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SCIENCE CHINA Technological Sciences Science China Press and Springer Verlag Berlin Heidelberg 2013 Corresponding author email mtds RESEARCH PAPER September 2013 Vol 56 No 9 2124 2131 doi 10 1007 s11431 013 5248 8 Compliance of hydraulic system and its applications in thrust system design of shield tunneling machine SHI Hu1 2 GONG GuoFang2 YANG HuaYong2 2 State Key Laboratory of Fluid Power Transmission and Control Hangzhou 310027 China Received January 4 2013 accepted April 7 2013 published online May 16 2013 As the most significant performance compliance of hydraulic system is defined as the capacity to accommodate the sudden change of the external load Due to the different requirements of the compliant tasks the existing method for mechanical sys tems cannot be used in the analysis and design of the hydraulic system In this paper the definition and expression of compli ance of hydraulic system are proposed to evaluate the compliance of the hydraulic system operating under sudden change load Because the unexpected geological conditions during excavation may exert sudden change load to the shield tunneling ma chine the compliance theory has found a right application in the thrust hydraulic system By analyzing the basic operating principle and the commonly used architectures of the thrust hydraulic system a compliance based thrust hydraulic system de sign method is presented Moreover a tunneling case is investigated in the paper as an example to expound the validation of design procedure In conclusion the compliance of the hydraulic system can be served as an evaluation of the capability in conforming to the load impact giving supports for the design of the thrust hydraulic system of shield tunneling machines compliance hydraulic system load impact thrust system design shield tunneling machine Citation Shi H Gong G F Yang H Y et al Compliance of hydraulic system and its applications in thrust system design of shield tunneling machine Sci China Tech Sci 2013 56 2124 2131 doi 10 1007 s11431 013 5248 8 1 Introduction Due to their high durability high power to weight ratios and rapid responses hydraulic drive systems have been playing a very important role in a diverse range of applica tions and industries Especially for the heavy duty machines and those operating under the worst or extreme conditions such as construction machinery hydraulic power transmis sion is the best and mostly exclusive solution An essential issue in such applications is the proper interaction between the actuator and the environment because it is inevitable for hy draulic systems to suffer considerably heavy impact loads In such situations the hydraulic system should be compliant with the external load applied on it and make a stable re sponse as much as possible to the environment while the energy of impacts is dissipated and the desired working pressure is achieved The transition between the normal conditions to impact response may involve undesirable im pact forces that drive a stable operating system into instabil ity or even cause great damage to the system Stabilizing the impact effect during the transitional motion can be ap proached from two viewpoints 1 4 i Study the dynamic response characteristics of the closed control system built up with pressure or flow feedback ii improve the system with the addition of an energy storage equipment to absorb hydraulic shock or load impact However until now no parameter or variable is available for defining and evaluating whether the system response characteristic is good enough to get through the specific Shi H et al Sci China Tech Sci September 2013 Vol 56 No 9 2125 severe working conditions either quantitatively or qualita tively The compliance of hydraulic system just deals with this issue encountered in hydraulic power transmission that is how effectively a given hydraulic system can reduce the harm due to the external impact load The compliance theory and the corresponding evaluation method for mechanical systems have been frequently con cerned by researchers Many research achievements have been applied to industry fields 5 8 Those investigations mainly cope with industrial robots and manipulators con sidering the stiffness or flexibility of the mechanisms and performing the compliance control to ensure the force or motion to be compliant to the operating environment e g inserting a bolt into a hole in an assembly process Unfor tunately the compliance in hydraulic systems is quite a dif ference so those employed in the design and analysis of a mechanical system are not applicable to the hydraulic sys tem Shield tunneling machine is a modern construction ma chine dedicated to building up tunnels through various geo logical conditions The thrust system is a key part of the machine driven by hydraulic system because of its large force 9 The underground conditions are so complicated and usually unpredictable that the thrust system may be exposed to extreme working conditions and encounter im pact load like force transmitted from tunneling face with rocks ahead of the machine Compliance of the thrust sys tem is one of the most pronounced issues that needs to be addressed during the thrusting process Some researchers have defined the compliance of shield tunneling machine for analysis and design They defined the stiffness of the mechanical system and the equivalent contact stiffness of the tunnel face 10 This definition mainly deals with the load transmission characteristics of the mechanical structure and parts so the related investigations cannot be applicable to the dynamic process of the hydraulic actuators due to their different focuses The main motive of this paper is to develop a definition and evaluation system for the compliance of the hydraulic system and apply it to the design of thrust hydraulic system of shield tunneling machine The article is organized as fol lows Section 2 describes the definition and the mathemati cal description of the compliance of the hydraulic system In Section 3 the compliance of the hydraulic system finds a typical application in analysis and design of the thrust hy draulic system of shield tunneling machine Compliance based thrust hydraulic system design for a specific con struction site characterized by complex geological layers is conducted in Section 4 including the compliant perfor mance comparison with the existing systems Finally con clusions are presented in Section 5 2 Compliance of hydraulic system In order to investigate the compliance of the hydraulic sys tem an index is defined by means of an expression with combination of the physical parameters The definition ac commodates many factors that determine the compliant performance of a hydraulic system 2 1 Definition and expression The compliance of a hydraulic system is an index for evalu ating the system capacity to accommodate the sudden load changes and load impacts It is denoted by the ratio of the product of general volume change and working pressure to the product of general volume and pressure variation of a given hydraulic system working under a severely changing load That is n c pV Ctt pV 1 where C represents compliance and is dimensionless V and V stand for general volume and its change respectively pn is normal working pressure p is pressure variation and tc is compliance duration The followings should be noted 1 The sudden load here means that the external force applied on the hydraulic sys tem is large enough to generate a very high working pres sure and open the relief valve in the system The small pressure fluctuation occurs under normal operating condi tion is not concerned in this study 2 The general volume change includes not only the expansion of the closed hy draulic chamber resulting from load impact but also the equivalent volume change that is the sum of the instantane ous flow rate through the relief valve over t duration In other words the volume and its change employed in this study are a dynamic rather than a static object The diagram demonstrating the relationship between load variation volume change and the work of the sudden load is shown in Figure 1 The upper and lower hatched areas refer to the general volume and pressure variation respectively In this way the compliance of the hydraulic system can be taken as an energy conversion and release process Accord ing to the knowledge in physics there exists an equation as p VpA xF x 2 where p is the working pressure of the hydraulic system A is the piston area of the hydraulic cylinder and x is the distance due to the piston yield to the sudden load In fact when the working pressure of the hydraulic sys tem is higher than the normal value after encountering sud den load the load peak begins to do work and leads to the general volume change Thereby the energy instantaneous ly accumulated under sudden load is dissipated It can be seen from Figure 1 that C is equal to the ratio of two hatched areas Obviously the larger C value indicates better compliance of the hydraulic system Eq 1 explains the compliance of the hydraulic system 2126 Shi H et al Sci China Tech Sci September 2013 Vol 56 No 9 Figure 1 Compliance principle of hydraulic system under sudden load in theory but the general volume is usually not measurable So it is very difficult to evaluate the compliance of a hy draulic system directly by this expression On the other hand when a hydraulic system is operating we would pay more attention to the interactions between the system and the environment The performance of the hydraulic system is mostly considered in a macroscopic view concerning the external force and the working pressure In order to evaluate the compliance of the hydraulic system to the specific sud den load quantitatively another variable is introduced to reveal the relationship between the external load change and the working pressure variation as shown in eq 3 It clear ly demonstrates the impact load transmission and decrease from external environment through hydraulic system as the diagram depicted in Figure 2 The compliance evaluation index can be defined as F C pA 3 where F is the variation of the external force acting on the hydraulic system p is the measured working pressure var iation of the hydraulic system and A is the effective acting area of the hydraulic actuator Figure 2 gives a simple graphical explanation of the ex pression in eq 3 Under the normal condition an external force F0 is applied on the hydraulic actuator Suddenly the external force changes into 2F0 Because of the compliance Figure 2 Schematic diagram of impact load transmission and decrease of the hydraulic system the equivalent force obtained by the working pressure conversion is 1 5F0 Therefore the com pliance evaluation index of the hydraulic system is 2 cacu lated by comparing the variation magnitudes Apparently compliance is closely related to the external load and is a load dependent characteristic attributed to a given hydraulic system In fact although eqs 1 and 3 describe the compliance of the hydraulic system from different aspects they are in agreement with each other in theory According to the defi nitions a larger general volume change and a smaller pres sure variation always mean larger values of both C and C The latter is a reflection of the former in terms of action and reaction load Based on the dynamic analysis of the hydrau lic response to sudden load 11 we can obtain CkC 4 where k is a coefficient related to the influencing factors to be discussed in the next section 2 2 Influencing factors According to eq 1 variable V is the most important fac tor to determine the compliance of a hydraulic system Suf fering the same load change a larger volume change allows the hydraulic system to release more instantaneously accu mulated energy achieving better compliance Based on the definition we can obtain ddd rL pV Vq tqtqt 5 where q is the general flow rate corresponding to the gen eral volume change during compliance time qr is the total flow rate through the pressure relief valve is the effec tive bulk modulus of the hydraulic fluid and qL is the other equivalent flow rate during compliance process including the leakage flow According to eq 5 for a basic hydraulic system the influencing factors of compliance mainly include effec tive bulk modulus of hydraulic oil structural parameters of pressure relief valve hydraulic pipelines and accumu lators in some cases By conducting the theoretical analy sis we can draw the following conclusions 11 1 Effective bulk modulus determines the response speed of the hydraulic system A higher effective bulk modulus makes the system respond to the load change more quickly consequently it reduces the compliance of the hydraulic system 2 For a pressure relief valve a larger opening diameter means a smaller hydraulic resistance Thereby it can ac commodate more overflow volume and increase the com pliance of the hydraulic system 3 The diameter and length of the hydraulic pipes as well as the volume of the accumulator are directly related to the Shi H et al Sci China Tech Sci September 2013 Vol 56 No 9 2127 volume of the closed operating chamber in the hydraulic system Apparently increasing volume can benefit the compliance of the hydraulic system 3 Thrust system and its compliance Shield tunneling machine performs excavation discharge erection and other procedures inside a steel cylindrical shield to achieve automation and factorization of tunnel construction As a key part of the shield machine the thrust system performs the task of pushing the machine ahead while tunneling Because of its large force the thrust system is exclusively driven by hydraulic system The shield ma chine mostly goes through unexpected geological layers so it is inevitable to encounter the suddenly changing load during thrusting The capability to get through these severe conditions is very significant to the thrust hydraulic system and it can be described by the system compliance When the thrust hydraulic system has bad compliance failure or even accidents may happen during tunneling So the compliance of the thrust hydraulic system is taken into account in this study as follows 3 1 Basic principle of thrust system Because the shield tunneling machine needs great power to move forward the actuators of the thrust system are basi cally composed of several groups of hydraulic cylinders installed at regular intervals in the circumferential direction of the cross section of cylindrical shield In response to its special function the thrust hydraulic system employed in the shield tunneling machine is a typical type of valve controlled cylinder hydraulic system in essence As shown in Figure 4 the control valves often fall into pressure and flow control types It is dependent upon two different con trol modes of the thrust system in order to meet the specific requirements under different operating conditions In some cases a compound control strategy is necessary to achieve better tunneling performance 12 Although the thrust sys tem consists of many groups of hydraulic cylinders the thrust cylinders are regulated by the same way So they can be treated as one entire cylinder whose sectional area equals the sum of each cylinder in a group In other words no matter how complex the thrust hydraulic system is its prin ciple can be simplified and expressed by the schematic in Figure 3 Accordingly the mathematical model of the valve controlled cylinder hydraulic system can be obtained as follows The flow equation of the cylinder is derived as L LtcL dd dd pxV qAC p tt 6 where qL is the cylinder flow A the effective working area Figure 3 Schematic of basic principle of thrust hydraulic system x the displacement of cylinder Ctc the coefficient of leakage V the total actuating volume and the effective bulk mod ulus The dynamics equation of the cylinder is 2 LvLimp dd dd xx ApMBFF tt 7 where M is the total mass of the moving parts Bv the vis cous damping coefficient FL the external load force and Fimp the sudden impact load exerted by outside environ ment 3 2 Architectures of thrust system Although the thrust hydraulic system is basically a valve controlled cylinder system the valve and the cylinder here refer to the valve groups and the cylinder groups respec tively Groups of valves and cylinders are employed in the thrust hydraulic system in order to generate large force to overcome the load applied on the tunneling face The thrust system not only performs the task of driving shield machine ahead while tunneling but also controls the posture of shield machine which ensures that the shield can advance along the expected path consequently for constructing the planned tunnel line In fact the former function is per formed by synchronous extension of all hydraulic cylinders of the thrust system and the latter control action is achieved by coordination control of many hydraulic cylinder groups 13 Generally the hydraulic cylinders of the shield tun neling machine in field application service are divided into four groups in the circumferential direction of the cross sec tion as shown in Figure 4 It shows a typical thrust cylinder distribution of the shield machine with a diameter of 6m There are 32 cylinders in all falling into group A group B group C and group D In practice the total number of the hydraulic cylinders is not invariable it is determined in the design stage and strongly dependent on the specific geolog ical conditions Finally there is a group of valves in each corresponding cylinder group as shown in Figures 5 to 7 where CV is short for control valve The yaw and pitch an gles of the shield tunneling machine can be controlled by coordination of actuators in group A along with group C and group B along with group D respectively 2128 Shi H et al Sci China Tech Sci September 2013 Vol 56 No 9 Figure 4 Hydraulic cylinder distribution on cross section of shield Figures 5 to 7 show the typical types of architectures of thrust