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An experimental study of the relationship between cutting efficiency and cuttings size in rock cutting using a PDC cutter

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Abstract

Rock cutting efficiency is the most common parameter used to evaluate the performance of polycrystalline diamond compact (PDC) bits. Many studies have shown that cuttings size might be used to evaluate rock breaking efficiency; however, there are few quantitative studies of the relationship between rock cutting efficiency and cuttings size in rock cutting when a PDC bit is used. Several linear cutting tests were conducted to explore the relationship between the mechanical specific energy (MSE) and cuttings size to solve this problem. The cuttings size distributions were also discussed. Then, the coarseness index (CI) was selected as the most appropriate indicator of cuttings size and its relationship with the MSE was investigated. In addition, rock cutting tests based on the Taguchi method were conducted to analyze cutting parameters such as the depth of cut (DOC), the back rake angle (θ) and the cutting speed (v) effects on the CI and MSE. The contribution of each parameter to the response was obtained. The results show that the distribution of cuttings size conforms to the Rosin–Rammler equation, and there is a significant relationship between the MSE and cuttings size. The MSE decreases with increased cuttings size, furthermore, the relationship between the MSE and the CI could be described by an exponent function. The Taguchi experiment results show that DOC and θ have significant impacts: the CI value increases with increased DOC, and the CI increases slightly with increased θ. The most influential factor on the CI is the DOC, followed by θ. However, within the range of experiments, the cutting speed has an insignificant effect on the CI value. This work is highly pertinent to better understanding of the relationship between rock cutting efficiency and cuttings size in rock cutting using a PDC cutter.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 51874327) and Scientific Research Starting Foundation of China University of Petroleum-Beijing at Karamay (RCYJ2016B-02-004).

Author information

Authors and Affiliations

  1. College of Mechanical and Transportation Engineering, China University of Petroleum-Beijing, Changping, Beijing, 102249, China

    Huihui Hou, Hongwu Zhu & Zhuo Yin

  2. Faculty of Engineering, China University of Petroleum-Beijing at Karamay, Karamay, Xinjiang, 834000, China

    Zhong Liu

  3. Faculty of Petroleum, China University of Petroleum-Beijing at Karamay, Karamay, Xinjiang, 834000, China

    Zhenquan Wang

Authors
  1. Huihui Hou
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  2. Zhong Liu
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  3. Hongwu Zhu
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  4. Zhenquan Wang
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  5. Zhuo Yin
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Correspondence to Hongwu Zhu.

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Technical Editor: Celso Kazuyuki Morooka.

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Appendix: The results of the experiments in Section 3

Appendix: The results of the experiments in Section 3

\(\theta\)(°)

DOC (mm)

Cuttings weight (mg)

Parameters of Rosin–Rammler equation

CI

 < 20

20–40

40–60

60–80

80–100

 > 100

\(n_{b}\)

\(r_{e}\)

\(R^{2}\)

(mesh)

(mesh)

(mesh)

(mesh)

(mesh)

(mesh)

 

(mm)

 

5

0.1

0.8

6.1

2.4

3.2

2.8

23.1

0.66

0.016

0.97

216.67

0.2

1.4

13.4

14.3

6.4

4.8

46.6

10.99

0.021

0.99

239.46

0.3

4.3

23.2

18.8

8.4

6.0

52.9

0.97

0.026

0.99

239.46

0.4

37.7

65.4

23.3

10.4

7.6

76.0

0.83

0.046

0.98

270.25

0.5

124.4

140.8

48.1

22.5

15.5

142.2

0.81

0.046

0.98

348.91

0.8

191.5

80.35

33.2

16.4

11.7

68.3

0.80

0.122

0.99

454.49

1.2

378.1

101.2

42.0

20.2

13.6

76.8

0.80

0.191

0.99

491.78

1.6

427.6

99.5

48.6

24.7

16.8

93.5

0.74

0.201

0.99

486.71

2.0

422.9

85.8

38.8

17.6

11.3

63.1

0.81

0.245

0.99

509.86

10

0.1

0

7.3

7.6

4.2

3.0

32.8

0.84

0.017

0.99

215.42

0.2

0.2

8.1

10.9

6.7

5.3

39.2

1.17

0.019

0.99

220.01

0.3

1.1

18.6

16.4

8.0

5.5

46.0

1.13

0.023

0.98

257.40

0.4

20.7

61.0

21.8

9.9

6.9

58.7

0.98

0.042

0.97

345.62

0.5

75.9

70.2

26.5

12.3

8.7

68.9

0.82

0.068

0.99

394.53

0.8

213.7

90.9

35.9

18.7

13.8

85.2

0.76

0.121

0.99

447.26

1.2

461.2

107.3

53.4

27.2

19.1

106.2

0.73

0.199

0.99

483.39

1.6

668.5

131.3

65.5

34.7

22.4

121.4

0.75

0.238

0.99

498.20

2.0

940.9

164.5

80.2

38.4

26.1

128.4

0.79

0.271

0.99

513.93

15

0.1

0

2.5

3.7

5.7

3.8

15.3

1.39

0.019

0.98

217.10

0.2

2.8

18.7

13.7

8.4

6.5

39.7

1.03

0.026

0.99

270.60

0.3

18.2

37.3

20.2

9.6

6.6

51.9

0.89

0.038

0.99

327.12

0.4

43.7

58.4

24.1

12.5

9.5

67.3

0.84

0.050

0.99

359.41

0.5

79.7

63.4

26.8

13.3

10.5

71.0

0.78

0.068

0.99

390.76

0.8

238.6

90.5

40.7

18.8

13.8

73.8

0.82

0.130

0.99

462.98

1.2

391.9

116.0

58.2

27.7

20.0

106.6

0.78

0.154

0.99

471.19

1.6

554.6

133.1

67.9

33.7

24.7

127.8

0.75

0.189

0.99

482.39

2.0

805.1

214.6

70.1

41.2

25.1

153.6

0.79

0.212

0.98

497.35

20

0.1

0

1.4

1.2

3.6

5.2

24.5

1.07

0.012

0.99

160.17

0.2

8.0

5.0

6.4

4.8

3.1

35.2

0.70

0.015

0.99

246.92

0.3

30.9

47.3

22.0

11.3

8.2

70.2

0.78

0.039

0.99

331.95

0.4

12.6

38.8

17.7

9.2

7.1

62.4

0.87

0.032

0.98

300.61

0.5

48.2

53.7

24.1

11.6

9.3

76.1

0.75

0.050

0.99

351.44

0.8

219.1

100.7

46.7

10.6

3.0

101.8

0.74

0.106

0.98

432.02

1.2

409.0

125.1

57.7

30.5

20.9

121.1

0.75

0.154

0.99

466.39

1.6

598.0

125.1

67.7

32.5

23.1

128.5

0.74

0.207

0.99

488.02

2.0

743.5

151.3

77.3

33.8

25.1

159.7

0.73

0.260

0.98

503.45

25

0.1

0

0

1.4

2.2

2.2

21.7

1.26

0.010

0.99

138.76

0.2

0

1.2

1.8

2.5

3.1

26.1

0.93

0.010

0.94

152.24

0.3

0

3.0

9.8

5.0

5.0

41.4

1.07

0.015

0.98

187.85

0.4

4.3

30.0

22.5

10.6

7.5

60.8

1.03

0.026

0.99

275.02

0.5

24.3

52.5

27.4

13.0

8.9

65.8

0.93

0.040

0.99

333.78

0.8

290.0

93.5

53.6

26.2

18.0

95.4

0.78

0.129

0.99

456.44

1.2

455.1

129.6

62.8

33.3

22.7

121.6

0.76

0.160

0.99

472.30

1.6

461.9

149.2

74.7

39.0

27.7

151.5

0.75

0.138

0.99

457.97

2.0

1238.6

184.1

99.1

48.0

33.2

182.0

0.71

0.328

0.99

512.12

1. CI is coarseness index, R2 is the correlation coefficient of the fitted curves of Rosin–Rammler equation. 2. Rosin–Rammler equation: \(R = {\text{100exp}}\left( { - \left( {r_{{\text{c}}} /r_{e} } \right)^{{n_{b} }} } \right)\), where R is the cumulative fraction of cuttings by weight retained on the sieve that of mesh size rc, re is the absolute grain size, nb is a constant describing the uniformity of the cuttings.

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Hou, H., Liu, Z., Zhu, H. et al. An experimental study of the relationship between cutting efficiency and cuttings size in rock cutting using a PDC cutter. J Braz. Soc. Mech. Sci. Eng. 43, 270 (2021). https://doi.org/10.1007/s40430-021-02984-9

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