Numerically investigating the crushing of sandstone by a tooth hob

doi:10.1007/s11709-023-0978-6

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (6) : 964-979 https://doi.org/10.1007/s11709-023-0978-6

RESEARCH ARTICLE

Numerically investigating the crushing of sandstone by a tooth hob

Dongning SUN^1,²(

), Baoning HONG^1,², Xin LIU^1,³, Ke SHENG^1,², Guisen WANG^1,², Zhiwei SHAO^1,², Yunlong YAO^1,²

¹. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing 210098, China
². Geotechnical Research Institute, Hohai University, Nanjing 210098, China
³. Institute of Tunnel and Underground Engineering, Hohai University, Nanjing 210098, China

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Abstract

To investigate the mechanical process that occurs between rocks and tooth hobs, the crushing of sandstone with a tooth hob was simulated using reconstructed multi-mineral mesoscopic numerical models of various grain-sized sandstone samples. When a piece of sandstone is crushed by the tooth of a hob rolling at a constant speed, the resultant reaction forces of the sandstone on the tooth first hinder and then contribute to the rolling of the hob. The absolute value of the longitudinal reaction force is significantly higher than that of the lateral reaction force. Because the tooth was subjected to reaction forces from the sandstone, forces and moments were applied to the hob in order to keep the hob rolling. The applied forces were equal in value and opposite in direction to the reaction forces of the sandstone on the tooth. Three typical curves of the work done by the applied forces and moment were obtained, and the contribution of the applied lateral force and moment to the total work done for crushing sandstones was variable; however, no work was done by the applied longitudinal force. Moreover, the applied longitudinal force and total work were positively correlated with the strength of sandstone samples. The total work, applied forces, and moment increased with the maximum penetration depth of the tooth in the sandstone.

Keywords sandstone tooth hob crushing process reaction force numerical simulation

Corresponding Author(s): Dongning SUN

About author:

^* These authors contributed equally to this work.

Just Accepted Date: 01 March 2023 Online First Date: 27 July 2023 Issue Date: 30 August 2023

Cite this article:

Dongning SUN,Baoning HONG,Xin LIU, et al. Numerically investigating the crushing of sandstone by a tooth hob[J]. Front. Struct. Civ. Eng., 2023, 17(6): 964-979.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-023-0978-6
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I6/964

Tab.1 Basic information regarding the sandstone samples

Fig.1 Full images and detailed views of the (a) very coarse, (b) coarse-, (c) medium-, and (d) fine-grained sandstone samples.

Fig.2 (a) Histogram showing the grain-size distributions; (b) grain-size distribution curves of the samples (VC: very coarse-grained sandstone; C: coarse-grained sandstone; M: medium-grained sandstone; F: fine-grained sandstone).

Fig.3 Results of the mineral composition analysis test.

Fig.4 Stress?strain curves of the different grain-sized sandstone samples: (a) very coarse-grained sandstone samples; (b) coarse-grained sandstone samples; (c) medium-grained sandstone samples; and (d) fine-grained sandstone samples.

Fig.5 (a) Failure modes of sandstone samples; (b) locally zoomed images of cracks.

Fig.6 Results of the Brazilian splitting test.

Fig.7 Reconstruction of the numerical model: (a) initial model; (b) Voronoi cell (each color block is a Voronoi cell); (c) final model (disks of the same color are bonded into a mineral grain).

Fig.8 Numerical models of different grain-sized sandstone samples.

Tab.2 Meso parameters of the contact between adjacent disks in the same grain

Tab.3 Calculation method for meso parameters of the contact between adjacent disks in two different grains

Fig.9 Comparison between the simulation results of the biaxial compression test and the experimental results of the triaxial compression tests: (a) very coarse-grained sandstone; (b) coarse-grained sandstone; (c) medium-grained sandstone; (d) fine-grained sandstone.

Fig.10 Simulation results of the Brazilian splitting tests.

Fig.11 Typical failure modes of the numerical models used in the (a) biaxial compression test and (b) Brazilian splitting test (each color block represents a fragment).

Fig.12 Illustration of the rock-crushing process: (a) dimensions of the tooth hob; (b) schematic diagram of the rock-crushing process by the tooth hob.

Fig.13 Numerical model of crushing sandstone using the tooth of a rolling hob.

Fig.14 Simulation results of the vertical penetration of hob in the coarse-grained sandstone model: rolling angle of the hob: (a) 0; (b) 0.5α; (c) 1.0α; (d) 1.5α; and (e) 2.0α (maximum penetration depth of the tooth into sandstone is 10 mm).

Fig.15 Force analysis of the hob in the rock-crushing process.

Fig.16 Lateral force varies with the variation in the rolling angle of the hob when the sandstone model and maximum penetration depth of the tooth in the sandstone are different: (a) maximum penetration depth of 3 mm; (b) maximum penetration depth of 5 mm; (c) maximum penetration depth of 10 mm; (d) maximum penetration depth of 15 mm.

Fig.17 Longitudinal force varies with variations in the rolling angle of the hob when the sandstone model and maximum penetration depth of the tooth in the sandstone are different: (a) maximum penetration depth of 3 mm; (b) maximum penetration depth of 5 mm; (c) maximum penetration depth of 10 mm; (d) maximum penetration depth of 15 mm.

Fig.18 Moment varies with the variation in the rolling angle of the hob when the sandstone model and maximum penetration depth of the tooth in the sandstone are different: (a) maximum penetration depth of 3 mm; (b) maximum penetration depth of 5 mm; (c) maximum penetration depth of 10 mm; (d) maximum penetration depth of 15 mm.

Fig.19 Work curves vary with variations in the rolling angle of the hob: (a) work curves when the medium-grained sandstone model is crushed by the hob (maximum penetration depth of 10 mm); (b) work curves when the coarse-grained sandstone model is crushed by the hob (maximum penetration depth of 3 mm); (c) work curves when the very coarse-grained sandstone model is crushed by the hob (maximum penetration depth of 5 mm) (work-F_Cx is the work done by lateral force, work-F_Cy is the work done by longitudinal force, work-M_C is the work done by moment, and total work is the sum of all other works).

Fig.20 Work curves vary with the variations in the maximum penetration depth of the tooth into the sandstone.

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