Five-axis linkage synchronous tool path interpolation method and system

A five-axis linkage synchronous tool path interpolation system, characterized in that it includes:

• a curve fitting module is used to fit the tool tip path curve and the tool axis path curve based on the quadratic NURBS curve according to the tool path information respectively, and the node vectors of the tool tip path curve and the tool axis path curve are obtained respectively;
• a speed planning module is used to plan the feed speed curve based on the relationship between the constraints of the CNC machine tool and the feed speed;
• 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;
• a tool tip curve interpolation point calculation module is used to interpolate the tool tip path curve from the i=0th interpolation point based on the feed speed curve, and calculate the i+1th interpolation point of the tool tip path curve based on the second-order Taylor expansion formula;
• a tool tip node vector interval judgment module is used to judge the tool tip node vector interval where the i+1th interpolation point of the tool tip path curve falls;
• a first-order derivative vector calculation module of the tool tip interpolation point is used to calculate 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 vector interval of the tool tip node;
• an angular progress calculation module is used to project three first-order derivative vectors onto the X0Y plane, and move the starting point to the same point, 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;
• a first-order derivative vector calculation module of the first tool axis interpolation point is used to calculate the vector interval of the tool axis node corresponding to the vector interval of the tool tip node on the tool axis path curve and the first-order derivatives vector of the interpolation points corresponding to the left and right endpoints of the vector interval of the tool tip node;
• a first-order derivative vector calculation module of the second tool axis interpolation point is used to determine the first-order derivative vector of the i+1th interpolation point of the tool axis path curve based on the angular progress;
• a proportional coefficient calculation module is used to calculate 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;
• the proportional coefficient is calculated according to the preset formula, which is:
• η
• 2
• =
• ❘
• "\[LeftBracketingBar]"
• QC
• ′
• (
• V
• k
• )
• ❘
• "\[RightBracketingBar]"
• ❘
• "\[LeftBracketingBar]"
• C
• ′
• (
• V
• k
• )
• ⁢
• C
• ′
• (
• V
• k
• +
• 1
• )
• ❘
• "\[RightBracketingBar]"
• 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;
• a tool axis curve interpolation point calculation module is used to calculate 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, 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.