Elliptical ball honing wheel for honing internal gear and design method thereof

Abstract

This application discloses an ellipsoidal honing wheel for high-power honing of internal gears and its design method, relating to the field of gear design. The method includes establishing a spatial meshing equation between the internal gear workpiece and the honing wheel; solving the spatial meshing equation to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece during meshing; determining the target intersection point between each instantaneous contact line and the nominal tooth tip surface of the honing wheel; determining the interference amount distributed along the axial direction of the honing wheel based on the positional relationship between each target intersection point and the tooth root circle of the internal gear workpiece; and correcting the nominal tooth tip surface of the honing wheel based on the interference amount. This addresses the problem in the prior art where the honing wheel easily interferes with the tooth root of the workpiece under large shaft angle conditions.

Description

Technical Field

[0001] This application relates to the field of gear design, and in particular to an ellipsoidal honing wheel for high-power honing of internal gears and its design method. Background Technology

[0002] Internal gears, as key components of mechanical transmission systems, are widely used in industrial robots, new energy vehicle drive systems, aerospace precision mechanisms, and high-precision machine tools. In the manufacturing process of internal gears, honing achieves higher tooth surface precision compared to gear turning, and effectively avoids thermal damage compared to gear grinding. However, the internal gear grinding process has relatively poor system rigidity and is prone to tooth surface vibration marks during processing, affecting surface quality.

[0003] In gear honing, a certain axial angle exists between the honing wheel and the workpiece. A larger axial angle enhances the sliding motion between the honing wheel and the workpiece tooth surface, allowing for higher rotational speeds and improving cutting efficiency and tooth surface texture. However, as the axial angle increases, the spatial meshing relationship between the honing wheel tooth surface and the workpiece tooth surface becomes more complex. Furthermore, the tooth tip edge region of the honing wheel designed using existing methods is prone to intruding into the root circle of the workpiece during meshing, resulting in overcutting interference. This interference not only excessively removes tooth root material and weakens tooth root strength but may also compromise the geometric accuracy of the machined tooth surface. Summary of the Invention

[0004] The purpose of this application is to provide an ellipsoidal honing wheel for high-power honing of internal gears and its design method, aiming to solve the problem that the honing wheel is prone to interference with the tooth root of the workpiece under the condition of large shaft intersection in the prior art.

[0005] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a design method for an ellipsoidal honing wheel used for high-power honing of internal gears, comprising: Establish the spatial meshing equation between the internal gear workpiece and the honing wheel; Solve the spatial meshing equation to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece during meshing; Determine the target intersection point between each of the instantaneous contact lines and the nominal tooth top surface of the honing wheel; The interference amount distributed along the honing wheel axis is determined based on the positional relationship between each of the target intersection points and the root circle of the internal gear workpiece. The nominal tooth tip surface of the honing wheel is corrected according to the interference amount to obtain an ellipsoidal honing wheel.

[0006] Secondly, this application provides an ellipsoidal honing wheel for high-power honing of internal gears, the honing wheel being obtained by the design method described in the first aspect; The honing wheel is designed with an ellipsoidal curved surface at the tooth tip.

[0007] According to the specific embodiments provided in this application, the following technical effects are disclosed: This application provides an ellipsoidal honing wheel for high-power honing of internal gears and its design method. By establishing a precise spatial meshing equation and solving the instantaneous contact line, the interference between the honing wheel tooth tip and the workpiece tooth root under the large shaft intersection angle condition can be accurately and quantitatively calculated, solving the problem that traditional design methods cannot accurately identify and quantify interference. Based on the calculated interference, the nominal tooth tip surface of the honing wheel is corrected point by point, generating an ellipsoidal surface with a specific contour. This design enables the honing wheel to effectively avoid interference with the workpiece tooth root during processing, thereby protecting the strength of the workpiece tooth root and ensuring the machining accuracy of the internal gear tooth surface. The designed ellipsoidal honing wheel has a smooth contraction shape with a larger middle and smaller ends in the axial direction at the tooth tip, which not only fundamentally eliminates the interference between the tooth tip and the tooth root, but also makes the honing wheel more stable when entering and exiting meshing, which is beneficial to improving the stability and efficiency of the processing. Attached Figure Description

[0008] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0009] Figure 1 This is a flowchart illustrating the overall implementation of a design method for an ellipsoidal honing wheel used for high-power honing of internal gears, according to one embodiment of the present invention. Figure 2 This is a schematic diagram of the spatial coordinate system between the workpiece and the honing wheel provided in one embodiment of the present invention; Figure 3 This is a schematic diagram of the instantaneous contact line and the intersection retention point provided in one embodiment of the present invention; Figure 4 This is a diagram showing the radial distance calculation results in one embodiment of the present invention; Figure 5 This is a diagram showing the calculation results of the interference amount in one embodiment of the present invention; Figure 6 This is a diagram showing the calculated actual contour curve of an ellipsoidal honing wheel in one embodiment of the present invention; Figure 7 This is a schematic diagram of the profile of the trimmed ellipsoidal honing wheel in one embodiment of the present invention; Figure 8 This is a schematic diagram of an ellipsoidal honing wheel model for electroplated CBN abrasive grains in one embodiment of the present invention. Detailed Implementation

[0010] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0011] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0012] This invention provides a design method for an ellipsoidal honing wheel used for high-power honing of internal gears, aiming to solve the problem in existing technologies where the honing wheel easily interferes with the tooth root of the workpiece under large shaft angle conditions. The method first establishes a spatial meshing equation between the internal gear workpiece and the honing wheel, accurately describing their contact relationship during motion. This step is fundamental to the entire design method, transforming the complex physical meshing process into a rigorous mathematical model, providing a theoretical basis for subsequent interference analysis.

[0013] In one specific embodiment, the design method for an ellipsoidal honing wheel used for high-power honing of internal gears specifically includes: Step S110: Establish the spatial meshing equation between the internal gear workpiece and the honing wheel.

[0014] Step S120: Solve the spatial meshing equation to determine the instantaneous contact line between the nominal tooth tip of the honing wheel and the internal gear workpiece during meshing.

[0015] Step S130: Determine the target intersection point between each instantaneous contact line and the nominal tooth top surface of the honing wheel.

[0016] Step S140: Determine the interference amount distributed along the honing wheel axis based on the positional relationship between each target intersection point and the root circle of the internal gear workpiece.

[0017] Step S150: Correct the nominal tooth top surface of the honing wheel according to the interference amount to obtain an ellipsoidal honing wheel.

[0018] Specifically, this method determines the instantaneous contact lines between the nominal tooth tip surface of the honing wheel and the internal gear workpiece during meshing by solving the spatial meshing equation. These instantaneous contact lines constitute the set of all potential contact points between the honing wheel and the workpiece tooth surface at different meshing moments. By analyzing these contact lines, a comprehensive understanding of their interaction across the entire tooth width can be obtained, which is a crucial step in identifying potential interference regions.

[0019] After obtaining the instantaneous contact lines, it is necessary to determine the target intersection points between each instantaneous contact line and the nominal tooth tip surface of the honing wheel. These target intersection points represent the outermost position that the honing wheel tooth tip edge may reach during meshing. By accurately locking these key points, subsequent interference analysis can be focused on the areas most prone to interference, thereby improving computational efficiency and accuracy.

[0020] Subsequently, based on the positional relationship between each target intersection point and the root circle of the internal gear workpiece, the interference amount distributed along the honing wheel axis is determined. Specifically, through coordinate transformation, these target intersection points determined in the honing wheel coordinate system are converted back to the workpiece coordinate system for analysis, calculating whether their radial positions exceed the boundary of the workpiece's root circle. In this way, the depth of penetration into the workpiece's tooth root at different axial positions of the honing wheel, i.e., the interference amount, can be quantitatively obtained.

[0021] Finally, the nominal tooth tip surface of the honing wheel is corrected based on the calculated interference. For axial positions with positive interference, the radius of the honing wheel is reduced accordingly at those positions. By correcting point by point across the entire axial range, a non-cylindrical profile, i.e., an ellipsoidal surface, is ultimately formed, which is larger in the middle and smaller at both ends. This profile correction based on precise calculations fundamentally eliminates the risk of interference while ensuring the accuracy of tooth surface machining and the strength of the tooth root, thus achieving optimized design of the honing wheel.

[0022] In some embodiments, establishing the spatial meshing equation between the internal gear workpiece and the honing wheel specifically includes: Based on the mathematical expression of the involute helical surface of the tooth surface of the internal gear workpiece, the tooth surface position vector and tooth surface normal vector of the internal gear workpiece with respect to the involute parameters are constructed in the first workpiece coordinate system, which is the initial fixed coordinate system of the internal gear workpiece.

[0023] Based on a transformation matrix regarding the rotation angle of the internal gear workpiece, the tooth surface normal vector of the internal gear workpiece in the first workpiece coordinate system is transformed into the tooth surface normal vector of the internal gear workpiece in the second workpiece coordinate system. The second working coordinate system is the motion-fixed coordinate system of the internal gear workpiece.

[0024] Determine the relative velocity equation at the contact point between the internal gear workpiece and the honing wheel.

[0025] Establish the spatial meshing equation: .

[0026] in, Let n be the equation for the relative velocity between the contact point of the internal gear workpiece and the honing wheel in the second workpiece coordinate system. h This is the normal vector of the tooth surface of the internal gear workpiece in the second workpiece coordinate system.

[0027] Specifically, the steps for establishing the spatial meshing equation between the internal gear workpiece and the honing wheel include a precise mathematical description of the workpiece's tooth surface. First, based on the mathematical expression of the involute helical surface of the internal gear workpiece's tooth surface, the tooth surface position vector and tooth surface normal vector of the internal gear workpiece with respect to the involute parameters are constructed in the first workpiece coordinate system. The first workpiece coordinate system is an initially fixed coordinate system set for the internal gear workpiece. This step provides the mathematical foundation for describing the workpiece's geometry.

[0028] Next, to describe the motion of the workpiece during meshing, a transformation matrix regarding the rotation angle of the internal gear workpiece is introduced. This transformation matrix converts the tooth surface normal vector of the internal gear workpiece in the first workpiece coordinate system into the tooth surface normal vector in the second workpiece coordinate system. The second workpiece coordinate system is a motion-fixed coordinate system that changes with the rotation of the workpiece. This transformation ensures that the normal vector information of the workpiece tooth surface in a unified reference system can always be obtained during the dynamic meshing process.

[0029] Simultaneously, in order to apply the gear meshing principle, it is necessary to determine the relative velocity equation of the contact point between the internal gear workpiece and the honing wheel. According to the fundamental law of gear meshing, the relative velocity vector of the contact point of the two tooth profiles must be perpendicular to the common normal at that point. Therefore, establishing the relative velocity equation is a necessary prerequisite for constructing the spatial meshing equation.

[0030] Finally, the tooth surface normal vector obtained above in the second workpiece coordinate system is... The relative velocity equation with the point of contact Combined, establish the spatial meshing equation: The physical meaning of this equation is that at any point of contact, the dot product of the workpiece tooth surface normal vector and the relative sliding velocity between the two tooth surfaces is zero. All points that satisfy this equation constitute the theoretical set of contact points, thus laying a solid mathematical foundation for subsequent solutions to the instantaneous contact line.

[0031] Furthermore, the relative velocity equation of the contact point between the internal gear workpiece and the honing wheel in the second workpiece coordinate system is: ; Where ω1 and ω2 are the angular velocity vectors of the internal gear workpiece and the honing wheel in the second workpiece coordinate system, respectively. O1 is the position vector of the contact point between the internal gear workpiece and the honing wheel in the second workpiece coordinate system, O2 is the position vector of the origin of the second honing wheel coordinate system in the second workpiece coordinate system, and the second honing wheel coordinate system is the initial fixed coordinate system of the honing wheel.

[0032] The provision of this specific formula allows for the direct substitution of parameters in the calculation of relative velocity, enhancing the operability of the method.

[0033] In some embodiments, solving the spatial meshing equation to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece during meshing specifically includes: By iterating through the rotation angles of the internal gear workpiece within one meshing cycle, the target involute parameters that make the spatial meshing equation valid are determined.

[0034] Transform the corresponding coordinate points of the target involute parameters in the second workpiece coordinate system to the second honing wheel coordinate system to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece.

[0035] Specifically, the process of solving the spatial meshing equation to determine the instantaneous contact line includes: First, traversing all possible angles of the internal gear workpiece within one meshing cycle, and for each given angle, solving for the target involute parameters that make the spatial meshing equation valid using numerical calculation methods. This step is equivalent to finding those points on the workpiece tooth surface that satisfy the meshing conditions at each instant. Then, the corresponding coordinate points of these obtained target involute parameters in the second workpiece coordinate system are transformed to the second honing wheel coordinate system using a coordinate transformation matrix, thereby determining the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece. By traversing all angles, a series of instantaneous contact lines can be obtained, completely depicting the contact trajectory throughout the entire meshing process.

[0036] In some embodiments, determining the target intersection point between each instantaneous contact line and the nominal tooth tip surface of the honing wheel specifically includes: On each instantaneous contact line, find the point whose radial distance is equal to the radius of the honing wheel's tooth tip circle to obtain the tooth tip circle intersection point.

[0037] The intersection point of the tooth tip circle that meets the physical requirements is retained as the target intersection point.

[0038] Specifically, on each obtained instantaneous contact line, points whose radial distance is equal to the radius of the honing wheel's addendum circle are mathematically determined to obtain the addendum circle intersections. These intersections are the critical points where the instantaneous contact line extends to the edge of the honing wheel's tooth tip. However, not all mathematically significant intersections have physical meaning; therefore, selection is necessary to retain those addendum circle intersections that satisfy the physical boundary conditions and actual meshing logic as the final target intersections. Through this step, the critical points most likely to experience interference can be precisely located.

[0039] In some embodiments, the interference amount distributed along the honing wheel axial direction is determined based on the positional relationship between each target intersection point and the root circle of the internal gear workpiece, specifically including: Transform the target intersection point from the second honing wheel coordinate system to the first workpiece coordinate system.

[0040] In the second workpiece coordinate system, the interference amount distributed along the honing wheel axis is determined based on the radial distance of the target intersection point and the root circle radius of the internal gear workpiece: ; in, δ i and m i Let represent the interference at the i-th axial position of the honing wheel and the radial distance to the target intersection point, respectively. r f This indicates the root circle radius of the internal gear workpiece.

[0041] Furthermore, the nominal tooth tip surface of the honing wheel is corrected based on the interference amount, specifically including: If the interference at the i-th axial position of the honing wheel is positive, then the radius of the nominal tooth tip surface of the honing wheel at the i-th axial position is reduced by the interference.

[0042] By traversing each axial position of the honing wheel, the design tooth tip circle of the honing wheel is obtained.

[0043] Specifically, the interference amount at each calculated axial position is assessed. If the interference amount at the i-th axial position of the honing wheel is positive, it indicates a risk of overcutting at that position, requiring the radius of the nominal tooth tip surface of the honing wheel at the i-th axial position to be reduced to minimize the interference. By traversing every axial position of the honing wheel and performing the above correction operation, a series of corrected radius points are obtained. Connecting these points forms the designed tooth tip circle profile of the honing wheel. This process ensures the accuracy and comprehensiveness of the correction, and the final profile effectively avoids all interference areas.

[0044] The design method of the ellipsoidal honing wheel for high-power honing of internal gears provided by the present invention will be described in detail below through a specific embodiment.

[0045] Reference Figure 1 In one specific embodiment, the design method of the ellipsoidal honing wheel for high-strength honing of internal gears includes: Step 1: Establish the spatial coordinate system between the workpiece and the honing wheel.

[0046] like Figure 2 As shown, the spatial coordinate system includes the workpiece's initial fixed coordinate system. S 1(O 1; x 1, y 1, z 1) and the fixed coordinate system of motion S 1′( O 1′; x 1′, y 1′, z 1′) Initial fixed coordinate system of the honing wheel S 2( O 2; x 2, y 2, z 2) and the fixed coordinate system of motion S 2′( O 2′; x 2′, y 2′, z 2′) and fixed reference coordinate system S g ( O g ; x g , y g , z g ).

[0047] Step 2: Based on the mathematical expression of the involute helical surface of the workpiece tooth surface, in the initial fixed coordinate system of the workpiece... S In step 2, the coordinate equations and normal vector equations of the left and right tooth surfaces of the workpiece are constructed.

[0048] For example, the workpiece is in the initial fixed coordinate system S The expression for the position vector of the left tooth surface in section 1 is: ; Workpiece in the initial fixed coordinate system S The expression for the left tooth surface normal vector in section 1 is: ; Workpiece in the initial fixed coordinate system S The expression for the position vector of the right tooth surface in section 1 is: ; Workpiece in the initial fixed coordinate system S The expression for the normal vector of the right tooth surface in section 1 is: ; in, Let any point on the standard tooth surface of the workpiece be in the initial fixed coordinate system. S The coordinates in 1, The starting angle of the involute. The standard involute development angle, The involute helix increment angle, The radius of the base circle, Let be the helical parameter, and .

[0049] It should be noted that the workpiece is in the initial fixed coordinate system S The position vectors of the left and right tooth surfaces in Figure 1 together constitute the coordinate system of the workpiece in the initial fixed coordinate system. S 1. The tooth surface position vector r1. And the workpiece in the initial fixed coordinate system. S The left and right tooth surface normal vectors in Figure 1 together constitute the coordinate system of the workpiece in the initial fixed coordinate system. S The tooth surface normal vector n1 in 1.

[0050] Step 3: Set the workpiece rotation angle The angle of the honing wheel Establish the initial fixed coordinate system of the workpiece. S 1 to the fixed coordinate system of the honing wheel S The homogeneous transformation matrix M2′1 of 2′ ), and determine the meshing equation. , Let be the equation of the relative velocity between the contact point between the workpiece and the honing wheel in the workpiece's fixed coordinate system. It is the normal vector of the tooth surface of the workpiece in its own motion-fixed coordinate system.

[0051] From the workpiece's initial fixed coordinate system S 1 to the fixed coordinate system of the honing wheel S The homogeneous transformation matrix M2′1 of 2′ It is determined by the following relationship: ; ; ; ; in, The center distance, The angle between the axes is denoted by .

[0052] relative speed Calculated using the following formula: ; Where ω1=(0,0, ω 1) T and ω2=(0,- ω 2sin Σ , ω 2cos Σ ) T These are the angular velocity vectors of the internal gear workpiece and the honing wheel in the workpiece's fixed coordinate system, respectively. Let be the position vector of the contact point between the internal gear workpiece and the honing wheel in the workpiece's motion-fixed coordinate system. Transformation matrix The top left corner of the 3×3 submatrix, O2 is the position vector of the origin of the honing wheel's motion-fixed coordinate system in the workpiece's motion-fixed coordinate system.

[0053] The meshing equations satisfy: ; .

[0054] Step 4: Calculate the workpiece rotation angle for one meshing cycle, and solve for the target involute parameters that satisfy the meshing equation using numerical methods. The coordinates of the corresponding points are transformed from the motion-fixed coordinate system of the workpiece to the motion-fixed coordinate system of the honing wheel to obtain the instantaneous contact line on the tooth surface of the honing wheel.

[0055] Step 5: On each instantaneous contact line, find the points where the radial distance is equal to the radius of the honing wheel's addendum circle, obtaining the addendum circle intersections. Then, restrict the range of the z-coordinate of these intersections, retaining only those points that satisfy | z |≤ z limit The point is taken as the target intersection point. In the embodiment, the target intersection point is as follows: Figure 3 As shown.

[0056] On each instantaneous contact line, the points satisfying the condition that the radial distance is equal to the radius of the honing wheel's addendum circle are obtained to obtain the addendum circle intersection points, specifically including: For each discrete point sequence P on the instantaneous contact line i =( x i , y i , z i ),in i =1,2,…, N Calculate the chord length between two adjacent points and sum them up to define the arc length parameter. s : ; This establishes a mapping relationship between discrete point coordinates and arc length, and calculates the radial distance of each point: ; Further search for the radial distance spanning the tip circle radius of the honing wheel. r a2 Adjacent pairs of points: (1) If there exists an adjacent point P i With P i+1 satisfy r i < r a2 and r i+1 > r a2 (or vice versa), then based on arc length s Perform linear interpolation to obtain the intersection point P of the tooth tip circles. int Coordinates: ; (2) If all of the current meshing lines r i < r a2 (The curve does not reach the tooth tip circle), indicating that the contact line does not naturally extend to the tooth tip circle. The last three points P in the direction of increasing arc length are used. N P N-1 、 P N-2 : ; Wherein, the coefficient is from The three points are determined by interpolation.

[0057] Construct about arc length s The equation: ; Solving the equation yields real solutions. s ext Substitute x ( s ), y ( s ), z ( s The coordinates of the intersection point of the extrapendicular tooth tip circle are obtained from the equation. .

[0058] Step 6: Using the inverse transformation matrix, transfer the selected target intersection points from the motion-fixed coordinate system of the honing wheel. S 2′ Transform back to the workpiece's initial fixed coordinate system S 1. Calculate the radial distance m of this point in the initial fixed coordinate system of the workpiece: ; ; ; .

[0059] The radial distance calculated in this embodimentm like Figure 4 As shown.

[0060] Step 7: Calculate the interference amount δ = m - r f ,in r f Let be the radius of the tooth root circle of the workpiece. δ If the value is greater than 0, it indicates that the honing wheel has penetrated the root of the workpiece tooth at that point, and the radius of the honing wheel at the corresponding point needs to be adjusted to reduce the interference. δ To form an ellipsoidal honing wheel profile.

[0061] Specifically, the actual profile of the ellipsoidal honing wheel satisfies: For each calculated target intersection point P (assuming it is at the i-th axial position of the honing wheel), the interference at that point is defined as follows: .

[0062] (1) If δ i ≤0 indicates that the honing wheel did not penetrate into the root of the workpiece tooth at this intersection point, and the tip circle radius of the honing wheel at this axial position remains at 0. r a2 ; (2) If δ i A value >0 indicates that the honing wheel penetrates the workpiece tooth root at this point, and the interference is [value missing]. δ i To prevent overcutting, the tip circle radius of the honing wheel at this axial position needs to be adjusted. r a2 Reduce interference δ i The revised design tooth tip circle radius: ; Finally, the design tip circle radius at each axial position of the honing wheel is calculated to obtain the design profile curve of the ellipsoidal honing wheel.

[0063] In this embodiment, the calculated interference result is as follows: Figure 5 As shown, the calculated design profile curve of the ellipsoidal honing wheel is as follows: Figure 6 As shown, the design profile of the trimmed ellipsoidal honing wheel is as follows: Figure 7 As shown.

[0064] Step 8: Use the calculated ellipsoidal correction data in 3D software to generate a corrected solid ellipsoidal honing wheel 3D model for the production and manufacturing of ellipsoidal honing wheels for internal gear high-strength honing.

[0065] Step 9: Select the corresponding type of superhard abrasive grains based on the material and heat treatment hardness of the internal gear workpiece, and solidify the superhard abrasive grain layer through electroplating or sintering processes.

[0066] Specifically, when the internal gear workpiece is carburized and quenched steel or high-hardness alloy steel with a hardness ≥ HRC50, CBN abrasive is selected for the superhard abrasive layer; when the internal gear workpiece is quenched and tempered steel or low-hardness alloy steel with a hardness < HRC50, microcrystalline corundum abrasive is selected; when the internal gear workpiece is cemented carbide or special materials such as ceramics, diamond abrasive is selected.

[0067] In one example, the design of an internal gear and honing wheel for an automotive transmission is used as the implementation object. The internal gear is made of 20CrMnTi carburized and quenched steel with a tooth surface hardness of HRC58-62, which belongs to high-hardness gear steel. Specific parameters are shown in Table 1. Table 1. Parameters of ellipsoidal honing wheel and internal gear workpiece

[0068] In this example, the tooth surface of the honing wheel is a standard involute helical surface, and its tooth tip rotation surface varies ellipsoidally along the axial direction. Specifically, in this example, there is varying degrees of interference at different axial positions, with smaller interference in the central region and gradually increasing interference towards the two edges. Correspondingly, the tooth tip circle radius of the honing wheel is continuously corrected along the axial direction: in the axial central region, the interference is approximately 0.05 mm, and the tooth tip circle radius is adjusted from the original design value r. a2 The radius of the tooth tip circle shrinks from 39.8 mm to approximately 39.75 mm; at both axial edges, the interference increases to approximately 0.5 mm, and the tip circle radius further shrinks to approximately 39.3 mm. The correction amount of the entire tip circle radius along the axial direction is precisely equal to the interference amount at the corresponding position, so that the corrected tip rotation surface presents a smooth, continuous curve with a larger middle and smaller ends on the axial section, and the overall outline has an ellipsoidal feature. In this example, the surface of the honing wheel teeth is coated with a CBN (cubic boron nitride) superhard abrasive layer through an electroplating process, with an abrasive grit size of 120 / 140 mesh and a uniform coating thickness controlled at 0.15 mm.

[0069] As can be seen from the above specific embodiments, the design method of the ellipsoidal honing wheel for high-power honing of internal gears provided by the present invention has the following technical effects: 1. By establishing an accurate spatial meshing equation and solving the instantaneous contact line, the interference between the honing wheel tooth tip and the workpiece tooth root under the large shaft intersection angle condition can be accurately and quantitatively calculated, solving the problem that traditional design methods cannot accurately identify and quantify interference.

[0070] 2. Based on the calculated interference, the nominal tooth tip surface of the honing wheel is corrected point by point, generating an ellipsoidal surface with a specific contour. This design enables the honing wheel to effectively avoid interference with the tooth root of the workpiece during processing, thereby protecting the strength of the tooth root and ensuring the machining accuracy of the internal gear tooth surface.

[0071] 3. The designed ellipsoidal honing wheel has a smooth, tapering shape with a larger center and smaller ends in the axial direction at the tooth tip. This not only fundamentally eliminates the interference between the tooth tip and the tooth root, but also makes the honing wheel more stable when entering and exiting the mesh, which is beneficial to improving the stability and efficiency of the machining process.

[0072] 4. By solidifying an ultra-hard abrasive layer selected according to the material properties of the workpiece onto the optimized ellipsoidal honing wheel tooth surface, the honing wheel can achieve efficient cutting capability for internal gears of different hardness and materials while avoiding tooth root interference, thus expanding the applicability of the high-strength honing process.

[0073] Reference Figure 8 This invention also provides an ellipsoidal honing wheel for high-power honing of internal gears. The honing wheel is obtained through the design method provided by this invention. Its most significant feature is that the tooth tip surface of the honing wheel is designed as an ellipsoidal curved surface. This special curved surface shape is not arbitrarily set, but is an inevitable result derived from the precise calculation and correction of interference under specific workpiece and machining parameters. This allows the honing wheel to maintain the involute characteristics of the tooth surface while exhibiting a smooth, tapering shape in the axial direction, larger in the middle and smaller at both ends. This effectively avoids interference between the tooth tip edge and the workpiece tooth root when meshing with the workpiece at a large axial angle, ensuring machining quality and workpiece strength.

[0074] In some embodiments, an ultrahard abrasive layer is bonded to the surface of the gear teeth of the honing wheel. This ultrahard abrasive layer directly undertakes the cutting task on the tooth surface of the internal gear workpiece. By bonding it to a precisely modified ellipsoidal honing wheel matrix, the honing wheel not only has a geometry that avoids interference, but also possesses efficient and high-precision machining capabilities, achieving a unity of geometric optimization and functional enhancement.

[0075] The abrasive grains in the superhard abrasive layer are selected from cubic boron nitride (CBN), microcrystalline corundum, and diamond; for example, CBN is preferred for high-hardness quenched steel workpieces. The superhard abrasive layer can be bonded to the surface of the gear teeth via electroplating or sintering. These specific material and process choices allow the honing wheel to better adapt to different processing requirements. For example, for internal gear workpieces of different hardness and materials, the most suitable abrasive grains and bonding methods can be selected to achieve optimal processing results, wear resistance, and economy, greatly improving the overall service performance and process applicability of the honing wheel.

[0076] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0077] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A design method of an ellipsoidal honing stone for a power honing of an internal gear, characterized by, include: Establish the spatial meshing equation between the internal gear workpiece and the honing wheel; Solve the spatial meshing equation to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece during meshing; Determine the target intersection point between each of the instantaneous contact lines and the nominal tooth top surface of the honing wheel; The interference amount distributed along the honing wheel axis is determined based on the positional relationship between each of the target intersection points and the root circle of the internal gear workpiece. The nominal tooth tip surface of the honing wheel is corrected according to the interference amount to obtain an ellipsoidal honing wheel.

2. The design method of an ellipsoidal honing stone for a ring gear superfinishing according to claim 1, characterized by, Establish the spatial meshing equation between the internal gear workpiece and the honing wheel, specifically including: Based on the mathematical expression of the involute helical surface of the tooth surface of the internal gear workpiece, the tooth surface position vector and tooth surface normal vector of the internal gear workpiece with respect to the involute parameters are constructed in the first workpiece coordinate system, where the first workpiece coordinate system is the initial fixed coordinate system of the internal gear workpiece. Based on a transformation matrix regarding the rotation angle of the internal gear workpiece, the tooth surface normal vector of the internal gear workpiece in the first workpiece coordinate system is converted into the tooth surface normal vector of the internal gear workpiece in the second workpiece coordinate system, where the second working coordinate system is the motion-fixed coordinate system of the internal gear workpiece. Determine the relative velocity equation of the contact point between the internal gear workpiece and the honing wheel; Establish the spatial meshing equation: 。 in, The equation for the relative velocity between the contact point of the internal gear workpiece and the honing wheel in the second workpiece coordinate system is given. Let be the tooth surface normal vector of the internal gear workpiece in the second workpiece coordinate system.

3. The design method of the ellipsoidal honing wheel for high-power honing of internal gears according to claim 2, characterized in that, The relative velocity equation of the contact point between the internal gear workpiece and the honing wheel in the second workpiece coordinate system is: ； Wherein, ω1 and ω2 are the angular velocity vectors of the internal gear workpiece and the honing wheel in the second workpiece coordinate system, respectively. O1 is the position vector of the contact point between the internal gear workpiece and the honing wheel in the second workpiece coordinate system, O2 is the position vector of the origin of the second honing wheel coordinate system in the second workpiece coordinate system, and the second honing wheel coordinate system is the motion-fixed coordinate system of the honing wheel.

4. The design method of the ellipsoidal honing wheel for high-power honing of internal gears according to claim 2, characterized in that, Solving the spatial meshing equation to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece during meshing specifically includes: By iterating through the rotation angles of the internal gear workpiece within one meshing cycle, the target involute parameter that makes the spatial meshing equation valid is determined. The corresponding coordinate points of the target involute parameters in the second workpiece coordinate system are transformed to the second honing wheel coordinate system to determine the instantaneous contact line between the nominal tooth tip surface of the honing wheel and the internal gear workpiece.

5. The design method of the ellipsoidal honing wheel for high-power honing of internal gears according to claim 2, characterized in that, Determining the target intersection point between each of the instantaneous contact lines and the nominal tooth tip surface of the honing wheel specifically includes: On each of the instantaneous contact lines, the point whose radial distance is equal to the radius of the tooth tip circle of the honing wheel is determined to obtain the tooth tip circle intersection point; The intersection point of the tooth tip circle that meets the physical requirements is retained as the target intersection point.

6. The design method of the ellipsoidal honing wheel for high-power honing of internal gears according to claim 4, characterized in that, The interference amount distributed along the axial direction of the honing wheel is determined based on the positional relationship between each target intersection point and the root circle of the internal gear workpiece, specifically including: Transform the target intersection point from the second honing wheel coordinate system to the first workpiece coordinate system; In the second workpiece coordinate system, the interference amount distributed along the axial direction of the honing wheel is determined based on the radial distance of the target intersection point and the root circle radius of the internal gear workpiece: ； in, δ i and m i These represent the interference at the i-th axial position of the honing wheel and the radial distance to the target intersection point, respectively. r f This indicates the root circle radius of the internal gear workpiece.

7. The design method of the ellipsoidal honing wheel for high-power honing of internal gears according to claim 6, characterized in that, The nominal tooth tip surface of the honing wheel is corrected based on the interference amount, specifically including: If the interference amount at the i-th axial position of the honing wheel is positive, then the radius of the nominal tooth tip surface of the honing wheel at the i-th axial position is reduced by the interference amount. By traversing each axial position of the honing wheel, the designed tooth tip circle of the honing wheel is obtained.

8. An ellipsoidal honing wheel for high-power honing of internal gears, characterized in that, The honing wheel is obtained by the design method according to any one of claims 1-7; The honing wheel is designed with an ellipsoidal curved surface at the tooth tip.

9. The ellipsoidal honing wheel for high-power honing of internal gears according to claim 8, characterized in that, The surface of the tooth portion of the honing wheel is solidified with an ultra-hard abrasive layer.

10. The ellipsoidal honing wheel for high-power honing of internal gears according to claim 9, characterized in that, The abrasive type of the superhard abrasive layer is selected from: cubic boron nitride abrasive, microcrystalline corundum abrasive and diamond abrasive; And / or, the superhard abrasive layer is solidified onto the surface of the gear tooth portion by an electroplating process or a sintering process.

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