Procedure and System for Profile Generation

Abstract

The present invention relates to a method for the profile generation of involute-based toothed shaft connections, comprising: determination of a circle described by the reference diameter d.sub.B′, distance-based generation of the shaft top circle using the reference diameter distance A.sub.dB, the shaft top circle being the quasi first element of the shaft profile; distance-based generation the hub top circle using the effective touching height h.sub.w, distance-based determination of the touching point between the shaft tooth flank and the shaft root fillet using the shaft form oversize of the reference profile C.sub.FP1 or the shaft form oversize C.sub.FP1 generation of the shaft root fillet, the shaft reference profile being already completely generated by means of this step in the case of full filleting of the shaft; constant-tangent generation of the shaft root circle for shaft root filleting, this step being required only in the case of partial filleting; and obtainment of the shaft profile.

Claims

1. Procedure for profile generation of involute splined shaft connection, comprising the steps a) determination of a circle described by the reference diameter d.sub.B, b) distance-based generation of the shaft tip circle using the reference diameter distance A.sub.dB, whereby the shaft tip circle represents the quasi first element of the shaft profile, whereby starting from the shaft tip circle in steps c), d) and e), the shaft profile generation is sequentially unidirectional inward, c) distance-based generation of the hub tip circle using the effective contact height h.sub.w, d) distance-based determination of the contact point between the shaft tooth flank and the shaft root rounding using the shaft form excess of the reference profile c.sub.FP1 or the shaft form excess c.sub.F1, e) generation of the shaft root rounding, whereby in the case of a shaft full rounding, the shaft reference profile is already completely generated with this step, f) tangential generation of the shaft root circle to the shaft root rounding, whereby this step is only required for partial rounding, and g) obtain the shaft profile.

2. Procedure according to claim 1, based on the shaft profile furthermore comprising the steps h) generation of the hub tip circle as the first element of the hub profile, whereby, starting from the shaft tip circle in steps i), j) and k), the hub profile generation is performed sequentially unidirectionally outward, i) distance-based determination of the contact point between the hub tooth flank and the hub root rounding using the hub form excess of the reference profile c.sub.FP2 or the hub form excess c.sub.F2, j) generation of the hub root rounding, whereby in the case of a hub full rounding, the hub profile is already completely generated with this step, k) tangential generation of the hub root circle to the hub root rounding, whereby this step is only required for partial rounding, and l) obtain the hub profile.

3. Procedure according to claim 1, whereby the reference diameter d.sub.B is freely selectable.

4. Procedure according to claim 1, whereby the module m is freely selectable.

5. Procedure according to claim 1, whereby the flank angle α is freely selectable.

6. Procedure according to claim 1, whereby the root rounding radii ρ.sub.f are freely selectable and the form excesses c.sub.F are freely selectable.

7. Procedure according to claim 1, whereby the effective contact height without profile modification h.sub.w(R.sub.hw=0) is freely selectable.

8. System for profile generation of involute splined shaft connections containing a shaft and a hub, comprising I) the shaft tip circle, which is completely defined by the shaft tip circle diameter d.sub.a1 for a given axis-congruent position, which is also valid for the reference profile and the nominal geometry: TABLE-US-00010 A.sub.dB input parameter according to invention d.sub.B input parameter d.sub.a1 d.sub.B + 2 .Math. A.sub.dB according to invention II) the shaft tooth flank, which is an involute, which is defined by its coordinates (x.sub.E; y.sub.E): TABLE-US-00011 m input parameter z.sub.1 input parameter α input parameter u.sub.E control variable d m .Math. z.sub.1 d.sub.b d .Math. cos α x.sub.E r.sub.b (cos u.sub.E + u.sub.E sin u.sub.E) x.sub.E r.sub.b (−sin u.sub.E + u.sub.E cos u.sub.E) III. the shaft partial rounding comprising III.1) the shaft root rounding, which in case of tangent continuity between the shaft tooth flank and the shaft root rounding and between the shaft root rounding and the shaft root circle is completely defined by the shaft root rounding radius ρ.sub.f1, whereby in case of a shaft partial rounding this is an input parameter, III.2) the shaft root circle, which is completely defined by the shaft root circle diameter d.sub.f1 for a predefined axis-congruent position and the required tangent continuity of the shaft root circle with the shaft root rounding: TABLE-US-00012 A.sub.dB input parameter according to invention A.sub.hw input parameter according to invention c.sub.F1 input parameter d.sub.B input parameter h.sub.w input parameter according to (R.sub.hw = 0) invention m input parameter R.sub.hw input parameter according to invention z.sub.1 input parameter α input parameter ρ.sub.f1 input parameter d m .Math. z.sub.1 x.sub.I1 .Math. m $\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ according to invention x.sub.I2 .Math. m −x.sub.I1 .Math. m according to invention x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) according to invention x.sub.M2 .Math. m −x.sub.M1 .Math. m according to invention x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m according to invention x.sub.2 .Math. m −x.sub.1 .Math. m resp. (x.sub.I2 + x.sub.M2) .Math. m according to invention y.sub.1 .Math. m R.sub.hw .Math. h.sub.w(R.sub.hw = 0) .Math. (1 − A.sub.hw) according to invention y.sub.2 .Math. m −y.sub.1 .Math. m according to invention d.sub.a2 −d + 2 .Math. x.sub.2 .Math. m + h.sub.w(R.sub.hw = 0) + 2 .Math. y.sub.2 .Math. m according to invention d.sub.b d .Math. cos α u.sub.E1 $\sqrt{{\left(\frac{-r_{a2}-c_{F1}}{r_b}\right)}^2-1}$ according to invention |{right arrow over (K)}.sub.M1| $\sqrt{\begin{array}{c}{\left(r_b\left(\cos u_{E1}+u_{E1}\sin u_{E1}\right)+{\rho }_{f1}\sin u_{E1}\right)}^2+\\ +{\left(r_b\left(-\sin u_{E1}+u_{E1}\cos u_{E1}\right)+{\rho }_{f1}\cos u_{E1}\right)}^2\end{array}}$ according to invention d.sub.f1 2 .Math. (|{right arrow over (K)}.sub.M1|− ρ.sub.f1) according to invention IV) the shaft full rounding comprising IV.1 the shaft root rounding, which in case of tangent continuity between the shaft tooth flank and the shaft root rounding is completely defined by the shaft root rounding radius at full rounding ρ.sub.f1.sup.V: TABLE-US-00013 A.sub.dB input parameter according to invention A.sub.hw input parameter according to invention c.sub.F1 input parameter d.sub.B input parameter h.sub.w input parameter according to (R.sub.hw = 0) invention m input parameter R.sub.hw input parameter according to invention z.sub.1 input parameter α input parameter π mathematical constant p m .Math. π d m .Math. z.sub.1 x.sub.I1 .Math. m $\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ according to invention x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) according to invention x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m according to invention s.sub.1 $\frac{p}{2}+2.Math.x_1.Math.m.Math.\tan \alpha$ α.sub.s1 $\frac{s_1}{r}$ according to invention α.sub.Er $.Math.{\tan }^{-1}\left(\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }\right)-\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }.Math.$ according to invention α.sub.E $\frac{{\alpha }_{s1}}{2}+{\alpha }_{\mathrm{Er}}$ according to invention α.sub.S $\frac{2\pi }{z_1}$ according to invention α.sub.KM1.sup.V $\left(-1\right).Math.\left({\alpha }_E-\frac{{\alpha }_S}{2}\right)$ according to invention x.sub.2 .Math. m −x.sub.1 .Math. m resp. (x.sub.I2 + x.sub.M2) .Math. m according to invention y.sub.1 .Math. m R.sub.hw .Math. h.sub.w(R.sub.hw = 0) .Math. (1 − A.sub.hw) according to invention y.sub.2 .Math. m −y.sub.1 .Math. m according to invention d.sub.a2 −d + 2 .Math. x.sub.2 .Math. m + h.sub.w(R.sub.hw = 0) + 2 .Math. y.sub.2 .Math. m according to invention d.sub.b d .Math. cos α u.sub.E1 $\sqrt{{\left(\frac{-r_{a2}-c_{F1}}{r_b}\right)}^2-1}$ according to invention ρ.sub.f1.sup.V $\frac{r_b\left(\begin{array}{c}\tan \left({\alpha }_{\mathrm{KM}1}^V\right)\left(\cos u_{E1}+u_{E1}\sin u_{E1}\right)+\\ +\sin u_{E1}-u_{E1}\cos u_{E1}\end{array}\right)}{\cos u_{E1}-\tan \left({\alpha }_{\mathrm{KM}1}^V\right)\sin u_{E1}}$ according to invention IV.2) the shaft root circle, which is not part of the shaft profile shape in case of shaft full rounding, but can nevertheless be calculated and then has the character of a design element, whereby in case of given axis-congruent position as well as the required tangent continuity of the shaft root circle with the shaft root rounding, the shaft root circle is completely defined by the shaft root circle diameter d.sub.f1: TABLE-US-00014 A.sub.dB input parameter according to invention A.sub.hw input parameter according to invention c.sub.F1 input parameter d.sub.B input parameter h.sub.w input parameter according to (R.sub.hw = 0) invention m input parameter R.sub.hw input parameter according to invention z.sub.1 input parameter α input parameter π mathematical constant d m .Math. z.sub.1 x.sub.I1 .Math. m $\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ according to invention x.sub.12 .Math. m −x.sub.I1 .Math. m according to invention x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) according to invention x.sub.M2 .Math. m −x.sub.M1 .Math. m according to invention x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m according to invention x.sub.2 .Math. m −x.sub.1 .Math. m resp. (x.sub.I2 + x.sub.M2) .Math. m according to invention y.sub.1 .Math. m R.sub.hw .Math. h.sub.w(R.sub.hw = 0) .Math. (1 − A.sub.hw) according to invention y.sub.2 .Math. m −y.sub.1 .Math. m according to invention d.sub.a2 −d + 2 .Math. x.sub.2 .Math. m + h.sub.w(R.sub.hw = 0) + 2 .Math. y.sub.2 .Math. m according to invention d.sub.b d .Math. cos α u.sub.E1 $\sqrt{{\left(\frac{-r_{a2}-c_{F1}}{r_b}\right)}^2-1}$ according to invention p m .Math. π s.sub.1 $\frac{p}{2}+2.Math.x_1.Math.m.Math.\tan \alpha$ α.sub.s1 $\frac{s_1}{r}$ according to invention α.sub.Er $.Math.{\tan }^{-1}\left(\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }\right)-\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }.Math.$ according to invention α.sub.E $\frac{{\alpha }_{s1}}{2}+{\alpha }_{\mathrm{Er}}$ according to invention α.sub.S $\frac{2\pi }{z_1}$ according to invention α.sub.KM1.sup.V $\left(-1\right).Math.\left({\alpha }_E-\frac{{\alpha }_S}{2}\right)$ according to invention ρ.sub.f1.sup.V $\frac{r_b\left(\begin{array}{c}\tan \left({\alpha }_{\mathrm{KM}1}^V\right)\left(\cos u_{E1}+u_{E1}\sin u_{E1}\right)+\\ +\sin u_{E1}-u_{E1}\cos u_{E1}\end{array}\right)}{\cos u_{E1}-\tan \left({\alpha }_{\mathrm{KM}1}^V\right)\sin u_{E1}}$ according to invention |{right arrow over (K)}.sub.M1| $\sqrt{\begin{array}{c}{\left(r_b\left(\cos u_{E1}+u_{E1}\sin u_{E1}\right)-{\rho }_{f1}^V\sin u_{E1}\right)}^2+\\ +{\left(r_b\left(-\sin u_{E1}+u_{E1}\cos u_{E1}\right)-{\rho }_{f1}^V\cos u_{E1}\right)}^2\end{array}}$ according to invention d.sub.f1 2 .Math. (|{right arrow over (K)}.sub.M1| − ρ.sub.f1.sup.V) according to invention V) the hub tip circle, which in case of a predefined axis-congruent position is completely defined by the hub tip circle diameter d.sub.a2, which is valid equally for reference profile and nominal geometry: TABLE-US-00015 A.sub.dB input parameter according to invention A.sub.hw input parameter according to invention d.sub.B input parameter h.sub.w(R.sub.hw = 0) input parameter according to invention m input parameter R.sub.hw input parameter according to invention z.sub.1 input parameter d m .Math. z.sub.1 x.sub.I1 .Math. m $\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ according to invention x.sub.I2 .Math. m −x.sub.I1 .Math. m according to invention x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) according to invention x.sub.M2 .Math. m −x.sub.M1 .Math. m according to invention x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m according to invention x.sub.2 .Math. m −x.sub.1 .Math. m resp. (x.sub.I2 + x.sub.M2) .Math. m according to invention y.sub.1 .Math. m R.sub.hw .Math. h.sub.w(R.sub.hw = 0) .Math. (1 − A.sub.hw) according to invention y.sub.2 .Math. m −y.sub.1 .Math. m according to invention d.sub.a2 −d + 2 .Math. x.sub.2 .Math. m + h.sub.w(R.sub.hw = 0) + 2 .Math. y.sub.2 .Math. m according to invention VI) the hub tooth flank, which is an involute, which is defined by its coordinates (x.sub.E; y.sub.E): TABLE-US-00016 m input parameter z.sub.1 input parameter α input parameter u.sub.E control variable d m .Math. z.sub.1 d.sub.b d .Math. cos α x.sub.E r.sub.b (cos u.sub.E + u.sub.E sin u.sub.E) x.sub.E r.sub.b (−sin u.sub.E + u.sub.E cos u.sub.E) VII) the hub root rounding comprising VII.1) the hub partial rounding with VII.1a) the hub root rounding, which in case of tangent continuity between the hub tooth flank and the hub root rounding and between the hub root rounding and the hub root circle is completely defined by the hub root rounding radius ρ.sub.f2, whereby in case of a hub partial rounding this is an input parameter VII.1b) the hub root circle, which is completely defined by the hub root circle diameter d.sub.f2 for a predefined axis-congruent position and the required tangent continuity of the hub root circle with the hub root rounding: TABLE-US-00017 A.sub.dB input parameter according to invention c.sub.F2 input parameter d.sub.B input parameter m input parameter z.sub.1 input parameter α input parameter ρ.sub.f2 input parameter d.sub.a1 d.sub.B + 2 .Math. A.sub.dB according to invention d m .Math. z.sub.1 d.sub.b d .Math. cos α u.sub.E2 $\sqrt{{\left(\frac{r_{a1}+c_{F2}}{r_b}\right)}^2-1}$ according to invention |{right arrow over (K)}.sub.M2| $\sqrt{\begin{array}{c}{\left(r_b\left(\cos u_{E2}+u_{E2}\sin u_{E2}\right)-{\rho }_{f2}\sin u_{E2}\right)}^2+\\ +{\left(r_b\left(-\sin u_{E2}+u_{E2}\cos u_{E2}\right)-{\rho }_{f2}\cos u_{E2}\right)}^2\end{array}}$ according to invention d.sub.f2 (−1) .Math. 2 .Math. (|{right arrow over (K)}.sub.M2| + ρ.sub.f2) according to invention VII.2) the hub full rounding with VII.2a) the hub root rounding, which in case of tangent continuity between the hub tooth flank and the hub root rounding is completely defined by the hub root rounding radius at full rounding ρ.sub.f2.sup.V: TABLE-US-00018 A.sub.dB input parameter according to invention A.sub.hw input parameter according to invention c.sub.F2 input parameter d.sub.B input parameter h.sub.w(R.sub.hw = 0) input parameter according to invention m input parameter R.sub.hw input parameter according to invention z.sub.1 input parameter α input parameter π mathematical constant p m .Math. π d m .Math. z.sub.1 x.sub.I1 .Math. m $\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ according to invention x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) according to invention x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m according to invention s.sub.1 $\frac{p}{2}+2.Math.x_1.Math.m.Math.\tan \alpha$ α.sub.s1 $\frac{s_1}{r}$ according to invention α.sub.Er $.Math.{\tan }^{-1}\left(\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }\right)-\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }.Math.$ according to invention α.sub.E $\frac{{\alpha }_{s1}}{2}+{\alpha }_{\mathrm{Er}}$ according to invention α.sub.KM2.sup.V (−1) .Math. α.sub.E according to invention d.sub.a1 d.sub.B + 2 .Math. A.sub.dB according to invention d.sub.b d .Math. cos α u.sub.E2 $\sqrt{{\left(\frac{r_{a1}+c_{F2}}{r_b}\right)}^2-1}$ according to invention ρ.sub.f2.sup.V $\frac{r_b\left(\begin{array}{c}\tan \left({\alpha }_{\mathrm{KM}2}^V\right)\left(\cos u_{E2}+u_{E2}\sin u_{E2}\right)+\\ +\sin u_{E2}-u_{E2}\cos u_{E2}\end{array}\right)}{\tan \left({\alpha }_{\mathrm{KM}2}^V\right)\sin u_{E2}-\cos u_{E2}}$ according to invention VII.2b) the hub root circle, which is not part of the hub profile shape in case of hub full rounding, but can nevertheless be calculated and then has the character of a design element, whereby in case of a given axis-congruent position as well as the required tangent continuity of the hub root circle with the hub root rounding, the hub root circle is completely defined by the hub root circle diameter d.sub.f2: TABLE-US-00019 A.sub.dB input parameter according to invention A.sub.hw input parameter according to invention c.sub.F2 input parameter d.sub.B input parameter h.sub.w(R.sub.hw = 0) input parameter according to invention R.sub.hw input parameter according to invention m input parameter z.sub.1 input parameter α input parameter π mathematical constant p m .Math. π d m .Math. z.sub.1 x.sub.I1 .Math. m $\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ according to invention x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) according to invention x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m according to invention s.sub.1 $\frac{p}{2}+2.Math.x_1.Math.m.Math.\tan \alpha$ α.sub.s1 $\frac{s_1}{r}$ according to invention α.sub.Er $.Math.{\tan }^{-1}\left(\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }\right)-\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }.Math.$ according to invention α.sub.E $\frac{{\alpha }_{s1}}{2}+{\alpha }_{\mathrm{Er}}$ according to invention α.sub.KM2.sup.V (−1) .Math. α.sub.E according to invention d.sub.a1 d.sub.B + 2 .Math. A.sub.dB according to invention d.sub.b d .Math. cos α u.sub.E2 $\sqrt{{\left(\frac{r_{a1}+c_{F2}}{r_b}\right)}^2-1}$ according to invention ρ.sub.f2.sup.V $\frac{r_b\left(\begin{array}{c}\tan \left({\alpha }_{\mathrm{KM}2}^V\right)\left(\cos u_{E2}+u_{E2}\sin u_{E2}\right)+\\ +\sin u_{E2}-u_{E2}\cos u_{E2}\end{array}\right)}{\tan \left({\alpha }_{\mathrm{KM}2}^V\right)\sin u_{E2}-\cos u_{E2}}$ according to invention |{right arrow over (K)}.sub.M2| $\sqrt{\begin{array}{c}{\left(r_b\left(\cos u_{E2}+u_{E2}\sin u_{E2}\right)-{\rho }_{f2}^V\sin u_{E2}\right)}^2+\\ +{\left(r_b\left(-\sin u_{E2}+u_{E2}\cos u_{E2}\right)-{\rho }_{f2}^V\cos u_{E2}\right)}^2\end{array}}$ according to invention d.sub.f2 (−1) .Math. 2 .Math. (|{right arrow over (K)}.sub.M2|+ ρ.sub.f2.sup.V) according to invention

9. Parameter reference diameter distance A.sub.dB, with which the function for free selection of the distance between the reference diameter d.sub.B and the shaft tip diameter d.sub.a1 is implemented in the system according to claim 8.

10. Use of the system according to claim 8 for profile modification, whereby the parameters referred to as x.sub.I1, x.sub.I2, previously x.sub.1, x.sub.2, are known, while the profile modification is based on the factors x.sub.M1, x.sub.M2, y.sub.1, y.sub.2, R.sub.hw, A.sub.hw and functionally interacts with the previously designated parameters of the profile shift.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0075] FIG. 1 is a reference profile according to the [DIN 5480] [Wild 20].

[0076] FIG. 2 is a derivation of the profile shift [Wild 20].

[0077] FIG. 3 illustrates the geometric relationships of involute splined shaft connections according to the [DIN 5480] in the shaft root area on the example of the connection.

[0078] FIG. 4 illustrates the geometric differences of the profile shaft connections compared in the research project [FVA 742 I] (same scale) [Wild 20].

[0079] FIG. 5 illustrates basic systematics of the inventive system for profile generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), on the example of the connection.

[0080] FIG. 6 illustrates an adjusted reference profile of the [DIN 5480] [Wild 20].

[0081] FIG. 7 illustrates requirement-specific design of toothed shaft connections according to (Tab. 2, Tab. 3) by selecting the reference diameter d.sub.B as well as the reference diameter distance A.sub.dB [Wild 20].

[0082] FIG. 8 illustrates the requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections , cf. (Tab. 2, Tab. 3), by the selection of the module m resp. the shaft number of teeth z.sub.1 on the example of the connection.

[0083] FIG. 9 illustrates the requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections by the selection of the flank angle a on the example of the connection.

[0084] FIG. 10 illustrates the requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the root rounding radii ρ.sub.f on the example of the connection.

[0085] FIG. 11 illustrates the requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the form excesses c.sub.F on the example of the connection.

[0086] FIG. 12 illustrates the requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the effective contact height without profile modification h.sub.w(R.sub.hw=0) on the example of the connection.

[0087] FIG. 13 is a not profile modified toothed shaft connection.

[0088] FIG. 14 illustrates a requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the profile modification controlling parameters R.sub.hw as well as A.sub.hw on the example of the connection.

DETAILED DESCRIPTION OF THE INVENTION

[0089] For a given occasion, in [Wild 20] based on a newly developed systematic for the profile generation of involute splined shaft connections, a new system for the nominal geometry generation of such connections was developed, cf. (Tab. 2, Tab. 3). The extensive derivations of its equations based on their functional correlation are given in [Wild 20]. The object of the present application is merely the presentation of the developed systematic for profile generation of involute splined shaft connections, cf. the section brief description of the invention for problem solving, of the resulting inventive system for nominal geometry generation of such connections as well as its immediate components. The two last-mentioned aspects will be discussed in the following. [Wild 20]

[0090] In analogy to the [DIN 5480], the reference profile shown in FIG. 6, revised in comparison to FIG. 1, serves as the basis for the definition of the in [Wild 20] inventive system for the nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3). From a cross-comparison between the figures mentioned above, it is evident that there is now a strict differentiation between shaft- and hub-specific quantities. From the input parameters listed in Tab. 1 of the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), this concerns the root rounding radii of the reference profile ρ.sub.fP as well as the form excesses of the reference profile c.sub.FP. [Wild 20]

[0091] The control of the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), is performed by the parameters listed in Tab. 1. In this regard, it should be noted that some of them are newly introduced, so their function is not yet commonly known. Concerning this, the reference diameter distance A.sub.dB, cf. FIG. 7, the effective contact height of the flanks in radial direction without profile modification h.sub.w(R.sub.hw=0), cf. FIG. 12, as well as the parameters reduction factor of the effective contact height R.sub.hw controlling the profile modification and the distribution key of the reduction of the effective contact height A.sub.hw, cf. FIG. 13 with FIG. 14, have to be named. Further, the inventive system for nominal geometry generation of involute splined shaft connections is completely presented in (Tab. 2, Tab. 3). In order of completeness, Tab. 4 provides equations for the calculation of further geometric quantities which are only of a descriptive but not of a determining character regarding the profile shape presented in (Tab. 2, Tab. 3). Their application is therefore optional. In the development of the inventive system for nominal geometry generation of involute splined shaft connections presented in (Tab. 2, Tab. 3), it was considered that connections of the [DIN 5480] are still generatable. The only question here is how the input parameters listed in Table 1 have to be selected so that geometry equivalence results. The corresponding values are summarized in Tab. 5. With reference to the results given in [Wild 20] on the shape stability of involute splined shaft connections according to (Tab. 2, Tab. 3), however, it may also be useful to simply generate geometrically compatible connection partners according to (Tab. 2, Tab. 3) with those according to [DIN 5480]. The values to be selected in this case for the input parameters listed in Table 1 are given in Table 6. [Wild 20]

[0092] Definition of the Input Parameters

[0093] The control of the inventive system for nominal geometry generation of involute splined shaft connections according to (Tab. 2, Tab. 3) is completely performed by the input parameters summarized in Tab. 1. [Wild 20]

TABLE-US-00001 TABLE 1 [Wild 20] Symbol Toothing data and calculation equations d.sub.B Freely selectable A.sub.dB Freely selectable (radial effectiveness) m Freely selectable z.sub.1 Freely selectable z.sub.2 −z.sub.1 α Freely selectable ρ.sub.f1 In the interval 0 ≤ ρ.sub.f1 ≤ ρ.sub.f1.sup.V freely selectable ρ.sub.f2 In the interval 0 ≤ ρ.sub.f2 ≤ ρ.sub.f2.sup.V freely selectable c.sub.F1 Freely selectable c.sub.F2 Freely selectable h.sub.w(R.sub.hw = 0) Freely selectable R.sub.hw In the interval 0 ≤ R.sub.hw < 1 freely selectable A.sub.hw In the interval 0 ≤ A.sub.hw < 1 freely selectable

[0094] Mathematical Formulation

[0095] The inventive system for nominal geometry generation of involute splined shaft connections is fully defined with the equations given in (Tab. 2, Tab. 3). These are compiled in such a way that, with appropriately selected input data, cf. Tab. 1, the equations only need to be applied in sequential order. Only exception in this respect is the calculation of the full rounding radii ρ.sub.f.sup.V. Here, it is recommended to always determine these before choosing the root rounding radii ρ.sub.f, so that the radii chosen by the user are ensured to be smaller than these and thus technically realizable in a feasible way. [Wild 20]

TABLE-US-00002 TABLE 2 [Wild 20] Symbol Toothing data and calculation equations d m .Math. z.sub.1 x.sub.I1 .Math. m [00002]$\frac{d_B-d-h_w\left(R_{\mathrm{hw}}=0\right)+2.Math.A_{\mathrm{dB}}}{2}$ x.sub.I2 .Math. m −x.sub.I1 .Math. m x.sub.M1 .Math. m A.sub.hw .Math. R.sub.hw .Math. h.sub.w(R.sub.hw = 0) x.sub.M2 .Math. m −x.sub.M1 .Math. m x.sub.1 .Math. m (x.sub.I1 + x.sub.M1) .Math. m x.sub.2 .Math. m −x.sub.1 .Math. m resp. (x.sub.I2 − x.sub.M2) .Math. m y.sub.1 .Math. m R.sub.hw .Math. h.sub.w(R.sub.hw = 0) .Math. (1 − A.sub.hw) y.sub.2 .Math. m −y.sub.1 .Math. m p m .Math. π s.sub.1 [00003]$\frac{p}{2}+2.Math.x_1.Math.m.Math.\tan \alpha$ α.sub.s1 [00004]$\frac{s_1}{r}$ α.sub.Er [00005]$.Math.{\tan }^{-1}\left(\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }\right)-\frac{\sqrt{1-{\cos }^2\alpha }}{\cos \alpha }.Math.$ α.sub.E [00006]$\frac{{\alpha }_{s1}}{2}+{\alpha }_{\mathrm{Er}}$ α.sub.S [00007]$\frac{2\pi }{z_1}$

TABLE-US-00003 TABLE 3 [Wild 20] Symbol Toothing data and calculation equations d.sub.b d .Math. cos α d.sub.a2 −d + 2 .Math. x.sub.2 .Math. m + h.sub.w(R.sub.hw = 0) + 2 .Math. y.sub.2 .Math. m u.sub.E1 [00008]$\sqrt{{\left(\frac{-r_{a2}-c_{F1}}{r_b}\right)}^2-1}$ α.sub.KM1.sup.V [00009]$\left(-1\right).Math.\left({\alpha }_E-\frac{{\alpha }_S}{2}\right)$ ρ.sub.f1.sup.V [00010]$\frac{r_b\left(\begin{array}{c}\tan \left({\alpha }_{\mathrm{KM}1}^V\right)\left(\cos u_{E1}+u_{E1}\sin u_{E1}\right)+\\ +\sin u_{E1}-u_{E1}\cos u_{E1}\end{array}\right)}{\cos u_{E1}-\tan \left({\alpha }_{\mathrm{KM}1}^V\right)\sin u_{E1}}$ d.sub.a1 d.sub.B + 2 .Math. A.sub.dB |{right arrow over (K)}.sub.M1| [00011]$\sqrt{\begin{array}{c}{\left(r_b\left(\cos u_{E1}+u_{E1}\sin u_{E1}\right)+{\rho }_{f1}\sin u_{E1}\right)}^2+\\ +{\left(r_b\left(-\sin u_{E1}+u_{E1}\cos u_{E1}\right)+{\rho }_{f1}\cos u_{E1}\right)}^2\end{array}}$ d.sub.f1 2 .Math. (|{right arrow over (K)}.sub.M1|− ρ.sub.f1) u.sub.E2 [00012]$\sqrt{{\left(\frac{r_{a1}+c_{F2}}{r_b}\right)}^2-1}$ α.sub.KM2.sup.V (−1) .Math. α.sub.E ρ.sub.f2.sup.V [00013]$\frac{r_b\left(\begin{array}{c}\tan \left({\alpha }_{\mathrm{KM}2}^V\right)\left(\cos u_{E2}+u_{E2}\sin u_{E2}\right)+\\ +\sin u_{E2}-u_{E2}\cos u_{E2}\end{array}\right)}{\tan \left({\alpha }_{\mathrm{KM}2}^V\right)\sin u_{E2}-\cos u_{E2}}$ d.sub.f2 (−1) .Math. 2 .Math. (|{right arrow over (K)}.sub.M2| + ρ.sub.f2) |{right arrow over (K)}.sub.M2| [00014]$\sqrt{\begin{array}{c}{\left(r_b\left(\cos u_{E2}+u_{E2}\sin u_{E2}\right)-{\rho }_{f2}\sin u_{E2}\right)}^2+\\ +{\left(r_b\left(-\sin u_{E2}+u_{E2}\cos u_{E2}\right)-{\rho }_{f2}\cos u_{E2}\right)}^2\end{array}}$

[0096] Supplementary, Geometric Parameters

[0097] In addition to the parameters listed in (Tab. 1, Tab. 2, Tab. 3), further geometric quantities with a merely descriptive character, i.e. not with an influence on the profile shape according to (Tab. 2, Tab. 3), can be specified. Their calculation is therefore optional. Without claiming to be complete, these are defined in Tab. 4. [Wild 20]

TABLE-US-00004 TABLE 4 [Wild 20] Symbol Toothing data and calculation equations c.sub.1 [00015]$\frac{-d_{f1}-d_{a2}}{2}$ c.sub.2 [00016]$\frac{-d_{a1}-d_{f2}}{2}$ d.sub.Ff2 −(d.sub.a1 + 2 .Math. c.sub.F2) d.sub.Ff1 −d.sub.a2 − 2 .Math. c.sub.F1 e.sub.2 s.sub.1 h.sub.w [00017]$h_w=\frac{d_{a1}-.Math.d_{a2}.Math.}{2}$ h.sub.1 [00018]$\frac{d_{a1}-d_{f1}}{2}$ h.sub.2 [00019]$\frac{-d_{f2}+d_{a2}}{2}$

[0098] Geometry Equivalence to the [DIN 5480]

[0099] In the inventive system for nominal geometry generation of involute splined connections, cf. (Tab. 2, Tab. 3), it is considered that geometrically equivalent connection partners to the [DIN 5480] are generatable. In this context, it is necessary to define how the input parameters listed in Tab. 1 have to be selected so that geometry equivalence between the previously named profile shapes results. The corresponding definitions are given in Table 5. [Wild 20]

TABLE-US-00005 TABLE 5 [Wild 20] Symbol Toothing data and calculation equations d.sub.B Select acc. to the [DIN 5480] A.sub.dB −0.1 .Math. m m Select acc. to the [DIN 5480] x.sub.I1 −0.05 ≤ x.sub.I1 ≤ 0.45 x.sub.I2 −x.sub.I1 z.sub.1 Select acc. to the [DIN 5480] z.sub.2 −z.sub.1 α 30°, cf. [DIN 5480] ρ.sub.f1 = ρ.sub.fP1 Select acc. to the [DIN 5480] ρ.sub.f2 = ρ.sub.fP2 Select acc. to the [DIN 5480] c.sub.F1 = c.sub.FP1 Due to the empirical character of the [DIN 5480], this value has to be adjusted until the shaft root circle diameter d.sub.f1 according to the [DIN 5480] is reached. c.sub.F2 = c.sub.FP2 Due to the empirical character of the [DIN 5480], this value has to be adjusted until the hub root circle diameter d.sub.f2 according to the [DIN 5480] is reached. h.sub.w(R.sub.hw = 0) 0.9 .Math. m R.sub.hw 0 A.sub.hw /

[0100] Geometry Compatibility to the [DIN 5480]

[0101] Although geometry equivalence between splined shaft connections according to (Tab. 2, Tab. 3) as well as according to the [DIN 5480] is possible by considering the contents listed in Tab. 5. However, with reference to [Wild 20], the aim can also be merely to generate compatibility between these profile shapes with further optimal geometric design of the connection partners. Under the aspect of shape stability, this is to be recommended. The above-mentioned requirement is ensured with consideration of the boundary conditions listed in Tab. 6. [Wild 20]

TABLE-US-00006 TABLE 6 [Wild 20] Symbol Toothing data and calculation equations d.sub.B Select acc. to the [DIN 5480] A.sub.dB −0.1 .Math. m m Select acc. to the [DIN 5480] x.sub.I1 −0.05 ≤ x.sub.I1 ≤ 0.45 x.sub.I2 −x.sub.I1 z.sub.1 Select acc. to the [DIN 5480] z.sub.2 −z.sub.1 α 30°, cf. [DIN 5480] h.sub.w(R.sub.hw = 0) 0.9 .Math. m R.sub.hw 0 A.sub.hw /

[0102] Requirement-Specific Design

[0103] With the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), unrestricted access to the parameters controlling this profile shape, cf. Tab. 1, is possible within the technically given limits. Thus, the connections originating from it can be fully aligned to the requirements placed on them. In the design examples, the given possibilities for adapting the nominal geometry of involute splined shaft connections according to (Tab. 2, Tab. 3) are visualized. It should be noted that with the available knowledge base, the requirement-specific parameter influences in wide areas can at least be estimated. For the aspect of shape stability, especially [Wild 20] should be referred to. [Wild 20]

[0104] Note on Standardization

[0105] With regard to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), it should be noted that in the context of a potentially normative transition, the definition of preferred values for the input parameters listed in Tab. 1 is useful, for example, to ensure the interchangeability resp. reproducibility of connection partners. However, the making of corresponding conventions or the submission of corresponding proposals is not the subject of the present application, but is a further activity. [Wild 20]

[0106] Design Examples

[0107] FIG. 7 to FIG. 14 show examples of the possibilities provided by the inventive system for generation of nominal geometry of involute based splined shaft connections, cf. (Tab. 2, Tab. 3), for the requirement-specific design of such connections. [Wild 20]

TABLE-US-00007 Symbols, designations and units Symbol Designations Unit A.sub.dB Reference diameter distance mm A.sub.hw Distribution key of the reduction of / the effective contact height c Tip clearance mm c.sub.F Form excess mm c.sub.Fmin Minimum form excess mm c.sub.FP Form excess of the reference mm c.sub.p Tip clearance of the reference mm d Pitch circle diameter mm d.sub.a Tip circle diameter mm d.sub.B Reference diameter mm d.sub.b Base circle diameter mm d.sub.E Coordinate of the involute in radial direction mm d.sub.Ff Root form circle diameter mm d.sub.f Root circle diameter mm e.sub.2 Nominal hub tooth gap mm h.sub.aP Tip height of the reference profile mm h.sub.aP0 Tip height of the tool reference profile mm h.sub.fP Root height of the reference profile mm h.sub.p Tooth height of the reference profile mm h.sub.w Effective contact height mm K Circle used to generate the root rounding radius / {right arrow over (K)}.sub.M Root circle centre point vector mm m Module mm p Pitch mm R.sub.hw Reduction factor of the effective contact height / s.sub.1 Nominal tooth thickness mm u.sub.E Control variable of the involute / x Profile shift factor / x.sub.I Initiation profile shift factor / x.sub.M Modification profile shift factor / y Gen. profile modification factor / z Gen. number of teeth / α Flank angle Rad α.sub.E Involute reallocation Angle Rad α.sub.Er Angle between x-axis and involute on the pitch circle Rad α.sub.KM Coordinate of the root circle centre Rad point in rotational direction α.sub.KM.sup.V Coordinate of the root circle centre in Rad rotational direction with full rounding α.sub.s Sector angle Rad α.sub.s1 Shaft tooth thickness angle on the pitch circle Rad ρ.sub.f Root rounding radius mm ρ.sub.f.sup.V Root rounding radius at full rounding mm ρ.sub.fP Root rounding radius of the reference profile mm var. Varied / voll. Fully rounded / 1 Shaft / 2 Hub / 3 Profile reference line /

LITERATURE

[0108] [DIN 323] Norm DIN 323, 1974-08-00: Normzahlen und Normreihen

[0109] [DIN 3960] Norm DIN 3960, 1987-03-00: Begriffe und Bestimmungsgrößen für Stirnräder (Zylinderräder) und Stirnradpaare (Zylinderradpaare) mit Evolventenverzahnung (Nachfolgedokument: DIN ISO 21771, 2014-08-00

[0110] [DIN 5480] Norm DIN 5480, 2006-03-00: Passverzahnungen mit Evolventenflanken und Bezugsdurchmesser

[0111] [ISO 4156] Norm ISO 4156, 2005-10-00: Passverzahnungen mit Evolventenflanken. Metrische Module, Flankenzentriert

[0112] [DFG ZI 1161] Ziaei, M., Selzer, M.: Entwicklung kontinuierlicher unrunder Innen- und Außenkonturen für formschlüssige Welle-Nabe-Verbindungen und Ermittlung analytischer Lösungsansatze, DFG-Zwischenbericht DFG ZI 1161

[0113] [FVA 742 I] Wild, J.; Mörz, F.; Selzer, M.: Optimierung des Zahnwellenprofils primär zur Drehmomentübertragung unter Berücksichtigung wirtschaftlicher Fertigungsmöglichkeiten, FVA-Forschungsvorhaben Nr. 742 I, Frankfurt/Main, 2018 (FVA-Heft 1316)

[0114] [Maiw 08] Waiwald, A.: Numerische Untersuchungen von unrunden Profilkonturen für Welle-Nabe-Verbindungen, Diplomarbeit, Westsächsische Hochschule Zwickau, 2008

[0115] [Wild 20] Wild, J.: Optimierung der Tragfähigkeit von Zahnwellenverbindungen, Technische Universitat Clausthal, Dissertation, (noch nicht veröffentlicht)

TABLE-US-00008 Figure captions 1 Reference profile according to the [DIN 5480] [Wild 20] 2 Derivation of the profile shift [Wild 20] 3 Geometric relationships of involute splined shaft connections according to the [DIN 5480] in the shaft root area on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m = 0.12; c.sub.F2/m = 0.02; R.sub.hw = 0; A.sub.hw = /) [Wild 20] 4 Geometric differences of the profile shaft connections compared in the research project [FVA 742 I] (same scale) [Wild 20] 5 Basic systematics of the inventive system for profile generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m = 0.12; c.sub.F2/m = 0.02; R.sub.hw = 0; A.sub.hw = /) [Wild 20] 6 Adjusted reference profile of the [DIN 5480] [Wild 20] 7 Requirement-specific design of toothed shaft connections according to (Tab. 2, Tab. 3) by selecting the reference diameter d.sub.B as well as the reference diameter distance A.sub.dB [Wild 20] 8 Requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the module m resp. the shaft number of teeth z.sub.1 on the example of the connection (Tab. 2, Tab. 3) − 45 × 0.6 × 74 (α = 30°; ρ.sub.f1/m = 0.48; c.sub.F1/m = 0.12; R.sub.hw = 0; A.sub.hw = /) left as well as (Tab. 2, Tab. 3) − 45 × 5 × 7 (α = 30°; ρ.sub.f1/m = 0.48; c.sub.F1/m = 0.12; R.sub.hw = 0; A.sub.hw = /) right with shaft focusing (same scale) [Wild 20] 9 Requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the flank angle α on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 20°; ρ.sub.f1/m = 0.56; c.sub.F1/m = 0.12; R.sub.hw = 0; A.sub.hw = /) left as well as (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 45°; ρ.sub.f1/m = 0.24; c.sub.F1/m = 0.12; R.sub.hw = 0; A.sub.hw = /) right with shaft focusing (same scale) [Wild 20] 10 Requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the root rounding radii ρ.sub.f on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.16; c.sub.F1/m = 0.12; R.sub.hw = 0; A.sub.hw = /) left as well as (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = voll.; c.sub.F1/m = 0.12; R.sub.hw = 0; A.sub.hw = /) right with shaft focusing (same scale) [Wild 20] 11 Requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the form excesses c.sub.F on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m = 0.12; c.sub.F2/m = 0.02; R.sub.hw = 0; A.sub.hw = /) left as well as (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m = 0.02; c.sub.F2/m = 0.02; R.sub.hw = 0; A.sub.hw = /) right with shaft focusing (same scale) [Wild 20] 12 Requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the effective contact height without profile modification h.sub.w(R.sub.hw = 0) on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m = 0.12; c.sub.F2/m = 0.02; R.sub.hw = 0; A.sub.hw = /) with shaft focusing [Wild 20] 13 Not profile modified toothed shaft connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m = 0.12; c.sub.F2/m = 0.02; R.sub.hw = 0; A.sub.hw = /) (same scale as FIG. 14) [Wild 20] 14 Requirement-specific design of toothed shaft connections according to the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), by the selection of the profile modification controlling parameters R.sub.hw as well as A.sub.hw on the example of the connection (Tab. 2, Tab. 3) − 45 × 1.5 × 28 (α = 30°; ρ.sub.f1/m = 0.48; ρ.sub.f2/m = 0.16; c.sub.F1/m − 0.12; c.sub.F2/m = 0.02; R.sub.hw = var.; A.sub.hw = var.) (same scale as FIG. 13) [Wild 20]

TABLE-US-00009 TABLES 1 Input parameters of the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3) [Wild 20] 2 Inventive system for nominal geometry generation of involute splined shaft connections [Wild 20] 3 Inventive system for nominal geometry generation of involute splined shaft connections (Continuation from Tab. 2) [Wild 20] 4 Further geometrical parameters not influencing the profile shapes originating from the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3) [Wild 20] 5 Definition of the input parameters listed in Tab. 1 of the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), for geometry equivalence with connections according to the [DIN 5480] [Wild 20] 6 Definition of the input parameters listed in Tab. 1 of the inventive system for nominal geometry generation of involute splined shaft connections, cf. (Tab. 2, Tab. 3), for geometry compatibility with connections according to the [DIN 5480] [Wild 20]