Wear Analysis of Disc Cutters of Full Face Rock Tunnel Boring Machine

ZHANG Zhaohuang,MENG Liang,and SUN Fei

1 School of Energy,Power and Mechanical Engineering,North China Electric Power University,Beijing 102206,China

2 Foreign Languages School,North China Electric Power University,Beijing 102206,China

1 Introduction*

Tunnel boring machine(TBM)[1]consists of full face rock TBM and shield.Chinese researchers have had a basic command of shield production techniques with the support of the Tenth“Five-Year Plan”and the Eleventh“Five-Year Plan”.Now the research on TBM has been carried out in“863 Program”of scientific administration，which is part of the Twelfth“Five-Plan”.Disc cutters are a type of rock-breaking tool,an important part of full face rock TBM,apt to wear out[2].The complexity of operating objects of TBM and the complexity of their interaction make the layout and employment of disk cutters in the limelight at home and abroad.In the past 40 years,researchers,through experiments on disc cutters in the labs,attempted to discover the empirical parameters for the layout of TBM and conducted field researches by collecting performance parameters of TBM in the field[3].In 1999 BARTON[4]put forth a model of predicting TBM performance by QTBM.ROSTAMI,et al[5],in 1993 developed the prediction model of disc cutters’cutting forces based on the performance of rocks.WIJK[6]developed a math model of predicting TBM performance in 1992.The prediction models of TBM performance mainly lie in the empirical experience and field data,thus its accuracy and reliability also depend on the accuracy and size of data.A case in point is BLINDHEIM[7]at Norwegian University of Science and Technology,who had a comprehensive research on the TBM performance prediction model and in 1979 developed the Norwegian hard rock prognosis system,which was later improved by LISLERUD[8](1988)and BRULAND[9](1999)respectively based on field data of Norwegian tunnels.Other models in the field,such as those by TARKOY[10](1975),NELSON,et al[11–12],are able to make an estimation of penetration and excavating rates in line with the whole hardness and forces of each disc cutter.The test of cutting the full-size rocks along with its physical properties test is likely to be the most reliable field test technique,which has been carried out with linear cutting machines.The forces acting on the cutters are measured out in the test of full-size disc cutters’linear rolling on large-size rock samples.BALCI[13]classified these researches into several types:theoretical model,semi-theoretical model,empirical model and field model.Among them the theoretical model is based on the analysis of forces needed for the excavation per unit volume of rock as well as performance such as compressive resistance,tensile strength,shear strength of rock and rock mechanical properties like rock quality designation.The characteristics of these models have been analyzed and summarized in Refs.[14–15].As a matter of fact,researchers have always been trying to find a more comprehensive,accurate and reliable method to predict TBM working performance.Some researchers[16]advocate that the most reliable way is to combine theoretical analysis with empirical study on the basis of some type of rock with a certain structure and measure out the forces acting on the cutters,and then to adjust the results in line with ground conditions and machine limitations.Rewarding attempts in this respect have been made in Refs.[17–20].All in all,the researchers abroad have had more researches and a deeper understanding of disc cutters’fragmenting rocks,which were mainly undertaken in the labs mostly adopting the method of linear rolling,whose results are beneficial to the life prediction,consumption and costs of TBM disc cutters in the field.Due to the development of China,importance has been attached to the research and application of disc cutters at home[21–22].However,those studies lack an available theoretical and empirical basis in terms of the research on disc cutters’wear and its measurement.Therefore,further theoretical and empirical study is necessary.

Based on the research results as well as macro and microscopical analysis,the wear coefficients for measuring disc cutter wear,such as radial wear coefficient,axial wear coefficient,and trajectory wear coefficient,have been advanced and tested in the trial excavation segment of some project.During the excavation segment,those wear coefficients are modified according to their penetration modification coefficients,discrepancy among the work of disc cutters with various penetration and different locations taken into account.The resultant wear coefficients are respectively referred to as comprehensive radial wear coefficient,comprehensive axial wear coefficient,and comprehensive trajectory wear coefficient,which are implemented to predict the disc cutter wear in various locations.Contrast between the predicted wear and actual wear of disc cutter in the excavation reveals that the wear predicted with comprehensive radial wear coefficient is highly in accord with that predicted with comprehensive trajectory wear coefficient,with accuracy up to 16.12%.

2 Measurement of Disc Cutter Wear

The cutter wear refers to the decrease in the radial length.Microscopically,the intermittently recurrent wear of a certain point on the cutter tip can result from the fragmentation of rocks by disc cutters per revolution.So,the wear capacity of disc cutters can be obtained by measuring the wear of a point on the cutter tip when they crush rocks,that is,radial wear coefficient;while macroscopically,a disc cutter’s wear is the result of interaction between the disc cutter and its working objects,and emerges in the excavation process of TBM in the field.So,the wear can also be obtained by measuring the wear of a cutter within unit excavation length,that is,axial wear coefficient.On the other hand,the analysis of disc cutters’rock fragmentation also reveals that in the excavation process,in terms of one disc cutter,the boring trajectory track of the continuously rolling rock fragmentation is in the form of spatial spiral.Therefore,the cutter wear also can be achieved by measuring the wear of a cutter which rolls on the spatial spiral,that is,trajectory wear coefficient.These three coefficients are called wear coefficients of TBM disc cutters.

2.1 Radial wear coefficient

In view of the analysis above,radial wear coefficient of disc cutters is defined as the radial wear at a point on the cutter tip during a penetration into the rock,expressed as krmm/time.

Assuming the total excavation length of TBM is L,and the depth made by cutter head each revolution is h,then the number of cutter head rotations is L/h;suppose the radius of a cutter is r and the radius of its trajectory is R,then the number of a cutter’s rotations within each revolution of the cutter head is R/r.Thus when the total excavation length of TBM is L,the number of rock-breaking on some point of the cutter is as many as(L/h)×(R/r).If the wear of a disc cutter is m,then

2.2 Axial wear coefficient

In accordance with what analyzed above,axial wear coefficient is defined as wear within unit excavation length of TBM.It is expressed as klmm/mm,then

2.3 Trajectory wear coefficient

During the operation of TBM,each disc cutter(suppose that it’s a geometric point)on the cutterhead moves in a spatial spiral(Fig.1).Suppose that rotation speed of the cutter head is ω,boring speed v,a coordinate is set as shown in Fig.1,where z is an axis of the tunnel,which is in the excavation direction of TBM.Plane xy is the initial plane of excavation,with point A the initial point to set about until point B after time t.Thus the trajectory track can be expressed as follows:

The trajectory length S is given by:

where Θ—Total rotation number of TBM disc cutters within the excavation length L,

The total rotation number M of disc cutters is given by

The TBM trajectory wear coefficient kmis defined as the wear of disc cutters after each revolution on the trajectory track.Thus

3 Determination of Wear Coefficient

3.1 Measurement of wear coefficient

Measurement of Disc cutter wear coefficient can be conducted in the trial excavation or some segment of a TBM project,with rock mass types,traits(crack and weak gravitational plane,and so on),rock performance parameters(tensile strength,compressive strength,shear strength,hardness)and excavation parameters(penetration,rotating speed of cutterhead)recorded,so as to provide a theoretical basis of the measurement of disc cutter wear for other similar projects.For instance,the TBM disc cutters employed in some tunneling subject and its relevant parameters are shown in Table 1[23–24].The average penetration during the excavation of 173 m segment is 7.87 mm,and the wear of each cutter is demonstrated in Table 1.The values of radial wear coefficient,axial wear coefficient and trajectory wear coefficient calculated and resulted from Eqs.(1),(2)and(6)are shown in Table 1.Based on the data in Table 1,the radial wear coefficients,axis wear coefficients,and trajectory wear coefficients of cutters installed in different locations are listed in Fig.2.Fig.2 reveals that radial wear coefficients,axial wear coefficients and trajectory wear coefficients are similar in their variation tendency,and radial wear coefficients are practically the same as trajectory wear coefficients.

Table 1.Relevant parameters and wear coefficients to trial boring section of some project by TBM

The conclusion that radial wear coefficient of a disc cutter is consistent with its trajectory wear coefficient can derive from Eq.(6).Thus Eq.(6)can be expressed as

Fig.2.TBM cutter wear coefficients in different cutter locations of some tunneling TBM project

3.2 Modification in wear coefficients

The factors that have impact on the wear coefficients of TBM disc cutters are multi-layered and involved,which,apart from the geometrical parameters of cutter and its physical property parameters,include geological stratigraphic parameters(rock mass type,rock mass features– crack and weak gravitational plane),rock performance parameters(tensile strength,compressive strength,shear strength and hardness)and excavation parameters(penetration and cutter rotating rates),and so on.Special empirical experiments(tests)are needed with respect to the effects on wear coefficients which cutters’geometrical parameters,physical property parameters of the materials,geological stratigraphical parameters and rock property parameters have.In fact,the effects of those parameters are not isolated but interact with one another.The wear of disc cutters made of some material and some geometrical features,when employed in the similargeological conditions,vary with their locations on the cutterhead.The inner cutters’wear always chimes with a certain rule;while transition cutters’wear is another story.

Assuming that in the trial excavation,the arc length in the rock covered by the inner cutters from the contact point to the utmost penetration is s0,and the arc length covered from the contact point to the utmost penetration in an excavation segment is s,and the modification of wear Coefficients in line with penetration is expressed as ks..

Thus,if the rock in the excavation segment has a better quality than in the trial one,then the cutter penetration in the excavation segment is comparatively smaller,that is,s＜s0,meanwhile there is more stress on the cutter edge in contact with rocks than that in the trial excavation,and the cutter wear increases,thus:ks＞1;if the rock in the excavation segment has a worse quality,the cutter penetration in the excavation segment is larger,that is,s＞s0,meanwhile there is smaller stress on the cutter edge in the excavation segment than in the trial excavation,and the cutter wear is lessened,thus:ks＜1.Therefore,the inner cutter wear coefficient modified in accordance with penetration is defined as ks,which is given by

The expression of s0is the same as Eq.(8),of which h needs to be replaced by h0that is cutter penetration in the trial excavation.

The wear of a transition cutter is sensitive to the penetration,as the plane where its edge is on and the plane where the rock breaking takes place form an obtuse angle larger than 90°,instead of being perpendicular to each other.Thus,the transition cutter wear coefficient modified in accordance with penetration is defined as

With reference to the analysis fore-mentioned,krs=krks,kls=klksand kms=kmksare respectively referred to as comprehensive radial wear coefficient,comprehensive axial wear coefficient and comprehensive trajectory wear coefficient.Comprehensive wear coefficient ksof inner cutter is calculated with Eq.(7)and comprehensive wear coefficient ksof transition cutter is calculated with Eq.(9).In view of Eqs.(1),(2)and(6),the disc cutter wear prediction equations are as follows respectively.

Equation of disc cutter wear mrpredicted with comprehensive radial wear coefficients is

Equation of disc cutter wear mlpredicted with comprehensive axial wear coefficients is

Equation of disc cutter wear mmpredicted with comprehensive trajectory wear coefficients is

4 Application Study of Wear Coefficient

To verify the accuracy and objectivity of wear measurment with the three wear coefficients of TBM disc cutters during the excavation process we experiment on a 5621 m excavation segment of a tunnel.In this segment,the average penetration of disc cutters is 5.02 mm.The wear of disc cutters in each location is shown in Table 2.According to the wear coefficients in Table 1,the wear of disc cutters in this segment predicted with Eqs.(10)–(12)is also shown in Table 2.Thus a correlation curve of predicted wears and cutter wears demonstrated in Fig.3,from which it can be observed that the wear of each disc cutter predicted with comprehensive radial wear coefficients and that predicted with comprehensive trajectory wear coefficients are highly compatible,and though the variation tendency in the wear predicted with comprehensive axial coefficients being in agreement with that predicted with comprehensive radial wear coefficients and trajectory wear coefficients,the prediction value is apparently smaller.Since the comprehensive axial coefficients of disc cutters mainly reflect the cutter wear variations in the radial direction of cutterhead(the direction in which disc cutters are installed on the cutterhead)and the wear of all disc cutters on the cutterhead in the excavation direction takes the average value,hence the wear of each cutter in the excavation direction has not been fully reflected,which is the main reason for the smaller prediction values.The trajectory track of disc cutters,when breaking rocks,is actually in the form of a spatial spiral,therefore,the axial wear coefficients fail to reflect the rock breaking of disc cutters fully and their wear situation objectively.

Fig.3.Contrast between calculated wear and wear of disc cutter

Radial wear coefficient and trajectory wear coefficient of disc cutters are actually two aspects of one issue.it is mainly about the rocks’acting upon disc cutters in terms of radial wear coefficients while the other way round in terms of trajectory wear coefficients.Therefore,the wear values predicted with the two methods are congruent.Axial wear coefficient is popularly used in the disc cutter wear prediction method in the current projects.The comprehensive axial wear coefficients of disc cutters in each location resulted from a segment with average penetration 7.87 mm and excavation length 173 m are used to predict the wear of corresponding disc cutters in the follow-up section(with average penetration 5.02 m,excavation length 5621 m)which then are compared with practical wear values,with the deviation(Δl),relative deviation(δl)and average relative deviation(δlp)obtained(Table 3).Table 3 indicates that the range resulted from the prediction of inner disc cutter wear with comprehensive axial wear coefficient takes place at location number 45,which is 317.89 mm and its corresponding relative deviation is 25.76%;the range resulted from the prediction of transition cutter wear is at location number 59,which is 1171.37 mm,and its corresponding relative deviation is 51.11%;average relative deviation value resulted from the prediction of the total inner cutter wear is 37.70%,that from the prediction of the total transition cutter wear 46.08% and that from the prediction of the total cutter wear 41.20%(close to 40%,objective accuracy of disc cutter wear predicted in the field).The wear of disc cutters predicted in the follow-up segment with comprehensive radial wear coefficient and comprehensive trajectory wear coefficient and the resulted deviation(Δrm),relative deviation(δrm)and average relative deviation(δrmp)are demonstrated in Table 3.Table 3 shows that the range resulted from the prediction of inner disc cutter wear with comprehensive radial wear coefficient and comprehensive trajectory wear coefficient is at cutter number 45,which is 119.47 mm and its corresponding relative deviation is 14.26%;the range resulted from the prediction of transition cutter wear is at number 61,which is 880.29 mm,and its corresponding relative deviation is 48.14%;average relative deviation value resulted from the prediction of the total inner cutter wear is 15.48%,that from the prediction of the total transition cutter wear 16.58% and that from the prediction of the total cutter wear 16.112%.Comparative analysis of the data indicates that in the trial segment the range resulted from the inner cutter wear predicted with comprehensive radial wear coefficient or comprehensive trajectory wear coefficient is less than that predicted with comprehensive axial wear coefficient by 317.89-119.47=198.42;the range from the transition cutter wear decreases by1171.37-8 80.29=291.08;the accuracy of inner cutter wear predicted with comprehensive radial wear coefficient or comprehensive trajectory wear coefficient at cutter number 45 is more than that predicted with comprehensive axial wear coefficient by 25.76%-16.38%=9.38%,accuracy of the actual inner cutter wear increased by 37.7%-1 5.48%=22.22%,accuracy of practical transition cutter wear going up by 46.08%-16.58%=29.5% and accuracy of the total cutter wear rising by 41.20%-16.12%=25.08%.Therefore,the accuracy of disc cutter wear(service life)prediction with comprehensive radial wear coefficient or comprehensive trajectory wear coefficient is conspicuously better than that predicted with comprehensive axial wear coefficient.

Table 3.Deviation of predicted wear of disc cutters in a 5621-meter segment of some TBM project and analysis

5 Conclusions

(1)The wear of disc cutters(service life)is measured with its radial wear coefficient,axial wear coefficient and trajectory wear coefficient.

(2)With various penetrations,radial wear coefficient,axial wear coefficient and trajectory wear coefficient of disc cutters are modified in line with their penetration modification coefficients;and the resultant wear coefficients are referred to as comprehensive radial wear coefficient,comprehensive axial wear coefficient and comprehensive trajectory wear coefficient respectively.

(3)The disc cutter wear predicted with comprehensive radial wear coefficient is highly in agreement with that predicted with comprehensive trajectory wear coefficient,and accurate(in a 5621 m excavation segment,progressive relative deviation is merely 16.12%),while the deviation of disc cutter wear predicted with axial comprehensive wear coefficient is larger(in the 5621 m excavation segment,progressive relative deviation is up to 41%).

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