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Research Papers

Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility

[+] Author and Article Information
Xianyin Duan

National Numerical Control System
Engineering Research Center,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: duanxianyin@gmail.com

Fangyu Peng

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
B418 Room,
East Building,
1037 Luoyu Road,
Wuhan, Hubei 430074, China
e-mail: zwm8917@263.net

Rong Yan

National Numerical Control System Engineering
Research Center,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: yanrong@hust.edu.cn

Zerun Zhu

National Numerical Control System
Engineering Research Center,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: eonpig@hust.edu.cn

Kai Huang

National Numerical Control System
Engineering Research Center,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: hk125gm@hust.edu.cn

Bin Li

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China
e-mail: libin999@hust.edu.cn

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June 15, 2014; final manuscript received September 18, 2015; published online October 27, 2015. Assoc. Editor: Allen Y. Yi.

J. Manuf. Sci. Eng 138(4), 041001 (Oct 27, 2015) (15 pages) Paper No: MANU-14-1327; doi: 10.1115/1.4031678 History: Received June 15, 2014; Revised September 18, 2015

In the tool orientation planning for five-axis sculptured surface machining, the geometrical constraints are usually considered. Actually, the effect of nongeometrical constraints on tool orientation planning is also important. This paper studied one nongeometrical constraint which was cutting force induced static deflection under different tool orientations, and proposed a cutter deflection model based on that. In the study of the cutting force, the undeformed chip thickness in filleted end milling was modeled by geometrical analysis and coordinate transformation of points at the cutting edge. In study of static flexibility of multi-axis machine, static flexibility of the entire machining system was taken into consideration. The multi-axis machining system was divided into the transmission axes-handle (AH) end and the cutting tool end. The equivalent shank method was developed to calculate the static flexibility of the AH end. In this method, static flexibility anisotropy of the AH end was considered, and the equivalent lengths of the AH end were obtained from calibration experiments. In cutter deflection modeling, force manipulability ellipsoid (FME) was applied to analyze the static flexibility of the AH end in arbitrary directions. Based on the synthetic static flexibility and average cutting force, cutter deflections were derived and estimated through developing program realization. The predicted results were compared with the experimental data obtained by machining 300 M steel curved surface workpiece, and a good agreement was shown, which indicated the effectiveness of the cutter deflection model. Additional experiments of machining flat workpiece were performed, and the relationship of cutter deflections and tool orientations were revealed directly. This work could be further employed to optimize tool orientations for suppressing the surface errors due to cutter deflections and achieving higher machining accuracy.

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Figures

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Fig. 1

Geometric model of the cutter. (a) Side view of general end mill; (b) side view of filleted end mill; (c) bottom view of filleted end mill (taking four-flute cutter as an example).

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Fig. 2

Illustration of undeformed chip thickness modeling in filleted end milling. (a) Geometric sketch of COC and its position; (b) geometric sketch of undeformed chip; (c) illustration of undeformed chip thickness; and (d) partially magnified view.

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Fig. 3

Multi axis machining system. (a) AH end; (b) static flexibility model of multi axis machining system; and (c) cutting tool end.

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Fig. 4

Deflection cuboid of the end of the EMS

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Fig. 5

Rotation transformation relationship among different coordinate systems

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Fig. 6

Flow chart for predicting cutter deflection

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Fig. 7

Simulation results of cutter deflection at one CC point. (a) ex; (b) ey; and (c) ez.

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Fig. 8

Experimental settings for obtaining cutting force coefficients

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Fig. 9

Fitting curves of test data from cutting force calibration. (a), (b), and (c) were results in tangential, radial, and axial directions, respectively.

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Fig. 10

Experimental settings for obtaining static flexibility parameters. (a), (b), and (c) were images in x, y, and z directions, respectively.

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Fig. 11

Calibration experiments data of static flexibility parameters: (a) in x direction and (b) in y direction

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Fig. 12

Verification experimental settings for obtaining cutter deflection

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Fig. 13

Model and photograph of workpiece in verification tests: (a) cylindrical surface and (b) flat surface

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Fig. 14

Comparison of predicted and measured cutter deflections for all of the conditions: (a) ex for conditions 1–4, (b) ex for conditions 5–8, (c) ey for conditions 1–4, and (d) ey for conditions 5–8

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Fig. 15

Error ratios (μex, μey) of predicted cutter deflections for all of the conditions: (a) μex forconditions 1–4; (b) μex for conditions 5–8; (c) μey for conditions 1–4; and (d) μey for conditions5–8

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Fig. 16

Cutter deflections in xt axis for different lead angles and tilt angles: (a) the lead angle kept constant and (b) the tilt angle kept constant

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Fig. 17

Cutter deflections in yt axis for different lead angles and tilt angles: (a) the lead angle kept constant and (b) the tilt angle kept constant

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