Envelope surface formed by cutting edge under runout error in five-axis flank milling

Yu, Liang; Wang, Yuhan; Jin, Yongqiao

doi:10.1007/s00170-013-5040-8

Cited by 10 publications

(5 citation statements)

References 24 publications

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“…Based on tangency condition in envelope theory and the body velocity representation in spatial kinematics, the analytical solution of the envelope surface of the taper tool can be derived. We refer the reader to Zhu et al's 25 work or our previous work 26 for more details. For completeness, the jth discrete characteristic point on envelope surface at the instant t i is given as follows…”

Section: Tool Envelope Surfacementioning

confidence: 99%

Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

Zhong

Wang

2017

Advances in Mechanical Engineering

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This article presents an approach to generate optimal couples of tool size and tool path for flank milling ruled surface with a conical cutter based on normal mapping, while at the same time keeping this couples within the given bounded constraints. For given initial pairs of taper tool and tool path, tool envelope surface is calculated. Then, the tool axis trajectory surface is related to envelope surface through the normal mapping. On this basis, the correspondence between the surface pair ''design ruled surface-envelope surface-tool axis trajectory surface'' is established, and it is used to obtain the signed flank milling error. By using this signed error, tool size and tool path optimization for flank milling is formulated as an optimization model subjected to bounds, and the trust-region-reflective least-squares method is used to solve this problem. Numerical example is given to confirm the validity of the proposed method.

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Section: Tool Envelope Surfacementioning

confidence: 99%

Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

Zhong

Wang

2017

Advances in Mechanical Engineering

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“…This will bring in some geometry errors, lead ing to poor machining accuracy. Yu et al [25] presents a cutter runout model including both axis offset eiTor and axis tilt error with four parameters. In order to integrate the cutter runout effect into envelope surface modeling and reduce the adverse effect of cutter runout on geometry accu racy, the expression of cutter edge in the spindle coordinate sys tem should be derived combined with the runout parameters.…”

Section: Expression Of Cutter Edge Combined With Runout Parametersmentioning

confidence: 99%

“…In this sense, it is a bivariate sphere-swept surface. [16,25]. Its ana lytical expression is derived in Ref.…”

Section: Rjs(z) Sin Cp{z)+zls(z)]t Xj a Zk A Z) + Y Ja Z)y'jaz)mentioning

confidence: 99%

“…As the actual cutter surface and swept envelope surface when con sidering the runout effect are no longer congruent with the nomi nal ones [16], some geometry errors and changes of process geometry parameters will be brought in. Yu et al [25] established an analytic model of the cutter swept enve lope surface considering the runout effect based on the spatial kine matics theory proposed by Zhu et al [26]. Based on calibration procedures using the measurement of cutting forces, the cutter runout parameters can be identified [18,19], This leaves the possibility to investigate the effect of cutter runout on milling process.…”

Section: Introductionmentioning

confidence: 99%

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Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank Milling Considering Cutter Runout

Zhu

2014

Journal of Manufacturing Science and Engineering

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State Key L a b o ra to ry o t M e cha n ical System and V ib ra tio n , S c h o o l o f M e cha n ical E n g in e erin g, S h a ng h ai Jia o T o n g U nive rsity, S h a ng h ai 2 0 0 2 4 0 , C hin a e -m a il: lzl@ s jtu .e d u .c n L i-M in Z h u 1 State Key L a b o ra to ry o f M e cha n ical System and V ib ra tio n , S c h o o l o f M e cha n ical E n g in e erin g, S h a ng h ai Jia o T o n g U nive rsity, S h a ng h ai 2 0 0 2 4 0 , C hin a e -m a il: z h u lm @ s jtu .e d u .c n Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank M illing Considering Cutter Runout Cutter runout is a common and inevitable phenomenon impacting the geometry accuracy in the milling process. However, most o f the works on tool path planning neglect the cut ter runout effect. In this paper, a new approach is presented to integrate the cutter runout effect into envelope surface modeling and tool path optimization fo r five-axis flank mill ing with a conical cutter. Based on the geometry model o f cutter runout which consists o f cutter axis and cutter tilt, an analytic expression o f cutter edge combined with four run out parameters is derived. Then the envelope surface formed by each cutter edge is con structed using the envelope theory o f sphere congruence. Due to the cutter runout effect, the envelope surfaces formed by the cutter edges are different from each other, and the valid envelope surface is the combination o f these envelope surfaces which contribute to the final machined surface. To measure the machining errors, the geometry deviations between the valid envelope surface and the design surface are calculated with the dis tance function. On the basis o f the differential property o f the distance function, tool path optimization considering cutter runout is modeled as a mixed-integer linear program ming (MILP) problem, which can be solved by the branch-and-bound method. Finally, numerical examples are given to confirm the validity and efficiency o f the proposed approach. The results show that the geometry errors induced by runout can be reduced significantly using the proposed method.

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“…In his method, component error and rotation error are considered as elements in error analysis. Yu et al 19 studied the machined surface formed by a specially designed cutting edge under cutter runout error, including axis runout error and tilt error, in flue-axis flank milling and studied special cases of the analytical model and the runout effect on the envelope surface. Liu et al 20 studied the spectral characteristics of milling force for chip load, tool wear, and tool runout in the end milling process to distinguish them from each other and proposed a new method of identifying tool eccentricity and wear with force.…”

Section: Introductionmentioning

confidence: 99%

Influence of tool rotation errors on flank machined surface

Cao

Yang

et al. 2017

Proceedings of the Institution of Mechanical Engineers, Part B:

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In flank milling, the machined metal surface is formed by the edge of the cutting tool and is thus affected by tool errors. Cutting tool rotation errors affect the movement of the tool teeth and thus change the trajectory of the tool edge. This change will also affect the cutting force, which will result in deformation in the cutting process. Previous studies focus mostly on the cutting tool runout error and ignore the effect of tool deformation. In this article, we built a mathematical model of the machining process that considers not only the tool runout error but also the tool tilt deformation error. Using this model, we analyzed how the tool rotation error will influence workpiece surface quality and surface frequency. Results show that feed rate and rotation errors will affect surface roughness, geometric error, and surface energy distribution.

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Envelope surface formed by cutting edge under runout error in five-axis flank milling

Cited by 10 publications

References 24 publications

Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

Optimizing tool size and tool path of five-axis flank milling with bounded constraints via normal mapping

Envelope Surface Modeling and Tool Path Optimization for Five-Axis Flank Milling Considering Cutter Runout

Influence of tool rotation errors on flank machined surface

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