Analog simplified analysis method and device for worm grinding wheel grinding gear and medium

Abstract

The invention provides an analogy simplified analysis method and device for a worm grinding wheel grinding gear and a medium, belongs to the field of grinding machining, deduces and calculates a single-time grinding material removal area of a specific tooth surface through analysis of movement and contact behaviors on a middle plane, and calculates a single-time grinding material removal area of the specific tooth surface on the basis of a material removal rate equivalent principle. The worm grinding wheel gear grinding process is equivalently simplified into plane grinding. According to the method, equivalence of movement and contact behaviors in the grinding process is considered, grinding force and thermal effect equivalent analysis is achieved based on the material removal rate equivalent principle, and obtained equivalent plane grinding process parameters directly reflect the grinding behavior, grinding force and thermal characteristics of a worm grinding wheel grinding gear; the complex worm grinding wheel gear grinding process can be subjected to equivalent simplified research on a plane grinding platform, the experiment cost is reduced, experiment result analysis is simplified, and optimization analysis of worm grinding wheel gear grinding process parameters is facilitated.

Description

Technical Field

[0001] This invention belongs to the field of grinding, specifically relating to an analogical simplified analysis method, equipment, and medium for grinding gears with worm gears. Background Technology

[0002] Worm wheel grinding of gears is a gear generating grinding method with advantages such as high machining accuracy and high production efficiency, and is widely used in mass gear grinding. Grinding, as one of the means of gear finishing, is often the final process in gear machining, directly determining the surface integrity of the tooth surface, and thus affecting the service performance of the gear.

[0003] Studying the impact of worm wheel grinding on the surface integrity of gears is crucial for improving gear grinding processes, controlling surface integrity, and enhancing gear performance. In engineering practice, numerous worm wheel grinding experiments are often conducted to optimize process parameters, but these experiments are costly, time-consuming, and lack clear guidance for process optimization. Analytical modeling and simulation analysis, on the other hand, can qualitatively and quantitatively analyze the impact of process parameters on surface integrity through in-depth analysis of the grinding mechanism, providing practical optimization solutions while reducing testing costs and offering greater applicability. The complex wheel-gear meshing motion and material removal process involved in worm wheel grinding make analytical modeling and simulation analysis of the grinding process challenging. Therefore, how to simplify the complex worm wheel grinding process of gears through appropriate equivalent simplification methods, so that subsequent analytical modeling and simulation analysis become feasible, is an urgent problem to be solved. At the same time, the equivalent simplification model is also conducive to simplifying the experimental process of worm wheel grinding of gears, reducing experimental costs, and simplifying the analysis of experimental results.

[0004] Scholars have studied the equivalent simplification method for worm wheel grinding of gears. The main approach is to simplify the complex meshing motion of worm wheel grinding of gears through equivalent simplification analysis, thereby simplifying the study of the grinding mechanism.

[0005] For example, the proposed equivalent simplified model of worm wheel grinding gears, which analyzes the motion and contact behavior in the grinding zone, is only an equivalent analogy of instantaneous grinding behavior and does not take into account the characteristics of grinding material removal rate. Therefore, it lacks equivalent analysis of grinding force and thermal load. Furthermore, the equivalent simplified model still involves the complex motion of the workpiece and grinding wheel between a pair of intersecting axes, which does not achieve a good simplification analysis effect. It cannot make full use of existing surface grinding and cylindrical grinding platforms, and the corresponding equivalent simplified test is still quite complicated. Summary of the Invention

[0006] This invention provides an analogical simplification analysis method for worm wheel grinding of gears. This invention solves the problem of high complexity in three-dimensional grinding analysis, and provides an efficient theoretical tool for grinding process parameter optimization, equipment selection, and surface integrity prediction, thereby improving the analysis efficiency of worm wheel grinding of gears.

[0007] The methods include: S101: Define an intermediate plane and equate the worm wheel grinding process of gears to the meshing of an equivalent grinding wheel spur rack and gear on the intermediate plane; wherein the intermediate plane is parallel to the helical gear normal section and perpendicular to the worm wheel normal section; S102: On the intermediate plane, the motion of the worm gear grinding gear is simplified by equivalent means, including deriving the hypothetical axial movement speed, actual grinding line speed and actual tooth surface grinding depth of the equivalent grinding wheel spur rack. S103: The contact behavior of the worm wheel grinding gear is simplified to the intersecting contact of two intersecting circular arc surfaces in space; wherein, the two intersecting circular arc surfaces correspond to the equivalent circular arc surface of the worm wheel and the equivalent circular arc surface of the gear, respectively. S104: Based on equivalent contact behavior, calculate the volume of material removed in a single grinding process on the preset tooth surface; S105: Based on the volume of the material removal area in a single grinding operation, calculate the material removal rate and the material removal rate per unit width for a single grinding operation; S106: Based on the similarity of the grinding process, the worm wheel grinding of the gear is equivalent to a plane grinding model. The grinding wheel radius, grinding wheel linear velocity and grinding depth of the equivalent plane grinding are set so that they are consistent with the equivalent arc surface radius, actual grinding linear velocity and actual tooth surface grinding depth of the worm wheel, respectively. S107: Calculate the feed rate of the equivalent surface grinding model based on the principle of equivalent material removal rate per unit width; S108: Determine the grinding mode of the equivalent surface grinding model as reverse grinding.

[0008] It should be further explained that S101 specifically includes the following steps: The relative spatial position of the worm grinding wheel and the gear is determined, including the angle between the axis of the worm grinding wheel and the end face of the gear. The angle is calculated by the helix angle β of the helical gear and the lead angle γ of the worm grinding wheel, that is, the angle is β-γ. Based on relative spatial position, the intermediate plane is defined as a plane that is parallel to the normal section of the helical gear and perpendicular to the normal section of the worm grinding wheel, wherein the normal section of the helical gear is a plane perpendicular to the gear tooth direction, and the normal section of the worm grinding wheel is a plane perpendicular to the grinding wheel axis. Analyzing the shape of the worm gear grinding wheel in the normal section, the normal section shape is approximately the standard straight rack tooth profile, which includes a straight tooth profile and a standard pressure angle. The cross-sectional shape of the worm grinding wheel on the intermediate plane is equivalent to the grinding wheel straight rack, and the equivalent grinding wheel straight rack has the same tooth profile parameters as the normal cross-section of the worm grinding wheel. Establish the correspondence between the rotational motion of the worm grinding wheel and the axial movement of the equivalent grinding wheel spur rack. That is, when the worm grinding wheel rotates around its axis, the equivalent grinding wheel spur rack moves along the gear axis, and the gear rotates around its own axis, forming a meshing motion.

[0009] It should be further explained that S102 specifically includes the following steps: Based on the lead p and rotational speed of the worm grinding wheel n w Calculate the hypothetical axial movement speed of the equivalent grinding wheel spur rack. V t ; The linear velocity of the gear rotation V g and the linear velocity of the worm wheel rotation V w It is decomposed into components parallel to the intermediate plane and normal components perpendicular to the intermediate plane, respectively. In the direction of the normal vector of the intermediate plane, the normal component of the linear velocity of the worm wheel rotation and the normal component of the linear velocity of the gear rotation are combined to obtain the actual grinding linear velocity. V s ; Analyze the direction of the equivalent grinding wheel spur rack feed S along the gear radial direction, and confirm that the feed direction is parallel to the defined intermediate plane; Based on the gear normal pressure angle α, the gear radial feed S is converted into the actual tooth surface grinding depth t.

[0010] It should be further explained that S103 specifically includes the following steps: Determine the contact point between the worm wheel and the gear on the pitch circle; Calculate the principal radius of curvature of the worm wheel at the contact point. r w1 ; Calculate the principal radius of curvature of the gear at the contact point. r g1 ; Ignoring the other principal radius of curvature of the worm grinding wheel r w2 And the other principal radius of curvature of the gear r g2 ; based on r w1 and r g1 Establish a contact model of two equivalent circular arc surfaces arranged with spatially intersecting axes.

[0011] It should be further explained that S104 specifically includes the following steps: The parameters required to calculate the volume of the material removal region in a single grinding cycle are determined, including the actual tooth surface grinding depth t obtained in S102 and the equivalent principal curvature radius of the worm wheel obtained in S103. r w1 And the axial feed rate f of the worm grinding wheel, and the total tooth height of the gear are... h a +h f ,in h a For tooth tip height, h f For tooth root height; Simulate the motion process of the gear rotating one revolution, and simultaneously record the feed amount f of the worm wheel along the axial direction. Determine the new grinding boundary and the old grinding boundary formed in this process, and clarify that the area between the two boundaries is the single grinding material removal area, and the shape of the area in the cross section along the tooth width direction is crescent-shaped. The crescent-shaped cross-section is analyzed using the differential method. The cross-section is divided into multiple differential regions, and the differential height of each region is calculated. h i The cross-sectional area of ​​the crescent-shaped section is obtained by summing the areas of each differential region, corresponding to the differential width l. S j Measure and determine the width span of the cross section. L hg ; The material removal length along the gear tooth profile is determined to be the total tooth height of the gear. h a +h f The area of ​​the crescent-shaped cross-section S j With full tooth height h a +h f Multiply by the product to calculate the volume V of the material removal area in a single grinding operation on a specific tooth surface.

[0012] It should be further explained that S105 specifically includes the following steps: The relevant parameters for calculating the material removal rate of a single grinding pass on the tooth surface are determined, including the volume of the material removal area obtained in S104. V Determined gear speed n g The meshing overlap required for full tooth high-generation envelope motion ε , and the actual tooth surface grinding width b; Equivalent grinding wheel spur rack and gear meshing overlap εThe number of teeth spanned required for the full-tooth high-generation envelope motion is used to obtain the generating motion time for a single grinding operation. t g :

[0013] Calculate the material removal rate of a single grinding operation on the tooth surface Q m Material removal rate per unit width Q mw : .

[0014] It should be further explained that S106 specifically includes the following steps: Compare the material removal area of ​​the gear grinding wheel with the shape of the undeformed grinding debris area of ​​the surface grinding wheel. Extract the radius of curvature of the equivalent circular arc surface of the worm grinding wheel calculated in S103. r w1 The grinding wheel radius r of the equivalent surface grinding model is set to r= r w1 ; Extract the actual grinding linear velocity Vs synthesized in S102, and convert it to the grinding wheel linear velocity of the equivalent surface grinding model. V ss Set as V ss =Vs; Extract the actual tooth surface grinding depth t calculated in S102, and use the grinding depth of the equivalent surface grinding model. a p Set as a p =t; Calculate the grinding contact arc length of the original worm wheel grinding process and the equivalent surface grinding model respectively, and verify r= r w1 , V ss =Vs、 a p Does the setting of =t satisfy the consistency between the two in terms of grinding contact arc length, grinding depth, and grinding linear speed?

[0015] It should be further explained that S107 specifically includes the following steps: Extract the material removal rate per unit width of the lower tooth surface in a single grinding operation calculated from S105. Q mw ,confirm Q mw The numerical accuracy and units are set to the material removal rate per unit width in the equivalent surface grinding model. Qsw The target value, i.e. Q sw = Q mw ; Determine the material removal rate per unit width in surface grinding Q sw The calculation formula is as follows:

[0016] Extract the equivalent surface grinding depth set in S106 a p Determine the actual grinding width b of the equivalent surface grinding, based on... Q sw = Q mw And the derivation of the feed rate for equivalent surface grinding. v ww ,get v ww = Q sw / a p The following formula is used for calculation. v ww To ensure that units are consistent during the calculation process; .

[0017] According to another embodiment of this application, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the analogous simplification analysis method for worm gear grinding.

[0018] According to yet another embodiment of this application, a storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the steps of the analogy simplification analysis method for worm gear grinding gears.

[0019] As can be seen from the above technical solutions, the present invention has the following advantages: The simplified analogy analysis method for worm gear grinding provided by this invention defines a mid-plane parallel to and perpendicular to the normal section of the helical gear and the normal section of the worm gear. This transforms the complex spatial helical involute meshing of the worm gear and gear into planar meshing of an equivalent grinding wheel spur rack and gear on the mid-plane. Without requiring complex spatial meshing theory or finite element simulation, analysis can be conducted using mature planar rack and gear meshing laws, avoiding the problems of large computational load and long processing time in spatial meshing. By deriving the hypothetical axial movement velocity, actual grinding linear velocity, and actual tooth surface grinding depth of the equivalent grinding wheel spur rack, the abstract grinding motion and contact behavior are transformed into quantifiable parameters. These parameters are directly related to subsequent contact analysis and material removal calculations, avoiding analysis errors caused by the fuzziness of motion and contact parameters in existing technologies.

[0020] This invention simplifies the helical contact between the worm gear and the gear into the intersecting contact of two staggered circular arc surfaces in space, and ignores the secondary principal curvatures that have a negligible impact on the contact. This simplification allows the contact arc length and radius of curvature of the contact area to be directly calculated through the geometric relationship of the circular arc surfaces, thereby establishing the correlation between contact parameters, contact stress, and grinding heat. This enables rapid analysis of force and thermal load changes without the need for complex contact simulations.

[0021] This invention addresses the irregular cross-section of the crescent-shaped material removal region by dividing it into multiple differential regions using a differential method. The total cross-sectional area is obtained by summing these differential areas, and the volume is calculated by combining this with the full tooth height. The calculated material removal rate per unit width is calculated by dividing by the grinding width to eliminate interference from different gear tooth widths, focusing the removal rate index on the force and heat load per unit width. This ensures that the equivalent plane grinding model accurately matches the force and heat state of the original grinding process. Based on the principles of shape similarity and comparable material removal rate per unit width, worm wheel grinding is equivalent to a plane grinding model: Let r = r w1 , V ss =Vs、 a p =t, calculate and verify the feed rate. v ww Within the limits allowed by the equipment, the reverse grinding method is determined. This preserves the core motion, contact, and thermomechanical characteristics of the original grinding process while avoiding the analytical problems caused by spatial meshing and complex contact. It can be directly used for optimizing process parameters, studying grinding thermomechanical properties, and analyzing surface integrity in worm wheel grinding. Attached Figure Description

[0022] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart illustrating a simplified analogy analysis method for worm gear grinding of gears; Figure 2 A schematic diagram of the four motions in the process of a worm gear grinding wheel grinding a gear; Figure 3 This is a schematic diagram of the middle plane; Figure 4 A simplified equivalent schematic diagram of the worm gear grinding process on the intermediate plane; Figure 5 A schematic diagram illustrating the derivation and calculation of the actual grinding linear velocity for worm gear grinding of gears; Figure 6 A schematic diagram illustrating the derivation and calculation of the actual tooth surface grinding depth for worm gear grinding; Figure 7 A schematic diagram of the helical surface meshing of the worm gear and gear surfaces in three-dimensional space; Figure 8 A simplified equivalent schematic diagram of the surface contact behavior between the worm gear and the gear. Figure 9 A schematic diagram of the cross-sectional shape of the area where grinding material is removed from the gear surface; Figure 10 A schematic diagram of the area where grinding material is removed from the entire tooth profile of a gear surface; Figure 11 A schematic diagram illustrating the analytical derivation and calculation of the cross-sectional shape of the area where grinding material is removed from the gear surface; Figure 12 This is a schematic diagram of an electronic device. Detailed Implementation

[0024] The analogical simplification analysis method for worm wheel grinding of gears provided by this invention aims to overcome the shortcomings of the above-mentioned equivalent analysis methods. Based on the kinematic equivalent analysis of worm wheel grinding of gears on the intermediate plane, the method derives and calculates the single-pass grinding material removal rate of the tooth surface considering the axial feed action of the worm wheel. Considering the similarity between worm wheel grinding of gears and surface grinding behavior, the method adopts the principle of equivalent material removal rate to achieve an equivalent simplification of the worm wheel grinding of gears to surface grinding. This method can better reflect the influence of changes in worm wheel grinding of gear process parameters on the grinding material removal rate in surface grinding processes. It is of great significance for studying the influence of worm wheel grinding of gear process parameters on grinding force, thermal load, and surface integrity through equivalent simplification.

[0025] The following will describe in detail the analogous simplified analysis method for worm gear grinding of gears involved in this application. Specific details such as particular system structures and technologies are presented for illustrative purposes rather than for limiting purposes, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details.

[0026] It should be understood that, when used in this specification, terms include indicating the presence of a described feature, integral, step, operation, element, and / or component, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. The terms include, encompass, have, and variations thereof mean including but not limited to, unless otherwise specifically emphasized.

[0027] The statements such as "one embodiment" or "some embodiments" described in this application mean that one or more embodiments of this application include the specific features, structures, or characteristics described in that embodiment. Therefore, the statements such as "in one embodiment," "in some embodiments," "in other embodiments," and "in still other embodiments" in this application do not necessarily refer to the same embodiment, but rather mean one or more, but not all, embodiments, unless otherwise specifically emphasized.

[0028] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Please see Figure 1 The diagram shows a flowchart of an analogical simplification analysis method for worm gear grinding of gears in a specific embodiment. The method includes: S101: Define an intermediate plane and equate the worm wheel grinding gear process to the meshing of an equivalent grinding wheel spur rack and gear on the intermediate plane; wherein the intermediate plane is parallel to the helical gear normal section and perpendicular to the worm wheel normal section.

[0030] In some embodiments, S101 specifically includes the following steps: Step S1011: Determine the relative spatial position of the worm wheel and the gear, including the angle between the axis of the worm wheel and the end face of the gear. This angle is calculated by the helical gear helix angle β and the worm wheel lead angle γ, i.e., the angle is β-γ.

[0031] Step S1012: Based on the relative spatial position, define the intermediate plane as a plane that is parallel to the normal section of the helical gear and perpendicular to the normal section of the worm grinding wheel, wherein the normal section of the helical gear is a plane perpendicular to the gear tooth direction, and the normal section of the worm grinding wheel is a plane perpendicular to the grinding wheel axis.

[0032] Step S1013: Analyze the shape of the worm grinding wheel in the normal section. Since the helix angle of the worm grinding wheel is small, its normal section shape is approximately the standard straight rack tooth profile, which includes a straight tooth profile and a standard pressure angle.

[0033] Step S1014: Equip the cross-sectional shape of the worm grinding wheel on the intermediate plane with an equivalent grinding wheel spur rack. This equivalent grinding wheel spur rack has the same tooth profile parameters as the normal cross-section of the worm grinding wheel, such as module and pressure angle.

[0034] Step S1015: Establish the correspondence between the rotational motion of the worm grinding wheel and the axial movement of the equivalent grinding wheel spur rack. That is, when the worm grinding wheel rotates around its axis, the equivalent grinding wheel spur rack moves along the gear axis, while the gear rotates around its own axis, forming a meshing motion.

[0035] As can be seen, this embodiment clearly defines the motion parameters for the worm gear grinding of the gear, including the worm gear speed nw and the gear speed. n g Radial feed rate S, axial feed rate f z For machining helical cylindrical gears, it is also necessary to determine the angle β between the worm wheel axis and the gear end face. γ and β are the helix angles of the helical gear, and γ is the lead angle of the worm gear grinding wheel.

[0036] In this embodiment, the intermediate plane is defined to simultaneously satisfy the geometric conditions of being parallel to the normal section of the helical gear and perpendicular to the normal section of the worm grinding wheel. The geometric characteristics of the worm grinding wheel are then analyzed. Because the helix angle of the worm grinding wheel is extremely small, its cross-sectional shape on the intermediate plane can be approximated as a standard spur rack. Finally, the rotational motion of the worm grinding wheel around its own axis is transformed into the axial movement of an equivalent grinding wheel spur rack on the intermediate plane, establishing the meshing relationship between the spur rack and the gear, making their meshing motion completely equivalent to the original meshing motion of the worm grinding wheel and the gear.

[0037] S102: On the intermediate plane, the motion of the worm gear grinding gear is simplified by deriving the hypothetical axial movement speed, actual grinding linear speed and actual tooth surface grinding depth of the equivalent grinding wheel spur rack.

[0038] S102 specifically includes the following steps: Step S1021: Based on the lead p and rotational speed of the worm grinding wheel n w Calculate the hypothetical axial movement speed of the equivalent grinding wheel spur rack.V t .

[0039] Step S1022: Change the linear velocity of the gear rotation V g and the linear velocity of the worm wheel rotation V w It is decomposed into components parallel to the intermediate plane and normal components perpendicular to the intermediate plane.

[0040] Step S1023: In the direction of the normal vector of the intermediate plane, synthesize the normal component of the linear velocity of the worm wheel rotation and the normal component of the linear velocity of the gear rotation to obtain the actual grinding linear velocity. V s .

[0041] Step S1024: Analyze the direction of the equivalent grinding wheel spur rack feed along the gear radial direction S, and confirm that the feed direction is parallel to the defined intermediate plane.

[0042] Step S1025: Based on the gear normal pressure angle α, convert the gear radial feed S into the actual tooth surface grinding depth t.

[0043] In some embodiments, based on the kinematic principles of vector decomposition and synthesis, spatial velocity is converted into in-plane components and synthesized to obtain the key grinding speed; combined with the geometric characteristics of the involute tooth profile, radial feed is converted into tooth surface normal depth, realizing the quantification of motion and contact parameters and ensuring that the parameters accurately reflect the actual grinding state. The parameter derivation process in this embodiment is directly related to the intermediate plane of S101 and the equivalent rack, ensuring the coherence of the technical logic and avoiding the disconnect between the parameters and the previous simplification.

[0044] S103: The contact behavior of the worm wheel grinding gear is simplified to the intersecting contact of two staggered circular arc surfaces in space; wherein the two staggered circular arc surfaces correspond to the equivalent circular arc surface of the worm wheel and the equivalent circular arc surface of the gear, respectively.

[0045] S103 specifically includes the following steps: Step S1031: Determine the contact point position of the worm wheel and gear on the pitch circle.

[0046] Step S1032: Calculate the principal radius of curvature of the worm wheel at the contact point. r w1 .

[0047] Step S1033: Calculate the principal radius of curvature of the gear at the contact point. r g1 .

[0048] Step S1034: Ignore the other principal radius of curvature of the worm wheel. rw2 And the other principal radius of curvature of the gear r g2 .

[0049] Step S1035: Based on r w1 and r g1 Establish a contact model of two equivalent circular arc surfaces arranged with spatially intersecting axes.

[0050] In some embodiments, the surface types of the worm grinding wheel and the gear are specified, both being helical involute surfaces. The worm grinding wheel has an Archimedean spiral surface, and its equivalent rack tooth profile in the intermediate plane is a straight line; therefore, the principal radius of curvature in that direction is... r w2 =0, the principal curvature radius in the other direction r w1 Let be the radius of curvature of the helix of the worm grinding wheel; consider the helical cylindrical gear as a worm with a very large lead, its principal radius of curvature in the tooth width direction is... r g2 Extremely large, retaining only the principal radius of curvature in the involute tooth profile direction. r g1 Then, the formula is used to calculate the value on the pitch circle. r w1 and r g1 Ultimately, secondary curvature is ignored. r w2 and r g2 The original spiral surface contact is simplified to... r w1 , r g1 The two intersecting circular arc surfaces with radii of curvature are in contact.

[0051] This embodiment simplifies the complex spatial spiral surface contact analysis into a problem that can be calculated using the geometric relationships of a circular arc surface, reducing the complexity of contact behavior analysis; the obtained equivalent circular arc surface curvature radius directly provides a geometric basis for the subsequent calculation of the volume of the material removal region, connecting subsequent steps.

[0052] S104: Based on equivalent contact behavior, calculate the volume of material removed in a single grinding process on the preset tooth surface.

[0053] S104 specifically includes the following steps: S1041: Determine the parameters required to calculate the volume of the material removal region in a single grinding pass, including the actual tooth surface grinding depth t obtained in S102 and the equivalent principal curvature radius of the worm wheel obtained in S103. r w1 And the axial feed rate f of the worm grinding wheel, and the total tooth height of the gear are... ha +h f ,in h a For tooth tip height, h f It is the height of the tooth root.

[0054] In this embodiment, by collecting key parameters obtained from previous analysis, a data foundation is provided for the geometric analysis and volume calculation of the material removal area, ensuring that the calculation process has clear parameter support.

[0055] S1042: Simulate the motion process of the gear rotating one revolution, synchronously record the feed amount f of the worm wheel along the axial direction, determine the new grinding boundary and the old grinding boundary formed in this process, clarify that the area between the two boundaries is the single grinding material removal area, and the shape of this area in the cross section along the tooth width direction is crescent-shaped.

[0056] In this embodiment, the combined motion of gear rotation and worm wheel axial feed is used to determine the cross-sectional profile of the material removal area by superimposing the boundaries of the motion trajectory, thus transforming the abstract grinding motion into a concrete geometric cross-sectional shape.

[0057] S1043: The crescent-shaped cross-section is analyzed using the differential method. The cross-section is divided into multiple differential regions, and the differential height of each region is calculated. h i The cross-sectional area of ​​the crescent-shaped section is obtained by summing the areas of each differential region, corresponding to the differential width l. S j At the same time, the width span of the cross section was measured and determined. L hg .

[0058] In this embodiment, the concept of differentiation is used to transform irregular geometric shapes into a superposition of regular small regions, thereby achieving accurate calculation of the area of ​​irregular cross-sections.

[0059] S1044: Determine the material removal length along the gear tooth profile as the total tooth height of the gear. h a +h f The area of ​​the crescent-shaped cross-section S j With full tooth height h a +h f Multiply by the product to calculate the volume V of the material removal area in a single grinding operation on a specific tooth surface.

[0060] In this embodiment, based on the geometric principle that the volume of a column = base area × height, the area where the three-dimensional material is removed is abstracted into a regular column, and the volume is derived using the previously calculated cross-sectional area and total tooth height.

[0061] In the embodiments, the minute axial feed of the worm wheel during a single grinding process of the tooth surface is explicitly ignored, ensuring that the calculation model focuses only on the influence of the main motion parameters on the volume of the material removal area, thus avoiding minor interference with the calculation results.

[0062] In this embodiment, by screening key influencing factors and excluding minute quantities that contribute negligibly to the calculation results, the calculation model is simplified while avoiding interference from irrelevant variables, ensuring that the model highlights the processing of key parameters. This guarantees the reliability of data sources and provides core volume parameters for subsequent material removal rate calculations.

[0063] S105: Based on the volume of the material removal area in a single grinding operation, calculate the material removal rate and the material removal rate per unit width for a single grinding operation.

[0064] S105 specifically includes the following steps: S1051: Determine the relevant parameters for calculating the material removal rate of a single grinding pass on the tooth surface, including the volume of the material removal area obtained in S104. V Determined gear speed n g The meshing overlap required for full tooth high-generation envelope motion ε , and the actual tooth surface grinding width b.

[0065] S1052: Equivalent meshing overlap ratio of grinding wheel spur rack and gear ε The number of teeth spanned required for the full-tooth high-generation envelope motion is used to obtain the generating motion time for a single grinding operation. t g :

[0066] S1053: Calculate the material removal rate of a single grinding operation on the tooth surface. Q m Material removal rate per unit width Q mw : .

[0067] This embodiment utilizes the relationship between the number of teeth, rotational speed, and time in a gear rotation to convert the required number of teeth to develop the full tooth profile into a specific time. Each rotation of the gear corresponds to z teeth rotating. n gThe number of teeth rotated per unit time is determined, and the generating time is obtained by dividing the number of teeth per unit time by the number of teeth per unit time. Based on the formula for material removal rate = volume removed / time, and combining the previously obtained V, the amount of material removed per unit time is directly obtained through division. By dividing by the grinding width, the overall material removal rate is normalized to a unit width index, so that the parameter focuses on the removal efficiency per unit width, rather than the overall volumetric efficiency, thus meeting the principle requirement of equivalent removal rate per unit width in surface grinding.

[0068] S106: Based on the similarity of the grinding process, the worm wheel grinding of the gear is equivalent to a plane grinding model. The grinding wheel radius, grinding wheel linear velocity and grinding depth of the equivalent plane grinding are set so that they are consistent with the equivalent arc surface radius, actual grinding linear velocity and actual tooth surface grinding depth of the worm wheel, respectively.

[0069] S106 specifically includes the following steps: S1061: By comparing the shape of the material removal area of ​​the gear in worm wheel grinding with the shape of the undeformed grinding debris area in surface grinding, it is clear that both are areas enclosed by circular arc boundaries, and the cutting paths of the abrasive grains along the contact arc segment are similar, thus establishing the basis for equivalent simplification based on shape similarity.

[0070] S1062: Extract the radius of curvature of the equivalent arc surface of the worm grinding wheel calculated in S103. r w1 The grinding wheel radius r of the equivalent surface grinding model is set to r= r w1 This ensures that the equivalent model is consistent with the wheel curvature characteristics of the original grinding process.

[0071] In this embodiment, the grinding contact arc length is determined by both the radius of curvature of the grinding wheel and the grinding depth. With a fixed grinding depth, a larger radius of curvature results in a longer contact arc length. This is achieved by using r= r w1 This ensures that the contact arc length of the equivalent model is consistent with that of the original process at the same grinding depth, thereby ensuring that the number of abrasive grains participating in cutting and the cutting path length are consistent.

[0072] S1063: Extract the actual grinding linear velocity Vs synthesized in S102, and convert it to the grinding wheel linear velocity of the equivalent surface grinding model. V ss Set as V ss =Vs, ensuring that the equivalent model is consistent with the abrasive cutting speed of the original grinding process.

[0073] In this embodiment, the grinding linear velocity is a key parameter determining the abrasive cutting state. Excessive linear velocity leads to a surge in grinding heat, while insufficient velocity reduces efficiency and increases cutting force; through… V ss=Vs ensures that the cutting speed of the abrasive particles on the workpiece in the equivalent model is consistent with the original process, making the cutting energy input and the force and heat generation laws similar.

[0074] S1064: Extract the actual tooth surface grinding depth t calculated in S102, and convert the grinding depth of the equivalent surface grinding model. a p Set as a p =t, ensuring that the equivalent model is consistent with the single grinding depth of the original grinding process.

[0075] In this embodiment, the grinding depth is the core geometric parameter of a single grinding cycle, directly related to the material removal amount and the cutting depth of the abrasive grains. A greater grinding depth results in a greater material removal amount per cycle and a higher abrasive grain cutting load. a p =t ensures that the equivalent model has the same single cutting depth as the original process, so that the basic load for single material removal is the same.

[0076] S1065: Calculate the grinding contact arc length of the original worm wheel grinding process and the equivalent surface grinding model respectively, and verify r= r w1 , V ss =Vs、 a p The setting of =t ensures consistency between the two in terms of grinding contact arc length, grinding depth, and grinding linear speed, eliminating parameter mismatch issues.

[0077] This embodiment verifies the consistency of contact arc length, linear velocity, and depth to ensure that the equivalent model fully matches the original process in key contact and motion characteristics. It promptly identifies and corrects deviations in parameter settings, ensuring that the core characteristics of the equivalent model are consistent with the original process, and providing a reliable parameter basis for feed rate calculation.

[0078] S107: Calculate the feed rate of the equivalent surface grinding model based on the principle of equivalent material removal rate per unit width.

[0079] S107 specifically includes the following steps: S1071: Extract the material removal rate per unit width of the lower tooth surface in a single grinding operation calculated in S105. Q mw ,confirm Q mw The numerical accuracy and units are set to the material removal rate per unit width in the equivalent surface grinding model. Q sw The target value, i.e. Q sw = Q mw .

[0080] In this embodiment, the force and thermal load of the grinding process are directly determined by the material removal rate per unit width. Q mw The larger the value, the greater the cutting force and heat input per unit width. Therefore, the equivalent model... Q sw With the original process Q mw Maintaining consistency ensures that the mechanical and thermal properties of both are equivalent.

[0081] S1072: Define the material removal rate per unit width in surface grinding. Q sw The calculation formula is as follows:

[0082] in Q sw With surface grinding depth a p Feed rate v ww Related.

[0083] This embodiment is based on the geometric and kinematic relationships of surface grinding, where the grinding wheel... a p Material removal in the depth direction, workpiece with v ww The product of depth per unit width and feed rate is the area of ​​material removed per unit time. This relationship is the basic theory for calculating the material removal rate in surface grinding.

[0084] S1073: Extract the equivalent surface grinding depth set in S106 a p Determine the actual grinding width b of the equivalent surface grinding and verify it. a p Units and Q mw Does the unit match?

[0085] S1074: According to Q sw = Q mw And the derivation of the feed rate for equivalent surface grinding. v ww ,get v ww = Q sw / a p The following formula is used for calculation. v ww To ensure that units are consistent during the calculation process;

[0086] S1075: Verify the calculated feed rate v ww The rationality of this was verified by comparing the feed rate range of conventional surface grinding equipment and checking the... v ww Are there any parameter errors during the calculation process?

[0087] The equivalent model in this embodiment must be practically feasible. v ww Within the operational capabilities of existing equipment, otherwise the model cannot be implemented. Secondary verification is used to eliminate parameter substitution errors, ensuring... v ww It not only satisfies theoretical equivalence but also conforms to actual production conditions. This ensures the practicality of the equivalent surface grinding model and avoids issues arising from... v ww The equipment's capabilities were exceeded, rendering the model unusable. A second verification was conducted to further improve its performance. v ww The accuracy.

[0088] S108: Determine the grinding mode of the equivalent surface grinding model as reverse grinding.

[0089] In some embodiments, the directional relationship of the original worm gear grinding wheel is analyzed. In a single grinding of the tooth surface, the axial feed speed of the equivalent grinding wheel spur rack is in the same direction as the actual grinding linear velocity.

[0090] This embodiment clarifies the criteria for determining the surface grinding mode. Reverse grinding refers to workpiece feed speed being opposite to the grinding wheel linear velocity, while forward grinding is when they are in the same direction. Based on the equivalent surface grinding wheel linear velocity Vss=Vs, the feed speed vww must be opposite to Vss. Matching the directional relationship between fz and Vs in the original process, the equivalent surface grinding mode is ultimately determined to be reverse grinding. This clarifies the complete process parameters for equivalent surface grinding, allowing the model to transition from parameter calculation to a practically executable grinding scheme. The determination of the grinding mode is based on the velocity direction of the original process, ensuring that the motion state of the equivalent model completely matches the actual grinding, thus improving the model's accuracy and practicality.

[0091] Furthermore, as a refinement and extension of the specific implementation of the above-described analogical simplified analysis method for worm gear grinding of gears, the method includes: Step 1: Analyze the worm gear grinding process, define the intermediate plane, and simplify it on the intermediate plane to the equivalent meshing of the grinding wheel spur rack and gear.

[0092] like Figure 2 As shown, the worm gear grinding process includes four types of motion: worm gear rotation speed...n w Gear speed n g Radial feed rate S Axial feed f z For machining helical cylindrical gears, the included angle between the worm wheel axis and the gear end face is... β-γ ,in β For the helix angle of helical gears, γ This is the lead angle of the worm gear grinding wheel.

[0093] like Figure 3 As shown, the intermediate plane is defined as: a plane parallel to the normal section of the helical gear and perpendicular to the normal section of the worm grinding wheel; the helix angle of the worm grinding wheel is very small, and its normal section shape is approximately that of a standard spur rack, therefore, as... Figure 4 As shown, the meshing of the worm grinding wheel and the gear can be equivalently regarded as the meshing of the equivalent grinding wheel spur rack and the gear on the intermediate plane; the rotation of the worm grinding wheel around the axis corresponds to the axial movement of the equivalent grinding wheel spur rack, and is accompanied by the corresponding rotational movement of the gear. This process is equivalent to the meshing motion of the worm grinding wheel and the gear.

[0094] Step 2: The motion of the worm wheel grinding gear is simplified equivalently on the intermediate plane.

[0095] The worm gear grinding wheel has a helical surface. One revolution along its helix results in a lead stroke in the axial direction, which is equivalent to the grinding wheel's spur rack advancing one lead stroke. This speed is the imaginary axial movement speed. V t :

[0096] In the formula: p For the worm gear grinding wheel lead; n w This refers to the rotational speed of the worm gear grinding wheel.

[0097] Within the tooth surface grinding removal area, the relative velocity between the worm wheel surface and the tooth surface is the actual grinding linear velocity. V s ,like Figure 5 As shown, the linear velocity of the gear rotation can be... V g and the linear velocity of the worm wheel rotation V w Project the decomposition onto the intermediate plane and its normal vector, and then perform a composite calculation in the direction of the normal vector of the central plane:

[0098] Grinding wheel radial feed S Parallel to the intermediate plane, no decomposition is required, such as... Figure 6As shown, the gear has an involute tooth profile and a radial feed rate. S The corresponding actual tooth surface grinding depth in the normal direction of the gear surface Actual tooth surface grinding depth ,in α This is the normal pressure angle of the gear.

[0099] In summary, the equivalent motion of the grinding wheel, spur rack, and gear in the intermediate plane includes: the actual grinding linear velocity. V s Gear rotational linear velocity V g1 Equivalent grinding wheel spur rack axial movement speed V t Radial feed of grinding wheel S .

[0100] Step 3: Based on the motion analysis of the equivalent grinding wheel spur rack and gear on the intermediate plane in Step 2, the contact behavior of the worm grinding wheel grinding the gear is simplified to the intersecting contact of two staggered circular arc surfaces in space.

[0101] The surface and tooth surface of the worm grinding wheel are both helical involute surfaces, such as... Figure 7 As shown, the worm grinding wheel belongs to the Archimedean spiral surface, and the equivalent grinding wheel rack on its intermediate plane has a straight tooth profile and a principal radius of curvature. r w2 =0, principal curvature radius r w1 Let be the helix radius of curvature of the worm grinding wheel; consider the helical cylindrical gear as a worm with extremely large lead, its principal radius of curvature is... r g2 Extremely large, with negligible curvature in the tooth width direction, and principal radius of curvature. r g1 Let be the radius of curvature of the involute tooth profile. For worm gears and gears on the pitch circle... r w1 and r g1 have:

[0102] In the formula: r w The radius of the worm gear grinding wheel; r g The pitch circle diameter of the gear; α t The end face pressure angle; β b The base circle helix angle.

[0103] Ignore the principal curvature of the worm wheel surface r w2 and principal curvature of tooth surface rg2 The contact between the worm gear and the gear on the pitch circle can be simplified equivalently to the intersection of two staggered circular arc surfaces in space, such as... Figure 8 As shown.

[0104] Step 4: Based on the simplified contact behavior of the worm wheel grinding gear in Step 3, consider the axial feed of the worm wheel when the gear rotates one revolution. f The volume of material removed in a single grinding pass on a specific tooth surface is derived and calculated. V and the corresponding grinding material removal rate Q m Grinding material removal rate per unit width Q mw .

[0105] For a specific tooth surface, as the gear continues to rotate one revolution, the worm wheel moves axially... f The feed rate creates a new material removal zone for full profile grinding. Axial feed rate. f The shape of the material removal area formed in the cross section along the tooth width is as follows: Figure 9 As shown in the shaded area, a crescent-shaped material removal region exists between the new and old grinding boundaries. The contact from the tooth root to the tooth tip is considered to be consistent with the pitch circle, and an enveloping motion is performed along the tooth profile to expand this crescent-shaped section to the entire tooth profile, forming the material removal region under a single grinding action on the tooth surface, as shown below. Figure 10 As shown. Here, we choose to ignore the minute axial feed of the worm wheel during a single grinding process of the tooth surface.

[0106] The shape of the crescent-shaped cross section can be considered as having a radius of... r w1 The grinding wheel cylinder at the depth of surface grinding t Down feed f The formed undeformed wear debris area, such as Figure 11 As shown, circle o The grinding boundary of 1 is ad feed f Back circle o The grinding boundary of 2 is be The area of ​​undeformed wear debris is edbe Analytical derivation of the calculation of width span L hg Calculating the cross-sectional area based on the differential method S j The material removal length along the tooth profile is the total tooth height. h a +h f Calculate the material removal volume in a single grinding cycle. V :

[0107] In the formula: h i For the first i Differential height of the region; l For the first i The differential width of the region; h a This refers to the tooth tip height; h f It is the height of the tooth root.

[0108] Equivalent grinding wheel spur rack and gear meshing overlap ε The number of teeth spanned required for the full-tooth high-generation envelope motion is used to obtain the generating motion time for a single grinding operation. t g :

[0109] Further obtain the material removal rate of a single grinding action on the tooth surface Q m Material removal rate per unit width Q mw :

[0110] Step 5: Analyze the similarity between worm wheel grinding of gears and surface grinding behavior. Based on the principles of equivalent contact and motion behavior in the grinding process and comparable material removal rates, derive and calculate the grinding wheel radius of the equivalent surface grinding model. r Grinding wheel linear velocity V ss Surface grinding depth a p Feed rate v ww By combining grinding methods (clockwise and counterclockwise), the process of worm wheel grinding gears is simplified to equivalent surface grinding.

[0111] The crescent-shaped material removal area on a specific tooth surface and the undeformed wear debris area in surface grinding are extremely similar in shape. Both processes involve abrasive cutting along the grinding contact arc. If the grinding wheel radius in the equivalent surface grinding model... r Equivalent cylindrical grinding wheel radius of worm grinding wheel r w1 Maintain consistency, grinding depth a p and actual tooth surface grinding depth t Maintain consistent grinding wheel linear speed V ss The actual grinding linear speed of worm gear grinding teeth V sIf they remain consistent, the grinding contact arc length and abrasive grinding behavior in the equivalent surface grinding and worm wheel gear grinding processes will remain consistent.

[0112] Unlike the unidirectional feed of surface grinding, the tooth surface grinding of gears by worm wheel involves feed effects in two directions (tooth width direction and tooth profile direction) in a single grinding operation. The material removal rate and the material removal rate per unit width determine the force and thermal load of the grinding process and directly affect the integrity of the machined surface. It is considered that the analogous equivalent of surface grinding should have the same material removal rate per unit width as the single grinding operation of tooth surfaces. The grinding material removal rate of surface grinding... Q s and material removal rate per unit width Q sw They are respectively:

[0113] In the formula: a p This refers to the grinding depth. b This refers to the grinding width; v w The feed rate is used. The principle of equivalent material removal rate is adopted to achieve equivalent analysis of the feed motion, i.e. Q mw =Q sw Analogous equivalent surface grinding feed rate v ww for:

[0114] In summary, the equivalent simplified analysis of surface grinding for single-pass grinding of tooth surfaces in worm gear grinding has been completed; the equivalent grinding wheel rack feed rate for single-pass grinding of tooth surfaces has been determined. f z and actual grinding line speed V s Since they are in the same direction, the feed rate for surface grinding should be opposite to the direction of the grinding wheel's linear velocity, i.e., the surface grinding method is reverse grinding.

[0115] Table 1 shows the main parameters of the gear and worm wheel in this embodiment, and Table 2 shows the process parameters of worm wheel grinding of gears and the corresponding equivalent plane grinding process parameters in this embodiment. As shown in Table 2, the equivalent simplified analysis method of the worm wheel grinding of gears in this embodiment shows that the material removal rate per unit width on a specific tooth surface reflects the influence of the change of grinding process parameters on the grinding behavior. The obtained equivalent plane grinding process parameters effectively reflect the differences between different grinding process parameters, realizing the equivalent simplified analysis of the complex worm wheel grinding of gears to the plane grinding process.

[0116] Table 1: Main parameters of gear and worm grinding wheels

[0117] Table 2: Process parameters for worm gear grinding and corresponding equivalent surface grinding process parameters

[0118] In summary, the analogical simplification analysis method for worm wheel gear grinding proposed in this invention can simplify the complex worm wheel gear grinding process into a plane grinding process based on the actual dimensional parameters of the worm wheel and gear, and the grinding process parameters. This method considers the equivalence of motion and contact behavior during the grinding process and applies the principle of equivalent material removal rate to equivalence of grinding force and thermal load. The equivalent plane grinding process parameters can better reflect the grinding behavior, grinding force, and thermal characteristics of worm wheel gear grinding. This method is applicable to the equivalent simplification study of the worm wheel gear grinding process on a plane grinding platform and can be used to further analyze the influence of grinding process parameters on grinding force, thermal load, and surface integrity.

[0119] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0120] like Figure 12 As shown, this application also provides an electronic device, including a display module 103, a memory 102, a processor 101, a communication module 104, and a computer program stored in the memory and executable on the processor 101. When the processor 101 executes the program, it implements the steps of an analogy-based simplified analysis method for worm gear grinding.

[0121] In embodiments of the present invention, electronic devices include, but are not limited to, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic devices may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the embodiments described and / or claimed herein.

[0122] In this embodiment, processor 101 may be implemented using at least one of an application-specific integrated circuit, a programmable logic device, a field-programmable gate array, a processor, a controller, a microcontroller, a microprocessor, or an electronic unit designed to perform the functions described herein. In some cases, such an implementation may be implemented within a controller. For software implementation, implementations such as processes or functions may be implemented with separate software modules that allow the performance of at least one function or operation. Software code may be implemented by a software application (or program) written in any suitable programming language, and the software code may be stored in memory and executed by the controller.

[0123] The display module 103 is used to display information input by the user or information provided to the user. The display module 103 may include a display panel, which may be configured in the form of a liquid crystal display, an organic light-emitting diode, or the like.

[0124] The memory 102 can be used to store software programs and various data. The memory 102 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0125] The communication module 104 transmits radio signals to and / or receives radio signals from at least one of a base station, an external terminal, and a server. Such radio signals may include voice call signals, video call signals, or various types of data sent and / or received according to text and / or multimedia messages.

[0126] The present invention also provides a storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the analogy simplification analysis method for worm gear grinding gears.

[0127] The storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example,, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0128] The storage medium stores a program product capable of implementing the methods described above in this specification. In some possible implementations, various aspects of this disclosure can also be implemented as a program product comprising program code that, when run on a terminal device, causes the terminal device to perform the steps described in the exemplary methods section of this specification according to various exemplary embodiments of this disclosure.

[0129] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of simplified analytical approach for worm grinding of gear, the method comprising: Comprise: S101: define the intermediate plane, and the worm grinding gear process is equivalent to the equivalent gear rack and gear meshing on the intermediate plane; wherein the intermediate plane is parallel to the normal profile of helical gear and perpendicular to the normal profile of worm grinding wheel; S102: on the intermediate plane, the equivalent simplified worm grinding gear movement, including the derivation of the equivalent straight rack gear bar imaginary axial moving speed, the actual grinding line speed and the actual tooth surface grinding depth; S103: the contact behavior of worm grinding gear is equivalent to the intersection of two intersecting circular arc surfaces in space; wherein the two intersecting circular arc surfaces correspond to the worm grinding wheel equivalent circular arc surface and the gear equivalent circular arc surface respectively; S104: based on the equivalent contact behavior, calculate the single grinding material removal area volume on the preset tooth surface; S105: based on the single grinding material removal area volume, calculate the material removal rate and the unit width material removal rate of single grinding action; S106: based on the grinding process similarity, the worm grinding gear is equivalent to the plane grinding model, the equivalent plane grinding wheel radius, the grinding wheel linear velocity and the grinding depth are set to be consistent with the worm grinding wheel equivalent circular arc surface radius, the actual grinding line speed and the actual tooth surface grinding depth respectively; S107: according to the unit width material removal rate equivalent principle, calculate the feed speed of the equivalent plane grinding model; S108: determine the grinding mode of the equivalent plane grinding model as reverse grinding.

2. The simplified analytical method for gear grinding with a worm-type grinding wheel as claimed in claim 1, wherein S101 specifically includes the following steps: determine the relative spatial position of the worm grinding wheel and the gear, including the angle between the worm grinding wheel axis and the gear end face, the angle is calculated by the helical gear helix angle β and the worm grinding wheel lead angle γ, that is, the angle is β-γ; based on the relative spatial position, define the intermediate plane as a plane parallel to the normal profile of helical gear and perpendicular to the normal profile of worm grinding wheel, wherein the normal profile of helical gear is a plane perpendicular to the tooth direction of gear, and the normal profile of worm grinding wheel is a plane perpendicular to the axis of worm grinding wheel; analyze the shape of worm grinding wheel in the normal profile, which is approximately a standard straight rack tooth profile, including straight tooth profile and standard pressure angle; the profile shape of worm grinding wheel on the intermediate plane is equivalent to the straight rack gear, and the equivalent straight rack gear has the same tooth profile parameters as the worm grinding wheel normal profile; establish the corresponding relationship between the worm grinding wheel rotation and the equivalent straight rack gear axial movement, that is, when the worm grinding wheel rotates around the axis, the equivalent straight rack gear moves along the gear axial direction, and the gear rotates around its own axis, forming the meshing movement.

3. The simplified analytical method for gear grinding with a worm-type grinding wheel as claimed in claim 1, wherein S102 specifically includes the following steps: According to the lead p and the rotational speed of the worm grinding wheel n w , the imaginary axial movement speed of the equivalent grinding wheel straight rack is calculated V t ; Rotational linear speed of the gear V g Rotational linear speed of the worm wheel V w are decomposed into a component parallel to the median plane and a normal component perpendicular to the median plane, respectively; In the direction of the intermediate plane normal vector, the normal component of the synthetic worm wheel grinding wheel rotational linear velocity and the normal component of the gear rotational linear velocity are obtained to get the actual grinding linear velocity V s ; analyze the equivalent straight rack gear along the gear radial feed S direction, confirm that the feed direction is parallel to the defined intermediate plane; according to the normal pressure angle α of gear, convert the gear radial feed S into the actual tooth surface grinding depth t.

4. The simplified analytical method for gear grinding with a worm-type grinding wheel as claimed in claim 1, wherein S103 specifically includes the following steps: determine the contact point position of worm grinding wheel and gear on the reference circle; Computing principal radii of curvature of a worm grinding wheel at a contact point r w1 ; Computing principal radii of curvature of a gear at a contact point r g1 ; ignoring the other principal radius of curvature of the worm wheel r w2 and the other principal radius of curvature of the gear r g2 ; Based on r w1 and r g1 Two equivalent circular-arc surface contact models of spatial staggered-axes arrangement are established.

5. The simplified analytical method for gear grinding with a worm-type grinding wheel as claimed in claim 1, wherein S104 specifically includes the following steps: Determine the parameters needed for calculating the volume of the single-grinding material removal region, including the actual tooth surface grinding depth t obtained in S102, the equivalent principal curvature radius of the worm grinding wheel obtained in S103, the axial feed amount f of the worm grinding wheel, and the total tooth height of the gear r w1 h a +h f wherein h a is the addendum height, h f is the dedendum height;​ The motion process of one circle of gear rotation is simulated, the axial feeding amount f of the worm grinding wheel is recorded synchronously, the new grinding boundary and the old grinding boundary formed in the process are determined, the area between the two boundaries is determined as the single grinding material removal area, and the shape of the area in the section along the tooth width direction is half-moon shape; The differential method is used to analyze the half-moon-shaped section, the section is divided into multiple differential regions, and the differential height of each differential region is calculated h i The corresponding differential width l is measured and determined, and the width span of the section is measured and determined S j , the cross-sectional area of the half-moon-shaped section is obtained by accumulating the areas of the differential regions L hg ; The material removal length along the gear tooth profile is determined as the full gear tooth height h a +h f The half-moon cross-sectional area S j is multiplied by the full tooth height h a +h f to calculate the single-grinding material removal area volume V on the specific tooth surface.

6. The simplified analytical method for gear grinding with a worm-type grinding wheel as claimed in claim 1, wherein S105 specifically comprises the following steps: determining a related parameter for calculating the single pass grinding material removal rate of the tooth surface, the related parameter including the single pass grinding material removal region volume obtained in S104 V , the determined gear rotation speed n g , the engagement coincidence degree required by the full tooth height generating envelope motion ε , and the actual tooth surface grinding width b; Meshing coincidence of equivalent gear rack and pinion ε The number of teeth across the tooth is required for the full tooth height generating envelope motion, to obtain the generating motion time of a single grinding action t g : Material removal rate for single pass grinding of tooth flanks Q m and material removal rate per unit width Q mw : 。 7. The simplified analytical method for gear grinding with a worm-type grinding wheel as defined in claim 1, wherein S106 specifically comprises the following steps: The material removal area of the worm grinding wheel grinding gear is compared with the undeformed chip area shape of plane grinding; The equivalent circular arc surface curvature radius of the worm grinding wheel calculated in the extraction S103 r w1 The radius r of the grinding wheel of the equivalent plane grinding model is set as r = r r w1 ; extracting the actual grinding line speed Vs of the synthesized in S102, the wheel line speed of the equivalent plane grinding model is set as V ss is set as V ss =Vs; The actual tooth surface grinding depth t calculated in the extraction S102 is substituted into the grinding depth of the equivalent plane grinding model a p is set to a p = t; The grinding contact arc length of the original worm grinding wheel grinding process and the equivalent plane grinding model is calculated respectively, and the consistency of the grinding contact arc length, grinding depth and grinding line speed of the two is verified. r w1 、 V ss =Vs、 a p =t is set to meet the consistency of the grinding contact arc length, grinding depth and grinding line speed of the two.

8. The simplified analytical method for gear grinding with a worm-type grinding wheel as claimed in claim 1, wherein S107 specifically comprises the following steps: Extracting the calculated single pass material removal rate per unit width of the dedendum flank surface in S105 Q mw , confirming the numerical accuracy and unit of the calculated single pass material removal rate per unit width of the dedendum flank surface in S105 Q mw , and setting it as the target value of the material removal rate per unit width in the equivalent plane grinding model Q sw Q sw = Q mw ;​ Determination of material removal rate per unit width in flat grinding Q sw The calculation formula is as follows, extracting the equivalent plane grinding depth set in S106 a p determining the actual grinding width b of the equivalent plane grinding according to Q sw = Q mw and deriving the feed speed of the equivalent plane grinding v ww , obtaining v ww = Q sw / a p calculating by using the following formula v ww ensuring the unit uniformity in the calculation process; 。 9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the analog simplified analysis method for the worm grinding wheel grinding gear according to any one of claims 1 to 8 when executing the program.

10. A storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to implement the steps of the analog simplified analysis method for the worm grinding wheel grinding gear according to any one of claims 1 to 8.

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