A roll profile design method for dressing face gear worm grinding wheel

Abstract

The present invention discloses a method for designing the rolling profile of a dressing worm grinding wheel for face gears, belonging to the field of gear manufacturing. A method of segmentally designing the rolling profile of a dressing worm grinding wheel for face gears is adopted. In this method, the specific structure of the roller is divided into: a base part, an extended involute part, a working involute part, and an extended straight part. At the same time, the curve shapes, lengths, and endpoint selection methods of the profiles of each part are described in detail, so that the dressed worm grinding wheel can reduce the interference with the grinding wheel during roller dressing on the premise of ensuring a complete enveloping of the face gear tooth surface.

Description

Technical Field

[0001] The present invention belongs to the field of gear manufacturing, especially for dressing the worm grinding wheel roller of face gear, and particularly relates to a method for designing the specific profile of the roller for forming and dressing the worm grinding wheel of straight-tooth face gear. Technical Background

[0002] The face gear is a core component of many aero-engines, which has the advantages of large transmission ratio, compact structure, large contact ratio, etc. Such a transmission pair can significantly improve the power density and reliability of the crossed-axis transmission system and reduce noise. It will be more widely applied to various high-speed and heavy-load working conditions. At present, the face gear grinding process in China is still not mature, and there are still problems to be solved, such as high requirements for machine tool control, low grinding efficiency, and great difficulties in roller manufacturing and grinding wheel dressing.

[0003] Compared with other grinding processes, the worm grinding wheel has high grinding efficiency and no principle error, and can avoid problems such as uncontrollable pitch error. Regarding the worm grinding wheel for face gear, Ken Beel developed a numerically controlled worm grinding machine for face gear and began to apply it abroad. In the method of dressing the worm grinding wheel, the dressing method based on the formed diamond roller is relatively easy to control and manufacture. Fan Jiahui of Nanjing University of Aeronautics and Astronautics proposed a method for controlling the allowance in worm grinding wheel grinding and a dressing method after the worm grinding wheel is worn. Tang Jinyuan of Central South University studied the basic principle of forming and dressing the worm grinding wheel of face gear and verified its feasibility. Guo Hui and Zhao Ning of Northwestern Polytechnical University took a six-axis numerically controlled worm grinding machine as the research equipment, developed a relatively complete set of worm grinding wheel grinding and dressing actions and analyzed their errors, and used the formed dressing with a parabola superimposed on the roller profile. Ran Quanfu of Chongqing University studied the motion control method of the formed roller and the worm grinding wheel when there is a virtual center distance. The above research provides an application basis for grinding face gear with worm grinding wheel and dressing the worm grinding wheel, but limited to theoretical design, the complete design structure of the formed roller and the problems existing in actual dressing are not discussed. Therefore, developing a roller structure that can ensure the surface integrity of the worm grinding wheel of face gear and better meet the dressing requirements is of great significance for improving the machining accuracy of face gear and developing and improving domestic face gear processing equipment. Summary of the Invention

[0004] The formed roller profile for dressing the worm grinding wheel of face gear mainly consists of four parts: the base part, the extended involute part, the working involute part, and the extended straight line part. The base part undertakes the role of connecting and supporting the whole roller. The specific width design depends on the machine tool structure, so as to ensure that there is no interference with other machine tool components during dressing, and at the same time reduce the volume, lower the cost, and improve the dynamic balance performance of the roller. The working involute is the core of the whole profile, and its shape is a standard involute. The positions of the upper and lower end points are determined by the shape and tooth height of the face gear. The involute equation is as follows:

[0005]

[0006] In the formula, r bs is the base circle radius of the gear shaper cutter, θ s is the Gauss coordinate of the tooth surface of the gear shaper cutter, and θ os is the half angle of the tooth space, and the calculation formula is:

[0007]

[0008] In the formula, Z s is the number of teeth of the gear shaper cutter, and α is the pressure angle of the pitch circle. Due to errors and wear during machining, and the root circle of the face gear may be changed according to actual machining requirements, it is necessary to extend its upper and lower ends. Since the upward extended part will affect the shape of the root circle, its shape needs to maintain an involute, that is, the extended involute part. There is no fixed requirement for its length, and it only needs to be coordinated with the base width. Generally, it is taken 1 - 3 mm higher than the upper end of the working involute. The lower end extended section mainly plays a role in protecting the working area and dressing the outer circle of the grinding wheel. Since the extended part will not affect the shape of the effective area of the grinding wheel, a straight line segment is used for convenient machining. To ensure that the tooth space depth is not too long, it is taken 1 - 3 mm, and the specific size can be appropriately adjusted according to the size of the roller. However, since the roller makes a complex spatial movement around the grinding wheel during dressing, an unreasonable design of the angle between the extended straight line and the radial direction may cause undercutting. Combining the above, the main parameters to be considered in designing a complete roller are the positions of the upper and lower ends of the working involute and the angle between the extended straight line of the roller and the radial direction.

[0009] Since the face gear can be formed by the envelope of the gear shaper cutter, and the involute of the roller corresponds to the tooth space shape of the gear shaper cutter, the positions of the upper and lower ends of the working involute are mainly determined by the shape and tooth height of the face gear. The following is the equation of the face gear formed by the envelope of the gear shaper cutter:

[0010]

[0011] Among them, φ s is the rotation angle of the gear shaper cutter at a certain moment, and among them, m 2s is the transmission ratio between the gear shaper cutter and the face gear. From the involute equation, it can be obtained that the closer to the upper part of the hob, θ s is larger, and its upper and lower ends are determined by the positions of the maximum and minimum θ s on the face gear. Studying the tooth surface graph, it can be obtained that the position of the maximum θ s is on the transition curve, and the θ s of all points on the curve are the maximum value θ smax , which is determined by the addendum circle radius of the designed gear shaper cutter. And the minimum value of θ s is at the highest point near the inner end of the face gear, and θ sminIt can be calculated by substituting the coordinates of the corresponding points into the face gear equation. To ensure a certain degree of fault tolerance, a θ' smin slightly smaller than θ smin can be selected so that the lower end of the involute is extended downward by a certain part to meet the trimming requirements.

[0012] The radial angle β between the extended straight line part and the roller needs to be designed in combination with the undercut phenomenon of the straight line on the grinding wheel. Since the larger the radial angle between the extended straight line part and the roller, the smaller the undercut of the roller, and when it is above a certain critical angle, there will be no undercut. Also, since the undercut amount increases towards both sides, without changing the thickness of the grinding wheel, it is only necessary to ensure that the modified roller design makes the angle above the corresponding critical angle on both sides of the roller to ensure no undercut occurs. The following gives an estimation method for the minimum value of the critical angle.

[0013] Since the undercut occurs near the bottom end of the roller, the fundamental reason is that on the surface within the range in the figure, the angle between the vector corresponding to the roller surface and the tangent vector of the worm grinding wheel surface is greater than the angle β between the straight line part of the roller and the axis. The equation of the worm grinding wheel (single-sided) formed by the envelope of the gear shaper cutter is:

[0014]

[0015] where φ w is the rotation angle of the worm grinding wheel at a certain moment, and from the transmission relationship:

[0016]

[0017] In the formula, Z w is the number of heads of the worm, and Z s is the number of teeth of the gear shaper cutter. Estimating β requires solving the maximum angle between and within the possible undercut range. The angle corresponding to the undercut range of the roller and the undercut range of the grinding wheel is calculated as:

[0018]

[0019] l d is the tooth space depth, R w is the maximum outer diameter of the grinding wheel, and φ max is the angle corresponding to the maximum thickness of the grinding wheel. The tangent vector can be approximated by the following method:

[0020]

[0021] The calculation of the corresponding change vector of the roller surface requires first solving the spatial transformation relationship between the gear shaper cutter and the worm grinding wheel as follows:

[0022]

[0023] Combined with the coordinate transformation of the roller relative to the gear shaper cutter, where λ0 is the helix angle of the worm grinding wheel, φ w To obtain the final relative position relationship between the roller and the worm grinding wheel as:

[0024]

[0025] L is the distance between the center of the roller and the center of the gear shaper cutter, and the calculation formula is:

[0026] L = r bs cosθ os +R - l

[0027] where R is the radius of the roller, l is the height of the extended straight line part, b is the thickness of a certain slice of the roller from the center, and the equation of the roller is based on b0 = r bs sinθ os For the upper half of the boundary line, it is the involute equation, and for the lower half, it is the conical surface. The roller model is constructed in cylindrical coordinates, and the roller model can be written as: [x d y d z d = f(R d , b, θ d ), R d is a parameter related to b determined by the roller profile, and its parametric equation is solved as:

[0028]

[0029] From the above, the minimum design angle can be solved as:

[0030] Description of the Drawings

[0031] Figure 1 is a schematic diagram of the roller structure;

[0032] Figure 2 is a schematic diagram of the tooth surface of the face gear;

[0033] Figure 3 is a schematic diagram of the relative position between the roller and the worm grinding wheel;

[0034] Detailed Description

[0035] This roller profile design method takes the face gear worm grinding wheel as the dressing object, improves the roller design theory, and avoids overcutting between the roller and the worm grinding wheel. The basic structure of this roller is as shown in the appendix Figure 1 shown. In this article, the following parameters in the table will be used as examples for design. The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0036]

[0037] Substituting the above parameters into the face gear equation, the tooth surface as shown in the appendix can be obtained. Figure 2 And by solving the broaching cutter equation backwards, the θ on the tooth surface can be obtained. smax = 0.7476, θ smin = 0.1559. Substituting θ smax = 0.7476, the coordinates of the upper end of the working involute relative to the center of the broaching cutter can be solved as: (42.4621, 6.7799). The distance from the center of the broaching cutter is equal to 43 mm, and the extended length is selected as 2.5 mm, that is, the distance from the upper end of the extended involute to the center of the broaching cutter is: 45.5 mm. From this, the coordinates of the upper end of the extended involute can be solved as (44.5577, 9.2120).

[0038] Substituting θ smin into the broaching cutter equation, the coordinates of the upper and lower segments (relative to the center position of the broaching cutter) are obtained. To ensure a certain redundancy, the lower end needs to be extended by a part. In this paper, due to the machine tool properties, it is extended by Δx = 0.2 mm, and the corresponding lowest point after extension is θ smin ′, which can be determined by the following broaching cutter equation.

[0039] Δx = r bs [sin(θ smin + θ os ) - θ smin cos(θ smin + θ os )] - r bs [sin(θ smin ′ + θ os ) - θ smin ′cos(θ smin ′ + θ os )]

[0040] Finally, θ smin ′ = 0.1118 is obtained. Substituting it into the broaching cutter equation, the coordinates of the lower end are solved as: (34.6052, 1.8413).

[0041] After determining the basic working area of the roller, it is necessary to determine the angle of the extended straight line with respect to the radial direction of the roller, that is, β in the appendix. Figure 1 From the equation of the worm grinding wheel, the worm grinding wheel model in the appendix can be obtained. Figure 3 Combined with the equation of the roller in the coordinate system of the worm grinding wheel, the appendix can be completely obtained. Figure 3The relative position of the middle roller and the worm grinding wheel. Enlarging the position of the roller and the worm grinding wheel, it can be observed that the working involute of the roller is tangent to the worm grinding wheel. If the straight line is not designed properly, overcutting will occur on both sides of the tangent position between the worm grinding wheel and the roller. From the estimation method of the vector representation meaning in the above text, β min = 19.86°. Selecting the extended straight line distance to be 1.5 mm, the coordinates of the lower end of the straight line segment can be obtained as: (33.1052, 1.2954). The complete roller curve coordinates can be obtained as shown in the following table.

[0042]

[0043] To verify the correctness of the estimation, first observe whether overcutting occurs in Figure 3 the attachment using different β. After many attempts, it is found that when β ≈ 15°, overcutting does not occur exactly. It is close to the estimated value and slightly less than the estimated value. This proves that this estimation method can approach the limit value while ensuring a certain redundancy.

[0044] To further verify the feasibility, in this paper, the dressing process is simulated by machining using β = 4° exceeding the limit value and the estimated value β min = 19.86°. The overcut marks in the simulation results disappear significantly, further proving the rationality of the design.

Claims

1. A method for designing the profile of a worm grinding wheel for face gear dressing, characterized in that Use this roller to dress the face gear worm grinding wheel formed by the envelope of a straight-tooth shaper cutter. Using the segmented design method, under the premise of ensuring a complete enveloped tooth surface, reduce the interference with the grinding wheel during roller dressing. The structure includes: a base part that plays a connecting and supporting role, an extended involute part that plays a connecting and redundant design role, a working involute part that mainly shapes the effective area of the grinding wheel, and an extended straight part that plays a role in protecting and dressing the outer circle of the grinding wheel. The working involute part of the roller is an involute, and its upper endpoint, i.e., θ s The maximum point corresponds to the transition curve on the face gear tooth surface, and the transition curve is formed by the envelope of the shaper cutter tooth tip. That is, the upper endpoint of the working involute part of the roller should be the same as the shaper cutter tooth tip point. The lower endpoint of the working involute is θ s The minimum point corresponds to the uppermost tooth point at the inner end of the face gear design standard surface. When calculating, first calculate the corresponding θ of this point from the face gear tooth surface equation smin , and then extend it downward by Δx to meet the subsequent trimming requirements. The corresponding θ smin ′ is calculated by the following equation: Δx = r bs [sin(θ smin + θ os ) - θ smin cos(θ smin + θ os )] - r bs [sin(θ smin ′ + θ os ) - θ smin ′cos(θ smin ′ + θ os )] where, Δx is the extended distance, r bs is the base circle radius of the gear shaper cutter, θ s is the Gauss coordinate of the tooth surface of the gear shaper cutter, θ os is the half angle of the tooth space of the gear shaper cutter, θ smax and θ smin are the maximum and minimum values of θ s . The extended straight line segment of the roller determines the tooth space depth of the part below the involute on the grinding wheel. To ensure that it plays a protective role while the tooth space is not too deep to affect the strength of the grinding wheel teeth, the length is taken as 1 - 3 mm; it is calculated through the following matrix: Among them, M wd is the coordinate transformation relationship matrix from the roller to the worm grinding wheel, M ws is the coordinate transformation relationship matrix from the gear shaper cutter to the worm grinding wheel, L is the distance between the center of the roller and the center of the gear shaper cutter, φ s is the rotation angle of the gear shaper cutter, b is the thickness from the center of the roller, R d is a parameter related to b determined by the roller profile, θ d is the angle between the profile section and the meshing surface of the roller and the worm grinding wheel. By estimating the maximum value of the angle between the tangent vectors on the roller and the worm grinding wheel within the undercut range, the minimum angle of β is determined when designing the roller: Among them, is the corresponding vector of the roller surface, is the tangent vector of the worm grinding wheel surface, β is the angle between the extended straight line segment of the roller and the radial direction of the roller, β min is the minimum angle of β designed for the roller.

2. The roller design method of a dressing face gear worm grinding wheel according to claim 1, characterized in that The shape and length of the extended base part that plays a connecting and supporting role need to be adapted to the machine tool, and the height of the extended involute part is 1-3 mm, with an involute shape and coordinated with the whole.

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