Machine Tool Rough Trajectory Smoothing for Redundant Drives
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing methods for determining a rough trajectory for machine tools with redundant drive devices are often computationally intensive and may not align with the physical capabilities of the machine, leading to extended machining times and inefficient operation.
Innovation Solution
A method that calculates a rough trajectory by determining rough trajectory nodal points with minimal gradient change, ensuring the distance between these points and the original contour nodal points satisfies a specified condition, allowing for high-speed operation of the low-dynamic drive with reduced acceleration and jerkiness, and is optimized using a quadratic program to minimize squared gradient differences.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing methods for determining rough trajectory are used, then the trajectory can be calculated, but the computational effort is high and machining time is extended
Solution Approach 1:
The trajectory calculation is segmented into two independent parts: rough trajectory determination using only contour nodal points and distances, and fine trajectory determination using full contour geometry. This segmentation allows the rough trajectory to be calculated quickly without extensive computational resources, while the fine trajectory refines the path later. The method divides the contour into segments between nodal points and processes each segment independently to determine rough trajectory nodal points.
Solution Approach 2:
The rough trajectory is calculated in advance as a preliminary path before fine trajectory optimization. By pre-determining the rough trajectory using simplified calculations based on nodal points and distance constraints, the system prepares a baseline path that satisfies basic requirements, allowing subsequent fine trajectory calculations to focus only on optimization rather than complete path determination.
2Speed
If the low-dynamic drive operates at high speed, then productivity increases, but acceleration forces become excessive
Solution Approach 1:
The system dynamically adjusts the trajectory characteristics by separating rough and fine trajectory components. The rough trajectory is designed with controlled gradient changes to limit acceleration forces on the low-dynamic drive, while the fine trajectory adds precision without significantly increasing acceleration demands. This dynamic separation allows the low-dynamic drive to operate efficiently within its acceleration capabilities.
Solution Approach 2:
The method changes the parameter of gradient difference between adjacent rough trajectory portion functions to minimize acceleration forces. By explicitly minimizing the difference in gradients between consecutive segments, the trajectory ensures smooth transitions that reduce acceleration demands on the low-dynamic drive, enabling higher overall speeds without exceeding force limits.
3Manufacturing precision
If the rough trajectory closely follows the contour, then machining precision improves, but the gradient changes increase causing more acceleration
Solution Approach 1:
The rough trajectory satisfies distance constraints to the contour at nodal points without requiring close following throughout the entire path. By applying distance constraints only at discrete nodal points rather than continuously, the method achieves sufficient precision while allowing larger gradient transitions between nodal points, thereby reducing acceleration forces. The fine trajectory then provides additional precision where needed.
Data Source
AI summary
The invention relates to a method for ascertaining a rough trajectory from a specified contour for controlling a machine tool which has at least two mutually redundant drive devices for carrying out superimposed movements, wherein the contour is determined by a contour function (Pj, pj) which is defined in portions by contour nodal points P0−Pn+1 and respective contour portion functions p0−pn, wherein a respective contour portion function pj connects two adjacent contour nodal points Pj, Pj+1, wherein the rough trajectory is determined by a rough trajectory function (Qj, qj) which is defined in portions by rough trajectory nodal points Q0−Qn+1 and respective rough trajectory portion functions q0−qn, wherein a respective rough trajectory portion function q connects two adjacent rough trajectory nodal points Qj, Qj+1, wherein, for each contour nodal point Pj, a respective assigned rough trajectory nodal point Qj is ascertained in such a manner that a difference in the gradients of the two adjacent rough trajectory portion functions qj−1, qj which contain this rough trajectory nodal point Qj is minimal and that the distance of the contour nodal point Pj from the rough trajectory nodal point Qj satisfies a specified distance condition.