Research Papers

Time-Efficient Trochoidal Tool Path Generation for Milling Arbitrary Curved Slots

[+] Author and Article Information
Ke Xu

College of Mechanical and
Electronic Engineering,
Nanjing University of Aeronautics
and Astronautics,
Nanjing 210016, China

Baohai Wu

School of Mechanical Engineering,
Northwestern Polytechnical University,
Xi'an 710129, China

Zhaoyu Li

Department of Mechanical and
Aerospace Engineering,
Hong Kong University of Science
and Technology,
Kowloon, Hong Kong

Kai Tang

Department of Mechanical and
Aerospace Engineering,
Hong Kong University of Science
and Technology,
Kowloon, Hong Kong
e-mail: mektang@ust.hk

1Corresponding author.

Manuscript received April 6, 2018; final manuscript received October 22, 2018; published online January 22, 2019. Assoc. Editor: Guillaume Fromentin.

J. Manuf. Sci. Eng 141(3), 031008 (Jan 22, 2019) (14 pages) Paper No: MANU-18-1216; doi: 10.1115/1.4042052 History: Received April 06, 2018; Revised October 22, 2018

Trochoidal (TR) tool paths have been a popular means in high-speed machining for slot cutting, owing to its unique way of cyclically advancing the tool to avoid the situation of a full tool engagement angle suffered by the conventional type of slot cutting. However, advantageous in lowering the tool engagement angle, they sacrifice in machining efficiency—to limit the tool engagement angle, the step distance has to be carefully controlled, thus resulting in a much longer total machining time. Toward the objective of improving the machining efficiency, in this paper, we propose a new type of TR tool path for milling an arbitrary curved slot. For our new type of TR tool path, within each TR cycle, rather than moving circularly, the tool moves in a particular way such that the material removal rate is maximized while the given maximum engagement angle is fully respected. While this type of TR tool path works perfectly only for circular slots (including straight ones), by means of an adaptive decomposition and then a novel iso-arc-length mapping scheme, it is successfully applied to any general arbitrarily curved slot. Our experiments have confirmed that, when compared with the conventional TR tool paths, the proposed new type of TR tool path is able to significantly reduce the total machining time by as much as 25%, without sacrificing the tool wear.

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Fig. 1

(a) Zigzag pocket milling and (b) parallel contouring pocket milling

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Fig. 2

The front curve and its corresponding tool trajectory

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Fig. 3

Definition of engagement angle in straight slot machining

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Fig. 4

(a) The negative form, (b) positive form, and (c) straight form

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Fig. 5

Step distance ds as an angle ((a) and (b)) and a translation (c)

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Fig. 6

Determination of the maximally allowed step distance ds: (a) straight slot and (b) curved slot

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Fig. 7

A penalty to deal with overcut situation during the optimization process

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Fig. 8

Optimized front curve and engagement angle of (a) straight form, (b) negative form, and (c) positive form; (d) the engagement angle of the conventional TR front curve for a straight slot

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Fig. 9

(a) Definition of a curved slot and (b) sharp corner on the upper boundary curve

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Fig. 10

Least-square circular fitting

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Fig. 11

Slot decomposition

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Fig. 12

(a) Isoparametric tool path generation and (b) iso-arc-length front curve generation

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Fig. 13

Joining the front curves of all the segments

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Fig. 14

Backward transition curve generation and the final tool path

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Fig. 15

(a) Optimized and (b) traditional TR tool path with Rt=6 and (c) optimized and (d) traditional TR tool path with Rt=3

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Fig. 16

Two test examples of freeform curved slot and their decompositions

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Fig. 17

Test slot 1: the nominal primitive segments

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Fig. 18

Test slot 1: (a) constant circular tool path and its simulated engagement angle, (b) adaptive circular tool path and its simulated engagement angle, and (c) time-efficient TR path and its engagement angle

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Fig. 19

Statistics of test slot 1

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Fig. 20

Test slot 2: the nominal primitive segments

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Fig. 21

Test slot 2: (a) constant circular tool path and its simulated engagement angle, (b) adaptive circular tool path and its simulated engagement angle, and (c) time-efficient TR path and its engagement angle

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Fig. 22

Statistics of test slot 2

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Fig. 23

The physical machining results by the three competitors

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Fig. 24

(a) A brand new cutter, and the tool wear for (b) constant circular path, (c) adaptive circular path, and (d) optimized TR path



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