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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: 21242131 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 & MEI XueSong1* 1 School of Mechanical Engineering, Xian Jiaotong University, Xian 710049, China; 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: 21242131, 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 14: (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 58. 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, nc, , pVCttpV (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 , FCpA (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 ,rLpVVq 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 LLtcLdd,ddpxVqAC ptt (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 2LvLimpdd,ddxxApMBFFtt (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 hydraulic system, where A, B, C, D represent the corresponding four groups respectively. All the three types have four control valve groups to control each group of ac-tuators. Like other industrial hydraulic systems, all of them are equipped with pressure relief valve to manage the sud-den load change conditions. Besides, there are some layout differences resulting in different compliance systems. In type I system, there is only one pressure relief valve for the whole cylinders. For every group, there is no relief valve. All actuators of the four groups share the same relief channel. In contrast, type II system has four pressure relief valves to serve every groups of actuators. When one group undergoes sudden load change, it can open its own relief valve easily and immediately. Quite different from the for-mer two types, type III only has one pressure relief valve for the whole system. The only relief valve must meet the re-quirements of both cylinder groups and main circuit of the hydraulic system. According to the influencing factors of compliance, pressure relief valve and hydraulic pipelines are closely Figure 5 Schematic diagram of thrust hydraulic system: Type I. Figure 6 Schematic diagram of thrust hydraulic system: Type II. Figure 7 Schematic diagram of thrust hydraulic system: Type III. related to the compliance of the thrust hydraulic system. Obviously, the three types of thrust hydraulic systems pre-sented above differ in these two aspects. For instance, the system in Figure 6 has more relief valves, which will defi-nitely contribute to the pressure response to sudden load change. The layout of the pipelines influences the volume in the compliance expression. 3.3 Comparison of typical types of thrust system In order to carry out further investigation into compliance of thrust hydraulic system and draw a detailed comparison among the compliance of the three types of thrust hydraulic systems, three types of shield tunneling machines working in different construction sites are introduced. They have the same nominal diameter and thrust speed. The corresponding type of thrust hydraulic system is adopted in these machines. The main parameters of the three type thrust hydraulic sys- Shi H, et al. Sci China Tech Sci September (2013) Vol.56 No.9 2129 tems are listed in Table 1 11. The compliance of the three systems can be calculated by means of eq. (1). However, it is difficult to obtain the ana-lytical solution of the variables in the definition expression due to the nonlinearity of the hydraulic system. Thanks to the numerical simulation technique, it makes the possibility. Here, we establish the models of every system and carry out simulation in AMEsim software environment to get the nu-merical solution of each variable. The sudden load is gener-ated by employing the collision model in the software. Firstly, the hydraulic cylinders are extending at the normal speed and pressure. Suddenly, the mass collides with the spring-damper model, and the compliant process to be ana-lyzed begins. The related parameters and their values were provided in ref. 11. It should be noted that the compliance process and the variables are varying with time during sud-den load response. We take into account the compliant characteristic at 0.1 s after the sudden load action. The cal-culation results are shown in Table 2. It can be seen that type II system has the best compliance of all and the C val-ue of type III system is the smallest. There is one relief valve for each group in type II system, and the general volume change in the definition expression is increased consequently. Table 1 Main parameters of three type thrust hydraulic systems Items Type I Type II Type III Cylinder group 3+4+4+5 6+8+8+10 4+4+4+8 Thrust speed (cm/min) 6 6 6 Shield diameter (m) 6.34 6.4 6.28 Nominal pressure (MPa) 31.1 35 35 Maximum pressure (MPa) 35 37 40 Parameters of cylinder (piston diameter/rod diameter stroke/mm) 300/200 1900 200/170 2200 260/220 2100 Table 2 Compliance comparison of three types of systems Items Compliant time (s) Compliance Type I 0.1 0.157 Type II 0.1 0.335 Type III 0.1 0.0825 4 Compliance based thrust system design Since the response characteristic of the thrust hydraulic system under sudden change load can be evaluated by com-pliance, we can design a desirable system for tunneling un-der a specific load condition by considering its compliance. In this section, we will deal with compliance based thrust system design and its applications. 4.1 Design procedure A good shield tunneling machine should be equipped with a thrust hydraulic system that is adaptable to the given geo-logical conditions and the corresponding external load. Compliance based thrust hydraulic system is design for ac-complishing such a purpose. The flow chart of design pro-cedure is shown in Figure 8. Before designing, we must get the geological information of the construction site in detail. Then, we can calculate the thrust load and choose the best system structure as well as parameters. In this step, the other characteristics of the thrust system such as stability required by customers are taken into account. The computation of compliance is conducted to specially concentrate on the working conditions with sudden change load, and the nor-mal condition is not concerned. When the system parame-ters are determined according to the specific condition, the key influencing factors will be considered consequently. We can obtain several groups of values to construct the possible hydraulic systems, and carry out computation of the poten-tial compliance. Among a series of optional systems, the system with the best compliance is finally adopted and veri-fied corresponding to the given geological conditions. In fact, the parameter value of the hydraulic system to be determined is not continuous, and the design standard estab-lished by authorized institutions must be followed. There-fore, computation of compliance is performed on the basis of combination of different series of standard parameter values. By combining the system parameter with the com-ponent parameter, a range of systems with relatively opti- Figure 8 Flow chart of compliance based thrust hydraulic system design. 2130 Shi H, et al. Sci China Tech Sci September (2013) Vol.56 No.9 mal compliance is obtained. By this way, the system with expected compliance can be found. 4.2 Case study A thrust hydraulic system with expected compliance is vital to the shield tunneling machine working in the extremely complex geological environment. As shown in Figure 9, along the designed tunnel axis, many different kinds of soils as well as rocks may cover, even rich underground water. Following the design procedure presented in Figure 9, we will design a thrust hydraulic system matching the loads resulting from the geological conditions shown in Figure 9. In order to make a clear comparison, the diameter of the shield tunneling machine to be considered in this design case is also about 6 m. It can be seen from Figure 9 that the shield tunneling machine has to excavate through six layers ranging from clay to granite during the 100th ring to the 400th ring. The soil hardness on every excavating face is not uniform. In addition, the shield tunneling machine is penetrating through the soil layer below water level. Tunneling in such complicated conditions, it is inevitable to undergo the sud-den change load. The actual load force exerting on the thrust system is depicted by the solid line in Figure 10. It can be seen that the load changes severely and the abnor-mally large change exists around the 250th ring. According to the compliance computation results, the system with type II structure is the best. Therefore, we in-troduce this basic structure into the designed system. As-suming that the thrust speed is 6 cm/min, we carry out the calculation. The hydraulic system consists of 16 cylinders grouped by the 3+4+4+5 mode. In order to improve the compliant performance, a relief valve with a cracking pres-sure of 37 MPa and an accumulator with a volume of 5 L are equipped for each group. The evaluation results based on the given geological condition are presented in Figure 10. Because the external loads are given in the case, the com-pliance evaluation index is preferable for calculation and comparison. As described before, the load changes so dra-matically that the maximum is 1.5 times as much as the normal level. Corresponding to eq. (3), if the sudden load change is expressed as a unit, then the thrust force to be produced by the system is 0.69. Accordingly, it can be seen from Figure 10 that the geological condition based compli-ance can be written as 1/0.69. In the sudden change section, the external load peak is decreased to 69% of the original due to compliance. In fact, this thrust hydraulic system has been employed on a shield tunneling machine of a large multifunctional tunneling test rig. It should be noted that the load force changes are rela-tively smoother except for the sudden change in the middle part. Based on the compliance definition, it is easy to de-duce that the compliance does not perform a function over these two sections. Moreover, the compliance evaluation results based on the given geological conditions are also presented in Figure 11. It has been shown in the results that the compliance evaluation indexes of types I, II and III are 1/0.86, 1/0.79 and 1/0.92, respectively during the sudden load change section. It is clear that the geological evaluation results according to eq. (3) are in good agreement with the computation results based on eq. (1). 5 Conclusions In this paper, the definition of compliance of hydraulic sys-tem and its corresponding expressions are proposed in terms of pressure and volume change of the hydraulic system. For the thrust hydraulic system of shield tunneling machine, the compliance based system design was investigated to cope with the problems encountered under extreme operating conditions because of worse geological environment. Thr- oughout theoretical analysis and typical geological condi-tion based computation of the thrust hydraulic system, con-clusions can be drawn as follows. Compliance proposed in this paper is a very effective evaluation index for such hydraulic systems undergoing the severely sudden change load, and should be taken as a sig-nificant characteristic necessary to be considered when de-signing a thrust hydraulic system. The thrust hydraulic system with a structure of type II has better compliance than those w
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