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关键词：: 中型四柱式液压机液压系统设计

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摘要

本设计为中型四柱式液压机，主机最大工作负载设计为2000KN。主机主要由上梁、导柱、工作台、移动横梁、主缸、顶出缸等组成。本文重点介绍了液压系统的设计。通过具体的参数计算及工况分析，制定总体的控制方案。经方案对比之后，拟定液压控制系统原理图。液压系统选用插装阀集成控制系统，插装阀集成控制系统具有密封性好，通流能力大，压力损失小等特点。为解决主缸快进时供油不足的问题，主机顶部设置补油油箱进行补油。主缸的速度换接与安全行程限制通过行程开关来控制；为了保证工件的成型质量，液压系统中设置保压回路，通过保压使工件稳定成型；为了防止产生液压冲击，系统中设有泄压回路，确保设备安全稳定的工作。此外，本文对液压站进行了总体布局设计，对重要液压元件进行了结构、外形、工艺设计，对主机、电气控制系统进行了简要设计。

通过液压系统压力损失和温升的验算，本文液压系统的设计可以满足液压机顺序循环的动作要求，能够实现塑性材料的锻压、冲压、冷挤、校直、弯曲等成型加工工艺。

关键词：液压系统；液压机；毕业设计

ABSTRACT

This paper design for the medium frame of hydraulic machines, the mainframe’s largest work load design for 2000KN. Mainframe mainly by the beam、guided、worktable、mobile beams、master cylinder、cylinder head out of components etc. This paper focuses on the hydraulic system design. Through specific parameters and hydraulic mechanic situation analyzes, formulation of a master control program. By contrast, developed hydraulic control system diagram.Hydraulic systems use cartridge valve integrated control system, integrated cartridge valve control system has good sealing, flow capacity, small pressure loss characteristics etc. To solve the master cylinder express entered the shortage of oil supply in the top of the mainframe installed oil tank. Master cylinder for the speed of access restrictions and security through the trip exchanging to control switches.To ensure the quality of the work-piece molding, in the hydraulic system installed packing loop through packing work-piece stability molding; To prevent hydraulic shocks, pressure relief system with a loop to ensure that this equipment can be a safe and stable work. In addition, the paper hydraulic station on the overall layout of the key components of the hydraulic structure、shape、technique for a specific design.

By the loss of hydraulic system pressure and temperature checked. Hydraulic system is designed to meet the hydraulic action sequence and cycle requirements can be achieved by forging plastic materials, stamping, cold extrusion, straightening, bending, and other molding processes.

Keywords: Hydraulic System ；Hydraulic Pressure machine；Graduation design

第1章绪论1

1.1 液压机现状概要1

1.2 本文拟达到的要求2

第2章四柱液压机总体方案设计3

2.1 四柱液压机主要设计参数3

2.2 四柱液压机工作原理分析3

2.2.1 四柱液压机的基本组成3

2.2.2 四柱液压机的工作原理4

2.3 四柱液压机工艺方案设计6

2.4 四柱液压机总体布局方案设计6

2.5 四柱液压机零部件设计7

2.5.1 主机载荷分析7

2.5.2 主机工作台设计10

2.5.3 控制台设计10

第3章四柱液压机液压系统设计10

3.1 液压传动的优越性概述11

3.2 液压系统设计要求11

3.2.1 液压机负载确定11

3.2.2 液压机主缸工艺过程分析12

3.2.3 液压系统设计参数12

3.3 液压系统设计12

3.3.1 液压机主缸工况分析12

3.3.2 液压机顶出缸工况分析15

3.3.3 液压系统原理图拟定16

3.3.4 液压系统基本参数计算21

3.4 液压系统零部件设计28

3.4.1 液压机主缸设计28

3.4.2 液压机顶出缸设计32

3.4.3 液压油管设计33

3.4.4 液压油箱设计35

3.5 液压站布局设计36

3.5.1 液压站设计需要考虑的问题36

3.5.2 液压站的结构设计36

3.6 液压系统安全、稳定性验算37

3.6.1 液压系统压力损失验算37

3.6.2 液压系统温升验算41

第4章四柱液压机电气系统设计42

4.1 电气控制概述42

4.2 四柱液压机电气控制方案42

4.2.1 四柱液压机电气控制方式选择42

4.2.2 电气控制要求与总体控制方案42

4.3 四柱液压电气控制电路设计43

4.3.1 四柱液压机主电路设计43

4.3.2 四柱液压机控制电路设计43

4.3.3 电气控制过程分析45

第5章四柱液压机安装调试和维护46

5.1 四柱液压机的安装47

5.2 四柱液压机的调试47

5.3 四柱液压机的保养维护47

结论48

参考文献49

致谢51

附录152

附录253

第1章绪论

1.1液压机现状概要

液压传动技术发展到今天已经有了较为完善、成熟的理论和实践基础。液压传动技术与传统的机械传动相比，操作方便简单，调速范围广，很容易实现直线运动并且还具有自动过载保护功能。液压传动容易实现自动化操作，采用电液联合控制后，可以实现更高程度的自动控制以及远程遥控。由于液压传动的工作介质是流体矿物油，有较大的沿程和局部阻力损失。当系统的工作压力比较高时，还会产生比较大的泄漏，泄漏的矿物油将直接对环境造成污染，有时候还容易引起安全事故。油液受温度的影响很大，因此液压油不能在很高或很低的温度条件下工作。由于液压油的可压缩性和泄漏，液压传动不能保证恒定的传动比和很高的传动精度，这是液压传动的最大不足之处。此外，液压传动的故障排除不如机械传动、电气传动那样容易，因而对使用和维护人员有较高的技术水平要求。虽然液压传动存在这些缺陷，但总体上优点还是盖过了缺点，因而应用还是很广泛。

液压机自19世纪问世以来得到了很快的发展，在工业生产中已经有了广泛的应用，成了产品压力加工成型不可或缺的机械设备。随着科学技术的日新月异，电子技术、液压技术的不断成熟，液压机也得到了更进一步的发展。到目前为止，液压机的最大公称压力已经达到了750MN，控制技术也由原来传统的继电器控制变为可编程控制器和工业计算机控制，这使液压机的运行平稳性、控制精度、产品质量有了保证，同时生产效率得到了很大的提高。

液压机加工与传统机械加工相比属于无屑加工，应用范围广泛，一般用于塑性材料的冷挤、校直、弯曲、冲裁、拉伸等。此外液压机还用于粉末冶金、翻边、压装等产品的成型加工工艺。液压机还能实现复杂工件和不对称工件的加工，产品废品率较低。液压机根据加工工件的不同性质，还可进行适当的压力行程调整，满足产品的加工要求。液压机主要由主机、液压系统、电气系统三部分组成。液压机的整个工作过程的实现，首先是由电气系统来控制液压系统，然后再由液压系统控制主机主缸和顶出缸的顺序动作。总的来说，液压机操作简单，维护方便。

虽然液压机目前应用十分广泛，但是潜在的问题还很多。液压机属于高压工作设备,进行压力加工时,随着压力的不断升高泄漏也会不断增大,这样不利于保证零件的加工精度，同时还会对环境造成污染。除此之外，液压机还存在如下缺陷，液压机压力加工完成后，卸压时存在很大的液压冲击，这样对液压元件及其它设备损害很大；按下启动按钮后，动作灵敏性不及电气控制；液压机出现故障不能够正常工作，故障不容易及时找到并排除，给维护带来了一定的技术难题和不便；液压机工作时产生的液压冲击、气蚀等现象，会缩短液压元件的使用寿命。

为了催生更大的生产力，液压机的设计需要改进。液压油路设计、控制系统的优化设计将是液压机今后值得研究的方向。

（1）油路设计方面

为了防止泄油和外界的污染，液压机油路的设计趋于集成化、封闭循环式，这样可以延长设备的使用寿命。除此之外，液压元件设计尽量标准化，集成化。集成液压系统减少了管路连接，可以降低泄漏和污染。液压元件的标准化给维护带来了方便。

（2）控制系统方面

液压机属于高压设备，控制系统除控制设备安全可靠的工作之外，还应该让控制精度变得更高，人机交互变得更简单，操作更方便，自动化、高速化、智能化程度更好。

综上所述，液压机的发展促进了生产力的发展。伴随着电气控制技术、液压传动技术的不断发展，液压机的自动化程度、加工精度将进一步得到提高，实现智能化控制。

1.2本文拟达到的要求

（1）液压机总体方案设计，其中包括主机的结构设计和工艺设计、零部件的结构设计和工艺设计、部件装配方案设计；

（2）通过液压系统总体设计方案的对比，确定合理的液压系统设计方案。主要包括液压系统原理图设计、液压元件结构、工艺设计、液压站总体布局设计；

（3）电气控制系统设计，包括主电路和控制电路电路图设计；

（4）设计方案确定时，必须考虑选用什么样的制造材料，达到什么样的表面加工质量，采用什么样的机械加工设备，选择什么样的热处理方式等；

（5）整个设备满足拆装方便，运输方便的要求；

（6）四柱液压机能够准确完成如下工作循环：主缸活塞滑块快速下行、主缸活塞滑块慢速加压、主缸保压、主缸卸压、主缸活塞滑块回程、顶出缸顶出、顶出缸退回等；

（7）设备达到总体布局合理，结构紧凑、工作稳定可靠、操作简单、维护方便、环境污染小、工作的时候噪音低、自动化程度高等，能够完成冲压、冷挤、校直、弯曲、粉末冶金压制成型、薄板拉伸、压装成型等加工工艺。

第2章四柱液压机总体设计

2.1四柱液压机主要设计参数

（1）拟设计的四柱液压机主要技术参数见表2.1

表2.1 液压机技术参数

参数项参数

公称力（最大负载）2000KN

工进时液体最大工作压力25MPa

主缸回程力400KN

顶出缸顶出力350KN

主缸滑块行程700mm

顶出活塞行程250mm

主缸滑块距工作台最大距离1100mm

主缸滑块快进速度0.08m/s

主缸滑块工进最大速度0.006m/s

主缸快退速度0.03m/s

顶出活塞顶出速度0.02m/s

顶出活塞退回速度0.05m/s

（2）四柱液压机的主要功能

通过液压传动系统传递动力，完成零件的压力成型加工。

（3）四柱液压机的适用范围

液压机主要用于冷挤、校直、弯曲、冲裁、拉伸、粉末冶金、翻边、压装等成型工艺。

2.2 四柱液压机工作原理分析

2.2.1 四柱液压机的基本组成

四柱液压机主要由主机、液压控制系统、电气控制系统三部分组成。其中主机包括工作台、导柱、滑块、上缸、顶出缸等结构；液压系统由控制元件、执行元件、辅助元件、动力装置、工作介质等组成；电气控制控制系统主要由继电器、接触器、按钮、行程开关、电器控制柜等组成。

2.2.2 四柱液压机的工作原理

（1）四柱液压机主机组成简图2.1

1-滑块 2-导柱 3-工作台 4-安装地基

5-顶出缸 6-主缸 7-上横梁 8-辅助油箱

图2.1 四柱液压机主机组成简图

（2）四柱液压机工作原理分析

四柱液压机的动作顺序通过电气系统、液压系统控制，控制顺序框图如图2.2。

图2.2 四柱液压机控制顺序图

从上面的控制顺序框图可以看出，液压机的工作原理由电气控制系统控制液压系统，液压控制系统再控制主机工作，主机动作触及行程开关，将信号反馈给电气控制系统，实现循环控制。

（3）四柱液压机工作循环分析

四柱液压机工作循环如图2.3所示。

图2.3 四柱液压机工作循环图

四柱液压机工作循环如图2.3（a），滑块在自重的作用下快速下行，碰到行程开关后由快进变为工进，随后进行加压、保压。保压时间完成后，滑块快速回程，直到回到原来的位置，停止运动；图2.3（b）表示顶出缸的工作循环过程，主缸快进、工进、保压、退回停止后，顶出缸才运动，将工件顶出。

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内容简介：: S adhan a Vol. 31, Part 5, October 2006, pp. 543556. Printed in IndiaEffect of bulk modulus on performance of a hydrostatictransmission control systemALI VOLKAN AKKAYAYildiz Technical University, Mechanical Engineering Department, 34349,Besiktas, Istanbul, Turkeye-mail: .trMS received 9 September 2005; revised 20 February 2006Abstract.In this paper, we examine the performance of PID (proportionalintegral derivative) and fuzzy controllers on the angular velocity of a hydrostatictransmission system by means of Matlab-Simulink. A very novel aspect is that itincludes the analysis of the effect of bulk modulus on system control. Simulationresultsdemonstratesthatbulkmodulusshouldbeconsideredasavariableparameterto obtain a more realistic model. Additionally, a PID controller is insufficient inpresence of variable bulk modulus, whereas a fuzzy controller provides robustangular velocity control.Keywords.Hydrostatic transmission; bulk modulus; PID (proportional integralderivative); fuzzy controller.1. IntroductionHydrostatic transmission (HST) systems are widely recognized as an excellent means ofpower transmission when variable output velocity is required in engineering applications,especially in field of manufacturing, automation and heavy duty vehicles. They offer fastresponse,maintainprecisevelocityundervaryingloadsandallowimprovedenergyefficiencyand power variability (Dasgupta 2000; Kugi et al 2000). A basic hydrostatic transmission isan entire hydraulic system. Generally, it contains a variable-displacement pump driven byan induction motor, a fixed or variable displacement motor, and all required controls in onesimple package. By regulating the displacement of the pump and/or motor, a continuouslyvariable velocity can be achieved (Wu et al 2004).Manufacturers and researchers continue to improve the performance and reduce the costof hydrostatic systems. Especially, modelling and control studies of hydrostatic transmissionsystemshaveattractedconsiderableattentioninrecentdecades.Somestudiesonthistopiccanbe found in the literature (Huhtala 1996; Manring & Luecke 1998; Dasgupta 2000; Kugi et al2000;Dasguptaetal2005).Variousrotationalvelocitycontrolalgorithmsforhydrostaticsys-temsaredevelopedandappliedbyLennevi&Palmberg(1995),Lee&Wu(1996),Piotrowska(2003). All these designs use the bulk modulus as a fixed value through a wide pressurerange. However, in practice, the bulk modulus is an essential part of dynamic behaviours of543544Ali Volkan Akkayathe hydraulic systems (McCloy & Martin 1980; Watton 1989). Due to temperature variationsand air entrapment, the bulk modulus may vary during the operation of the hydraulic sys-tems (Eryilmaz & Wilson 2001). A little entrapped air is enough to reduce the bulk modulussignificantly (Merrit 1967; Tan & Sepehri 2002). Moreover, system pressure plays an impor-tant role on the bulk modulus value (Wu et al 2004). Some effects of instabilities induced bybulk modulus nonlinearities such as pressure oscillations in the form of pressure waves canbe detrimental to operation of hydraulic systems and may result in reduced component life,loss of performance, disturbance in control systems, reduced efficiency and increased acous-tic noise. In spite of these adverse effects, there are few studies about bulk modulus withinhydrostatic transmission systems. Yu et al (1994) developed an on-line parameter identifica-tion method, determining the effective oil bulk modulus within an actual hydraulic system bymeasuring the propagation of a pressure wave through a long pipe. Marning (1997) devel-oped a linear relation between oil bulk modulus and pressure for a HST system. However, todate, nothing has appeared in the literature that addresses the effect of bulk modulus dynam-ics incorporated into a hydrostatic transmission model on control design process of the HSTsystem. In fact, models of hydrostatic transmission systems with variable bulk modulus havemore complex dynamic behaviour than normal. Moreover, having servo control of the sys-tem, dynamics of bulk modulus becomes more important because the closed-loop systemitself raises the issue of stability.Bulk modulus cannot be determined directly and hence needs to be estimated. Based onthis estimation, corrective actions may be taken in control applications for HST systems. Thecomplex dynamic interactions between variable bulk modulus and the control action is inves-tigated using modelling and simulation analysis. Simulation tests are particularly beneficialwhen preparing a model of a real system is complicated and time-consuming. A servo hydro-statictransmissioncontrolsystemisagoodexampleforthisissue.Thedeterminationofstaticand dynamic behaviours using simulation tests is possible without expensive prototypes. Thesimulation also makes a shorter product-designing cycle possible.This study focuses on control performance of a typical HST system. A nonlinear modelof the system is studied by means of Matlab-Simulink software. The system model is acombination of each individual component model consisting of pump, valve, hydraulic hoseand hydraulic motor. In addition, the variable bulk modulus is presented to describe theeffects of this phenomenon on system dynamics and control algorithm. For this purpose, twodifferent hydraulic hose Simulink models are incorporated separately into the system model.In addition, the models are utilized in the control design process. The control of the angularvelocity of the hydraulic motor coupled with load is achieved by PID (proportional integralderivative) and fuzzy types of controller. In the first model, bulk modulus is assumed to havea fixed value and angular velocity control of the HST system is carried out with the classicalPID control algorithm. In the second model, bulk modulus is defined as a variable parameterdependingonentrappedairandsystempressure.Thisnewmodelisappliedonvelocitycontrolof the HST system under the same PID control parameters. In the following, fuzzy controllerisimplementedinthisnewmodelinordertojudgeitscapabilityagainstvariablebulkmodulusnonlinearity. The simulation results of two control approaches are then compared to analysethe differences in the performance of the HST system in terms of bulk modulus dynamics.2. Mathematical modelThe physical model of the HST system considered for this study is shown in figure 1. Thevariable displacement pump driven by an induction motor supplies hydraulic power to a fixedEffect of bulk modulus on performance of a transmission control system545Figure 1.Hydrostatic transmission system.displacementhydraulicmotorfordrivingload.Toprotectthesystemfromexcessivepressure,a pressure relief valve is used.From a research objective point of view, the descriptions of a system mathematical modelshould be as simple as possible. At the same time, it must include important characteristics ofthe real event. One way to understand the system is to separate the system into componentsfor the purpose of modelling. Using a fundamental knowledge of physics, for instance themomentequilibriumandcontinuityequation,amodelthatrepresentsthedynamicsbehaviourofeachcomponentcanbederivedatthecomponentlevels.Havingunderstoodeachindividualcomponent,wecanunderstandtheoverallsystembyinterconnectingthecomponentstogetherto obtain an overall system model (Prasetiawan 2001). In this paper, the model of eachcomponent used for the HST system is developed using earlier methods (Jedrzykiewicz et al1997, 1998).2.1 Variable-displacement pumpIt is assumed that the angular velocity of the prime mover (induction motor) is constant.Therefore, angular velocity of the pump shaft is constant. Pump flow rate can be adjustedwith variable displacement via the swashplate displacement angle and can be given asQp= kpvp,(1)where, Qpis pump flow rate (m3/s), is displacement angle of swashplate (), kpis pumpcoefficient (m3/s), vpis pump volumetric efficiency () which is assumed not to depend onpump rotation angle.2.2 Pressure relief valveTo simplify, pressure relief valve dynamics is not taken into consideration. Therefore, twoequation as below are given for passing flow rate through pressure relief valve (m3/s) in thestate of opening and closing.Qv= kv(P Pv), if P Pv,(2)Qv= 0, if P Pv,(3)546Ali Volkan Akkayawhere, kvis slope coefficient of valve static characteristic (m5/Ns), P is system pressure (Pa)and Pvis valve opening pressure (Pa).2.3 Hydraulic hoseAs in traditional modelling, the pressurized hose that connects the pump to the motors ismodelled as volume with a fixed bulk modulus in this section. Variable bulk modulus arediscussed in the following subsection.The fluid compressibility relation can be given as in (4). Equation (5) provides the pressurevaluefromagivenflowrate.Itisassumedthatpressuredropinthehydraulichoseisnegligible.Qc= (V/)(dP/dt),(4)(dP/dt) = (/V)Qc,(5)where, Qcis flow rate deal with fluid compressibility (m3/s), V is the fluid volume (m3)subjected to pressure effect, is fixed bulk modulus (Pa).2.3a VariablebulkmodulusFluidisanimportantelementofhydrostaticsystemsandenablespower transmission, hence it can influence the dynamic behaviours of the system and thecontrol system. The bulk modulus of non-aerated hydraulic oil depends on temperature andpressure, for mineral oils with additives its value ranges from 1200 to 2000MPa. Moreover,system pressure and entrapped air affect the bulk modulus value. If a hydraulic hose is usedratherthanasteelpipe,thebulkmodulusofthissectionmaybeconsiderablyreduced.Owingto these reasons, the parameters influencing bulk modulus value must be included in the HSTmodel for more accurate system dynamics.The equation which gives the variable bulk modulus of fluid-air mixture in a flexiblecontainer is as follows (McCloy & Martin 1980):1v=1f+1h+VaVt1a,(6)where, the subcripts a, f and h refer to air, fluid, and hose respectively. It is assumed that theinitial total volume Vt= Vf+Va, and that f? a. Thus bulk modulus will be less than anyf, h, or Vt/Vaa. The bulk modulus of the fluid fis obtained from the manufacturersdata. The adiabatic bulk modulus used for air is (Cp/Cv)P = 14P. With these assumptions,(6) can be rewritten as in,1v=1f+1h+s14 P,(7)where, s is entrapped air percent in the total volume (s = Va/Vt).2.4 Hydraulic motor and loadFlow rate used in the hydraulic motor (m3/s) can be written as inQm= km/vm,(8)where, kmis hydraulic motor coefficient (m3), is angular velocity of hydraulic motor (1/s)andvmisvolumetricefficiencyofthemotor().Itisassumedthathydraulicmotorefficiencydoes not depend on its shaft rotation angle. Hydraulic motor torque (Nm) can be written as,Mm= kmt?Pmm,(9)Effect of bulk modulus on performance of a transmission control system547where, kmtis motor torque coefficient (m3), ?P is pressure drop in hydraulic motor (Pa)and mmis mechanical efficiency of hydraulic the motor (). The torque produced in thehydraulic motor (Nm) is equal to the sum of the moments from the motor loads and can begiven as,Mm= MI+ MB+ Mo,(10)where,MI,MBandMoarethemomentsresultingfromloadinertia,frictionforceandmachineoperation respectively. These moments can be denoted asMm= Im(d/dt) + B + Mo,(11)where, Imis the inertia of the hydraulic motor shaft (Nms2), B is viscous friction coefficientof motor and its shaft (Ns/m), and is angular velocity of motor shaft (1/s). Equation (11)can be used to determine the angular velocity of the hydraulic motor shaft. This equation isrearranged for angular velocity asd/dt = (Mm B Mo)/Im.(12)2.5 Hydrostatic transmission systemThe fundamental mathematical models of the system components and phenomena occurringin hydrostatic systems are conveniently combined to obtain the overall HST system model.Accordingly, a hydrostatic transmission is modelled as a lumped system. In the developmentof the dynamic model of the system, it is assumed that static and dynamic features of thetransmissiondonotdependuponthedirectionofhydraulicmotorrotationandthetransmissionis a state of thermal balance. Leakage flows in pump and motor are not taken into accountduring the modelling.The mathematical model of the HST system consists of two equations as below:equality of flow rate:Qp= Qm+ Qc+ Qv,(13)moment:Mm= MI+ MB+ Mo.(14)Using (5) and (12), the following are then obtained,dP/dt = (/V)(Qp Qm Qv),(15)d/dt = (Mm B Mo)/Im.(16)A commonly available general purpose simulation package Matlab/Simulink is used tosolve the nonlinear equations. The Simulink model based on the component mathematicalmodels of HST system is given in figure 2. The component models can be easily modifiedin accordance width specific constructions. Accordingly, when bulk modulus is rebuilt in thehydraulic hose component with regard to (7), the second model can be generated.548Ali Volkan AkkayaFigure 2.Simulink model of hydrostatic transmission system.3. Control applicationsMost publications related to the HST control are related to the speed control of the hydraulicmotorconnectedtotheload.Inordertoachievethisgoal,differentclosed-loopcontroldesignstrategiescanbeused.However,Lee&Wu(1996)showedthatusingonlypumpdisplacementto regulate load speed is the most effective of all the methods they tested. In addition, Re et al(1996) concluded that the sole use of pump displacement actuation to control one load speedof a system with variable-displacement pump and motor is the most efficient, and should bealways preferred whenever possible. For this reason, in the HST systems being considered inthis study, the output angular velocity is controlled by the flow rate supplied to the hydraulicmotor, and this flowrate is adjusted by the swashplate angle of the variable-displacementpump. Swashplate dynamics are not taken into consideration in the control application inthis study for the sake of simplicity. In addition, the swashplate control system usually hasfaster dynamics than the rest of the system, and therefore neglecting its dynamics is justified(Watton 1989).Topreciselycontroltheangularvelocityofthehydraulicmotorinhydrostatictransmissioncontrol systems, an appropriate controller must be designed in advance. In industrial appli-cations, classical control methods such as PI, PID are being used for velocity control of HSTsystems.ItiscrucialtodeterminecontrollerparametersaccuratelybecausePIDcontrolmeth-ods have linear characteristics. They are sometimes insufficient to overcome nonlinearitieswhich exist in the nature of the HST systems for high precision applications (Tikkanen et al1995; Prasetiawan 2001). In particular, the bulk modulus ought to be regarded as a source ofsignificant nonlinearity for this type of controller. Thus, the controller has to be very robustto account for such wide variation. Use of knowledge-based systems in process control isincreasing, especially in the fields of fuzzy control (Tanaka 1996). Unlike classical controlmethods, the fuzzy controller is designed with linguistic terms to cope with the nonlineari-ties. Therefore, this control method is also applied to judge its capacity to reduce the adverseeffect of variable bulk modulus.3.1 PID controlThe structure of the PID control algorithm used for the angular velocity control of HSTsystem is given in (17) and (18) below. Ziegler-Nichols method is implemented for tuningcontrol parameters, such as proportional gain (Kp), derivative time constant (d) and integraltime constant (i) (Ogata 1990). After fine adjustments, the optimal control parameters areEffect of bulk modulus on performance of a transmission control system549Figure 3.Simulink model of HST system for PID control.determined for the reference angular velocity. Figure 3 shows the Simulink model of thePID-controlled HST system.uv(t) = Kpe(t) + Kpdde(t)dt+Kpi?e(t) dt,(17)e(t) = r .(18)3.2 Fuzzy controlFuzzy logic has come a long way since it was first presented to technical society, whenZadeh (1965) first published his seminal work. Since then, the subject has been the focusof many independent research investigations. The attention currently being paid to fuzzylogic is most likely the result of present popular consumer products employing fuzzy logic.The advantages of this method are its applicability to nonlinear systems, simplicity, goodperformance and robust character. These days, this method is being applied to engineer-ing control systems such as robot control, flight control, motor control and power systemssuccessfully.In fuzzy control, linguistic descriptions of human expertise in controlling a process arerepresented as fuzzy rules or relations. This knowledge base is used by an inference mecha-nism, in conjunction with some knowledge of the states of the process in order to determinecontrol actions. Unlike the conventional controller, there are three procedures involved in theimplementation of a fuzzy controller: fuzzification of inputs, and fuzzy inference based onthe knowledge and the defuzzification of the rule-based control signal. The structure of thefuzzy controller is seen in figure 4.An applied fuzzy controller needs two input signals. These signals are error (e) and deriva-tive of error (de) respectively. The usual overlapped triangular fuzzy membership functionsare used for two input signals (e,de/dt) and the output signal (u). Figure 5 shows the struc-ture of the membership functions of input and output signals. Input signals are transformedat intervals of 1,1 by scaling factors which are Ge and Gde.In the fuzzification process, all input signals are expressed as linguistic values which are:NB negative big, NM negative medium, NS-negative small, ZE-zero, PS-positive small,PM-positive medium, PB-positive big. After input signals are converted to fuzzy linguisticvariables, these variables are sent to the inference mechanism to create output signals.550Ali Volkan AkkayaFigure 4.Structure of a fuzzy controller.Theinferenceprocessconsistsoffortyninerulesdrivenbythelinguisticvaluesoftheinputsignals. These fuzzy rules written as a rule base are shown given in table 1. The rule base isdeveloped by heuristics with error in motor angular velocity and derivation of error in thisvelocity. For instance, one of the possible rules is: IF e = PS and de = NB THAN u = NM.Thisrulecanbeexplainedasinthefollowing:Iftheerrorissmall,angularvelocityofhydraulicmotor is around the reference velocity. Significantly big negative value of derivation of errorshows that the motor velocity is rapidly approaching the reference position. Consequently,controller output should be negative middle to prevent overshoot and to create a brake effect.Asarule-inferencemethod,theMamdaniMethodisselectedbecauseofitsgeneralacceptance(Tanaka 1996).Defuzzification transforms the control linguistic variables into the exact control output. Indefuzzification, the method of centre of gravity is implemented (Tanaka 1996), asu =n?i=1WiBi/n?i=1Wi(19)Figure 5. Triangular fuzzy member-shipfunctions,(a)einputsignal,(b)deinput signal, (c) u output signals.Effect of bulk modulus on performance of a transmission control system551Table 1. Rule base for fuzzy control.deeNBNMNSZEPSPMPBNBNBNBNBNMNMNSZENMNBNBNMNSNSZEPSNSNBNMNSNSZEPSPMZENMNSNSZEPSPSPMPSNMNSZEPSPSPMPBPMNSZEPSPSPMPBPBPBZEPSPMPMPBPBPBwhere, u is the output signal of the fuzzy controller, Wiis the degree of the firing of the ithrule,Biisthecentroidoftheconsequentfuzzysubsetofithrule.Realvaluesofcontroloutputsignal (uv) are determined by the scaling factor of Guv. As a result, the fuzzy controllerbuilt-in Fuzzy Logic Toolbox of the Matlab program has been added to the Simulink modelof hydrostatic transmission system for simulation analysis (figure 6).4. Simulation results and discussionThe validity of the influence of bulk modulus dynamics on HST control system has beentestedincomputersimulations.Inordertocarryoutsimulation,somephysicalandsimulationparameters corresponding to HST system are taken from work of McCloy & Martin (1980)and Jedrzykiewicz et al (1997, 1998), and other control parameters are as given in table 2.OpenlooppressureandangularvelocityresponsesoftheHSTsystemaregiveninfigures 7aand b respectively, under fixed bulk modulus and variable bulk modulus. Comparing the sim-ulation results shows that the model including variable bulk modulus shows flexible dynam-ics and decreasing system stiffness (figure 7a). Moreover, a degree of aeration less than 1%brings about considerable changes of velocity and pressure responses because the aeration ofthe working fluid results in decrease of fluid bulk modulus and changes its characteristics asa function of pressure.The dynamic behaviour patterns in figure 8 are obtained from PID control. It is observedfrom figure 8a that the system model including the fixed bulk modulus is in good agreementwith reference velocity. In contrast to this, the simulation result of the model with variablebulk modulus show oscillations in the transient regime. The reason is that the bulk modulusFigure 6.Simulink model of HST system for fuzzy controller.552Ali Volkan AkkayaTable 2. Physical and simulation parameters.Moments resulting from machine operationMo(Nm)150Viscous friction coefficientB (Ns/m)15Displacement angle of swashplatea ()16 for open-loopInertia of hydraulic motor shaftIm(Nms2)004Opening pressure value of valvePv(Pa)12 106Fluid volume subjected to pressure effectV (m3)14145 104Pump coefficientkp(m3/s)2688 105Hydraulic motor coefficientkm(m3)3979 105Motor torque coefficientkmt(m3)3979 105Slope coefficient of relief valvekv(m5/Ns)02 109Pump volumetric efficiencyvp(%)97Mechanical efficiency of hydraulic motormm(%)95Bulk modulus of fluidf(Pa)149 109Bulk modulus of hoseh(Pa)47 107Degree of entrapped airs (%)05Reference angular velocityr(1/s)7Proportional gain constantKp()70Derivative time constantd()00002875Integral time constanti()000115Scaling factor of errorGe ()01Scaling factor of derivative of errorGde ()00001Scaling factor of control signalGu ()1500Figure7. OpenloopresponsesofHSTsystemunderfixedandvariable(a)systempressure,(b)angularvelocity.Effect of bulk modulus on performance of a transmission control system553Figure 8.PID control responses of HST system for fixed and variable bulk modulus (a) angularvelocity, (b) system pressure, (c) variable bulk modulus.value becomes lower than that of the fixed one (figure 8b) and changes with system pressure(figure 8c). The same characteristic is seen for increasing load moment at 003s. The aboveresults indicate that with change in the bulk modulus, peak pressure as well as fluctuation ofthe fluid pressure increase in closed loop control applications. This increases the settling timeof the systems responses. This may cause to failure of the stability of the system. Therefore,it is necessary to revise the control parameters or apply a more robust controller in terms ofvariable bulk modulus.Fuzzy and PID control responses of HST system under the variable bulk modulus aredepicted in figure 9. Simulation results of fuzzy controller show good performance comparedwith PID controller in tracking referenced velocity (figure 9a). In addition, fuzzy controllerrejects the effect of loading on pressure dynamics (figure 9b). Figure 9c indicates that fuzzycontroller minimizes the fluctuations of bulk modulus value. This is the reason why thefuzzy response is more robust. Figure 9d shows that PID controller can work safely up to200Hz,whereasafuzzycontrolleriscapableofenduring400Hz.Therefore,afuzzycontroller554Ali Volkan AkkayaFigure 9.Fuzzy and PID control responses of HST system under variable bulk modulus. (a) Angularvelocity, (b) system pressure, (c) variable bulk modulus, (d) velocity bode diagram.increases the stability conditions of a hydraulic transmission system in presence of variablebulk nonlinearity.5. ConclusionThe effects of bulk modulus nonlinearity on the performance of a hydrostatic transmissioncontrol system have been analysed through system modelling and simulation. This study hasEffect of bulk modulus on performance of a transmission control system555demonstrated that omitting the bulk modulus dynamics in hydrostatic transmission controlsystems may lead to major errors in system response and have implications on the safety ofoperation. Therefore, bulk modulus should be considered as a variable parameter to obtaina more realistic overall model and to determine more accurate control parameters in PIDcontroller. Analysis including bulk modulus dynamics in an HST-control system model withthis control design feature has not been described in the literature to date. Therefore, it maybe useful for early design of an HST system used for PID control application. In addition, itis clearly seen that a fuzzy controller has the capability of eliminating the adverse effects ofvariablebulkmodulus.Thiswillalsobenefitthecontroldesignprocessintermsofdevelopinga robust controller. For future research, model development will be expanded to includeswashplate dynamics, valve dynamics and more complex flow and torque models of thepump and the motor. Furthermore, an adaptive control method will be applied for changeablevelocity reference and load moment.List of symbolsBviscous friction coefficient of motor and its shaft Nms;Bicentroid of the consequent fuzzy subset of ith rule;HSThydrostatic transmission;Iminertia of hydraulic motor shaft Nms2;kppump coefficient m3/s;kmhydraulic motor coefficient m3;kmtmotor torque coefficient m3;kvslope coefficient of static characteristic of relief valve m5/Ns;MBmoments resulted from friction force Nm;MImoments resulted from load inertia Nm;Mmhydraulic motor torque Nm;Momoments resulted from machine operation Nm;Psystem pressure Pa;Pvopening pressure value of valve Pa;Qcflow rate deal with compressibility m3/s;Qmflow rate used in hydraulic motor m3/s;Qpflow rate of pump m3/s;Qvpassing flow rate through relief valve m3/s;uvoutput signal of fuzzy controller;Vfluid volume subjected to pressure effect m3;Widegree of firing of ith fuzzy rule;displacement angle of swashplate ;bulk modulus Pa;mmmechanical efficiency of hydraulic motor ;vppump volumetric efficiency ;vmvolumetric efficiency of motor ;angular velocity of motor 1/s;?Pmpressure drop in hydraulic motor Pa.556Ali Volkan AkkayaReferencesDasgupta K 2000 Analysis of a hydrostatic transmission system using low speed high torque motor.Mech. Mach. Theory 35: 14811499Dasgupta K, Chattapadhyay A, Mondal S K 2005 Selection of fire-resistant hydraulic fluids throughsystem modelling and simulation. Simul. Model. Pract. Theory 13: 120Eryilmaz B, Wilson B H 2001 Improved tracking control of hydraulic systems. Trans. ASME: J.

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