US 11,994,838 B1
Five-axis linkage synchronous tool path interpolation method and system
Jian Gao, Guangzhou (CN); Guixin Zhang, Guangzhou (CN); Yuheng Luo, Guangzhou (CN); Lanyu Zhang, Guangzhou (CN); Haixiang Deng, Guangzhou (CN); Yun Chen, Guangzhou (CN); and Xin Chen, Guangzhou (CN)
Assigned to GUANGDONG UNIVERSITY OF TECHNOLOGY, Guangzhou (CN)
Filed by GUANGDONG UNIVERSITY OF TECHNOLOGY, Guangzhou (CN)
Filed on Feb. 22, 2024, as Appl. No. 18/583,904.
Application 18/583,904 is a continuation of application No. PCT/CN2023/093939, filed on May 12, 2023.
Claims priority of application No. 202211629012.1 (CN), filed on Dec. 14, 2022.
Int. Cl. G05B 19/4103 (2006.01)
CPC G05B 19/4103 (2013.01) [G05B 2219/34169 (2013.01)] 8 Claims
OG exemplary drawing
 
1. A five-axis linkage synchronous tool path interpolation method, characterized in that it includes:
according to the tool path information, the tool tip path curve and the tool axis path curve are respectively fitted based on the quadratic NURBS curve, and the node vectors of the tool tip path curve and the tool axis path curve are obtained respectively;
according to the relationship between the constraints of the CNC machine tool and the feed speed, the feed speed curve is planned; the constraints of the CNC machine tool include sampling point speed constraints, centripetal acceleration constraints, centripetal jerk constraints, chord error constraints and contour error constraints;
according to the feed speed curve, the tool tip path curve is interpolated from the i=0th interpolation point, and the i+1th interpolation point of the tool tip path curve is calculated according to the second-order Taylor expansion formula;
the tool tip node vector interval is determined where the i+1th interpolation point of the tool tip path curve falls;
the first-order derivative vector of the i+1th interpolation point of the tool tip path curve and the first-order derivative vector of the interpolation point corresponding to the left and right endpoints of the tool tip node vector interval are calculated;
the three first-order derivative vectors are projected onto the X0Y plane and the starting point is moved to the same point; the first angle between the first-order derivative vector at the i+1th interpolated point of the tip path curve and the first order derivative vector at the left end of the vector interval of the tool tip node, and the second angle between the first-order derivative vector at the left end of the vector interval of the tool tip node and the first-order derivative vector at the right end of the vector interval of the tool tip node are calculated respectively in the X0Y plane; the first angle is divided by the second angle to get the angle progress;
the first angle between the first-order derivative vector at the i+1th interpolated point of the tip path curve and the first order derivative vector at the left end of the vector interval of the tool tip node, and the second angle between the first-order derivative vector at the left end of the vector interval of the tool tip node and the first-order derivative vector at the right end of the vector interval of the tool tip node are calculated respectively in the X0Y plane;
the tool axis node vector interval corresponding to the tool tip node vector interval on the tool axis path curve and the first-order derivative vector of the interpolation points corresponding to the left and right endpoints of the tool tip node vector interval are calculated;
the first-order derivative vector of the i+1th interpolation point of the tool axis path curve is determined according to the angular progress;
the intersection point of the first-order derivative vector of the i+1th interpolation point of the tool axis path curve and the first-order derivative curve of the tool axis path curve is calculated; the proportional coefficient is calculated according to the preset formula, which is:

OG Complex Work Unit Math
among them, η2 is the proportional coefficient, Vk is the left end point of the tool tip node vector interval, Vk+1 is the right end point of the tool tip node vector interval, Q is the intersection point of the first-order derivative vector of the i+1th interpolation point of the tool axis path curve and the first-order derivative curve of the tool axis path curve, C′(Vk) is the first-order derivative vector of the interpolation point corresponding to the left end point of the vector interval of the tool tip node, and C′(Vk+1) is the first-order derivative vector of the interpolation point corresponding to the right end point of the vector interval of the tool tip node;
the i+1th interpolation point of the tool axis path curve linked to the i+1th interpolation point of the tool tip path curve is calculated based on the proportional coefficient, and the tool axis path curve is interpolated;
the calculation formula for calculating the i+1th interpolation point of the tool axis path curve linked to the i+1th interpolation point of the tool tip path curve based on the proportional coefficient is:
vi+1=Vk+η2(Vk+1−Vk)
among them, vi+1 is the i+1th interpolation point of the tool axis path curve.