^{1}

^{1}

^{2}

^{2}

^{1}

^{1}

^{2}

The rock cutting process with a circular sawblade and the rock breaking mechanism of rock are studied with a numerical simulation method in this paper. The influence of cutting parameters of the circular sawblade on cutting force, rock damage, and specific cutting energy in the process of circular sawblade cutting rock is researched. The cutting force increases with the feed speed and an increase in cutting depth and decline in rotation speed. Cutting rock with double circular sawblades can reduce cutting force. However, the specific cutting energy declines with the increase in cutting depth and the decline in the distance between the double circular sawblades. Cutting parameters have a great influence on the damage range of rock. The research results can be applied to rock processing with a circular sawblade.

Natural stone is an important building material, and the circular sawblade is widely applied in natural stone processing. The influences of circular sawblade cutting parameters on the cutting performance are studied. Many experts and scholars at home and abroad have penetrated into research on cutting rock with a sawblade.

The brittleness of the rock makes rock processing very difficult. Diamond sawblade is the best choice in rock processing. Therefore, many scholars have investigated cutting rock with a sawblade. Zhang et al. explored the wear performance of diamond tools with different sawing trajectories in stone processing with experiments [

Kahraman et al. predicted the sawability of carbonated rock with the artificial network from shear strength parameters [

Many scholars have researched the influence of operation and rock parameters on the diamond saws cutting performance and specific cutting energy with experimental and theoretical methods. However, few research studies are based on the method of numerical simulation to investigate the damage of rock with a circular sawblade cutting rock. Therefore, this paper establishes the numerical simulation models to research the influence of various parameters on the cutting performance of a circular sawblade, with feed speeds of 0.10, 0.15, 0.20, 0.25, and 0.30 m/min and rotation speeds of 1000, 1500, 2000, 2500, and 3000 r/min, the cutting depths set as 10, 20, 30, 40, 50, and 60 mm, and the distance of double diamond sawblades set as 10, 20, 30, 40, and 50 mm.

The rotation speed direction of a circular sawblade has a great effect on the cutting performance. It is defined that the feed speed and the rotation speed in the same direction is the forward cutting while the opposite direction is the reverse cutting. There are two kinds of cutting force models of circular sawblade cutting rock with two directions of rotation speed, as is shown in Figure

Force model of a circular sawblade cutting rock: (a) The force model of a circular sawblade cutting rock with forward cutting; (b) the force model of a circular sawblade cutting rock with reverse cutting.

The tangential force and normal force are the main components of cutting force in a circular sawblade cutting rock. However, the axial force is much smaller than tangential force and normal force. The axial force is neglected during a circular saw cutting rock in the calculation for formulas. The cutting force can be obtained by the equation as follows:

The contact angle

The angle

The tangential force

The value of

In order to research the rock damage and the circular sawblade cutting performance, the geometric model of a circular sawblade cutting rock is established with Solidworks software, and then, the geometric model is imported to the ANSYS/LS-DYNA software to establish the circular sawblade cutting rock numerical simulation model.

The diameter of the circular sawblade is 380 mm, and it has 24 segments with the length of 40 mm, height of 15 mm, and thickness of 3.4 mm. The rock is a cuboid which is 500 mm in length, 150 mm in width, and 125 mm in height. The hexahedral element SOLID164 is used to mesh the circular sawblade and the rock, and the smallest size of rock element is 1 mm. The model is meshed by local mesh refinement that can reduce the number of grids to improve calculation speed, as well as to ensure the computation accuracy. The key parameters of rock material are plotted in Table

The related parameters of rock material [

Parameters | Mass density (kg/m^{3}) | Young’s modulus (GPa) | Uniaxial compressive strength (MPa) | Brazilian tensile strength (MPa) |
---|---|---|---|---|

Value | 2.7e3 | 45.5 | 120.7 | 12.1 |

Constrains are applied to the numerical simulation model. The full constraints are applied to the bottom surface, the displacements constraints in the

The numerical simulation model of a circular sawblade cutting rock.

The RHT model is divided into three stages: the elastic stage, linear strengthening stage, and damage softening stage. The standardized pressure expression is

The equivalent stress of the elastic limit plane of the initial material is obtained by the equivalent stress on the failure plane, with the expression as follows:

Because the RHT constitutive model introduces the linear reinforcement phase equation, it can describe the strain hardening effect of brittle materials such as concrete and rock. In the linear strengthening stage, the yield stress obeys the linear strengthening model. The function expression is

At the beginning of the elastic phase and the linear reinforcement of the plastic strain, there is no accumulated damage. Only when the equivalent stress strength exceeds the equivalent stress beyond the failure stress intensity, the material begins to accumulate damage and, then, enters the softening stage of damage. The ratio of the cumulative equivalent plastic strain increase to the ultimate failure equivalent plastic strain is defined as the damage variable

The stress state equation with various different load angles is as follows:

The residual stress surface is introduced in the RHT concrete model, and the equivalent stress intensity is

In the process of circular sawblade cutting rock, the failure modes of rock elements is complex, including compressive failure, tensile failure, and shear failure. Under the action of compressive, tensile, and shear stresses, the damage of rock element appears and increases, while with the rock damage reaching 1, the rock element will fail and be deleted. The rock fragments are difficult to be presented; therefore, the amount of the rock fragments is a positive correlation with rock removal volume. Therefore, the rock fragments are evaluated by rock removal volume.

Owing to the grid independence of the simulation model having great influence on the accuracy of simulation results, it is necessary to verify the grid independence. When the relative change rate of cutting force is within the set range scope, the results can be considered reliable and accurate. Finally, the appropriate rock mesh density is selected for the numerical simulation. The relative change rate curve of cutting force under different mesh densities is presented in Figure

Independence test of the rock mesh density.

When the mesh number reaches 144330, the relative change rate is less than 0.11%, which is within 0.15%. The increase of mesh number has little effect on the relative change rate of the cutting force. Therefore, when the mesh number is more than 144330, the results of numerical simulation can be considered accurate.

In order to verify the numerical simulation of a circular sawblade cutting rock, in this paper, the experimental results [

The results of numerical simulation and experiment.

The circular sawblade cuts rock with constant rotation speed and feed speed, with the feed speed of 0.30 m/min, rotation speed of 2000 r/min, and the cutting depth of 30 mm. It is obvious that the force appears and increases as the circular sawblade contacts the rock. The rock element is damaged with circular sawblade compression and tension. The damage value of some rock elements reaches 1 which is acted by the circular sawblade with continuing cutting. While the damage value of rock element reaches 1, the element would fail and be deleted. The rock damage nephograms in the process of circular sawblade cutting rock are plotted in Figure

Rock damage nephograms of a circular sawblade cutting rock at various cutting distances: (a) Rock damage nephogram of 7 mm cutting distance; (b) rock damage nephogram of 9 mm cutting distance; (c) rock damage nephogram of 12 mm cutting distance; (d) rock damage nephogram of 21 mm cutting distance; (e) rock damage nephogram of 27 mm cutting distance; (f) rock damage nephogram of 45 mm cutting distance; and (g) rock damage nephogram of 70 mm cutting distance.

The cutting force has a larger peak value when the circular sawblade cuts the rock at the beginning, as shown in Figure

Force curves of rock cutting with a circular sawblade.

The circular sawblade cuts rock with the feed speed of 0.30 m/min, rotation speed of 2000 r/min, and the cutting depth of 30 mm. The direction of rotation speed has great effects on the cutting performance. The rock damage nephograms with different rotation speed directions are shown in Figure

The rock damage nephograms with various cutting models: (a) the rock damage nephogram with forward cutting; (b) the rock damage nephogram with reverse cutting.

The force curves of the circular sawblade cutting rock with the forward cutting and reverse cutting are presented in Figure

Force curves of the circular sawblade cut rock with forward and reverse cutting: (a) the cutting force of the circular sawblade cutting rock; (b) the normal force of the circular sawblade cutting rock; (c) the tangential force of the circular sawblade cutting rock; and (d) the axial force of the circular sawblade cutting rock.

To investigate the influence of feed speed on the cutting force, the circular sawblade cutting rock numerical with the rotation speed of 2000 r/min, the cutting depths of 10, 30, and 50 mm, and the feed speeds of 0.10, 0.15, 0.20, 0.25, and 0.30 m/min are built. The average force curves with various feed speeds are presented in Figure

Force curves of the circular sawblade cutting rock with various feed speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.

Force curves of the circular sawblade cutting rock with various rotation speeds: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of the circular sawblade cutting rock.

The results of the circular sawblade cutting rock with the feed speed of 0.3 m/min, rotation speed of 1000, 1500, 2000, 2500, and 3000 r/min, and cutting depth of 10, 30, and 50 mm are shown in Figure

Cutting depth is an important cutting parameter which influences cutting force and rock damage. The simulation models with the feed speed of 0.30 m/min, the cutting depths of 10, 20, 30, 40, 50, and 60 mm at the rotation speeds of 1000, 2000, and 3000 r/min are applied to researching influence of cutting depth on cutting force. The cutting force of the circular sawblade cutting rock increases obviously with the increase in cutting depth, as shown in Figure

Force curves of the circular sawblade cutting rock with various cutting depths: (a) the cutting force curve of the circular sawblade cutting rock; (b) the normal force curve of the circular sawblade cutting rock; (c) the tangential force curve of the circular sawblade cutting rock; and (d) the axial force curve of circular sawblade cutting rock.

The average force curves of double circular sawblades cutting rock with various distances between the double circular sawblades are shown in Figure

Force curves of the average value of double circular sawblades with various distances: (a) the cutting force curve of double circular sawblades cutting rock; (b) the normal force curve of double circular sawblades cutting rock; (c) the tangential force curve of double circular sawblades cutting rock; and (d) the axial force curve of double circular sawblades cutting rock.

The forces of the single and double circular sawblades

Single sawblade | Cutting force (N) | Normal force (N) | Tangential force (N) | Axial force (N) | |||||
---|---|---|---|---|---|---|---|---|---|

501.51 | 227.85 | 446.71 | 6.91 | ||||||

Distance | 1# | 2# | 1# | 2# | 1# | 2# | 1# | 2# | |

Double circular sawblade | 10 | 317.6 | 309.9 | 107.5 | 106.3 | 297.4 | 289.5 | 14.8 | 15.6 |

15 | 335.3 | 323.0 | 115.0 | 118.8 | 313.9 | 299.3 | 13.2 | 12.8 | |

20 | 341.9 | 363.6 | 134.7 | 131.7 | 313.5 | 338.2 | 11.0 | 10.6 | |

25 | 396.7 | 378.3 | 142.2 | 140.4 | 369.9 | 350.8 | 9.4 | 9.2 | |

30 | 408.2 | 387.1 | 159.1 | 158.1 | 375.6 | 352.9 | 8.0 | 8.3 | |

35 | 426.5 | 421.5 | 168.0 | 163.0 | 391.8 | 388.5 | 6.6 | 6.5 | |

40 | 429.7 | 441.8 | 175.0 | 177.6 | 392.3 | 404.3 | 6.2 | 5.8 | |

50 | 464.1 | 468.6 | 179.5 | 185.2 | 427.9 | 430.3 | 5.6 | 6.1 |

The results of a single circular sawblade cutting rock are shown in Table

The rock damage area is greatly affected by feed speed, as shown in Figure

Rock damage nephogram with various feed speeds: (a) feed speed of 0.10 m/min; (b) feed speed of 0.15 m/min; (c) feed speed of 0.20 m/min; (d) feed speed of 0.25 m/min; and (e) feed speed of 0.30 m/min.

In order to research the influence of rotation speed on rock damage, it is defined in the circular sawblade cutting rock in the rotation speeds as 1000, 1500, 2000, 2500, and 3000 r/min, as shown in Figure

Rock damage nephogram with various rotation speeds: (a) rotation speed of 1000 r/min; (b) rotation speed of 1500 r/min; (c) rotation speed of 2000 r/min; (d) rotation speed of 2500 r/min; and (e) rotation speed of 3000 r/min.

With the increase in cutting depth, the damage of rock increases. As shown in Figure

Rock damage nephogram with various cutting depths: (a) cutting depth of 10 mm; (b) cutting depth of 20 mm; (c) cutting depth of 30 mm; (d) cutting depth of 40 mm; (e) cutting depth of 50 mm; and (f) cutting depth of 60 mm.

The distance of the double circular sawblades affects the cutting performance. The damage field distributions of the double circular sawblades with various distances between the double circular sawblades are shown in Figure

Rock damage nephogram with various distances between double circular sawblades: (a) distance between doubled circular sawblades of 10 mm; (b) distance between doubled circular sawblades of 15 mm; (c) distance between doubled circular sawblades of 20 mm; (d) distance between doubled circular sawblades of 25 mm; and (e) distance between doubled circular sawblades of 30 mm.

The distance between the double circular sawblades affects the rock damage during circular sawblade cutting rock, as shown in Figure

The specific energy consumption is an important index to evaluate the cutting performance of a circular sawblade. The cutting energy of a circular sawblade cutting rock is defined as the product of tangential force and relative moving distance of the circular sawblade, and the specific cutting energy is defined as the ratio of the cutting energy consumption to rock removal volume.

The specific cutting energy of the circular sawblade cutting rock with various cutting parameters is shown in Figures

The relationship of the specific cutting energy and cutting depth.

Relationship between the specific cutting energy consumption and the distance between the circular sawblades.

The regression results to predict the specific cutting energy.

Variables | Cutting parameters | Regression equation | Correlation coefficient | ||
---|---|---|---|---|---|

SE-CD | RS = 1000 r/min | ^{2} − 0.04554 | 0.89530 | 602.2663 | 1.2383 |

SE-CD | RS = 2000 r/min | ^{2}-0.05062 | 0.95913 | 1556.879 | 2.8962 |

SE-CD | RS = 3000 r/min | ^{2} − 0.07476 | 0.99008 | 7631.371 | 2.7548 |

SE-DD | FS = 0.3 m/min | ^{2} + 0.01443 | 0.95239 | 3850.399 | 1.0724 |

RS = 2000 r/min |

SE = specific energy, CD = cutting depth, DD = distance between the double circular sawblades

The process of the circular sawblade cutting rock is studied in this paper. The influence of cutting parameters and the direction of the circular sawblade on the cutting performance are explored.

Cutting parameters have a great effect on the cutting performance. The cutting force increases with the feed speed, and cutting depth increasing and declines with the increase of rotation speed. The increasing distance of double sawblades causes the cutting force to increase and, then, maintain stable.

The damage and rock removal volume of the rock are influenced by the cutting parameters of the circular sawblade. When the damage of rock reaches 1, the rock elements will fail and be deleted. Therefore, the rock removal volume is closely related to rock damage. The forward cutting and reverse cutting have different influences on rock damage and cutting force. The fluctuation of the forward cutting force curve is much smaller than that of the reverse cutting force curve.

The cutting parameters of the circular sawblade influence the specific cutting energy. The specific cutting energy decreases with the increase in cutting depth, and the specific cutting energy increases with the increase of the distance between double circular sawblades.

The results of the researches could be used to guide rock processing.

The data used to support the findings of this study are included within the article.

There are no conflicts of interest regarding the publishing of this paper.

This work was supported by the projects of the National Natural Science Fund of China (Grant nos. 51674155 and 51974170) and the Natural Science Foundation of Shandong Province (Grant no. ZR2019BEE069).