Five-Axis Tool Path Interpolation for Accurate Tool Axis Synchronization
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing five-axis NURBS curve interpolation methods often result in deviations between the actual tool direction and the desired direction, leading to poor contour accuracy in processed parts due to their dependence on shape consistency between tool tip and tool axis curves.
Innovation Solution
A five-axis linkage synchronous tool path interpolation method that fits tool tip and tool axis paths using quadratic NURBS curves, calculates interpolation points based on second-order Taylor expansion, and determines derivative vectors to establish a proportional coefficient for accurate tool axis path curve interpolation, independent of shape consistency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If the same parameter method is used to link tool tip curve and tool axis curve (vi+1=ui+1), then the calculation is simple, but the actual tool direction deviates from the desired direction
Solution Approach 1:
The patent changes the parameter relationship from direct equality (vi+1=ui+1) to a proportional relationship based on arc length parameters. The tool axis parameter vi+1 is calculated as vi + η·(ui+1-ui), where η is a proportional coefficient that adjusts the parameter increment based on the actual geometric relationship between tool tip and tool axis curves, thereby maintaining directional accuracy while preserving calculation simplicity.
Solution Approach 2:
The patent introduces an intermediary element - the proportional coefficient η - that mediates the relationship between tool tip parameter ui and tool axis parameter vi. This coefficient acts as a scaling factor that adjusts the parameter progression of the tool axis curve to match the geometric progression of the tool tip curve, eliminating direct parameter coupling while maintaining synchronization.
2Manufacturing precision
If the interval synchronization method is used to set the relationship between vi+1 and ui+1, then the deviation is reduced, but the method is extremely dependent on the shape consistency of the two curves
Solution Approach 1:
The patent transforms the rigid interval synchronization approach into a flexible proportional synchronization approach. Instead of fixing the parameter relationship based on predetermined intervals that assume shape consistency, the method dynamically adjusts the parameter increment using the proportional coefficient η, allowing the tool axis parameter vi+1 to scale appropriately regardless of the specific geometric shapes of the curves.
Solution Approach 2:
The patent introduces dynamics into the parameter synchronization by making the relationship between vi+1 and ui+1 adaptive rather than static. The proportional coefficient η allows the parameter progression to dynamically adjust to different curve shapes and geometries, enabling the method to handle various tool tip and tool axis curve configurations without requiring shape consistency.
3Manufacturing precision
If parametric interpolation is used instead of linear interpolation, then accuracy and efficiency are improved, but the complexity of the interpolation calculation increases
Solution Approach 1:
The patent employs parametric interpolation using NURBS (Non-Uniform Rational B-Splines) curves to represent both the tool tip path and tool axis path. By using uniform quadratic NURBS curves with appropriate node vectors, the method achieves high interpolation accuracy while controlling computational complexity through the use of standard, well-established mathematical formulations.
Solution Approach 2:
The patent uses NURBS curves as a universal mathematical representation that can accurately model complex tool paths and tool axis movements simultaneously. The same NURBS framework and basis functions are applied to both the tool tip curve C(u) and tool axis curve C(v), providing a unified, multi-functional approach that handles both position and orientation interpolation with consistent accuracy and computational efficiency.
Data Source
AI summary
A five-axis linkage synchronous tool path interpolation method and system, which utilizes the strict proportional coefficient relationship between points, control points and parameters on the first-order derivative curve of the spline curve, more accurate tool axis path curve interpolation points from the parameters of the tool tip path curve are calculated. There is no need to calculate the tool axis path curve interpolation points according to interval synchronization. It is not affected by the shape consistency of the tool tip path curve and the tool axis path curve.