Method for producing trochoidal inner and outer contours of polygon profiles using rolling processes

Abstract

Method for producing arbitrary trochoidal inner and outer contours and trochoidal hollow and solid profiles with arbitrary nominal diameters, arbitrary number of corners and arbitrary profile eccentricity sizes by applying rolling processes of arbitrary design with tools, wherein their shape is determined by the parameterized representation of the underlying hypotrochoidal profiles by the reference profile according to formula x ( a ) = D m 2 ⋅ [ an − 1 − ε ⋅ sin ( a ) ] , y (a) = D m 2 ⋅ ε ⋅ cos (a), is defined.

Description

[0001] The invention relates to a method for producing trochoidal inner and outer contours for polygonal profiles used as shaft-hub connections, employing rolling processes with novel reference and wheel profiles as tool geometries for producing these contours. The reference profile and wheel profile were developed from the geometry of the hypotrochoidal profile. These reference and wheel profiles, as tools (hobbing cutters, cutting combs, cutting wheels, and form cutters), enable the production of hypotrochoidal or epitrochoidal outer and inner contours using established rolling processes such as gear hobbing, gear shaping, gear skiving, gear planing, forming processes, and similar methods. The reference profiles can also be used to manufacture cutting wheels as tools for, for example, gear shaping of inner and outer contours.

[0002] Since the representation of the reference profile is parametric, the reference profile or the wheel profile can be used for any nominal diameter, for any number of corners / sides and for any eccentricity size of the hypotrochoidal profiles.

[0003] The application of the developed reference profiles to the upper cutting edge (lower profile side, see below) Fig. 5) creates a hypotrochoid outer contour (see Fig. 6 above). The application of the developed reference profiles to the lower cutting edge (upper profile side, see above).

[0004] Fig. 5) creates an epitrochoidal contour (see below). Fig. 6 below). The same applies to the application of this idea to wheel profiles. Therefore, the invention extends without limitation to applications for the production of epitrochoidal outer and inner contours using the manufacturing methods mentioned above.

[0005] The geometry of hypotrochoids can generally be generated by the non-slip rolling of a rolling circle on the inside of a base circle ( Fig. 1: shown as an example for page number n = 3). From this, the following general description (1) for the hypotrochoids is derived: x(a)=Dm2⋅cos(a)+e⋅cos[(n−1)⋅a] y(a)=Dm2⋅sin(a)+e⋅sin[(n−1)⋅a] where D m denotes the profile diameter of the hypotrochoid, e the eccentricity, n the number of sides and α the parameter angle.

[0006] Hypotrochoidal profiles are used in various technical fields, for example as positive-locking connections, and exhibit favorable mechanical stress conditions (elastic stresses) when transmitting torque. However, the production of such profile contours generally requires a special-purpose machine. Therefore, contour manufacturing has so far been associated with significantly higher production costs compared to conventional round contours.

[0007] A special grinding machine was developed by Fortuna Werke for the production of standardized P3G profiles with three flanks, similar to hypotrochides. This machine was based on the predecessor machine developed by Ernst Krause & Co. for epitrochides with three flanks [Ernst Krause & Co.: From the “K-profile” to the “polygon”. Reprint from “Austrian Machine Market and Electrical Industry”, 4th year, issue 14 / 15, August 1949].

[0008] Hypotrochoidal profiles are currently manufactured industrially on CNC machines. The two existing methods are a) twin-spindle turning [Maximov, JT: A new method of manufacture of hypocycloidal polygon shaft joints, Journal of Materials Processing Technology 166 (2005) 144-149 and Gold, PW In eight seconds to the polygon: Economical non-circular turning process for the production of polygon-shaft-hub connections. “antriebstechnik” Issue 6, 2006.] and b) the oscillating non-circular turning process [Jörg, R. High-performance non-circular turning and joining of positive-locking shaft-hub connections, 8th VDI Conference on Shaft-Hub Connections 2018 Dimensioning- Manufacturing-Applications, Stuttgart, 26-27 November 2018.]. Both processes require not only the appropriate tools, but also special, more expensive equipment for a suitable CNC lathe.

[0009] US 2016 / 0245388 A1 relates to an internal gear and a manufacturing process for it using a die forming process, wherein a die comprising a plurality of teeth is pressed against the workpiece while it is rotated by a drive unit.

[0010] According to the invention, the problem of producing trochoidal inner or outer contours is solved by the application of rolling processes. The shape (contour) of the tools required for this is determined according to the following description of the reference profile.

[0011] The problem is solved by a method for producing arbitrary trochoidal inner and outer contours or trochoidal hollow and solid profiles with arbitrary nominal diameters, arbitrary number of corners and arbitrary profile eccentricity sizes by applying rolling processes of arbitrary form with tools, wherein their shape is defined by the parameterized representation of the underlying hypotrochoidal contour by the reference profile according to formula (2).

[0012] The problem is further solved by a method for producing arbitrary trochoidal inner and outer contours or trochoidal hollow and solid profiles with arbitrary nominal diameters, arbitrary number of corners and arbitrary profile eccentricity sizes by applying rolling processes of arbitrary form with tools, wherein their shape is defined by the parameterized representation of the underlying epitrochoidal contour by the reference profile according to formula (3).

[0013] The class of rolling processes proposed here offers both a new, more cost-effective alternative for producing trochoidal internal and external contours of components and for manufacturing the necessary tools (e.g., cutting wheel or rolling needle) for the internal contours. This manufacturing method has not been used previously due to the lack of a suitable reference profile.

[0014] Based on the geometry description shown above (1), the geometry of the corresponding tool (profile bar) was developed. Fig. Figure 2 shows the hypotrochoid and the corresponding profile bar as an example for n = 5.

[0015] If the hypotrochoidal contour is specified, the reference profile for the tool (bar geometry) for producing a specified hypotrochoidal outer profile can be described by the following equations (2): x(a)=Dm2⋅[an−1−ε⋅sin(a)], y(a)=Dm2⋅ε⋅cos(a) with D m : Profile diameter of the hypotrochoids, ε=2⋅eDm relative eccentricity.

[0016] Fig. 3 and Fig. 4 show for the in Fig. The two examples shown are two further intervention positions.

[0017] Looking at the lower side of the reference profile ( Fig. 5) provides a further tool for producing the conjugate contours of the hypotrochoids, the so-called epitrochoid contours. The geometry of the epitrochoids can generally be generated by the non-slip rolling of a circular wheel on the outside of a base circle. The relationship between the two conjugate profiles with the reference profile defined in (2) is exemplified for a hypotrochoid with n = 10 and an epitrochoid with n = 5 in Fig. Figure 6 shows that such an epitrochoidal profile can also be used as a cutting wheel to produce hypotrochoidal profiles (outer contour). Fig. 7) Thus, various types of rolling processes, which are normally used for the production of commercially available gears (for example according to [DIN 867: Reference profiles for involute gears on spur gears (cylindrical gears) for general mechanical engineering and heavy machinery construction, edition 1986-02.]), can also be used for hypotrochoidal profiles as well as for epitrochoidal profiles.

[0018] If the epitrochoidal contour is specified, the reference profile for the tool (rod geometry) for producing the specified epitrochoidal profile can be described by the following equations: x(a)=Dm2⋅[an+1−ε⋅sin(a)], y(a)=Dm2⋅ε⋅cos(a), with Dm: profile diameter of the epitrochoids, ε=2⋅eDm relative eccentricity

[0019] If the contour of the tool (rod geometry) is to be considered as a reference point, the reference profile for producing the hypotrochoid or epitrochoid profile can be described by the following equations: x(a)=Dm2⋅[an−ε⋅sin(a)], y(a)=Dm2⋅ε⋅cos(a), with Dm=2⋅ns⋅m, where m describes a so-called module for the profile.

[0020] Description (4) applies in the case where the matable hypo- and epitrochoidal profile contours (for example as profile running gears) are to be produced based on a profile module m in the sense of a gear drive.

[0021] The parametric descriptions of the reference profile for hypotrochoidal profiles given above enable the use of the rolling method for any size and any eccentricity.

[0022] A manufactured hypotrochoidal profile can also be used directly as a tool or cutting wheel for producing hypotrochoidal internal contours with a larger number of corners but with the same corner size ( Fig. 8).

[0023] The invention is to be described in the following Fig. 1 to 8 will be explained in more detail.

[0024] The Fig. Figure 1 shows the generation of a hypotrochoidal profile (H-profile) by rolling a rolling circle on the inside of a base circle. Here, the diameter ratio, or the number of profile sides, is chosen to be three.

[0025] The Fig. Figure 2 shows the reference profile as a tool in engagement with a hypotrochoidal profile (H-profile) as the workpiece. The reference line touches the pitch circle of the profile in all positions. v represents the linear velocity of the reference line and ω describes the angular velocity of the pitch circle, while the Fig. Figure 3 shows a hypotrochoidal profile and a profile bar in a second angular position. v represents the linear velocity of the reference line and ω describes the angular velocity of the pitch circle. Fig. Figure 4 shows a hypotrochoidal profile and a profile bar in a third angular position. v represents the linear velocity of the reference line and ω describes the angular velocity of the pitch circle.

[0026] The Fig. 2 to 4 refer to applications of the rolling process and the application of all hypotrochoidal profiles generated using the "top side" of the described reference profile for each profile diameter and for each profile eccentricity and for each number of corners / sides, where the generated hypotrochoidal profile represents the outer contour of a component, e.g. a shaft.

[0027] The Fig. Figure 5 shows the upper and lower profile bars for producing the hypotrochoid profiles (H-profiles) and their conjugated so-called epitrochoid profiles (E-profiles) and the Fig. 6. The relationship between the two conjugate profiles with the reference rod is exemplified for a hypotrochoid with n = 10 and an epitrochoid with n = 5, while the Fig. Seven epitrochoidal profiles (E-profiles) are shown as a tool / cutting wheel for producing hypotrochoidal profiles (H-profiles).

[0028] The Fig. Paragraphs 5 to 7 refer to applications of the rolling process and the application of all epitrochoidal profiles generated using the "bottom side" of the described reference profiles, which are defined by the conjugate profile according to equation (3), for each profile diameter and for each profile eccentricity and for each number of corners / sides, wherein the generated epitrochoidal profile represents the outer contour of a component or the contour of an epitrochoidal tool (cutting wheel or broach of any size, eccentricity and number of cutting edges) for the secondary production of a trochoidal inner or outer contour, as well as for the production of the matable hypo- and epitrochoidal profile contours (for example as profile wheels) according to equation (4) for inner and outer profile pairs, which also includes a profile module for each profile eccentricity and for each number of corners / sides.

[0029] The described geometries are used as geometries of tools such as profile bars, cutting wheels or milling tools, as well as forming tools in all rolling processes, such as gear milling, gear turning, gear grinding, gear planing, gear shaping, gear peeling, profile broaching, as well as forming rolling processes, but also in similar processes, such as form milling, for the production of internal and external contours of hypotrochoidal and epitrochoidal profiles with any nominal diameters, any number of corners and any eccentricity sizes, as well as the aforementioned manufacturing methods for the production of trochoidal internal and external profiles with any positive or negative profile shift as well as without profile shift in the corresponding rolling processes.

[0030] The geometries described above are also used as geometries of tools for all the manufacturing methods described above for the production of trochoidal inner and outer profiles with inclined or helical axial profiles of the inner and outer contours to be produced, as well as for the production of trochoidal inner and outer profiles with cylindrical or conical outer surfaces.

[0031] Furthermore, the aforementioned geometries and the geometries of tools for producing trochoidal internal and external profiles "with" or "without" foot or head shortening, as well as for producing profiles with oblique or helical (non-prismatic) shapes, can also be used.

[0032] The Fig.Figure 8 shows a hypotrochoidal profile as a tool or cutting wheel for producing hypotrochoidal internal contours (hollow contours) with a larger number of corners and with the same corner size.

[0033] The geometries described and mentioned, and the geometries of tools, are generated using numerical approximations of equations (2), (3) and (4) in any form and any kind, for example, by point clouds, as well as any approximate values ​​using CAD and CAE systems to produce the corresponding profiles mentioned.

Claims

[1] Method for producing arbitrary trochoidal internal and external contours and trochoidal hollow and solid profiles with arbitrary nominal diameters, arbitrary number of corners and arbitrary profile eccentricity sizes by applying rolling processes of arbitrary design with tools, wherein their shape is determined by the parameterized representation of the underlying hypotrochoidal profiles by the reference profile according to formula x(a)=Dm2⋅[an−1−ε⋅sin(a)], y(a)=Dm2⋅ε⋅cos(a), is defined. [2] Method for producing arbitrary trochoidal inner and outer contours and trochoidal hollow and solid profiles with arbitrary nominal diameters, arbitrary number of corners and arbitrary profile eccentricity sizes by applying rolling processes of arbitrary design with tools, wherein their shape is determined by the parameterized representation of the underlying epitrochoidal profiles by the reference profile according to formula x(a)=Dm2⋅[an+1−ε⋅sin(a)], y(a)=Dm2⋅ε⋅cos(a), is defined. [3] Application of the method according to claim 1 for producing a hypotrochoidal profile for the outer contour of a component in the form of a shaft, generated using the “top side” of the described reference profile. [4] Application of the method according to claim 2 for producing an epitrochoidal profile generated using the “lower side” of the reference profile for the outer contour of a component or the contour of an epitrochoidal tool in the form of a cutting wheel or broach of any size, eccentricity and number of cutting edges. [5] Application of the method according to claim 1 or 2 for the production of a matching hypo- and epitrochoidal profile contour for inner and outer profile pairs using the described reference profiles, which also includes a profile module for each profile eccentricity and for each number of corners / sides. [6] Application of the method according to claim 1 or 2 for the production of trochoidal inner and outer profiles with any positive or negative profile shift as well as without profile shift. [7] Application of the method according to claim 1 or 2 for the production of trochoidal inner and outer profiles with cylindrical or conical outer surfaces. [8] Application of the method according to claim 1 or 2 for the production of trochoidal inner and outer profiles with oblique or helical axial direction of the inner and outer contours to be produced. [9] Application of the method according to claim 1 or 2 for the production of trochoidal inner and outer profiles “with” and “without” foot or head trimming. [10] Application of the method according to claim 1 or 2 for the production of profiles with inclined or helical shapes.

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