Abstract
In precision machining of free-form surfaces at high speed, it is very important to ensure part accuracy and machining properties. To achieve this, this paper develops a guide spline-based feedrate scheduling method for machining along curvilinear paths with simultaneous constraints of chord errors and ac/deceleration. Based on two metrics about feedrate scheduling from the view of geometric and kinematic properties, the nonlinear relationships between the arc-length parameter and path parameter are subsequently established with a parameter correction spline. Then a guide spline associated with the modified curvature radius of paths is constructed to the schedule feedrate. It is shown that determining the largest safe feedrate with constant chord error can be reduced to the issue of changing the feedrate proportionally with the square root of path curvature radii and ensuring the safe feed acceleration can be converted into the issue of presetting the largest slope of guide spline. The simulation results prove that the proposed feedrate scheme has potential applications in the field of finish machining.
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Abbreviations
- δ :
-
Maximum allowable cusp height
- ρ :
-
Curvature radius
- a :
-
Dc/acceleration
- u :
-
Toolpath parameter
- \( s^{ \wedge } \) :
-
Near arc-length parameter
- r(u) :
-
Parametric expression of a curvilinear path
- V :
-
Control point vector of B-spline spline
- t :
-
Time variable
- q i :
-
Control point of parametric correction spline
- κ:
-
Curvature at some path point
- ν:
-
Feedrate of the moving cutter
- T s :
-
Sampling time
- s :
-
Arc-length parameter
- ς :
-
Slope at some point of a given path
- μ i :
-
Knot value of the given knot vector
- N i,k :
-
Basis function of B-spline curve
- d i :
-
Control point of guide spline
- S :
-
Vector of sampling data of arc length
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Acknowledgements
This work is supported by NSFC under grant number (50405044) and national fundamental research program under grant number (2005CB724100). These supports are greatly appreciated. The authors thank Prof. Liu Jian for his kind helps. Also, the authors would like to thank the reviewers’ valuable comments.
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Sun, Y., Jia, Z., Ren, F. et al. Adaptive feedrate scheduling for NC machining along curvilinear paths with improved kinematic and geometric properties. Int J Adv Manuf Technol 36, 60–68 (2008). https://doi.org/10.1007/s00170-006-0817-7
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DOI: https://doi.org/10.1007/s00170-006-0817-7