Iterative Gear Tooth Deformation Calculation for Static Transmission Error
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Solution Overview
Problem
Current methods for determining static transmission error (STE) in gearboxes are either overly approximate or computationally expensive, particularly when dealing with non-standard tooth profiles, leading to inefficient design phases and potential wear, noise, and vibrations in critical applications.
Innovation Solution
An iterative method that calculates the deformation of meshing teeth by identifying the changing point of contact under load, using angular constraints and rotations to simulate real engaging conditions, allowing for accurate computation of STE without the high computational costs associated with finite element analysis.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If finite element analysis (FEM) is used to calculate STE, then measurement precision is improved, but productivity deteriorates due to extremely high computational cost and time consumption
Solution Approach 1:
The patent extracts only the essential elements needed for STE calculation - specifically the deformation at the contact point between teeth - rather than performing a complete FEM analysis of the entire gear structure. This selective extraction maintains accuracy for the critical measurement while dramatically reducing computational burden by avoiding analysis of non-essential regions.
Solution Approach 2:
The calculation process is segmented into distinct steps: first calculating tooth deformation using simplified models, then determining the contact point position based on that deformation, and finally computing STE. This segmentation allows each step to use the most appropriate calculation method for that specific task, avoiding the overhead of full FEM while maintaining necessary precision.
2Productivity
If simplified formulas are used to compute STE, then productivity is improved through rapid computation, but measurement precision deteriorates due to extreme approximation
Solution Approach 1:
The patent applies partial action by computing deformation only at the specific contact point region rather than throughout the entire tooth structure. This localized approach provides sufficient precision for STE calculation without the excessive computational effort of analyzing the complete gear geometry, achieving a balance between speed and accuracy.
Solution Approach 2:
The method changes the calculation parameters from full geometric models to simplified deformation parameters at the contact point. By focusing on the critical parameter (contact point displacement) rather than complete geometric fidelity, the calculation achieves adequate precision for STE while dramatically improving computation speed.
3Measurement precision
If iterative cycles are applied to establish load split, then measurement precision is improved, but device complexity increases due to additional computational iterations
Solution Approach 1:
The patent performs preliminary calculation of tooth deformation before determining the contact point position and load distribution. This preliminary action establishes a foundation that simplifies subsequent iterative steps, as the deformation state is already known and can be used directly in contact point calculations rather than requiring simultaneous solution of all variables.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables a reasonably accurate and faster calculation of STE, allowing for adjustments to tooth profiles to minimize errors, thereby reducing maintenance needs and operational issues in aerospace and automotive applications.
Implementation Method 1
the mathematical model for the computation of the elastic deformations of the meshing teeth under load
Data Source
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AI summary
A method for determining the deformation of loaded teeth (1, 2) of a gear (A, B) has been realized after checking that the point of contact (E), in which the force transmitted under load is concentrated, moves and distances itself from the contact line (L) due to the deformation of teeth. In particular, for each angular position of the meshing wheels, an iterative process identifies the contact point as a result of the deformation since at each new position of the load, the relative deformation must be recalculated up to convergence because it depends on the position of the load. The method allows in particular the determination of the static transmission error (STE), of modified tooth profiles to minimize the STE and the realization of the relative toothed wheels.