tooth height direction is (ε 1i ,ε 2i ), the change of this parameter is Δ i , then the change of the characteristic quantity is (Δ i ε 1i ,Δ i ε 2i ), the change of the characteristic quantity of another parameter is recorded as (Δ j ε 1j ,Δ j ε 2j ), let Δ j =1, we can always make Δ j =-ε 1j / ε li or Δ i =-ε 2j / ε 2i , so that the characteristic change brought by the common change of the two parameters is (0,Δ i ε 2i +ε 2j ) or (Δ i ε li +ε lj ,0), that is, by controlling the proportional relationship between the changes in the two parameters, the tooth length or tooth height characteristics are eliminated, thereby achieving separate corrections for the measured tooth surface tooth length inclination and tooth height inclination. During error correction, the parameters with low sensitivity are selected for proportional calculation and combination.

[0032] The beneficial effects of the present invention are:

[0033] The tooth surface error correction method for spiral bevel gears of the present invention is a technology that can ensure tooth surface accuracy and is particularly important in spiral bevel gear processing. However, the double helix method, which processes concave and convex surfaces on both the large and small wheels simultaneously, increases the difficulty of counter-adjustment. The present invention proposes a method for calculating the difference surface, which can input the error between the actual tooth surface and the theoretical tooth surface into a computer. Based on the actual difference surface, the shape features of sensitive difference surfaces are extracted and arranged and combined. The difference surface changes caused by parameter changes are divided into changes in the tooth length direction and the tooth height direction. This achieves separate correction of the measured tooth surface in the tooth length direction and the tooth height direction, simplifying the difficulty of counter-adjustment. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments and in conjunction with the accompanying drawings, wherein

[0035] Figure 1 A program for calculating sensitive difference surfaces

[0036] Figure 2 Schematic diagram of the difference surface calculation principle

[0037] Figure 3 Schematic diagram of the difference surface shape feature

[0038] Figure 4 The concave-convex surface sensitivity difference surface of a processing parameter

[0039] Figure 5 The result after error correction

[0040] Figure 6 The processing result is the poor surface DETAILED DESCRIPTION

[0041] To illustrate the features of the present invention, the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0042] Example:

[0043] Combine Figures 1 to 6 The embodiment of the present invention provides a double helical spiral bevel gear tooth surface error correction method, comprising the following steps:

[0044] Step (1), obtaining basic design parameters of the tooth surface of the spiral bevel gear;

[0045] Table 1 shows the basic design parameters of the tooth surface, machine tool processing parameters and cutter head parameters of the double helical spiral bevel gear pinion.

[0046] Table 1 Basic design parameters of spiral bevel gears

[0047]

[0048] Step (2): Based on the basic design parameters of the tooth surface, the tooth surface modeling is performed to obtain the theoretical tooth surface and the discretization points are not described here. The actual measured point data of the tooth surface measurement obtained by measuring the spiral bevel gear using CMM is shown in Table 2.

[0049] Table 2 Coordinate measuring machine measurement data

[0050]

[0051]

[0052] Step (3), calculating the difference surface, defining the difference surface features as tooth length features and tooth height features, and defining the shape features of the corresponding rows or columns as tilted or curved;

[0053] The difference surface is the surface formed by the distance from the measured point on the tooth surface to the theoretical tooth surface. The R and L values ​​of each discrete point Pt(xt,yt,zt) can be calculated. If the rotation axis is the z-axis, the R and L calculation formulas are:

[0054]

[0055] If there are i rows and j columns of tooth surface measurement points Pt(i, j), the corresponding tooth surface points Rt(i, j) and Lt(i, j) can be obtained by substituting them into formula (1). By inputting the basic tooth surface design parameters, machine tool processing parameters, and cutter head parameters obtained in step 1 through CAGE software, the tooth surface point R(i, j) corresponding to the theoretical tooth surface direction and its normal vector N(i, j) can be obtained. The distance d′(i, j) between Pt and R is calculated, and the normal error can be approximately calculated as:

[0056] d(i,j)=d'(i,j)·N(i,j) (2)

[0057] i is the x-axis variable, j is the y-axis variable, and d is the z-axis variable, and the difference surface can be obtained.

[0058] The difference surface features are defined as tooth length features and tooth height features, i.e. row direction features and column direction features. Figure 2 As shown, extract the endpoints P1, Pj and the middle point Pj / 2 of each row or column of data. If the extreme values ​​of the three data appear at the endpoints, that is:

[0059] P1≥P i / 2 ≥P i ∨P1≤P i / 2 ≤P i (3)

[0060] The shape feature of the corresponding row or column is recorded as the tilt, and the difference between the extreme values ​​is the tilt; if an extreme point appears in the middle of the three data, that is:

[0061] P1≥P i / 2 ∧P i / 2 ≤P i ∨P1≤P i / 2 ∧P i / 2 ≥P i (4)

[0062] The shape feature of the corresponding row or column is recorded as curvature, and the difference between the extreme values ​​is recorded as curvature.

[0063] Step (4) performing sensitivity analysis on the difference surface to obtain the variation trend of the tooth surface error after the adjustment parameters of each machine tool and the cutter head parameters change, i.e., the sensitive difference surface, and decompose this variation trend into the tooth length direction and the tooth height direction;

[0064] The main purpose of sensitivity analysis is to obtain the changing trend of tooth surface error after changes in various machine tool adjustment parameters and cutter head parameters, and to decompose this changing trend into the tooth length and tooth height directions. Since the tooth surface equation of spiral bevel gears is highly nonlinear, and sensitivity is essentially a linear characteristic, when calculating sensitivity, the change in machine tool processing parameters should be as small as possible or as close to the linear region as possible. The present invention believes that when the tooth surface error is as small as possible, the change in machine tool processing parameters is approximately linear. Therefore, when calculating sensitivity, the change in tooth surface error must not be greater than the actual tooth surface error.

[0065] like Figure 3 As shown in the figure, the procedure for calculating the sensitivity difference surface is as follows: Input the maximum error of the tooth surface measured e max , machine tool adjustment parameter X, parameter change Δ=0.05X; change the machine tool adjustment parameter to X=X+Δ; calculate the difference surface and maximum error e max' ; if e max' <e max , record the data; otherwise, change the machine tool adjustment parameters to Δ=-0.5Δ; calculate the difference surface and the maximum error e max' ;Record data.

[0066] like Figure 4 As shown in Figure 1, this is the sensitive difference surface for the mounting angle parameters. Analysis shows that the calculated shape features of the sensitive difference surface are all tilted, with no curved features. This is because curved features can be understood as secondary features, while tilt is a primary feature. Adding primary features together makes it difficult to obtain secondary features (the effect of multiple parameter corrections is considered additive). Therefore, it can also be seen that the measured difference surface with curved features will not appear.

[0067] Step (5): The sensitivity difference curve of each parameter has features in the tooth length direction and the tooth height direction. These features are extracted and divided by the parameter change to obtain the sensitivity. That is, each parameter has sensitivity in the tooth length direction and the tooth height direction. By selecting parameters with low sensitivity and performing proportional calculation and combination, the features in the tooth length direction and the tooth height direction are eliminated, thereby achieving separate correction of the measured tooth surface tooth length inclination and tooth height inclination.

[0068] The sensitivity of a parameter in the tooth length direction and tooth height direction is (ε 1i ,ε 2i ), the change of this parameter is Δ i , then the change of the characteristic quantity is (Δ i ε 1i ,Δ i ε 2i ), the change of the characteristic quantity of another parameter is recorded as (Δ j ε 1j ,Δ j ε 2j ), let Δ j =1, we can always make Δ j =-ε 1j / ε li or Δ i =-ε 2j / ε 2i , so that the characteristic change brought by the common change of the two parameters is (0,Δ i ε 2i +ε 2j ) or (Δ i ε li +ε lj ,0), that is, by controlling the proportional relationship between the changes in the two parameters, the tooth length or tooth height characteristics are eliminated, thereby achieving separate corrections for the measured tooth surface tooth length inclination and tooth height inclination. During error correction, the parameters with low sensitivity are selected for proportional calculation and combination.

[0069] like Figure 5 The final error correction result of the method proposed in the present invention is shown in Table 3, where the maximum error is 2 μm. The processing parameter correction results are shown in Table 3.

[0070] Table 3. The calculated processing parameter counter-adjustment in this paper

[0071]

[0072]

[0073] After processing using the calculated results, the actual measured difference surface results of the tooth surface are as follows Figure 6 As shown, it can be seen that the maximum error of the tooth surface is 6.3μm, the error is reduced by 67%, and the surface accuracy is significantly improved.

[0074] The above embodiments and accompanying drawings are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. The present invention has been described in detail with reference to preferred embodiments. Those skilled in the art should understand that any changes, modifications, additions, or substitutions made by those skilled in the art within the spirit and scope of the present invention do not depart from the spirit of the present invention and are intended to fall within the scope of the claims. Other related technical structures not fully disclosed in the present invention constitute prior art in the art.

Claims

1. A method for correcting tooth surface errors of spiral bevel gears using a double helical machining method, characterized in that: The following steps are involved: Step (1): Obtain the basic design parameters of the tooth surface of the spiral bevel gear; Step (2): Based on the basic design parameters of the tooth surface obtained in step (1), the theoretical tooth surface is obtained by tooth surface modeling, and then discretized to obtain the tooth surface preset grid for tooth surface error calculation in CMM measurement. The CMM is used to measure the spiral bevel gear to obtain the actual measured point data of the tooth surface and the tooth surface error; Step (3): Calculate the difference surface based on the theoretical tooth surface obtained in step (2) and the measured points on the tooth surface, and define the difference surface features as tooth length features and tooth height features. The tooth length feature refers to the row-direction feature of the gear tooth surface, and the tooth height feature refers to the column-direction feature of the gear tooth surface. The shape feature of the corresponding row or column is set as tilted or curved. Step (4): Perform sensitivity analysis on the difference surface obtained based on step (3) to obtain the change trend of the tooth surface error after the adjustment parameters of each machine tool and the cutter head parameters change, that is, the sensitive difference surface, and decompose this change trend into the tooth length direction and the tooth height direction; Step (5): Based on the sensitivity difference surface of each parameter obtained in step (4), there are features in the tooth length direction and tooth height direction. These features are extracted and divided by the parameter change to obtain the sensitivity, that is, each parameter has sensitivity in the tooth length direction and tooth height direction. By selecting parameters with low sensitivity for proportional calculation and combination, the features in the tooth length direction and tooth height direction are eliminated, thereby realizing the separate correction of the measured tooth surface tooth length inclination and tooth height inclination.

2. The tooth surface error correction method of a spiral bevel gear using a double helical machining method according to claim 1, characterized in that: In step (3), the specific steps are: 3.1) The difference surface is the surface formed by the distance from the measured point on the tooth surface to the theoretical tooth surface. The R and L values ​​of each discrete point Pt(xt,yt,zt) can be calculated. R refers to the middle value in the tooth height direction, and L refers to the middle value in the tooth length direction. If the rotation axis is the z-axis, the R and L calculation formulas are: If there are i rows and j columns of tooth surface measurement points Pt(i,j), the corresponding tooth surface points Rt(i,j) and Lt(i,j) can be obtained by substituting them into the above formula. By inputting the basic tooth surface design parameters, machine tool processing parameters and cutter head parameters obtained in step (1) through CAGE software, the tooth surface point R(i,j) corresponding to the theoretical tooth surface direction and its normal vector N(i,j) can be obtained. The distance d´(i,j) between Pt and R is calculated, and the normal error is approximately calculated as: i is the x-axis variable, j is the y-axis variable, and d is the z-axis variable, and the difference surface can be obtained; 3.2) Define the difference surface features as tooth length features and tooth height features, i.e., row-wise features and column-wise features. Extract the endpoints P1, Pj, and the middle point Pj / 2 of each row or column. If the extreme values ​​of the three data appear at the endpoints, then: The shape feature of the corresponding row or column is recorded as the tilt, and the difference between the extreme values ​​is the tilt; if an extreme point appears in the middle of the three data, that is: The shape feature of the corresponding row or column is recorded as curvature, and the difference between the extreme values ​​is recorded as curvature.

3. The tooth surface error correction method of a spiral bevel gear using a double helical machining method according to claim 2, characterized in that: In step (4), the specific steps of calculating the sensitivity difference surface are: Enter the maximum error of the measured tooth surface , machine tool adjustment parameters , parameter change ; Change the machine adjustment parameters to ; Calculate the difference surface and maximum error ;if , record the data; otherwise, change the machine tool adjustment parameters to ; Calculate the difference surface and maximum error ;Record data.

4. The tooth surface error correction method of a spiral bevel gear using a double helical machining method according to claim 1, characterized in that: In step (5), the specific steps are: The sensitivity difference surface of each parameter has features in the tooth length and tooth height directions. These features are extracted and divided by the parameter change to obtain the sensitivity. The tooth length and tooth height directions of the measured results are adjusted separately. The sensitivity of a parameter in the tooth length direction and tooth height direction is , the change of this parameter is , then the change of the characteristic quantity is , the change of the characteristic quantity of another parameter is recorded as ,make , you can always make or , so that the characteristic change brought about by the common change of the two parameters is or That is, by controlling the proportional relationship between the changes in the two parameters, the tooth length direction characteristics or the tooth height direction characteristics are eliminated, thereby realizing the separate correction of the measured tooth surface tooth length inclination and tooth height inclination. When correcting the error, the parameters with low sensitivity are selected for proportional calculation and combination.

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