Predictive plots for conical pick performance using mechanical and elastoplastic properties of rocks

Serdar Yasar

Department of Mining Engineering, Karadeniz Technical University, Trabzon, 61080, Turkey

Keywords:Performance prediction Rock cutting tests Specific energy Cutting force Plasticity index

ABSTRACT Conical picks are by far the most widely used drag type cutting tools employed on partial face rock excavation machines.The cutting force and specific energy are two important design parameters for the conical pick performance, and the rock cutting testing is considered as the promising tool for determining these parameters. In the absence of an instrumented cutting rig, researchers generally rely on empirical predictive plots. For this, this paper suggests predictive plots for estimating the cutting force and specific energy, in consideration of the cutting depth to define the cuttability with conical picks. In this context,rock cutting tests were carried out on six volcanic rock samples with varying cutting depths using the unrelieved and relieved cutting modes. The cutting force and specific energy were correlated with the uniaxial compressive strength, Brazilian tensile strength, elasticity modulus, and plasticity index. Predictive plots were proposed for different cutting depths in the unrelieved and relieved cutting modes and exponential relationships were obtained among the cuttability parameters, and mechanical and elastoplastic properties of rocks.

1. Introduction

Mechanical excavation machines have been widely used for excavation of underground structures both in mining and civil purposes since 1950s. Conical picks are the most dominant rock cutting tools employed on partial rock excavation machines such as roadheaders, continuous miners, and shearer-loaders. Cuttability estimation of rocks plays a key role in the performances of mechanical excavators.The specific energy(SE)and cutting force(FC)are regarded as two important cuttability parameters in terms of the performance of cutting tool,which determines the operational accomplishment of an excavation machines(Mellor,1975).Several methods have been utilized for estimation of the performance of cutting tool including numerical methods, empirical models,theoretical models and rock cutting tests, where the rock cutting testing is regarded as the soundest method of cuttability estimation. In the absence of an instrumented cutting test, empirical models are needed,which correlate SE and FC with the mechanical properties of rocks. SE is defined as the energy consumed for cutting a unit volume of rock,which is also the significant indicator of rock cutting efficiency. SE is determined by

where SE is the specific energy(MJ/m3),FC is the mean cutting force(kN) and, and Q is the volume of the excavated rock material (m3/km).

The unrelieved and relieved cutting modes, as shown in Fig.1,demonstrates the variation of SE with ratio of cutter spacing (s) to cutting depth(d).Three cases are illustrated in this figure:cases(a)and (b) showing the relieved cutting conditions and case (c)demonstrating the unrelieved cutting mode. In case (a), picks are located close to each other that picks overcrush the rock with excessive amount of energy consumed.In case(c),picks are located far from each other that there is no interaction between succeeding pick and picks cut the rock in an isolated manner.In case(b),picks are placed so effective to each other that picks interact with following picks and this point is regarded as the optimum cutting condition.

The optimum SE (SEopt), as shown in Fig.1, indicates the optimum cutting condition for a selected rock type. This point contributes to valuable information for performance prediction, and SEoptcan be used for the performance prediction of any mechanical excavator(Rostami et al.,1994).

Fig.1. Variation of SE with s/d ratio for relieved cutting of rocks and cutting traces.

The cutting force, in addition to SE, is critically important for performance of picks. Since each pick has a mechanical strength,the maximum cutting force FC′is an important indicator for utilization of picks.Also,the cutting force might be used for cutter head configuration using the relieved cutting data.

Theoretical works are concentrated on finding FC′experienced by the pick and explaining the rock fragmentation mechanism.The first theoretical model for conical picks was proposed by Evans(1984), assuming that the uniaxial compressive strength (UCS)(σc)and the tensile strength(σt)are dominant in rock cutting with conical picks. Ranman (1985) used chip geometry to explain the rock fragmentation mechanism of conical picks and developed a model.Roxborough and Liu(1995)modified Evans’theory to boost the force prediction ability.Goktan(1997) improved Evans’theory to address some limits, for example, FC′does not reduce to zero when pick angle is reduced to zero,even though it should be,and σcseems to be inversely proportional to FC′but not reasonable.Goktan and Gunes (2005) modified the original Evans’ theory to consider the angle of attack in force prediction equation due to the fact that other models did not take the angle of attack in account and they assumed that the pick attacked the rock perpendicularly where practically it is not possible.Bao et al.(2011)and Wang and Su (2019) used edge-chipping data to evaluate the pick cutting force in conical pick cutting. Li et al. (2018a) used linear elastic fracture mechanics to evaluate the cutting force based on a deficiency of previous models that these models evaluated the cutting force at the moment of breakage, even though cutting force was formed during the crack initiation phase. All theoretical models suffer from some oversimplified assumptions that result in insufficient explanation of cutting phenomenon and this also leads to the over- or under-estimation of force prediction under actual field conditions (Yasar and Yilmaz, 2018).

As an alternative method, numerical modeling has been adopted to simulate rock cutting(e.g.Menezes et al.,2014).Some results are also reported on the performances of conical pick cutting mechanics using numerical modeling and expert systems (Su and Akcin, 2011; Tang and Wang, 2014; Li et al., 2017, 2019; Jiang and Meng, 2018).

In addition to aforementioned methods, for simplicity upon application,researchers tried to correlate the parameters obtained from conical pick experiments with some physico-mechanical properties of rocks. Copur et al. (2001) correlated SEoptwith σc, σtand product of σcand σt,and found linear correlations among these parameters.Copur et al.(2003)utilized the punch penetration test results to predict some cuttability parameters,such as SEoptand FC.Balci et al. (2004) studied the relationships between SEoptand several mechanical properties of rock and ores,such as σc,σt,static and dynamic elasticity modulus, and Schmidt hammer rebound value. Bilgin et al. (2006) correlated SEoptand FC with numerous properties of rocks and suggested several empirical equations for further studies. Tumac et al. (2007) determined SEoptusing Shore hardness number and deformation coefficient.Tiryaki et al.(2010)suggested some empirical equations for determination of FC using previously published data. Yilmaz et al. (2014) obtained some fitting equations through correlating FC, SEoptand hybrid dynamic hardness values. Wang et al. (2017) developed empirical models based on principal component and ridge regression method by compiling the previously published data. Wang et al. (2018) proposed predictive plots to estimate SE using σcand σtin conical pick cutting. In addition to the empirical models, the effect of the confining stress on the performance of conical picks is also reported(e.g. Li et al., 2018b; Wang et al., 2019).

Previous studies on conical pick cutting showed that FC increases linearly with increasing cutting depth (Bilgin et al., 2006;Yasar and Yilmaz, 2019). However, there is always an offset on the y-axes(FC axes)both for drag pick cutting(Yasar and Yilmaz,2018)and disc cutting (Pan et al., 2019), which accentuates the importance of the evaluation of correlations based on the cutting depth.Additionally,it is well known that cutting depth in field conditions can change during cutting action, due to the trajectory of the cutting tool (Hekimoglu, 1991). Even though empirical models were proposed based on the rock strength properties (UCS, tensile strength,Schmidt hardness,etc.),all of them were concentrated on the relationships for a certain cutting depth with normalizing FC which may yield improper predictions.Furthermore,the plasticity index obtained from iterative impacting using a Schmidt hammer has rarely been used for the rock cuttability assessment.

Based on this, this study concentrates on rock cutting tests on selected volcanic rocks using conical picks,and suggests predictive plots with special reference to the cutting depth for site engineers with partial face machines. Six volcanic rock samples (two andesites and four tuffs)were subjected to cutting tests with vertical rock cutting rig (VRCR). Cutting tests were realized both in the unrelieved (isolated) and relieved (interaction) cutting modes. The maximum cutting force (FC′), the mean cutting force (FC), and the specific energy (SE) were recorded during the cutting tests. Variations of FC and SE with rock strength with cutting depth were investigated. Predictive plots were suggested using the UCS, Brazilian tensile strength, tangent elasticity modulus, and plasticity index (outcome of iterative impacting with the Schmidt hammer).

2. Rock characterization and cutting tests

2.1. Selected rock samples

Partial face machines are generally used to excavate the formations having intact rock strength (UCS) between 50 MPa and 100 MPa. In this study, in consideration of the performances ofpartial face machines, rocks having UCS between 50 MPa and 100 MPa were selected for controlled rock cutting tests. These samples include two andesites(A1 and A2)and four tuffs(T1,T2,T3 and T4). These volcanic rock samples contain no visible discontinuity and flaw, thus they can be considered as being homogenous to some extent.

Table 1Results of mechanical and elastoplastic tests.

Fig. 2. Main components of the experimental setup.

Fig. 3. Conical pick used in this study and its specifications.

Table 2Results of conical pick tests in the unrelieved cutting mode(Yasar and Yilmaz,2019).

Table 3Results of conical pick tests in the relieved cutting mode demonstrating the optimum cutting conditions (Yasar and Yilmaz, 2019).

2.2. Mechanical and elastic properties of rocks

UCS (σc) and Brazilian tensile strength (σbt) tests were conducted to determine the mechanical properties of rocks and to provide the basic input data for predictive plots. Both tests were carried out according to the recommendations of ISRM (2007),where UCS tests were repeated at least five times and tensile strength tests were replicated ten times.Loading rates for UCS and Brazilian tensile strength tests were 1 kN/s and 0.2 kN/s,respectively.

Tangent moduli of elasticity (E) of the rocks were determined simultaneously with the UCS tests using an extensometer mounted compressometer. Tangent moduli of elasticity were calculated using the axial strain and the axial stress corresponding to the 50%of the ultimate strength of the rocks. Five replications were accomplished, and results were averaged.

2.3. Plasticity index

Fig. 4. Variations of FC with (a) σc and (b) PI in the unrelieved cutting mode.

McFeat-Smith (1977) proposed a coefficient of deformation(plasticity index)based on the repetitive Shore hardness testing on the same location of a rock sample. It has been stated that after repetitive impacts, a plastically deformed surface was formed as a result of work hardening. McFeat-Smith (1977) used Shore scleroscope for impact testing and determining plasticity index.Furthermore,McFeat-Smith and Fowell(1977)used plasticity index along with cone indenter hardness to estimate the specific energy in rock cutting.A digital Schmidt hammer of Proceq(SilverSchmidt)was used in this study for this purpose instead of the Shore scleroscope which is not a very common testing arrangement nowadays. Twenty impacts were achieved on the same spot of the rock sample. Plasticity index is calculated by

where PI is the plasticity index,Q2is the 20th rebound number,and Q1is the first rebound number.Higher PI means higher plasticity of the rock.Results of the mechanical and elastoplastic rock properties are listed in Table 1.

2.4. Rock cutting tests

Rock cutting tests were carried out using VRCR. Basic components of the testing system are demonstrated in Fig. 2. VRCR is a mobile testing apparatus designed as an attachment to hydraulic testing machines. A cutting tool is attached under the piston of VRCR and this piston moves downwards and upwards with movement of the hydraulic bending machine piston.As the cutting tool enters into rock, the tool experiences cutting force and the force component is measured by the load-cell of bending machine.

Cutting tests were conducted using the relieved and unrelieved cutting modes for simulation of field cutting conditions and isolated cutting. Isolated cutting tests were applied with varying cutting depths(d)from 1 mm to 9 mm.It is seen that SE reached to a horizontal asymptote at d = 9 mm approximately, which was accepted as a cut-off value. Each test level was repeated at least three times and all results were averaged.The conical pick used in this study is shown in Fig. 3 along with photos referencing the cutting tests.Results of the unrelieved cutting tests are tabulated in Table 2.

Since SE reached to minimum at d=9 mm,the relieved cutting tests were carried out with a fixed value of d = 9 mm (Yasar and Yilmaz, 2019). Pick spacing (s) values were changed to determine the optimum cutting condition for the selected rock sample.The s/d ratios were selected as 2,3,4,5 and 8.Results of relieved cutting tests for optimum conditions are presented in Table 3.

3. Discussion

It is clear from the previous study(Yasar and Yilmaz,2019)that the FC-d and FC′-d plots for each rock have a trend of linearity.These results match with previous studies that showed the linear trend of FC and FC′with d(e.g.Hurt and Laidlaw,1979;Hurt,1980;Roxborough et al., 1981; Inyang, 2002; Bilgin et al., 2006). As an exception, Demou et al. (1983) presented an exponential relation between FC′and d with the exponent of near 1.3, which was discussed by Inyang (2002). Although FC and FC′increase linearly,there is a constant which should be taken in account when normalizing the cutting forces with d. This constant should be investigated in further studies and is is not the goal of this paper.

Fig. 5. Variations of SE with (a) σc, (b) σbt, (c) E and (d) PI in the unrelieved cutting mode.

In Fig. 4, variations of FC with σcand PI for different cutting depths are demonstrated. One can see that FC shows exponential trends with rock mechanical and elastoplastic properties. FC increases with increasing σcand with decreasing PI, which demonstrates the plasticity of the representative rock sample.Correlations among FC and σbtand E are not plotted in Fig. 4 due to the low coefficients of determination and will be summarized later.Furthermore,since FC′/FC ratios vary between 1.93 and 2.62 and FC′shows similar trends with FC, correlations between FC′and rock mechanical and elastoplastic properties are not given in a graph form; however, the corresponding predictive equations will be highlighted later.

While correlations with the UCS (σc) give the highest coefficients of determination (R2), the tensile strength exhibits the lowest R2values.According to the results of this rock sample group,σcand PI are the best indicators for the cutting force in the unrelieved cutting mode. The trend between FC and σbtfor changing d values shows very poor correlation, due to the high FC value experienced during the cutting of sample A2, even though this sample has a σbtvalue very close to sample T3.For both σcand σbt,the trends are not linear but exponential.In all theoretical models(Evans,1984;Roxborough and Liu,1995;Goktan,1997;Goktan and Gunes,2005),in some empirical models(Bilgin et al.,2006),it has been stated that FC in the unrelieved cutting mode increases linearly with σcor σbt; however, experimental results in this study show contrary results.The mismatch between the empirical studies on the model might be due to the rock/ore type employed in this study. Different rock/ore types can show different cutting characteristics.

Variations of SE with σc, σbt, E and PI for changing d values are plotted in Fig.5.It shows that the SE values increase exponentially with σc, σbtand E with varying coefficients of determination and decrease exponentially with increasing plasticity of the rocks.Bilgin et al.(2006)found power relation between SE and E.Tumac et al. (2007) showed an inverse power relation between SE and PI from Shore hardness testing.Coefficients of determination for σc-PI plots are enhanced with the increase in d,and correlations exhibit the highest R2values at d = 9 mm.

Relieved cutting test results have implications with respect to field cutting conditions,since picks on cutting heads cut the rock by interacting with the neighborhood cutter.Hence,these results gain importance for cutter head design when determining the optimum pick spacing in the cutter head and for performance prediction as well (Rostami et al., 1994). The optimum spacing may only be determined by rock cutting tests, thus experimental results have utmost significance for this aspect. One can see from the results(Table 3) that the optimum s/d ratio varies between 3 and 5 for these rock groups, which is consistent with the previous studies(Evans,1984;Bilgin et al.,2006).Based on this,empirical estimation of SE, FC′and FC are showed in this study using σc, σbt, E and PI.Variations of FC′and FC with σc, σbt, E and PI are plotted in Fig. 6.These curves have a trend similar to that in Fig. 4. FC has exponential trends with σcand σbt.Bilgin et al.(2006),however,showed a power relationship of FC with σcand σbt, and this may be due to usage of different kinds of rocks/ores which belong to different lithologies. Both FC′and FC show better correlation with σcrather than σbtwith R2= 0.91 and 0.93, respectively. Exponential correlations have been retrieved between FC and FC′with E and PI.

Fig. 6. Variations of FC and FC′ with (a) σc, (b) σbt, (c) E and (d) PI in the relieved cutting mode under optimum cutting conditions.

Table 4Overall summary of proposed equations.

Fig. 7 presents the variations of SEoptwith σc, σbt, E and PI.Variation of SEoptwith σcshows a high correlation value with R2=0.93.Similar to previous results,σcshows the best correlation with the dependent variable (SEopt). One may estimate FC′, FC and SEoptempirically only using σcand PI with a high coefficient of determination. However, one should consider the critical comments on the uniaxial compression test, since some researchers stated that the uniaxial compression test suffers from some limits such as influence of sample dimensions, condition of the sample ends,and loading rate effect(Fowell,1993;Fowell et al.,1994).Due to these problems, we should be careful when using empirical models. However, in the absence of an instrumented cutting test,these equations may contribute to valuable tips for practice users.In addition to the graphical illustration of the relationships among parameters, all proposed predictive plots are summarized in Table 4.

In addition to the obtained correlations between dependent and independent variables, this study introduces some other findings.First, the necessity of the proposed relationships between dependent (FC, FC′and SE) and independent (σc, σbt, E and PI) variables with respect to the cutting depth (d) is disclosed, since there is a certain offset on the y-axis of FC-d plot.Furthermore,correlations of the same parameter with cutting depth values show different coefficients of determination. On the other hand, for the first time,plasticity index or deformation coefficient (PI) is determined through a Schmidt hammer, while previous studies used Shore hardness testing to determine the PI parameter(e.g.McFeat-Smith and Fowell,1977;Tumac et al.,2007).However,Schmidt hammers are, nowadays, much more widespread and widely used in rock mechanics applications.It has been showed that PI can be used for FC, FC′and SE estimation both in the unrelieved and relieved cutting modes successfully. The plasticity of this rock group, to some extent, is the indicator for the strength of the rock samples; while sample A2 has the highest compressive strength, this rock sample showed the lowest plasticity. Finally, plasticity index (PI) is a nondestructive testing technique and is also the cheapest and easiest testing procedure among other mechanical testing procedures.

4. Conclusions

The conical pick cutting tests were conducted on six different volcanic rock samples both in the unrelieved and relieved cutting modes. Dependent variables (FC, FC′and SE) obtained from these tests were correlated with rock properties such as UCS, tensile strength, tangent elasticity modulus, and plasticity index. The correlation study was accomplished with focus on the cutting depth that all of the relationships were presented for varying cutting depths. Some results are highlighted below:

(1) FC′and FC increase linearly with increasing d with high coefficients of determination, and there is significant offset in the y-axis (FC) which entails the cutting depth-oriented correlations.

(2) Parameters FC,FC′and SE show exponential correlations with σc,σbt, E and PI in all cutting depths and cutting modes.

(3) Compressive strength (σc) exhibits the highest coefficient of determination for estimation of all cuttability parameters.

(4) Application of the PI index is presented using the Schmidt hammer.

(5) PI with the Schmidt hammer seems to be a promising tool for estimation of the cuttability parameters, showing a better performance than the elasticity modulus and tensile strength. It is a very useful tool since it is a non-destructive testing method.

It should be noted that all these correlations are pertinent to the rock group used in this study, covering the partial-face excavation machine applicability range. Suggested predictive plots will be useful for the site engineers who deal with the excavation machines employing conical picks. The cutting performance of a conical pick can be estimated using simple rock mechanics tests or non-destructive tests such as PI in a simple manner. Besides, it is noteworthy that one of the most reliable methods for rock cuttability assessment is rock cutting testing. However, in the absence of an instrumented cutting test,empirical models could serve as a useful guide for rock cuttability estimation.On the other hand,the normal force component at this stage is not possible to be measured with the present design of the VRCR.Further studies are needed on modification of the system for measurement of the normal force component.

Declaration of competing interest

The author declares that he has no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The author greatly acknowledges the anonymous reviewers who have helped to improve the quality of this paper.