# A Study of Digging Productivity of an Electric Rope Shovel for Different Operators

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Approach

#### 3.1. Field Studies

#### 3.2. Statistical and Clustering Analysis

_{1}, c

_{2}, …, c

_{k}] $\in \text{}{\mathbb{R}}^{\mathrm{d}}$ are defined.

## 4. Analysis of Results

#### 4.1. Productivity

_{0}and t

_{1}are the start and the end of digging respectively, F

_{b}is the bail force (bail pull) and crowd rate is the rate of change of crowd arm angle with respect to horizon. It should be noted that all these KPIs are being estimated by the commercial monitoring system on-board the shovel using a suit of sensors such as load cells and gyro sensors. As Equation (2) shows the digging energy estimated by the monitoring system on-board the shovel is an equivalent mechanical energy $\left(\text{tons}\times \text{rad}\right)$ during the digging part of the cycle. The equivalent digging energy is measured at the bail and is a measure of mechanical energy transferred to the bucket teeth. This energy is provided by electrical DC motors on-board the shovel. A summary of the aforementioned KPIs for all of the operators is presented in Table 1.

#### 4.2. Clustering of Shovel Cycles

#### 4.3. Operator Digging Practice

- Constant crowd speed until the desired dipper depth of penetration is achieved (the first part of the digging);
- Once the dipper penetrates into the bank, digging is mainly accomplished by hoist action, and the crowd speed is approximately zero.

_{1}, a

_{2}, a

_{3}, a

_{4}are the numerical ratings of digging energy, loading rate, crowd speed and hoist speed, respectively. Because of high variability in digging energy, a weighted average based on the percentage of cycles within each class can be used to calculate the numerical rating of digging energy (a

_{1}):

_{1}, p

_{2}, p

_{3}, p

_{4}denote the percentage of cycles in low, average, high and extremely high energy classes, respectively.

## 5. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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Operator | Statistics | Payload (tons) | Dig Time (s) | Swing Time (s) | Swing Angle (°) | Return Time (s) | Return Angle (°) | Productive Cycle Time (s) | Waiting Time (s) | Equivalent Digging Energy (tons × rad) | Loading Rate (tons/s) | Mucking Rate (tons/s) |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Operator A 589 Cycles | Mean | 98.3 | 16.4 | 8.2 | 68.8 | 8.6 | 62.3 | 33.3 | 18.9 | 266,265.5 | 6.2 | 3.0 |

COV | 0.17 | 0.20 | 0.31 | 0.36 | 0.24 | 0.36 | 0.15 | 1.94 | 0.36 | 0.26 | 0.19 | |

Min | 13 | 8 | 2 | 9 | 1 | 0 | 21 | 0 | 36,461 | 1 | 0 | |

Max | 133 | 24 | 18 | 180 | 27 | 173 | 53 | 373 | 588,114 | 15 | 6 | |

Operator B 1629 Cycles | Mean | 104.1 | 16.5 | 8.5 | 66.8 | 8.1 | 61.8 | 33.1 | 18.9 | 231,875.7 | 6.5 | 3.2 |

COV | 0.14 | 0.18 | 0.33 | 0.32 | 0.33 | 0.43 | 0.16 | 2.18 | 0.32 | 0.20 | 0.16 | |

Min | 11 | 8 | 2 | 1 | 0 | 0 | 18 | 0 | 6717 | 1 | 0 | |

Max | 139 | 24 | 30 | 166 | 36 | 175 | 67 | 411 | 617,241 | 15 | 6 | |

Operator C 1633 Cycles | Mean | 98.6 | 15.7 | 8.5 | 70.8 | 8.5 | 64.6 | 32.7 | 17.0 | 204,946.2 | 6.5 | 3.1 |

COV | 0.16 | 0.20 | 0.32 | 0.32 | 0.30 | 0.38 | 0.15 | 2.03 | 0.34 | 0.22 | 0.19 | |

Min | 17 | 8 | 1 | 2 | 1 | 0 | 16 | 0 | 19,629 | 1 | 0 | |

Max | 137 | 24 | 23 | 172 | 46 | 161 | 70 | 540 | 491,753 | 15 | 6 | |

Operator D 671 Cycles | Mean | 97.0 | 15.3 | 7.6 | 66.8 | 8.5 | 58.8 | 31.4 | 12.8 | 253,197.2 | 6.4 | 3.1 |

COV | 0.21 | 0.21 | 0.31 | 0.37 | 0.31 | 0.37 | 0.16 | 2.46 | 0.37 | 0.22 | 0.19 | |

Min | 11 | 8 | 2 | 4 | 1 | 0 | 19 | 0 | 22,938 | 1 | 1 | |

Max | 139 | 24 | 23 | 165 | 32 | 131 | 59 | 476 | 557,642 | 17 | 5 | |

All Data 4522 Cycles | Mean | 100.3 | 16.0 | 8.3 | 68.5 | 8.4 | 62.5 | 32.7 | 17.4 | 230,100.6 | 6.4 | 3.1 |

COV | 0.16 | 0.20 | 0.32 | 0.34 | 0.31 | 0.40 | 0.16 | 2.14 | 0.36 | 0.22 | 0.18 | |

Min | 11 | 8 | 1 | 1 | 0 | 0 | 16 | 0 | 6717 | 1 | 0 | |

Max | 139 | 24 | 30 | 180 | 46 | 175 | 70 | 540 | 617,241 | 17 | 6 |

Digging Energy Class | Energy Range ($\times {10}^{5}$) $\left(tons\times rad\right)$ | Percentage of Cycles (All Data) | Percentage of Cycles (Operator A) | Percentage of Cycles (Operartor B) | Percentage of Cycles (Operator C) | Percentage of Cycles (Operator D) |
---|---|---|---|---|---|---|

Low Energy | <1.57 | 18 | 14.2 | 14.4 | 24 | 15.2 |

Average Energy | 1.57–2.36 | 37 | 22.6 | 39.1 | 44 | 25.4 |

High Energy | 2.36–3.23 | 33 | 34.2 | 36.2 | 27 | 37.5 |

Extremely High Energy | >3.23 | 12 | 29 | 10.3 | 5 | 21.9 |

Operator | Cycle # | 1 | 2 | 3 | 4 | 5 | Mean | Standard Deviation | Coefficient of Variation |
---|---|---|---|---|---|---|---|---|---|

Operator A | Crowd Speed (m/s) | 0.460 | 0.523 | 0.567 | 0.599 | 0.402 | 0.510 | 0.080 | 0.157 |

R-squared | 0.994 | 0.986 | 0.986 | 0.989 | 0.959 | ||||

Hoist Speed (m/s) | 0.692 | 0.816 | 0.518 | 0.528 | 0.571 | 0.625 | 0.127 | 0.204 | |

R-squared | 0.954 | 0.966 | 0.992 | 0.983 | 0.995 | ||||

Operator B | Crowd Speed (m/s) | 0.379 | 0.654 | 0.553 | 0.462 | 0.493 | 0.508 | 0.103 | 0.202 |

R-squared | 0.988 | 0.996 | 0.986 | 0.992 | 0.947 | ||||

Hoist Speed (m/s) | 0.782 | 0.617 | 0.766 | 0.591 | 0.792 | 0.709 | 0.097 | 0.137 | |

R-squared | 0.983 | 0.961 | 0.978 | 0.942 | 0.970 |

Parameters | Class | |||
---|---|---|---|---|

Rating | ||||

Loading Rate (tons/s) | <5.4 | 5.4–6.9 | 6.9–8.8 | >8.8 |

4 | 6 | 8 | 10 | |

Digging Energy | Low | Average | High | Extremely High |

5 | 4 | 3 | 2 | |

Hoist Speed (m/s) | <0.6 | 0.6–0.7 | 0.7–0.8 | >0.8 |

1 | 2 | 3 | 4 | |

Crowd Speed (m/s) | <0.3 | 0.3–0.4 | 0.4–0.5 | >0.5 |

0.5 | 0.4 | 0.3 | 0.2 |

Patarameters | Loading Rate (tons/s) | Digging Energy | Hoist Speed (m/s) | Crowd Speed (m/s) | N |
---|---|---|---|---|---|

Average Value | |||||

a_{i} | |||||

Operator A | 6.2 | 266,265.5 | 0.625 | 0.510 | 7.2 |

6 | 3 | 2 | 0.2 | ||

Operator B | 6.5 | 231,875.7 | 0.709 | 0.508 | 14.4 |

6 | 4 | 3 | 0.2 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Babaei Khorzoughi, M.; Hall, R.
A Study of Digging Productivity of an Electric Rope Shovel for Different Operators. *Minerals* **2016**, *6*, 48.
https://doi.org/10.3390/min6020048

**AMA Style**

Babaei Khorzoughi M, Hall R.
A Study of Digging Productivity of an Electric Rope Shovel for Different Operators. *Minerals*. 2016; 6(2):48.
https://doi.org/10.3390/min6020048

**Chicago/Turabian Style**

Babaei Khorzoughi, Mohammad, and Robert Hall.
2016. "A Study of Digging Productivity of an Electric Rope Shovel for Different Operators" *Minerals* 6, no. 2: 48.
https://doi.org/10.3390/min6020048