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Research Papers

Minimax Optimization Strategy for Process Parameters Planning: Toward Interference-Free Between Tool and Flexible Workpiece in Milling Process

[+] Author and Article Information
Xiao-Ming Zhang

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China
e-mail: zhangxm.duyi@gmail.com

Dong Zhang

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of Science and
Technology,
Wuhan 430074, China

Le Cao, Tao Huang, Han Ding

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
Huazhong University of
Science and Technology,
Wuhan 430074, China

Jürgen Leopold

Precision Engineering Department,
Fraunhofer Institute for Machine Tools and
Forming Technology,
Chemnitz 09661, Germany

1Corresponding author.

Manuscript received May 26, 2016; final manuscript received October 31, 2016; published online December 21, 2016. Assoc. Editor: Xiaoping Qian.

J. Manuf. Sci. Eng 139(5), 051010 (Dec 21, 2016) (11 pages) Paper No: MANU-16-1301; doi: 10.1115/1.4035184 History: Received May 26, 2016; Revised October 31, 2016

In milling of flexible workpieces, like axial-flow compressor impellers with thin-wall blades and deep channels, interference occurrence between workpiece and tool shaft is a great adverse issue. Even though interference avoidance plays a mandatory role in tool path generation stage, the generated tool path remains just a nominally interference-free one. This challenge is attributed to the fact that workpiece flexibility and dynamic response cannot be considered in tool path generation stage. This paper presents a strategy in process parameters planning stage, aiming to avoid the interference between tool shaft and flexible workpiece with dynamic response in milling process. The interference problem is formulated as that to evaluate the approaching extent of two surfaces, i.e., the vibrating workpiece and the swept envelope surface generated by the tool undergoing spatial motions. A metric is defined to evaluate quantitatively the approaching extent. Then, a minimax optimization model is developed, in which the optimization objective is to maximize the metric, so as the interference-free can be guaranteed while constraints require the milling process to be stable and process parameters to fall into preferred intervals in which material removal rate is satisfactory. Finish milling of impeller using a conical cutter governed by a nominally interference-free tool path is numerically simulated to illustrate the dynamics responses of the spatially distributed nodal points on the thin-wall blade and approaching extent of the time-varying vibrating blades to the tool swept envelope surface. Furthermore, the present model results suggest to use an optimal process parameters set in finish milling, as a result improving machining efficiency in addition to ensuring the interference-free requirement. The model results are verified against milling experiments.

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References

Figures

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Fig. 5

(a) Conical tool geometry, (b) radius r as a function of parameter a, and (c) tool swept envelope surface

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Fig. 3

Point-to-surface distance

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Fig. 1

Milling of a thin-wall flexible blade: (a) programed cutter locations and (b) unwanted interference between tool and vibrating blade

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Fig. 4

Flow chart of the optimization procedures

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Fig. 6

Reference frame for tool motion

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Fig. 7

Diagram of getting the vibration response of workpiece surface in milling process

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Fig. 8

Coordinate representation of milling process: fixed coordinate system XYZ, process coordinate system FCN, and tool coordinate system xyz. The orientation of cutter is defined by lead angle α and tilt angle γ.

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Fig. 10

Tool path for NC machining of impeller blade: (a) cutter contact point trajectory and (b) discrete cutter locations

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Fig. 14

Comparison of cutting forces: (a) simulation results and (b) experimental results, with process parameters: Ω = 7450 rpm and f = 0.09 mm/tooth, iteration 6 in Table 3

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Fig. 15

Comparison of accelerations: (a) simulation results and (b) experimental results, with process parameters: Ω = 7450 rpm and f = 0.09 mm/tooth, iteration 6 in Table 3

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Fig. 16

Scallop height area in finish milling

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Fig. 9

Experiments: (a) experimental setup and (b) impeller geometry

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Fig. 11

Changes of dynamic metric Φ with respect to time t: Φ(w*,t), where w*=(7450 rpm,0.09 mm/tooth)T, Iteration 6 in Table 3. The arrow points to the minimum of the metric Φ(w*,t).

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Fig. 12

Spatial distributions of distances between S and X in the milling process, with process parameters: Ω = 7450 rpm and f = 0.09 mm/tooth, Iteration 6 in Table 3

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Fig. 13

(a) Interference occurrence, with process parameters: Ω = 6500 rpm and f = 0.1 mm/tooth, resulting in dynamic metric Φ=−15.7 μm and (b) interference-free surface, with process parameters: Ω = 7450 rpm and f = 0.09 mm/tooth, resulting in dynamic metric Φ=53.6   μm, iteration 6 in Table 3

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