Involute Spline Profile Generation for Closed-Form Geometry Control
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Solution Overview
Problem
The existing system for generating reference profiles of involute splined shaft connections, as defined by DIN 5480, does not provide a mathematically closed formulation of geometric relationships, leading to geometrical anomalies and limitations in parameter variation, which restricts the ability to achieve optimal shape stability and load capacity.
Innovation Solution
A new systematic approach for profile generation that allows for mathematically closed formulation of profile shapes, enabling parametric access to all geometry-determining parameters and requirement-specific geometric alignment, including the use of the reference diameter distance AdB to freely select the distance between the reference diameter and the shaft tip circle diameter, and the application of profile modification factors to adjust the shaft and hub geometries.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the existing system for generating reference profiles according to DIN 5480 is used, then the shaft connections can be produced with standardized dimensions, but geometrical anomalies occur and parameter variation is restricted
Solution Approach 1:
The patent introduces a new parameter system that allows independent variation of profile parameters (such as tip radius, root radius, flank angles) while maintaining mathematical consistency. This enables continuous parameter optimization without the discrete constraints of standardized systems, resolving the contradiction between precision and adaptability.
Solution Approach 2:
The patent transitions from a static, fixed reference profile system to a dynamic, continuously adjustable profile generation system. The new approach allows real-time modification of profile parameters based on specific application requirements while maintaining geometric integrity through mathematical relationships.
2Ease of manufacture
If the reference profile system with fixed geometric relationships is used, then production is simplified, but shape stability and load capacity are limited
Solution Approach 1:
The patent enables optimization of strength-critical parameters such as tooth root radius, tip radius, and contact angles while maintaining manufacturing simplicity through automated calculation based on the new mathematical model. This allows higher load capacity without significantly complicating the production process.
Solution Approach 2:
The patent performs preliminary optimization of profile geometry through mathematical formulation before manufacturing, identifying optimal parameter combinations that maximize load capacity. This preliminary design phase eliminates the need for iterative trial-and-error manufacturing adjustments.
3Ease of operation
If standardized reference diameters are used, then mounting of rolling bearings is facilitated, but the distance between reference diameter and shaft tip circle cannot be freely selected
Solution Approach 1:
The patent introduces a dynamic relationship between reference diameter and shaft tip circle diameter through a controllable offset parameter. This allows the distance to be adjusted continuously while maintaining compatibility with standardized bearing mounting requirements, resolving the contradiction between ease of operation and design freedom.
4Ease of manufacture
If empirical elements are used in profile generation, then manufacturing processes are simplified, but mathematical closed formulation is not achieved
Solution Approach 1:
The patent replaces empirical, experience-based profile generation methods with a rigorous mathematical model that provides closed-form solutions. This substitution eliminates the need for iterative empirical adjustments while maintaining manufacturing simplicity through algorithmic calculation of all profile parameters.
Data Source
AI summary
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 dB′, distance-based generation of the shaft top circle using the reference diameter distance AdB, 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 hw, 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 CFP1 or the shaft form oversize CFP1 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.