Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds

Timar, Sebastian; Farouki, Rida T.

doi:10.1016/j.rcim.2006.07.002

Cited by 37 publications

(11 citation statements)

References 15 publications

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“…Using the idea in refs. [7,10], we can show that the velocity obtained with our method is globally time-optimal in the case of single period turning.…”

Section: The Algorithm Of Look-ahead Schemementioning

confidence: 75%

“…In recent years, spline interpolation [4][5][6][7] has become the research hotspot in the field of CNC interpolation. In refs.…”

Section: Introductionmentioning

confidence: 99%

“…In refs. [6][7][8], the authors considered the optimal interpolation control method under the CNC machine's maximal acceleration and jerk constraints. However, for splines of degree three or higher, the calculations are too complicated.…”

Section: Introductionmentioning

confidence: 99%

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High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

Zhang

Sun

Gao

et al. 2011

Sci. China Technol. Sci.

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CNC machining plays an important role in mechanical manufacturing. A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine. For the consecutive micro-line segments interpolation, the velocities at the junction of two segments are the bottlenecks for the machining efficiency. This paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode, which utilizes the maximal acceleration capabilities of the NC machine while satisfying the machining precision. A new and more efficient look-ahead method and a feedrate override method are also proposed to boast the global machining speed. The proposed algorithm has been implemented on Blue Sky NC System, and experimented in real material manufacturing. Compared with several existing algorithms, the current algorithm can improve the manufacturing time ranging from 50% to 180%, depending on the machining parameters, and also results in better machining quality. In addition, the algorithm also satisfies the need of real-time interpolation.CNC, micro-line segment, multi-period turning, look-ahead scheme, real-time interpolation, feedrate override Citation:Zhang L X, Sun R Y, Gao X S, et al. High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining.

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“…Using the idea in refs. [7,10], we can show that the velocity obtained with our method is globally time-optimal in the case of single period turning.…”

Section: The Algorithm Of Look-ahead Schemementioning

confidence: 75%

“…In recent years, spline interpolation [4][5][6][7] has become the research hotspot in the field of CNC interpolation. In refs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

Zhang

Sun

Gao

et al. 2011

Sci. China Technol. Sci.

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show abstract

“…The planning results are obtained using the velocity-limited curve (VLC) and the switch points that are found by forward recursive and reverse iterations. Timar and colleagues 5,6 extended the PPM to CNC feedrate planning. The problem of computing the feedrate variations for minimising the movement time along a path described by a polynomial parametric function was solved by considering both fixed and speed-dependent axis acceleration bounds derived from the drive motor current and voltage ratings.…”

Section: Introductionmentioning

confidence: 99%

Convex optimisation method for time-optimal feedrate planning with complex constraints

Fan

Fang

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part B:

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Time-optimal feedrate planning theory has been widely applied in high-speed machining to improve machining efficiencies with a specified trajectory accuracy by fully exploiting the capabilities of high-speed computer numerical control machine tools. Reasonable and effective constraints conforming to practical situations are necessary conditions for obtaining optimal planning results. In this article, complex constraints, such as the motor torque constraint, the contour error constraint, the friction error constraint, the instruction velocity constraint and the smooth velocity constraint, are investigated in depth. Moreover, an efficient convex optimisation method is developed to address the time-optimal feedrate planning problem with these complex constraints. The experimental results from two feedrate planning tests and the computational efficiency for a test trajectory demonstrate the validity, stability and high efficiency of the proposed approach.

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“…There are three kinds of algorithms generating time-optimal interpolations of G01 codes. The first kind is by smoothing the trajectory globally, making time-optimal interpolation on the smooth trajectory, and then sampling along the smooth trajectory for each interpolation period [6], [11], [14]. The second kind is by smoothing the trajectory locally, i.e., at each vertex of the input piecewise linear trajectory, constructing a smooth curve blending the two edges of the vertex, then making time-optimal interpolation and sampling on the smooth trajectory [3], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Discrete Interpolation of G01 Codes in 2D Machining under Bounded Accelerations

Gao

Zhang

et al. 2012

Math.Comput.Sci.

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Abstract. In this paper, a new algorithm is proposed to interpolate G01 codes in 2D milling. Without resorting to smooth curve approximation, the algorithm makes full use of the acceleration bounds to change directions with optimal velocities at the cutter location points designated by the G01 codes, and then makes global lookahead and optimization to generate time-optimal interpolation of the G01 codes. The algorithm is realized and tested on NC wood carving machine, showing that when compared with the classical equalvelocity corner-turning method, the current method can reduce the machining time by 14%-115%, while maintaining better details than the classical method. Mathematics Subject Classification (2000). Primary 93C55; Secondary 49K30.

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Time-optimal traversal of curved paths by Cartesian CNC machines under both constant and speed-dependent axis acceleration bounds

Cited by 37 publications

References 15 publications

High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

High speed interpolation for micro-line trajectory and adaptive real-time look-ahead scheme in CNC machining

Convex optimisation method for time-optimal feedrate planning with complex constraints

Discrete Interpolation of G01 Codes in 2D Machining under Bounded Accelerations

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