当前位置：搜档网 › Thrust distribution characteristics of thrust systems of shield machines based

Thrust distribution characteristics of thrust systems of shield machines based

Journal of Mechanical Science and Technology 30 (1) (2016) 279~286

https://www.sodocs.net/doc/b79913902.html,/content/1738-494x(Print)/1976-3824(Online)

DOI 10.1007/s12206-015-1231-6

Thrust distribution characteristics of thrust systems of shield machines based on

spatial force ellipse model in mixed ground?

Kongshu Deng1,2,*, Yuanyuan Li3 and Zhurong Yin1

1Engineering Research Center of Advanced Mining Equipment, Ministry of Education, Hunan University of Science and Technology,

Xiangtan City, 411201, China

2Hunan Provincial Key Laboratory of High Efficiency and Precision Machining of Difficult-to-Cut Material,

Hunan University of Science and Technology, Xiangtan City, 411201, China

3School of Arts, Hunan University of Science and Technology, Xiangtan City, 411201, China

(Manuscript Received March 27, 2015; Revised July 5, 2015; Accepted August 21, 2015)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Abstract

The objective of this research is to investigate force distribution characteristics for propelling system of tunneling machines in mixed ground. First, a mechanical model for pushing system in composite strata is constructed. Then, eccentricity trunk is determined using spatial force ellipse eccentricity to measure the degree of uniformity of forces applied on rear segments in a thrust system. Finally, the eccentricity trunk is used to the thrust system of a tunneling machine applied in engineering. Force distribution performance of various arrangements with equal quantities of jacks is discussed in detail. Results from virtual prototype simulation prove the numerical analyti-cal results. A theoretical foundation and support is provided for the design of non-equidistant pushing system of tunneling machines un-der composite stratum.

Keywords: Thrust distribution; Propelling system; Eccentricity trunk; Eccentricity ring; Mixed ground

1. Introduction

Earth pressure balance (EPB) tunneling has frequently in-creased in recent years [1]. Shield tunneling has been success-fully applied to urban tunneling construction under various ground conditions in response to the escalating needs of up-grading and expanding existing infrastructures. The shield machine can be considered as the most commonly used mechanized tunneling technology [2].

A simplified diagram of an EP

B shield machine is illus-trated in Fig. 1. The rotating cutters fixed on a cutter-head excavate the soil, which passes into the pressurized head chamber, during tunneling. The entire machine is pushed ahead by hydraulic cylinders composed of thrust system that applies pressure on the rear segments [3, 4]. The screw con-veyor removes the excavated soil from the head chamber. It does not only drive the shield ahead during tunneling, but also controls the machine to ensure that the shield can advance along the expected path to construct the planned tunnel line

[5].

A complex working environment is created by inconsisten-cies in resistance surrounding the machine caused by the ani-sotropy of the excavation interface rocks and the weight of the machine. The offset load on segments would be easily gener-ated under such special conditions. Consequently, problems caused by meandering routes, ground subsidence, and ma-chine failure would be more likely to occur. Therefore, the analysis and design of the thrust system are highly significant [6].

Hydraulic cylinders in the current driving system of an EPB shield machine are parallel to the axis of the shield and are equidistant along the circumference. The structure could pro-duce a huge change-of-direction load during tunneling be-cause of the curved excavation and heterogeneous geologic conditions. Consequently, non-equidistant driving system should be preferred under some special conditions such as non-homogeneous oil, large changing-direction load on the body of the machine, and overweight cutting-head. Studies have shown different possible deformation characteristics and natural frequencies in various driving system configurations with similar numbers of hydraulic cylinders [7, 8]. Spatial force ellipse transmission characteristics have been examined in single stratum in Refs. [9, 10]. Although force deformation behavior for driving system in mixed ground has been dis-cussed in detail in Ref. [11], few studies have investigated the force performance of thrust systems with various arrange-ments in composite strata.

*Corresponding author. Tel.: +86 731 138********, Fax.: +86 731 58290624 E-mail address: dengkongshu@https://www.sodocs.net/doc/b79913902.html,

? Recommended by Associate Editor Beomkeun Kim

? KSME & Springer 2016

280 K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286

The article first presents the mechanical model for the push-ing system of a tunneling machine. Then, the eccentricity trunk is established based on the spatial force ellipse eccen-tricities as scales for even degree of force distribution. Finally, force distribution performance of the different layouts of a driving system is discussed using the eccentricity trunk to the propelling system in an engineering application. Results from virtual prototype simulation corroborated the numerical ana-lytical results. This study could provide a theoretical founda-tion and support for the design of a new thrust system of shield tunneling machines under composite stratum.

2. Construction of mechanical model for thrust sys-tem in mixed ground Hydraulic cylinders of a propelling system are laid out in

the circular direction of a shield, in accordance with Ref. [12] (Fig. 2). The circular center of the pushing hydraulic cylinders is considered as the coordinate origin, and the z -axis is parallel to the center line of the hydraulic cylinder and opposite to the driving direction. The y -axis is perpendicular to the z -axis and points to the ground. The x -axis is determined by the right-hand rule. Thus, a Cartesian coordinate system is constructed. In Fig. 2, F z is the resultant resistance in the z -direction, whereas M x and M y are the drag torques in the x- and y -directions, respectively. F i (i = 1, 2,..., N ) is the thrust of the i th hydraulic cylinder in the driving system, and the system has N jacks.

According to the mechanical mode in Fig. 2, the following dynamical equations can be obtained, as follows:

10N

i z

i F F

=-=? (1) 10N

i i y

i F x M =+=?

(2) 1

i i

x i F y

M =-=?

(3)

where (x i , y i ) denotes the i th hydraulic cylinder layout coordi-nates in the thrust system.

3. Construction of eccentricity trunk for a propelling system in composite strata To force uniformity on segments, the optimization function is as follows:

11.2N i i F F -=??D =-?÷è?

(4)

In Eq. (4), F - can be expressed as follows:

i z

i F F F

N -

=? (5)

where N is the number of hydraulic cylinders of the pushing system.

Forces i F will be more uniform when the value of D is minimum,. According to Eqs. (1)-(4), the Lagrange function can be derived as follows:

121131N N i z i i y i i N i i x i L F F x F M y F M l l l ===????

=D +-+++

?÷?÷è?è?

??-?÷è?

???. (6)

The partial differential form for Eq. (6) can be obtained as follows:

1230z i i i i L F

F x y F N

l l l ?=-+++=?. (7)

The hydraulic cylinders are spaced along the circumference. Thus, the following equation can be obtained:

222i i x y r +=

(8)

where r is the radius of the layout of the jacks.

Combining Eqs. (1)-(3) and (7), the force ellipse matrix can

Fig. 1. Earth pressure balance tunneling machine.

Fig. 2. Mechanical model of a propelling system.

K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286 281

be obtained as follows:

111111231 (1)

000...000...0001 (0110)

...1

1z y N x

N N z N

N z F F M x x M y y F F x y N x y F N l l l éù

êú

éùéù-ê

úêúêúêú

êúêúêú

êúêúêú=êúêúêú

êúêúêú

êúêúêúêúêúêúêúêú????êú

M M M M M M M . (9)

Combining Eqs. (7)-(9), the following equations can be ob-tained:

max 1z F

F N l =-+,

(10) min 1z F

F N

l =--

(11)

The plane α is constituted by Eq. (7), and the cylinder sur-face β is constructed using Eq. (8) (Fig. 3). The space point (x i , y i , z i ) is on the closed spatial ellipse curve line of intersection between the plane α and cylinder surface β. F i is the value of the force of the i th hydraulic cylinder at the stress point coor-dinates (x i , y i ). The spatial ellipse is defined as the force ellipse that represents the law of thrust distribution for thrust system in tunneling machines.

According to Eqs. (10) and (11), the parameters of the force spatial ellipse can be written as follows:

a = (12)

b r = (13)

e =

(14)

where a represents the major axis for the force spatial ellipse, b is the minor axis, and e is the eccentricity of the ellipse.

The degree of the offset load is reflected by the eccentricity of the force ellipse in Eq. (14). The offset load in the thrust system becomes progressively larger with increasing eccen-tricity.

Matrix A is assumed to be the inverse matrix of the coeffi-cient matrix of Eq. (9). Thus, the matrix equation can be re-written as follows:

1123z y x N z z F F M M F F A N F N l l l éùêúéù-êúêúêúêúêúêú

êú=êúêúêúêúêúêúêúêúêú??êú??

M M (15)

where 11

1213212223313233.........N N N N N N a a a a a a A a a a ++++++éùêúêú=êúêúêú??

M M M M . The following two Lagrange parameters can be obtained by

solving Eq. (15), as follows:

2212223z y x b F b M b M l =++ (16)

3313233z y x b F b M b M l =++ (17)

where 3212124

1N N N i

i b a a

+++==+

?, 2222N b a +=-, 2323N b a +=,

3313134

1N N N i

i b a a

+++==+

?, 3232N b a +=-, and 3333N b a +=.

The following equation can be obtained by introducing Eqs. (16) and (17) into Eq. (14):

()()2

2221222331323321z y x z y x e b F b M b M b F b M b M e +++++=-. (18)

In Ref. [10], the relationship between force distribution el-lipse eccentricity and configurations for systems is discussed in single stratum. No pure single stratum exists in tunneling construction conditions, and composite strata are always en-countered by mechanized excavating equipment. Conse-quently, all generalized net external forces F z , M x , and M y are not constants but rather variable parameters with limits de-rived from corresponding construction geological survey. As indicated in Eq. (18), if eccentricity e is given, an elliptic cy-lindrical surface called eccentricity ring will be made by M

M y , and F z that constitute a three-dimensional (3D) coordinate system (Fig. 4). One eccentricity ring manifests that eccentric-

Fig. 3. Spatial force ellipse model for thrust system.

282 K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286

ity for any point in the eccentricity ring is reciprocal to each other. Given an array of eccentricities , a family of elliptic cylindrical surfaces called eccentricity trunk is formed.

The majority of driving systems applied in engineering is often spaced in layout. For simple control and low cost in practical application, all hydraulic cylinders are divided into four groups that can be controlled individually by adjusting pressure and displacement of each group [13].

The jacks are placed evenly in a circle with radius r . Thus, Eqs. (19)-(21) can be given as follows:

0N N

i i i i x y ====??

(19)

10N

i i

i x y

==?

(20)

221

N N

i i i i Nr x y ====

??. (21)

The following set of coefficients for Eq. (20) can be ob-tained by inserting Eqs. (19)-(21) into Eqs. (9) and (15), as follows:

213123320b b b b ==== (22)

22332

b b Nr ==-. (23)

The following Eq. (24) can be obtained from the set of equations produced by substituting Eqs. (22) and (23) in Eq. (18), as follows: 222

24242441x y

e M M N r N r e +=-. (24)

From Eq. (24), for an equidistant pushing system in a tun-neling machine, one spatial cylinder surface corresponding to an eccentricity value e will be constructed in 3D space com-posed of M x , M y , and F z . Then, a series of cylindrical surfaces could be defined by the different eccentricities. The center-line of the eccentricity trunk is the z -axis. The radii of all cylinder

surfaces are dependent on the number of jacks N and ar-rangement radius r for hydraulic cylinders.

4. Case comparison study

Basic structural parameters for a shield machine with a di-ameter of 6.34 m are r = 2.85 m, N = 22, W = 200 t, and L = 7420 mm [14], as shown in Fig. 5. W and L represent the weight and length of the main machine, respectively.

For simplicity of control, all cylinders in the engineering application are divided into four groups, namely, groups A, B, C and D (Fig. 6). Groups A and C compromised six cylinders each, whereas groups B and D compromised five cylinders each. The pressure and velocity of each group are regulated to control the large machine during excavation. Many tunnels have been constructed using this configuration. The non-spacing systems are presented in Table 1, corresponding to the spacing driving system in Fig. 6.

The angle between the line connecting the center to the i th hydraulic cylinder and the positive x axis is θi that is defined as the coordinate angle for each jack (Fig. 6). Coordinate an-gles of the parameters are arranged for the driving system when the radius of the layout has been decided. The jacks are distributed evenly, and the angle contained by the two lines of the adjacent jacks is constant (Fig. 6). The coordinate angles of all hydraulic cylinders in Nos. 2-5 non-spacing systems are listed in Table 1.

The eccentricity trunk in Fig. 7 is constructed by inserting

all coordinate angles for spacing driving systems into Eq. (18).

Fig. 4. Eccentricity model for propelling system.

Fig. 5. EPB shield with a diameter of 6.34 m.

Fig. 6. No.1 of the four-group spacing propelling system.

K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286 283 The center of the eccentricity trunk is the z-axis, and eccentric-

ity ring is circular in shape. All parameters displayed in Table

1 for the four different driving systems are introduced into Eq.

(20). The eccentricity trunks for the non-equidistant layout

propelling systems from No. 2 to No. 5 are drawn in Figs. 8-

11, respectively. All eccentricity trunk figures indicate that the

closer each eccentricity ring is from the center of the eccen-

tricity trunk, the faster is the decrease in eccentricity. Al-

though the propelling systems have similar numbers of hy-

draulic cylinders, the location and shape for each eccentricity

trunk depends on the configuration parameters. Thus, different

arrangements with similar numbers of jacks would have dis-

tinct force distribution performance according to the limits for

the external net force M x, M y, and F z obtained from given

mixed ground conditions. Different arrangements of the pro-

pelling system are fit for different cases. The best arrangement

is therefore preferred as the ground of limits for each net force.

4.1 Numerical analysis

The shield machine with a diameter of 6.34 m is assumed to

work under the following conditions. The tunneling soil body

and the weight of cutter-head in machine would produce drag

force F Z varying from 0.9 ′ 103 t to 1.1 ′ 103 t. The resistive

momenta M x and M y range from -258.5 tm to -231.4 tm and -709.8 tm to -657.1 tm, respectively. All parameters are inserted into the eccentricity model, with force ellipse eccentricity of 0.3 as a limit (Fig. 18). The external forces are only in the ec-centricity ring for No. 5 system. Hence, the No. 5 non-distance thrust system should be preferred under the given conditions. 4.2 Simulation analysis in ADAMS

A 3D simulation model for each system can be established based on the parameters for the 6.34-m diameter shield ma-chine and all coordinate angles listed in Table 1. A 3D virtual prototype of No. 5 non-spacing propelling system is built in

Table 1. Phrase angles for Nos. 2-5 non-spacing systems.

Fig. 7. Eccentricity trunk for No.1 spacing propelling system. Fig. 8. Eccentricity trunk for No.2 non-spacing propelling system. Fig. 9. Eccentricity trunk for No.3 non-spacing propelling system.

284 K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286

ADAMS based on to all parameters for the shield machine in Table 1 (Fig. 13). The numerical analysis thrusts in Figs. 15-17 are compared with the simulation results for the 1st , 6th and

th hydraulic cylinders in the No. 5 pushing system under the simulated resistances displayed in Fig. 14. The simulation results are very consistent with the numerical calculation. The spatial force ellipse eccentricities for the five driving systems under the given conditions are obtained during shield excava-tion through the simulation in ADAMS (Fig. 18). Eccentrici-ties for Nos. 1-4 systems are much larger than 0.3, except for the No. 5 system. This result suggests that the thrust transmis-sion performance for No. 5 system would be superior to those of the other systems under the given conditions. Therefore, the simulation results prove that the No. 5 system should be pre-ferred over the other systems under given conditions.

Therefore, results from the analysis of a propelling system

Fig. 10. Eccentricity trunk for No.4 non-spacing propelling system.

Fig. 11. Eccentricity trunk for No.5 non-spacing propelling system.

Fig. 12. Relationship between external forces and five systems at ec-centricity ring equal to 0.3.

Fig. 13. Virtual prototype for No.5 uneven system.

Fig. 14. Simulated resistances for 3D virtual prototype.

Fig. 15. Comparison of thrust for No.1 jack.

K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286 285

showed the following:

(1) Different arrangements with similar numbers of jacks in the pushing system have distinct eccentricity trunks that indi-cate the force distribution performance.

(2) The preferred layout may be determined by analyzing the relationship between eccentricity ring and external net generalized forces.

(3) Simulation results verify the eccentricity trunk model of the numerical analysis of a propelling system.

5. Conclusions

This paper presents a mechanical model for a propelling system of a shield machine in mixed ground. The eccentricity trunk could be found based on the mechanical and the spatial force ellipse distribution model for the thrust system. Force distribution characteristics for the propelling system are inves-tigated in detail by applying the eccentricity trunk to a practi-cal system used in real engineering projects. The following conclusions can be drawn by comparing the force perform-ance of the propelling systems in composite strata:

(1) Although the number of a driving system has been de-termined, different arrangements would result in distinct ec-centricity trunks, thereby indicating the varied flexibility in mixed ground.

(2) An eccentricity model for the thrust system can be con-firmed by virtual prototype simulation in ADAMS.

(3) Optimal layout pushing system can be established by analyzing the relationship between eccentricity ring in trunk and external net forces.

Acknowledgements

This research is sponsored by the China Hunan Provincial Science & Technology Department Research Project (No. 2015JC3110), and the Hunan University of Science and Tech-nology Ph.D. Research Foundation (No. E51387).

References

[1] D. Peila, P. Andrea and C. Alessio, Earth pressure balance

tunnelling in rock masses: Laboratory feasibility study of the conditioning process, Tunnelling and Underground Space Technology , 35 (2013) 55-66.

[2] R. Vinai, C. Oggeri and D. Peila, Soil conditioning of sand

for EPB applications: A laboratory research, Tunnelling and Underground Space Technology , 23 (2008) 308-317.

[3] D. Peila, C. Oggeri and L. Borio, Using the slump test to as-sess the behavior of conditioned soil for EPB tunneling, Envi-ronmental and Engineering Geoscience , 15 (2009) 167-174. [4] A. S. Merritt and R. J. Mair, Mechanics of tunnelling ma-chine screw conveyor: model tests, Geotechnique , 56 (2006) 605-615.

[5] H. Y. Yang et al., Electro-hydraulic proportional control of

thrust system for shield tunneling machine, Automation in Construction , 18 (2009) 950-956.

[6] L. T. Wang et al., Modeling and analysis of thrust force for

EPB shield tunneling machine, Automation in Construction , 27 (2012) 138-146.

[7] K. S. Deng et al., Research on characteristics of deformation

in thrust system for EPB shield machines, Tunnelling and Underground Space Technology , 26 (2011) 15-21.

[8] X. Q. Tang et al., Research on natural frequency characteris-tics of thrust system for EPB machines, Automation in Con-struction , 22 (2012) 491-497.

[9] K. S. Deng et al., On the analysis of force transmission per-

formance for the thrust systems of shield tunneling machines,

Fig. 16. Comparison of thrust for No. 6 jack.

Fig. 17. Comparison of thrust for No.1 jack.

Fig. 18. Eccentricities for five systems.

286K. Deng et al. / Journal of Mechanical Science and Technology 30 (1) (2016) 279~286

ICIRA (2009) 268-278.

[10]K. S. Deng et al., Force transmission characteristics for the

non-equidistant arrangement thrust systems of shield tunneling machines, Automation in Construction, 20 (2011) 588-595. [11]K. S. Deng et al., Study on deformation characteristics

under variable stiffness for propelling mechanism of EPB shield machines in mixed ground, Journal of Mechanical Science and Technology, 28 (2014) 3679-3685.

[12]K. S. Deng, Research on characteristics and layout optimi-

zation for thrust system in EPB shield machines. Ph.D. The-sis, Tsinghua University, Beijing (2010).

[13]F. X. Zhang, Shield tunnelling method, China Communica-

tions Press (2004) (in Chinese).

[14]R. Min and J. Huang, Φ 6.34m EBP machine, Building

Construction, 12 (2002) 46-49 (in Chinese).

Kongshu Deng received his Bachelor

of Science degree in Mechanical Engi-

neering from Inner Mongolia University

of Science and Technology, Baotou,

China in 2002. He obtained his M.Sc.

degree from Beijing Jiaotong University,

Beijing, China in 2006 and the Ph.D.

degree from Tsinghua University, Bei-jing, China, in 2010. His two later degrees are also in me-chanical engineering. He is currently an associate professor at the Engineering Research Center of Advanced Mining Equipment, Ministry of Education, Hunan University of Sci-ence and Technology, China. His research interests include the design and analysis of the new thrust system for tunneling machines.

Thrust distribution characteristics of thrust systems of shield machines based

相关文档

最新文档