Curvilinear tooth bevel gear driving design based on digital profile wheel and machining method thereof

Abstract

The application discloses a kind of curve tooth bevel gear driving design based on digital profile wheel and its processing method, according to the big gear of curve tooth bevel gear, determine the digital profile wheel parameter;Combining the tooth trace form and cutter disc parameters of curve tooth bevel gear, determine the digital profile wheel tooth surface;Further determine the big wheel reference tooth surface;According to the big wheel reference tooth surface and the predetermined transmission law of big wheel and small wheel, determine the small wheel theoretical tooth surface;According to tooth surface contact spot, the tooth surface of profile wheel is corrected, and the corrected digital profile wheel tooth surface is obtained;The big wheel theoretical tooth surface is enveloped using the corrected digital profile wheel, and the curve tooth bevel gear pair is obtained, the design method makes the obtained tooth surface pair to drive according to predetermined law, weakens the influence of modification on transmission law, is favorable to the control of gear pair vibration noise, while reducing the machining difficulty of gear, with greater use value and popularization value.

Description

Technical Field

[0001] This invention relates to the field of bevel gear machining, specifically to the active design and machining method of curved bevel gears based on digital profiling wheels. Background Technology

[0002] Curved bevel gears, also known as spiral bevel gears, are mainly used to transmit motion between intersecting or staggered shafts. They are widely used in industries such as aviation, shipbuilding, automobiles, tractors, and machine tools. Due to their complex tooth surfaces and the difficulty in designing and manufacturing them, they have always been a focus of research for gear processing companies and professionals in the field.

[0003] Curved bevel gears mainly fall into two categories: circular arc bevel gears and cycloidal bevel gears. The former features a reduced tooth height and a circular tooth line, machined using a single-indexing end-face milling method, with Gleason & Co. (USA) as a representative. The latter has equal tooth height and an extended epicycloid tooth line, machined using a continuous-indexing end-face hobbing method, with Klingberg (Germany) and Oerlikon (Switzerland) as representatives. Currently, both companies' machine tools can machine both cycloidal and circular arc bevel gears.

[0004] With the rapid development and increasing sophistication of CNC technology, the machining capabilities of five-axis CNC machine tools have become increasingly advanced. Based on the concept of digital forming wheels, Chinese scholars developed the principle of digital forming wheel machining and corresponding gear machining machines. Subsequently, foreign machine tool manufacturers also developed corresponding gear machining processes based on this principle, forming their own software packages. However, the tooth surface design of these gears still follows the design method based on traditional rocking table machine tools, failing to break free from the limitations of the machine tool's rocking table and cutter head, and can only machine bevel gears with circular arc teeth and cycloidal teeth.

[0005] In the digital prototyping gear machining principle system, the tooth curve is no longer limited to circular arcs and cycloids, but can be more curved forms such as involutes and logarithmic curves. Simultaneously, the design of the tooth surface is no longer limited to modifications based on the rocker table and cutter head; it can be actively designed and modified according to the transmission law to obtain tooth surface pairs with better transmission quality. Therefore, based on the digital prototyping gear, it is necessary to study a general design method for curved bevel gears to achieve controllable gear machining. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention provides an active design and processing method for curved bevel gears based on digital production wheels.

[0007] This invention is achieved through the following technical solution:

[0008] An active design method for curved bevel gears based on digital profilers includes the following steps:

[0009] Step 1: Determine the parameters of the digital production wheel based on the large gear of the curved bevel gear;

[0010] Step 2: Determine the tooth surface of the digital production wheel based on the tooth profile and cutter head parameters of the curved bevel gear, combined with the parameters of the digital production wheel;

[0011] Step 3: Determine the reference tooth surface of the large wheel based on the digitally generated tooth surface;

[0012] Step 4: Determine the theoretical tooth surface of the small gear based on the reference tooth surface of the large gear and the predetermined transmission law of the large and small gears;

[0013] Step 5: Correct the tooth surface of the generating gear obtained in Step 2 according to the planned tooth surface contact area to obtain the corrected digital generating gear tooth surface.

[0014] Step 6: Use the corrected digital profile wheel to envelop the theoretical tooth surface of the large gear to obtain the curved bevel gear.

[0015] Preferably, the parameters of the digital production wheel are as follows:

[0016] The vertex of the face cone of the digital feed wheel coincides with the vertex of the pitch cone of the large wheel. The formulas for the number of teeth, helix angle, and midpoint cone distance of the digital feed wheel are as follows:

[0017] Number of teeth on the feed gear:

[0018] Helix angle of the feed wheel: β mC =β mG

[0019] Cone distance at the midpoint of the feed wheel: R mC =R mG

[0020] Among them, z G δ represents the number of teeth on the larger gear in the machined gear pair. 0G β is the cone angle of the larger pitch of the gear pair being machined. mG R is the helix angle at the midpoint of the large wheel. mG The cone distance is the midpoint of the large wheel.

[0021] Preferably, the tooth profile of the curved bevel gear in step 2 includes circular arcs and extended epicycloids, and the cutter head parameters include the cutter head radius and the number of cutter heads.

[0022] Preferably, the numerical expression for the tooth surface of the gear in step 2 is as follows:

[0023] When the tooth line is an arc, the radial vector of the tooth surface is as follows:

[0024]

[0025] When the tooth line is an extended epicycloid, the tooth surface radial vector is as follows:

[0026]

[0027] Among them, (x k ,y k ,z k ) represents the coordinates of the cutting edge profile curve of the cutting tooth, which is a function of parameter u. Md and Q0 represent the radial and angular tool positions of the cutter head, respectively, and θ c θ and θ' are the rotation angles of the feed wheel and the cutter head, respectively.

[0028] Preferably, in step 3, the reference tooth surface of the large wheel is the envelope of the digitally generated gear teeth, and its expression is as follows:

[0029]

[0030] in, and These are the rotation angles when the gear forms an envelope and when the large gear is generated, respectively. If the large gear is machined using a forming method, then...

[0031] Preferably, the predetermined transmission law mentioned in step 4 is the rotational law of a pair of tooth surfaces during the complete meshing process of the large and small gears of the gear pair, which is represented by the transmission ratio function i:

[0032]

[0033] in, For the small wheel's turning angle, Functions of second order or higher;

[0034] Preferably, the theoretical tooth surface of the pinion is the envelope of the tooth surface of the gear according to the transmission ratio, and the expression is as follows:

[0035]

[0036] in, These are the rotation angles when the teeth of the pinion and gear mesh, t and t, respectively. z1 t z2 These are the distances where the apex of the pitch cone of the small wheel and the large wheel exceeds the point where their axes intersect, respectively, and E is the offset distance of the gear pair.

[0037] Preferably, the planned tooth surface contact area in step 5 includes the position of the tooth surface reference point, the trend of the base point trace, and the shape and size of the contact patch.

[0038] Preferably, the correction of the tooth surface of the production wheel in step 5 includes tooth profile and tooth profile correction;

[0039] The tooth profile modification is achieved by pressure angle modification, tooth profile drum modification, or tooth tip edge modification.

[0040] The tooth profile modification is achieved by using helical angle modification, tooth profile drum shape, or both ends bevel modification.

[0041] Preferably, step 6 determines the theoretical tooth surface of the large gear based on the envelope of the corrected tooth surface of the producing gear.

[0042] A method for machining gears designed using a digital profiling wheel-based active design method for curved bevel gears.

[0043] The gear is rough-cut and grooved in layers using a finger end mill. During the grooving process, the finger end mill feeds in the tooth height direction and cuts along the tooth line, using a reciprocating cutting method to complete the rough grooving.

[0044] Then, a tapered finger milling cutter is used for tooth surface finishing. During the finishing process, the tapered finger milling cutter moves along the tooth line to cover the tooth surface.

[0045] Compared with the prior art, the present invention has the following beneficial technical effects:

[0046] The active design method for curved bevel gears using digital forming wheels of this invention is based on the machining principle of digital forming wheels. The tooth lines of the bevel gears are no longer limited to circular arcs and cycloids. By adopting an active design concept, the resulting tooth surface pairs mesh according to a predetermined transmission law, which greatly weakens the influence of profile modification on the transmission law and helps control the vibration and noise of the gear pairs. At the same time, during the gear machining process, the manufacturing difficulty of the cutting tools is greatly reduced, and there is no longer a need for specially designed gear machine tools, which greatly reduces the manufacturing difficulty of curved bevel gears and reduces the machining cost. Attached Figure Description

[0047] Figure 1 This is a schematic diagram illustrating the machining principle of the curved bevel gear planar forming wheel of the present invention.

[0048] Figure 2 This is a flowchart illustrating the tooth surface design and machining process of the present invention.

[0049] Figure 3 This invention relates to the design of the contact area of ​​the large gear tooth surface.

[0050] Figure 4 This is an ease-off diagram of the large gear tooth surface profile difference surface of the present invention;

[0051] Figure 5 This is a schematic diagram of the roughing and finishing of the gear tooth surface according to the present invention. Detailed Implementation

[0052] The present invention will now be described in further detail with reference to the accompanying drawings. These descriptions are intended to explain the invention and not to limit it.

[0053] Figure 1This is a schematic diagram of the forming principle of curved bevel gear teeth. After using the conical surface as the pitch surface of the quasi-hyperboloid gear, the tooth surface of the quasi-hyperboloid gear can be enveloped by a planar gear with the T-plane as the pitch cone surface. The imaginary gear with a pitch cone angle of 90° is called the planar forming wheel, i.e., the digital forming wheel.

[0054] See Figure 2 A method for the active design and machining of curved bevel gears based on digital production wheels includes the following steps:

[0055] Step 1: Determine the parameters of the digital production wheel based on the large gear of the curved bevel gear;

[0056] The vertex of the face cone of the feed gear coincides with the vertex of the pitch cone of the large gear. Number of teeth on the feed gear: The helix angle and midpoint cone distance of the feed wheel are equal to those of the large wheel, β mC =β mG R mC =R mG .

[0057] Among them, z G δ represents the number of teeth on the larger gear in the machined gear pair. 0G β is the cone angle of the larger pitch of the gear pair being machined. mG R is the helix angle at the midpoint of the large wheel. mG The cone distance is the midpoint of the large wheel.

[0058] Step 2: Determine the tooth surface of the digitally generated bevel gear based on the tooth profile and cutter head parameters;

[0059] The tooth line forms of curved bevel gears include, but are not limited to, commonly used circular arcs and extended epicycloids. The cutter head parameters include the cutter head radius and the number of cutter head heads z0, i.e., the number of cutter tooth sets.

[0060] Digital representation of gear tooth surface, taking commonly used circular arc teeth and extended epicycloid teeth as examples, if the tooth line is a circular arc, then the tooth surface radial vector is:

[0061]

[0062] If the tooth profile is an extended epicycloid, then the tooth surface radial vector is:

[0063]

[0064] Among them, (x k ,y k ,z k ) represents the coordinates of the cutting edge profile curve of the cutting tooth, which is a function of the parameter u, M d Q0 and θ represent the radial and angular tool positions of the tool head, respectively. c θ and θ' are the rotation angles of the feed wheel and the cutter head, respectively;

[0065] Step 3: Calculate the reference tooth surface of the large wheel based on the digitally generated tooth surface;

[0066] The reference tooth surface of the large gear is the envelope of the tooth surface of the producing gear, and its expression is:

[0067]

[0068] in, and These are the rotation angles when the gear forms an envelope, representing the production path and the rotation angle when the large gear expands. If the large gear is machined using a forming method, then in the formula...

[0069] Step 4: Determine the theoretical tooth surface of the small gear based on the reference tooth surface of the large gear and the predetermined transmission law of the large and small gears;

[0070] The predetermined transmission law, the rotational law of a pair of gear teeth during the complete meshing process of the large and small gears in a gear pair, is commonly represented by the transmission ratio function i:

[0071]

[0072] in, For the small wheel's turning angle, Functions of second order or higher;

[0073] The theoretical tooth surface of the smaller gear is the envelope of the reference tooth surface of the larger gear according to a predetermined transmission ratio in a predetermined transmission law, which can be expressed as:

[0074]

[0075] in, These are the rotation angles when the teeth of the pinion and gear mesh, t and t, respectively. z1 t z2 These are the distances where the pitch cone apex of the small gear and the large gear exceed the point where their axes intersect, respectively; E is the gear pair offset distance.

[0076] Step 5: Correct the tooth surface of the production gear obtained in Step 2 according to the tooth surface contact pattern requirements to obtain the corrected digital production gear tooth surface.

[0077] First, plan the tooth surface contact area, see Figure 3 This includes the position of the tooth surface reference point, the trend of the base point trace, and the shape and size of the contact patch; then, the tooth profile (tooth contour) and tooth direction are modified on the tooth surface of the production wheel in step 2. The tooth profile modification can be done by pressure angle modification, tooth profile bulging, tooth tip edge modification, etc., and the tooth direction modification can be done by helix angle modification, tooth direction bulging, and end beveling, etc. Among them, the tooth direction bulging can be done by parabolas of order 4 or above;

[0078] Step 6: Use the corrected digital production wheel to enclose the theoretical tooth surface of the large gear, and complete the active design of the curved bevel gear.

[0079] Specifically, using the modified tooth surface of the production gear in step 5, the theoretical tooth surface of the large gear is calculated according to the formula in step 3. The modification effect of the large gear tooth surface is as follows: Figure 4 As shown;

[0080] See Figure 5 The machining method of the above-designed curved bevel gear will be described below.

[0081] Step 7: Layered roughing and grooving based on general finger end mills: Use a bar-shaped cutter of appropriate size, feed in the tooth height direction, and cut along the tooth line to complete the roughing and grooving; adopt a high-efficiency dry cutting method with small depth of cut, fast feed, and no idle stroke; the roughing cutter can be one or multiple.

[0082] Step 8: Tooth surface finishing based on tapered finger end mill. A specially designed tapered finger end mill is used to cover the tooth along the tooth line. When machining by generating method, a common tapered end mill with a straight cutting edge can be used. When machining large wheels by forming method, because a modified digital forming wheel is used, the cutting edge curve of the tool needs to be specially designed according to the forming process.

[0083] In the digital gear machining principle system, the tooth line of this invention is no longer limited to circular arcs and cycloids, but can be more curve forms such as involutes and logarithmic curves. Simultaneously, the design of the tooth surface is no longer limited to modifications based on the rocker table and cutter head; it can actively design and modify the tooth surface according to the transmission law, resulting in a tooth surface pair with better transmission quality. Adopting an active design concept, the resulting tooth surface pair is transmitted according to a predetermined law, weakening the influence of modification on the transmission law and facilitating the control of gear vibration and noise. Using general-purpose finger-shaped milling tools to machine the tooth surface greatly reduces the difficulty of tool manufacturing. Furthermore, using general-purpose five-axis CNC machine tools eliminates the need for specially designed gear machine tools; only corresponding software packages need to be developed to process bevel gears with various tooth lines. This method can be further extended to various types of gear machining, possessing pioneering theoretical significance, broad application prospects, and enormous economic benefits. It realizes a completely new and independently controllable gear machining method, thoroughly breaking away from foreign technology systems.

[0084] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for active design of curved bevel gears based on digital generation wheels, characterized in that, Includes the following steps: Step 1: Determine the parameters of the digital production wheel based on the large gear of the curved bevel gear, as follows: The vertex of the face cone of the digital feed wheel coincides with the vertex of the pitch cone of the large wheel. The formulas for the number of teeth, helix angle, and midpoint cone distance of the digital feed wheel are as follows: Number of teeth on the feed gear: Helix angle of the feed wheel: Cone distance at the midpoint of the feed wheel: in, The number of teeth of the larger gear in the gear pair being machined. The cone angle of the larger pitch of the gear pair being machined. The helix angle is the midpoint of the large wheel. The cone distance at the midpoint of the large wheel; Step 2: Determine the tooth surface of the digital production wheel based on the tooth profile and cutter head parameters of the curved bevel gear, combined with the parameters of the digital production wheel; The tooth profile includes circular arcs and extended epicycloids, and the cutter head parameters include the cutter head radius and the number of cutter heads. The digital production gear tooth surface expression: When the tooth line is an arc, the radial vector of the tooth surface is as follows: When the tooth line is an extended epicycloid, the tooth surface radial vector is as follows: in, Let be the coordinates of the cutting edge profile curve of the cutting tooth, which is a function of the parameter u. and These are the radial and angular tool positions of the cutter head, respectively. and These are the rotation angles of the feed wheel and the cutter head, respectively. Step 3: Determine the reference tooth surface of the large gear based on the digitally generated gear tooth surface. The reference tooth surface of the large gear is the envelope of the digitally generated gear teeth, and its expression is as follows: in, and These are the rotation angles when the forming wheel and the large gear form an envelope, respectively. If the large gear is machined using a forming method, then... ; Step 4: Determine the theoretical tooth surface of the small gear based on the reference tooth surface of the large gear and the predetermined transmission law of the large and small gears; The predetermined transmission law refers to the rotational law of a pair of tooth surfaces during the complete meshing process of the large and small gears in a gear pair, using a transmission ratio function. i To indicate: in, For the small wheel's turning angle, Functions of second order or higher; The theoretical tooth surface of the pinion is the envelope of the tooth surface of the gear according to the transmission ratio, and the expression is as follows: in, , These are the rotation angles when the teeth of the pinion and gear mesh. These are the distances where the pitch cone apex of the small gear and the large gear exceed the point where their axes intersect, respectively; E is the gear pair offset distance. Step 5: Correct the tooth surface of the generating gear obtained in Step 2 according to the planned tooth surface contact area to obtain the corrected digital generating gear tooth surface. Step 6: Use the corrected digital profile wheel to envelop the theoretical tooth surface of the large gear to obtain the curved bevel gear.

2. The active design method for curved bevel gears based on digital production wheels according to claim 1, characterized in that, The planned tooth surface contact area described in step 5 includes the position of the tooth surface reference point, the trend of the base point trace, and the shape and size of the contact patch.

3. The active design method for curved bevel gears based on digital production wheels according to claim 1, characterized in that, The correction of the tooth surface of the production gear described in step 5 includes tooth direction and tooth profile correction; The tooth profile correction is achieved by pressure angle correction, tooth profile drumming, or tooth tip edge correction. The tooth direction correction adopts helical angle shaping, tooth direction drum-shaped, or two-end bevel shaping.

4. The active design method for curved bevel gears based on digital production wheels according to claim 1, characterized in that, Step 6: Determine the theoretical tooth surface of the large gear based on the envelope of the corrected production gear tooth surface.

5. A method for machining a gear designed according to the active design method for curved bevel gears based on digital profiling wheels as described in any one of claims 1-4, characterized in that, The gear is rough cut and slotted in layers using a finger end mill. During the slotting process, the finger end mill feeds in the tooth height direction and cuts along the tooth line. The rough cutting and slotting is completed by reciprocating cutting. Then, a tapered finger milling cutter is used for tooth surface finishing. During the finishing process, the tapered finger milling cutter moves along the tooth line to cover the tooth surface.

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