Tooth turning machining method for cycloid-like internal meshing gear

Abstract

The invention relates to the technical field of gear machining, and discloses a gear turning method of a cycloid-like internal meshing gear, which comprises the following steps of: establishing a tooth profile mathematical model based on an arc meshing line, determining a tooth crest and tooth root conjugate tooth profile equation of an external gear and an internal gear, and establishing a four-coordinate system and a spatial motion relation; an innovative variable-domain directional search coupling dichotomy algorithm is adopted, a blade curve is accurately solved on the axial section of Z = 0, and the problem of unstable calculation caused by tooth surface singular points is solved; a parameterized tool is designed, linkage cutting of the tool and a workpiece and control of cutting parameters are achieved by means of a five-axis numerical control machine tool, the precise machining effect is finally obtained, the gear bearing capacity is improved, the transmission stability is improved, the single-piece machining time is only 30 minutes, and the technical bottlenecks that a traditional method is low in machining efficiency and prone to over-cutting and under-cutting are broken through. The method is suitable for the precision transmission field of aerospace, new energy automobiles and the like, and the high-precision industrial manufacturing problem of the cycloid-like gear is practically solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of gear machining, in particular, especially relates to a kind of gear machining method of cycloidal internal gear meshing, it is suitable for the high-efficiency, high-precision processing scene of cycloidal (HCR) internal gear meshing. BACKGROUND

[0002] Cycloidal internal gear meshing has high coincidence degree, stable transmission and strong bearing capacity due to the adoption of cycloidal conjugate curve design for tooth profile, and has broad application prospects in precision transmission systems such as aerospace, high-end machine tools and new energy vehicles. Compared with traditional involute gears, cycloidal internal gear meshing significantly increases the number of simultaneously meshing teeth by optimizing the tooth profile curve, effectively reduces the tooth surface contact stress, and prolongs the service life of the gear.

[0003] Gear machining is a kind of efficient gear machining technology, which realizes continuous cutting through synchronous rotation of the cutter and the workpiece, has the advantages of high machining efficiency, high tooth surface precision and wide machining range, and has become one of the mainstream technologies for high-end gear machining. However, the tooth profile of cycloidal internal gear meshing is composed of multiple conjugate curves, and there are singular points on the tooth surface (the tangent vector is 0 at the intersection point of the curves, and the normal vector direction is uncertain), the meshing principle and motion relationship are significantly different from conventional involute gears, which makes it difficult for existing gear machining technology to be directly adapted: The traditional gear cutter design method is based on involute tooth profile, which cannot match the complex surface of cycloidal tooth profile, and machining problems such as overcutting and undercutting are prone to occur; The singular points of cycloidal tooth surface make it difficult to solve the meshing equation, and the existing numerical method cannot accurately obtain the cutter blade curve; The coordinate system transformation and motion relationship of cycloidal internal gear meshing are complex, and the existing machining mathematical model cannot accurately describe the relative motion of the cutter and the gear.

[0004] Therefore, it is urgent to develop a gear machining method for cycloidal internal gear meshing, which can overcome the above technical bottlenecks and meet the batch production needs of cycloidal internal gear meshing in the industrial field. SUMMARY

[0005] A gear machining method for cycloidal internal gear meshing, which optimizes cutter design, accurately calculates machining motion trajectory and reasonably configures cutting parameters, effectively avoids machining interference and improves chip removal, thereby realizing efficient, high-precision and stable machining of high-coincidence internal gears.

[0006] The technical means adopted by the present application are as follows: A gear machining method for cycloidal internal gear meshing, comprising the following steps: S1: based on the circular arc meshing line of the intersection point of the pitch circle and the intersection point of the addendum circle, in the fixed coordinate system S fA mathematical model of tooth profile is established, and the addendum curve and dedendum curve of the external gear and the internal gear are derived; S2: A tool-gear motion model is established by four types of coordinate systems (S f , S p , S2, S t ), an axis intersection angle a and a center distance a are set, and an angular velocity ratio ω 2 / ω t = Z t / Z 2 is determined; S3: Based on the spatial meshing equation V M N M =0, the tooth surface is divided into three continuous solving regions, and the variable field directional search combined with the bisection method is used to solve the tool blade curve on the Z=0 plane; S4: The tool and the workpiece are configured on a five-axis numerical control machine tool, and the cycloid tooth profile is cut by linkage according to the preset cutting parameters and the motion model.

[0007] Further, in S1, in order to improve the gear coincidence degree, the circular arc connecting the intersection point of the pitch circle of the external gear and the cycloid internal gear and the intersection point of the addendum circle is selected as the meshing line. According to the geometric principle, the circular arc radius and the maximum radian are calculated, and the circular arc meshing line equation is established in the fixed coordinate system S f ( Z f the axis is coincident with the gear rotation axis, X f the axis is the shortest distance direction of the two gear axes). Based on the gear meshing principle and coordinate transformation, combined with the correlation between the angular displacement of the external gear and the pitch circle radii of the internal and external gears, the addendum curve of the external gear, the addendum curve of the cycloid internal gear, the dedendum curve of the external gear, and the dedendum curve of the cycloid internal gear are derived, forming a complete cycloid internal meshing gear tooth profile model.

[0008] Further, in S2, four types of coordinate systems are set to clearly define the relative position relationship: a fixed coordinate system S f (referencing gear rotation), a fixed coordinate system S p (referencing tool rotation), a moving coordinate system S 2 (fixedly connected with the internal gear), and a moving coordinate system S t (fixedly connected with the tool). The angle between the two rotation axes is the axis intersection angle α , the shortest distance is the center distance a , and the moving coordinate systems are coincident with the corresponding fixed coordinate systems in the initial state.

[0009] Furthermore, in S3, according to the principle of spatial meshing, when any point on the cutting edge of the tool is tangent to the gear tooth surface at point M, the normal vector N of point M on the tooth surface... M The relative velocity V between the cutting tool and the gear at point M M A vertical relationship must be satisfied, that is: V M ·N M =0. In the formula, V M Let N be the relative velocity vector between the cutting tool and the gear at point M. M Let M be the normal vector of the tooth surface (obtained by the cross product of the tangent vectors of the tooth surface, no normalization is required).

[0010] Furthermore, a variable-domain oriented search method combined with the bisection method is adopted to solve the cutting edge curve in stages. The tooth tip curve and tooth root curve of the cycloidal tooth surface are divided into three continuous solution regions, and the known constants in each region are clearly defined. Z 2. Z t , α , a , m etc.) and variables ( φ 2: Gear rotation angle, θ Meshing line parameter angle, z (axial parameters); The variable domain method narrows the solution space, given a known solution ( φ 2(N) , θ (N) After that, determine the search direction for the next solution based on the trend of the previous solution: like θ (N) > θ (N-1) ,but θ (N+1) ∈[ θ (N) -Δ θ , θ (N) +Δ θ ]; like φ 2 (N) > φ 2 (N-1) ,but φ 2(N+1) ∈[ φ 2(N) -Δ φ , φ 2(N) +Δ φ ]; where Δ θ Δ φ The step size parameter is determined through trial and error to ensure that only one solution exists in each search interval. Bisection method, given the solution accuracy ξ = 0.001mm, for each search interval [a, b], solve the engagement equation according to the following steps f ( φ 2, θ , z )=V M N M =0: Verification f (a) f (b)<0, ensure that there is a zero point in the interval; Calculate the midpoint c = (a + b) / 2 in the interval, solve f (c); If | f (c)|<ξ, then c is the approximate zero point; if f (a) f (c)<0, let b = c; if f (c) f (b)<0, let a = c; Repeat steps S2-S3 until | a-b|<ξ, get the approximate solution of the variable, that is, the point on the blade curve.

[0011] Further, according to the blade curve obtained by solving, combined with the tool design parameters (modulus 4mm, number of teeth 24, addendum coefficient 1.25, dedendum coefficient 1.25, shaft intersection angle 8°, center distance 95.5283mm, pitch circle diameter coefficient 1.0098, coincidence 3.417), adopt SolidWorks and other three-dimensional modeling software to build three-dimensional model of gear cutting tool.

[0012] Further, in gear cutting, the blade of involute gear can select any curve on the entire engagement surface, as long as the curve passes through the entire tooth surface. Therefore, the design of involute gear cutting tool is relatively simple, and the tool manufacturing is also easy to realize. For HCR gear, the points that can become engagement points are concentrated near Z = 0, and most of them cannot completely engage with the tooth surface. After several derivations, the most suitable point for the tool blade is the point of Z = 0.

[0013] Further, in S4, according to the designed tool parameters and the deduced motion relationship, the tool, the fixture and the hypoid gear blank are installed on the five-axis CNC machine tool with C1 axis (tool rotation axis) and B axis (tool swing angle axis), and the cutting parameters (cutting speed 120 m / min, feed rate 0.1 mm / r, and back engagement amount 0.2 mm) are set. The Siemens 840D numerical control system is used to control the linkage of each motion axis, to realize the synchronous rotation and accurate feeding of the tool and the gear, and to complete the complete cutting of the hypoid tooth profile. After processing, the three-coordinate measuring instrument is used to detect the key indicators such as tooth profile accuracy and tooth spacing deviation, to ensure that the design requirements are met. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0015] Figure 1 is a process flow diagram for the machining method; Figure 2 is a relative position and motion coordinate system of the machine tool-blank-tool; Figure 3 is a generation diagram of the tool cutting edge curve; Figure 4 is a process diagram of the establishment of the machine tool and the blank. DETAILED DESCRIPTION

[0016] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the drawings and in combination with the embodiments.

[0017] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions of the embodiments of the present application will be described clearly and completely below in combination with the drawings of the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. The description of the at least one exemplary embodiment is actually only illustrative, but not as any limitation on the present application and its application or use. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0018] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, devices, components and / or combinations thereof, but do not preclude the presence or addition of one or more other features, steps, operations, devices, components and / or combinations thereof.

[0019] The relative arrangement of components and steps, numerical expressions, and numerical values set forth in the examples are not intended to limit the scope of the present application unless otherwise specifically stated. It is to be understood that the drawings are not necessarily to scale of the various parts shown in the drawings. Techniques, methods, and apparatus known to those of ordinary skill are not discussed in detail because they would be considered as too general. In all examples shown and discussed herein, any specific value should be interpreted as merely an example, and not as a limitation. Thus, other examples of the example embodiments can have different values. It is noted that like numbers and letters on the figures identify like parts throughout the disclosure, and thus, once defined, do not need to be discussed again in connection with subsequent figures.

[0020] In the description of the present application, it is to be understood that the orientation or positional relationships indicated by orientation words such as "front, back, upper, lower, left, right", "horizontal, vertical, perpendicular, horizontal" and "top, bottom" are generally based on the orientation or positional relationships shown in the drawings, and are only for the convenience of describing the present application and simplifying the description. Without the opposite indication, these orientation words do not indicate and imply that the indicated device or element must have a particular orientation or be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the scope of protection of the present application: the orientation words "inner, outer" refer to the inner and outer relative to the contour of each component.

[0021] For purposes of the description hereinafter, spatially relative terms, such as "above", "below", "up", "down", "right", "left", "vertical", "horizontal", "top", "bottom", "lateral", "longitudinal", "transverse", "forward", "rearward", "radial", "peripheral" and the like, can be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientations depicted in the figures. For example, if a device described herein is inverted or rotated 90 degrees, then an element described as "above" or "up" another element or feature would then be oriented "below" or "down" the other element or feature. Thus, the exemplary term "above" can encompass both an orientation of above and below. The device can be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. The terms "first", "second", "third", etc. used herein are used to distinguish one element from another, and do not necessarily have an ordinal meaning.

[0022] In addition, it should be noted that the use of "first", "second", etc. words to qualify parts, is only for the convenience of distinguishing the corresponding parts, and the above words have no special meaning unless otherwise stated, and therefore cannot be understood as limiting the scope of protection of the present application.

[0023] The embodiment is aimed at gear cutting of large modulus meshing gears, and the specific implementation is as follows: Embodiment parameters: Parameter of the cycloid inner gear: modulus m = 4 mm, number of teeth Z 2 = 46, addendum coefficient h a* = 1.0, dedendum coefficient h f* = 1.25, pitch circle radius R 2 = 92 mm, number of teeth of the outer gear Z 1 = 72, pitch circle radius of the outer gear R 1 = 144 mm, modulus 7.232; Parameter of the gear cutting tool: modulus m = 4 mm, number of teeth Z t = 24, addendum coefficient h a* = 1.25, dedendum coefficient h f* = 1.25, center distance a = 95.5283 mm, shaft intersection angle α = 8°, pitch circle diameter coefficient k = 1.0098, modulus 3.417; Machining equipment: five-axis numerical control machine tool (with C1 axis and B axis), numerical control system Siemens 840D.

[0024] The specific implementation steps are as follows: S1: Calculate the circular arc meshing line parameters: according to the pitch circle and the addendum circle parameters of the external gear and the internal gear, the circular arc meshing line radius R=[specific value] is obtained, and the maximum radian θ max =[specific value], the circular arc meshing line equation is established. The circular arc meshing line equation is substituted into the angular displacement equation of the external gear, and the coordinate transformation matrix is combined to sequentially derive the external gear addendum profile curve, the internal gear addendum profile curve, the external gear dedendum profile curve and the internal gear dedendum profile curve, and form a complete profile model.

[0025] S2: Determine the coordinate system parameters: set the fixed coordinate system S f , S p and the moving coordinate system S 2、 S t , the shaft intersection angle α =8°, and the center distance a =95.5283mm. According to the coordinate system definition and the relative position, the transformation matrix of S 2 to S f , S f to S p , S p to S t is derived, and then the total transformation matrix of S 2 to S t is obtained. According to the number of teeth of the internal gear Z 2=46 and the number of teeth of the cutter Z t =24, the angular velocity relationship ω 2 / ω t = Z t / Z 2=12 / 23.

[0026] S3: Divide the tooth surface into three solving regions, set the φ 2 range [-7°, 5°], θ range [-37°, 33°], z =0; adopt the variable field method to determine the solution space (Δ θ =3°, Δ φ= 0.5°), dichotomy accuracy ξ = 0.001 mm, a plurality of points on the blade curve are obtained; in SolidWorks, a three-dimensional model of the cutter is constructed according to the blade curve and cutter parameters, and the cutter is machined.

[0027] S4: mounting the designed gear cutting tool, fixture and cycloid-like gear blank on the five-axis CNC machine tool, importing the NC machining code written based on the motion relationship, setting the cutting speed 120 m / min, the feed amount 0.1 mm / r, the back engagement amount 0.2 mm, and starting the machining. During the machining process, the CNC system controls the X, Y and Z axes to realize the adjustment of the tool position, the B axis adjusts the tool shaft intersection angle, the C axis (workpiece rotation) and the C1 axis (tool rotation) are synchronously rotated according to the angular velocity relationship 12:23, and the Z axis continuously feeds according to the preset feed amount, so as to complete the cutting of the cycloid-like tooth profile. After the machining is completed, the three-coordinate measuring instrument is used for detection, the tooth profile accuracy reaches IT5 level, and the tooth surface roughness Ra is 0.6 μm, which meets the design requirements.

[0028] Implementation effect: the cycloid-like internal meshing gear processed in the embodiment has a coincidence degree of 7.232, the transmission stability is improved by more than 50% compared with the involute gear, the bearing capacity is improved by more than 40%, the processing efficiency is improved by 4 times compared with the gear shaping, and the single-piece processing time is shortened from 2 hours to 30 minutes.

[0029] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for machining the teeth of a cycloidal internal meshing gear, characterized in that, Includes the following steps: S1: The circular arc meshing line based on the intersection of the pitch circle and the addendum circle, in the fixed coordinate system S f A mathematical model of the tooth profile is established to derive the tooth tip profile curve and tooth root profile curve of the external and internal gears. S2: Through four types of coordinate systems (S f S p S2, S t Establish a tool-gear motion model, set the shaft intersection angle α and center distance a, and determine the angular velocity ratio. ω 2 / ω t = Z t / Z 2; S3: Based on the spatial meshing equation V M N M =0, the tooth surface is divided into three continuous solution regions, and the tool cutting edge curve on the Z=0 plane is solved by variable domain orientation search combined with the bisection method; S4: Configure the cutting tool and workpiece on a five-axis CNC machine tool, and cut the cycloidal tooth profile in conjunction with the preset cutting parameters and motion model.

2. The method for machining cycloidal internal meshing gears according to claim 1, characterized in that, The circular arc meshing line in S1 satisfies the following: its radius R is determined by the pitch circle parameters of the external and internal gears, and its maximum radian θ... max Solved using geometric constraints; the fixed coordinate system S f In the middle, Z f The shaft and the gear's rotation axis coincide, X f The shaft is along the direction of the shortest distance between the axes of the two gears.

3. The method for machining cycloidal internal meshing gears according to claim 1, characterized in that, The four types of coordinate systems in S2 include: fixed coordinate system S f (Refer to gear rotation), fixed coordinate system S p (Reference tool rotation), motion coordinate system S2 (fixed internal gear), motion coordinate system S t (Fixed tool); The initial state of each moving coordinate system coincides with the corresponding fixed coordinate system.

4. The method for machining cycloidal internal meshing gears according to claim 1, characterized in that, The variable-domain directional search method in S3 includes: like θ (N) > θ (N-1) ,but θ (N+1) ∈[ θ (N) -Δ θ , θ (N) +Δ θ ]; like φ 2 (N) > φ 2 (N-1) ,but φ 2(N+1) ∈[ φ 2(N) -Δ φ , φ 2(N) +Δ φ ]; where Δ θ Δ φ This is the step size parameter.

5. The method for machining cycloidal internal meshing gears according to claim 1, characterized in that, The bisection method in S3 includes: given an accuracy ξ=0.001mm, verifying f(a)·f(b)<0 through zero point and solving the cutting edge curve points through midpoint iteration.

6. The method for machining cycloidal internal meshing gears according to claim 1, characterized in that, The gear-turning cutter designed in S3 meets the following parameters: module m =4mm, number of teeth Z t =24, tooth addendum coefficient h a* =1.25, tooth root height coefficient h f* =1.25, center distance a =95.5283mm, axial angle α =8°, pitch circle diameter factor k =1.0098.

7. The method according to claim 1, characterized in that, The five-axis linkage control in S4 includes: the tool rotation axis C1 and the workpiece rotation axis C rotate synchronously at an angular velocity ratio of 12:23; the B axis adjusts the tool axis intersection angle α, and the Z axis continuously feeds at a feed rate of 0.1 mm / r.

8. A numerical control system implementing the method of claims 1-7, characterized in that: The Siemens 840D system is used to control the C1, B, C, and Z axes in a coordinated manner to achieve synchronous rotation of the tool and workpiece and precise feeding.

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