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A local tool path smoothing method with optimized curvature
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A local and smoothing technology, which is applied in the field of local tool path smoothing and G3 continuous optimization of curvature, can solve the problems of curvature optimization, large peak value of acceleration and jerk, and inability to guarantee jerk, so as to increase stability and reduce Effect of Curvature Peaks
Active Publication Date: 2022-03-11
NORTHWESTERN POLYTECHNICAL UNIV
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Although the G2 continuity and precision control of the smooth trajectory can be achieved, the jerk continuity during the machining process cannot be guaranteed, and the curvature optimization has not been performed.
[0004] The typical characteristics of the above literature are: the smoothed tool trajectory of the literature method meets the accuracy requirements and certain continuity requirements, but the curvature is not optimized, and the optimal smooth trajectory cannot be achieved, which will cause the peak acceleration and jerk during processing. Larger, affecting processing efficiency
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Embodiment 1
[0065] Example 1 is used to verify the advantage of the present invention in terms of curvature of the smoothed track. Example 2 is used to verify the advantages of the present invention during processing.
[0066] Example 1:
[0067] (1) The selected angles in the experiment are θ k =15°, θ k =30°, θ k =45°, θ k =60° corner, take l=10mm, the coordinates of the points forming the corner are [p k-1 ;p k ;p k+1 ]=[00; l 0; l+lcos(π-θ)lsin(π-θ)], the selected tolerance value ε w = 0.1 mm.
[0068] (2) Pass the corner angle value θ according to step (8) k Determine the control vertex distribution proportional coefficients μ, ν.
[0069] (3) Calculate the control vertex P k,2 and P k,3 the distance d between k,3
[0070]
[0071] (4) Calculate d k,1 and d k,2 Value of: d k,1 =μd k,3 、d k,1 =μd k,3
[0072] (5) Calculate the control vertex P of the trajectory after smoothing k,i (i=0,1,2,...,6),
[0073] P k,3 =p k
[0074] P k,0 =p k -(d k,1 +d k,2 ...
Embodiment 2
[0087] (1) The verification test is selected from the point [p k-1 ;p k ;p k+1 ]=[00; 100; 10+10cos(π-30°)10sin(π-30°)] to form a trajectory for smoothing, where the unit length of the coordinate axis is 1mm. Selected tolerance value ε w =0.1mm, the machining feed rate is 3mm / s.
[0089] (3) Pass the corner angle value θ according to step (8) k Determine the control vertex distribution proportional coefficients μ, ν.
[0090] (4) Calculate the distance d k,3
[0091] (5) calculate d k,1 and d k,2 Value of: d k,1 =μd k,3 、d k,1 =μd k,3 .
[0092] (6) Calculate the control vertex P of the trajectory after smoothing k,i (i=0,1,2,...,6)
[0093] P k,3 =p k
[0094] P k,0 =p k -(d k,1 +d k,2 +d k,3 )m k
[0095] P k,1 =p k -(d k,2 +d k,3 )m k
[0096] P k,2 =p k -d k,3 m k
[0097] P k,4 =p k -d k,3 no k
[0098] P k,5 =p k -(d k,2 +d k,3 )n k
[0099] P k,6 =p k -(d k,1 +d k,2 +d k...
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Abstract
The invention relates to a local tool pathsmoothing method for optimizing curvature. The method first establishes a five-degree quasi-uniform B-spline with 7 control vertices and symmetrically distributed control vertices to realize G3 continuity at the junction of straight lines and curves. By minimizing the strain energy and jerk energy of the curve and optimizing the curvature of the curve, a smooth trajectory with optimal curvature can be obtained. By establishing the fitting function relationship between the corner angle value and the distribution ratio of the control vertices, the analytical solution of the local corner smooth trajectory is realized, and the analytical solution of the local corner smooth trajectory is realized, the curvature peak value is greatly reduced, and the stability in the processing process is increased. sex.
Description
technical field [0001] The invention relates to a method for smoothing local tool paths, in particular to a method for smoothing local tool paths with G3 continuity and optimized curvature. Background technique [0002] Document 1 "S.Tulsyan, Y.Altintas, Local toolpath smoothing for five-axismachine tools, International Journal of Machine Tools and Manufacture, 2015, 96:15–26." discloses a G3 continuous local toolpath smoothing method , this method achieves G3 continuity by inserting five quasi-uniform B-splines between the corners formed by two adjacent straight line segments when smoothing the trajectory of the straight line segment formed by the tool tip position points, and can achieve the accuracy of the smoothed trajectory control. However, when solving the control vertex distribution satisfying G3 continuity, only a group of feasible solutions that are easy to calculate are selected, and the curvature of the curve is not optimized. [0003] Document 2 "X.Beudaert, S...
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