CHINESE JOURNAL OF MECHANICAL ENGINEERING Vol. 26,aNo. *,a2013 ·1·

DOI: 10.3901/CJME.2013.**.***, available online at www.springerlink.com; www.cjmenet.com; www.cjmenet.com.cn

Design Theory of Full Face Rock Tunnel Boring Machine Transition Cutter Edge Angle and Its Application

ZHANG Zhaohuang 1, *, MENG Liang 2 , and SUN Fei 2

1 School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing 102206, China 2 School of Foreign Languages, North China Electric Power University, Beijing 102206, China

Received October 24, 2012; revised January 29, 2013; accepted February, 2013

Abstract: At present, the inner cutters of a full face rock tunnel boring machine (TBM) and transition cutter edge angles are designed on the basis of indentation test or linear grooving test. The inner and outer edge angles of disc cutters are characterized as symmetric to each other with respect to the cutter edge plane. This design has some practical defects, such as severe eccentric wear and tipping, etc. In this paper, the current design theory of disc cutter edge angle is analyzed, and the characteristics of the rock­breaking movement of disc cutters are studied. The researching results show that the rotational motion of disc cutters with the cutterhead gives rise to the difference between the interactions of inner rock and outer rock with the contact area of disc cutters, with shearing and extrusion on the inner rock and attrition on the outer rock. The wear of disc cutters at the contact area is unbalanced, among which the wear in the largest normal stress area is most apparent. Therefore, a three­dimensional model theory of rock breaking and an edge angle design theory of transition disc cutter are proposed to overcome the flaws of the currently used TBM cutter heads, such as short life span, camber wearing, tipping. And a corresponding equation is established. With reference to a specific construction case, the edge angle of the transition disc cutter has been designed based on the theory. The application of TBM in some practical project proves that the theory has obvious advantages in enhancing disc cutter life, decreasing replacement frequency, and making economic benefits. The proposed research provides a theoretical basis for the design of TBM three­dimensional disc cutters whose rock­breaking operation time can be effectively increased.

Key words: disc cutter, three­dimensional mode, edge angle, full face rock tunnel boring machine (TBM), flat­face cutterhead

1 Introduction ∗

The theory of rock­breaking mechanism of full face rock tunnel boring machine (TBM) disc cutter provides a basis not only for the development of TBM, but also for the prediction of construction time and the cost of a project [1–2] . Hence, it has always been in the limelight in the field at home and abroad and a considerable amount of work has been carried out by the researchers. WIJK [3] developed a mathematical model for the excavation performance of a TBM. ROSTAMI, et al [4] , also developed a model for the cutting force estimation of disc cutters based on the intact rock properties. BARTON [5] developed a predictive formulation of TBM performance using an appropriate rock mass quality index (QTBM). Empirical performance prediction models are mainly based on the past experience and the statistical interpretation of the previously recorded field data on whose quality and amount the accuracy and reliability of these models rely. A case in point is the Norwegian hard rock prognosis system developed by the BLINDHEIM [6] , who did a comprehensive study to develop a TBM performance prediction model at the Norwegian

* Corresponding author. E­mail: zh_zhaohuang@163.com This project is supported by National Natural Science Foundation of

China (Grant No. 51075147) © Chinese Mechanical Engineering Society and Springer­Verlag Berlin Heidelberg 2013

University of Science and Technology (NTNU). Based on field data collected from Norwegian tunnels, LISLERUD [7]

and BRULAND [8] improved this model. NELSON, et al [9–10] , and TARKOY [11] developed models to estimate basic penetration and advance rates by using total hardness and thrust per cutter. The most reliable production estimation technique presently available probably are full­scale laboratory disc cutting tests combined with physical property tests, where the cutter forces are measured for a series of spacings and penetrations in large rock samples with a linear cutting machine (LCM). BALCI [12] classified these researches as theoretical, semi­theoretical, empirical models and field trial of real machines, among which the theoretical models are based on the analysis of the forces required to excavate a unit volume of rock and their relation with the intact rock properties such as rock compressive, tensile and shear strength, rock mass properties like rock quality designation (RQD). Examples of theoretical and semi­theoretical works can be found in Refs. [13–25]. And the characteristics of these models have been analyzed and summarized in Refs. [26–27]. However, a comprehensive, accurate, and reliable production estimation methodology is still being under investigation by researchers. Several potentially different approaches tend to be combined in practice. The most reliable prediction method in competent rock formation presently

YZHANG Zhaohuang, et al: Design Theory of Full Face Rock Tunnel Boring Machine Transition Cutter Edge Angle and Its Application ·2·

combines theoretical and empirical methods by measuring cutter forces and then adjusting the results for ground conditions and machine limitations (GERTSCH, et al [28] ), which have been tested in Refs. [29–31]. After analyzing the movement of the disc cutter rotating

around its own axis as well as around the axis of the cutter head, the project researchers held that the motion of a disc cutter is three­dimensional, combining two types of rotation. The rock­breaking models of disc cutters involved in the researches at home and abroad may be divided into empirical model, one­dimensional model, two­dimensional model, and three­dimensional model. An in­depth research on the two­dimensional model of rock breaking has been under way. GERTSCH, et al [32] , conducted a test on the linear groove of different penetration depths and spacing, by using disc cutter 17″ and K red granite to measure the normal force, rolling force, and side force. Owing to the complexity of the interaction between rock and disc cutters, much attention has been paid to the one­dimensional model and the two­dimensional model. The three­dimensional model of rock breaking, however, should be studied on a larger scale to obtain more accurate results. Therefore, we establish a three­dimensional model and a corresponding theory. Under the guidance of this theory, the transition disc cutter edge angle has been determined and experimental researches have been carried out.

2 Three­dimensional Model Theory of Transition Disc Cutter

Since 1950s foreign scholars have made an in­depth study of the one­dimensional rock­breaking model of TBM disc cutters. The edge angle can be 60°, 75°, 90°, 120°, or 160°, varying with the rock­breaking performance of each disc cutter. In the late 1980s, scholars at home and abroad came to devote themselves to the study of the two­dimensional rock­breaking model, hence the invention of a flat­edge (Constant Cross Section or CCS) disc cutter. Since 1990s, our researchers have been focusing on the theory and experiment of the three­dimensional model. Fig. 1 shows the rock­breaking work of a TBM transition disc cutter, with the front view being the rock­breaking operation of transition disc cutters in the clockwise direction of a working TBM. If point A on the cutter is taken as an observation point, and the velocity of bulk movement is Ae v and the velocity of relative movement Ar v , they can be expressed as follows:

, ,

Ae

Ar

v v r

ωρ ω

= ′ = (1)

where ω —Rotary speed of cutter head (rad/s), ρ—Polar radius of point A at the rock­breaking

edge of disc cutter (m), ω ′ — Rotary speed of disc cutter(rad/s),

sin , i R r

r α

ω ω − ′ =

Ri—Orbit radius of disc cutter observed (m), r—Radius of disc cutter (m), α—Installation angle of disc cutter (Fig. 1).

Fig. 1. Rock breaking of TBM transition disc cutter

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·3·

Hence the three­dimensional model theory of the rock­breaking movement of the TBM transition disc cutter.

3 Design Theory of Transition Disc Cutter Edge Angle

TBM transition disc cutters’ tipping and invalidation as a result of excessive wear can often be observed in its working process. Experimental study and actual observation show that the invalidation results from the sideslip of transition disc cutters during the rock­breaking movement, which then produces great side friction on the disc cutter edge. This friction results in the tipping as well as the friction wear of the disc cutter. Therefore, the key to designing the transition disc cutter edge angle is to reduce the sideslip of the rock­breaking edge to the minimum, that is, to prevent the sideslip at the spot of the largest impact load or to make slippage as small as possible. In other words, the rock­breaking velocity vector of the transition disc cutter of the largest impact load should coincide with the plane of the disc cutter edge. According to Fig. 1, the bulk movement velocity vector

of the transition disc cutter at point A Ae v coincides with or is parallels to the XY coordinate plane, which causes sideslip of the disc cutters. The bulk movement velocity can be divided into (see Fig. 1 (c))

sin sin , cos cos ,

Aex Ae

Aey Ae

v v v v

Φ ωρ Φ Φ ωρ Φ

= = = = (2)

where Aex v —Projection of the bulk movement velocity vAe on x­axis,

Φ —Polar angle of Point A on the rock­breaking disc cutter edge,

Aey v —Projection of the bulk movement velocity vAe on y­axis.

Aex v , a component of the bulk movement velocity of point A on x­axis, is subdivided into Aex v ⊥ vertical to the disc cutter active face and / / Aex v parallel to the active face (see Fig. 1(c), O A ′ is the radius of the disc cutter, its plane being the disc cutter active face), denoted as

/ /

cos sin cos , sin sin sin .

Aex Aex

Aex Aex

v v v v

α ωρ Φ α α ωρ Φ α

⊥ = = = =

(3)

/ / Aex v parallel to the disc cutter active face, is then further subdivided into / /o Aex v acting towards the centric axis of disc cutter rotation and / / r Aex v acting along its relative velocity (see Fig. 1(c)). Thus,

/ / o / /

/ / r / /

cos sin sin cos , sin sin sin sin .

Aex Aex

Aex Aex

v v v v

θ ωρ Φ α θ θ ωρ Φ α θ

= = = = (4)

Aey v , a component of the bulk movement velocity of the rock­breaking point A on y­axis, is divided into o Aey v

pointing to the disc cutter rotation center and r Aey v acting along the relative movement velocity (see Fig. 1 (c)). Thus,

o

r

sin cos sin , cos cos cos .

Aey Aey

Aey Aey

v v v v

θ ωρ Φ θ θ ωρ Φ θ

= = = = (5)

No relative slip is generated in the movement of the disc cutter along the relative movement velocity, into which, therefore, there will be no more investigation here. According to Fig. 1, the component of the bulk movement velocity of rock­breaking point A on the transition disc cutter in the direction of radius is composed of the velocity component o Aey v and the velocity component / /o , Aey v expressed as

o o / /o cos sin sin sin cos . A Aey Aex v v v ωρ Φ θ ωρ Φ α θ = − = − (6)

Suppose the rock­breaking point A on the transition disc cutter edge in question has the largest impact load. The rock­breaking velocity vector of the largest impact load point on the transition disc cutter should coincide with the disc cutter active face. Thus, the tangent of the angle Θ between the slip velocity of point A and the disc cutter active face at the moment is expressed as

o

sin cos tan cos sin sin sin cos sin cos

, cos sin sin sin cos

Aex

A

v v

ωρ Φ α Θ ωρ Φ θ ωρ Φ α θ

Φ α Φ θ Φ α θ

⊥ = = = −

−

(7)

from which

sin cos arctan .

cos sin sin sin cos Φ α

Θ Φ θ Φ α θ

= −

(8)

Empirical tests and theoretical analyses discover that when the disc cutter works on such hard rock as mixed granite and compound gneiss, the application point of normal force and rolling force acting on the disc cutter edge in contact with the rock lies at two­thirds of the penetration depth, pointing to the rotating center of the disc cutter, with the geometrical relationship shown in Fig. 1. We can yield

2 sin , 3 cos

3 cos cos , 3 cos

h r

r h r

θ α

α θ α

= − =

(9)

2

2

2 (3cos ) sin ,

2 tan / 3 2 / (3cos ) tan 3

cos , 2 tan / 3 2 / (3cos )

i i

i

i i

rh R R h rh

R h R R h rh

α Φ

α α

α Φ

α α

= − + − = − +

(10)

YZHANG Zhaohuang, et al: Design Theory of Full Face Rock Tunnel Boring Machine Transition Cutter Edge Angle and Its Application ·4·

where h is the cut depth of the disc cutter (per revolution). With reference to the characteristics of the rock to be

broken, the edge angle of the transition disc cutter established by strength theory isϕ . Then two side­edge angles in θ and wi θ can be respectively expressed as

in

wi

, 2

. 2

ϕ θ Θ

ϕ θ Θ

= − = +

(11)

Those are the calculation formula of the inner cutting edge angle and the outer cutting edge angle of the transition disc cutter designed in accordance with the three­dimensional model theory. For the effect drawing of the transition disc cutter thus designed, see Fig. 2.

4 Practical Application

The radial layout chart or plane expansion graph of a certain TBM disc cutter is demonstrated in Fig. 3. There are

eleven transition disc cutters with the radius being 216 mm (its arrangement parameter shown in Fig. 3. According to the recorded empirical boring data, the average cut depth is 6 mm. The calculation parameters and results of Eqs. (8)–(10) are presented in Table 1.

Fig. 2. Effect drawing for theoretical application

Fig. 3. Layout of disc cutters on a certain TBM cutter head

Table 1. Calculation parameters and results of a certain type of TBM transition disc cutter

Installation angle α/rad

Orbit radius Ri/mm

cosθ sinθ cosΦ sinΦ cosα sinα tanα Deflection angle Θ/rad

Deflection angleΘ/(°)

0.090 122 3 890 0.990 703 0.136 360 0.999 971 0.007 572 0.995 942 0.090 000 0.090 367 0.055 521 3.181 104 0.179 534 3 952 0.990 589 0.137 190 0.999 972 0.007 499 0.983 927 0.178 571 0.181 489 0.054 253 3.108 447 0.268 945 4 013 0.990 395 0.138 597 0.999 972 0.007 461 0.964 052 0.265 714 0.275 622 0.052 593 3.013 361 0.357 571 4 072 0.990 116 0.140 602 0.999 972 0.007 459 0.936 750 0.350 000 0.373 632 0.050 585 2.898 334 0.446 076 4 129 0.989 736 0.143 273 0.999 972 0.007 497 0.902 147 0.431 429 0.478 224 0.048 245 2.764 227 0.535 185 4 184 0.989 236 0.146 727 0.999 971 0.007 577 0.860 174 0.510 000 0.592 903 0.045 575 2.611 233 0.624 000 4 236 0.988 591 0.151 059 0.999 970 0.007 705 0.811 548 0.584 286 0.719 964 0.042 626 2.442 275 0.715 128 4 286 0.987 736 0.156 613 0.999 969 0.007 896 0.755 009 0.655 714 0.868 485 0.039 329 2.253 372 0.801 746 4 330 0.986 686 0.163 181 0.999 967 0.008 144 0.695 453 0.718 571 1.033 242 0.035 965 2.060 668 0.885 586 4 369 0.985 369 0.171 064 0.999 964 0.008 462 0.632 836 0.774 286 1.223 517 0.032 520 1.863 237 0.958 920 4 400 0.983 88 0.179 554 0.999 961 0.008 820 0.574 405 0.818 571 1.425 078 0.029 369 1.682 720

Average 2.534 453

With reference to the characteristics of the rock to be broken, the edge angle ϕ of the transition disc cutter established by strength theory is 35°. If 2.5 , Θ = ° as is

demonstrated in Table 1, the two side­edge angles are computed with Eq. (13):

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·5·

in

wi

35 2.5 15 , 2 2

35 2.5 20 . 2 2

ϕ θ Θ

ϕ θ Θ

° = − = − ° = ° = + = + ° =

o

o (13)

Based on the aforementioned theoretical calculation and analysis, the design effect drawings of inner and outer edge

angles of the transition disc cutter are shown in Fig. 2. To validate the theory, Ref. [33] introduces the test

contrasting the cutter ring of the inner cutter and that of the disc cutter as designed in the theory of transition disc cutter edge angle, which are used in the transition zone respectively. Test results are shown in Table 2.

Table 2. Empirical test of theoretical results

Cutter number 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 8.17* 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8.19 29 31 32 32 32 33 34 34 30 29 25 11 11 5/4/6 5/4/6 5/4/6 8.20 36 37 39 38 38 39 40 40 38 37 34 16 16 10/6/8 10/6/8 10/6/8 8.20** 15 0 0 0 0 0 0 0 0 0 0 16 16 10/6/8 10/6/8 10/6/8 8.21 24 18 18 13 13 13 13 15 12 19 24 22 22 15/8/12 15/8/12 15/8/12 8.24 29 26 26 18 18 18 18 20 18 24 27 25 25 20/18/19 20/18/19 20/18/19

Note: The wearing capacities of 63, 64, and 65 are wearing capacity of inner diameter/wearing capacity of pitch diameter/wearing capacity of outer diameter, respectively; *—Layout of disc cutters: transition cutter rings are those of inner cutter; **—Replacement of disc cutters: all replaced by gauge cutter rings at cutter spacing 51–60.

Table 2 reveals the wear characteristics and the lifetime characteristics of the inner cutter ring used in the transition zone as well as those of the transition disc cutter ring designed according to the transition disc cutter edge angle theory, whose contrastive analyses are shown in Table 3 and Table 4.

Table 3. Life and replacement rule of the common cutter ring in the transition zone

Parameter New

cutter ring Changing cutter No. 1

Changing cutter No. 2

Changing cutter No. 3

L

Number of cutter spacing N

51–65 51–60 51–65 51–60 L

Cutter ring life L/m/frequency

0 70–80 130–140 70–80 L

Table 4. Life and replacement rule of the newly designed cutter ring

Parameter New cutter

ring Changing cutter No. 1

Changing cutter No. 2

L

Number of cutter spacing N

51–65 51–65 51–65 L

Cutter ring life L/m/frequency

0 160–170 160–170 L

It is demonstrated in Table 3 and Table 4 that the design of transition cutter ring in line with the three­dimensional model theory not only boosts the service life of cutter ring but also reduces the frequency of cutter replacement in the transition zone, thus saving more time and making more profits.

5 Conclusions

(1) The rock­breaking movement of a TBM disc cutter is practically three­dimension spatial motion. When the disc cutter is working on such hard rock as mixed granite and

compound gneiss, the largest impact load of the rock­breaking edge occurs at two­thirds of the cut depth. (2) The disc cutter, whose design takes the velocity

vector plane of the largest impact load of the rock­breaking edge as the symmetric plane of the disc cutter edge, not only has a much longer lifespan, but also greatly reduces the frequency of tipping.

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Biographical notes ZHANG Zhaohuang, born in 1963, PhD, is a professor at North China Electric Power University, China. His research interests include full face rock tunnel boring machine and renewable energy equipment. Invention award by China Society of Rock Mechanics and Engineering (rank 1); Hebei Province Scientific and Technical Advance second prize (rank 1); 15 patents by Chinese State Patent Office (rank 1); 2 academic works (rank 1); 50 academic papers, of which there are 20 EI papers. Tel: +86­10­61772485; E­mail: zh_zhaohuang@163.com

MENG Liang, born in 1972, PhD, is a lecturer at North China Electric Power University, China. His academic interests extended to TBM . Tel: +86­10­82022269; E­mail: ml7218@hotmail.com

SUN Fei, born in 1972, master, is a lecturer at North China Electric Power University, China. His academic interests extended to TBM . Tel: +86­10­61772817; E­mail: sunfei@ncepu.edu.cn