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O+P Fluidtechnik 3/2016

O+P Fluidtechnik 3/2016


MEASUREMENT FORSCHUNG UND ENTWICKLUNG PEER REVIEWED ACCURACY ESTIMATION OF A NOVEL SETUP FOR ONLINE BULK MODULUS MEASUREMENT IN HYDRAULIC SYSTEMS Dr. Chuan Ding, Univ.-Prof. Dr.-Ing. Hubertus Murrenhoff This paper presents an online measuring setup for the effective bulk modulus of hydraulic oil. After a brief review, its structure and corresponding mathematic model are introduced carefully to reveal working principles. Subsequently, the error of this method is also analysed to evaluate the feasibility. As a conclusion, the calculated error here is larger than expected due to the limitation of flow meter accuracy. 74 O+P – Ölhydraulik und Pneumatik 3/2016

MEASUREMENT ROLE OF BULK MODULUS IN HYDRAULIC SYSTEMS As the intermedium of power transmission, hydraulic oil, like the blood in a human body, plays an important role in a hydraulic system and its characteristics influence the dynamic performance and even the efficiency of a whole system. The bulk modulus, as one of the critical parameters of hydraulic oil, represents the stiffness of hydraulic oil under pressure. It is also considered as the reciprocal of the compressibility coefficient of hydraulic oil [1]. In a hydrostatic system, the transmitted energy is reproduced by the hydraulic oil acting as a spring. This means a lower bulk modulus of hydraulic oil will cause more energy losses on compressing the fluid and reduce the efficiency of energy transmission [2, 3]. On the other side, regarding the dynamic performance of the hydraulic system, the value of bulk modulus characterizes and the stiffness determines the natural frequency for known systems and loads [4]. Hence, it is hard to avoid the bulk modulus while analyzing hydraulic control systems in a detailed way. Unfortunately, this parameter is unsuitable for online measurement and has usually been determined under an ideal condition or even assumed as a constant to simplify the realization of system analysis [5]. In real applications, the bulk modulus of hydraulic oil changes not only with pressure and temperature but also with the percentage of entrained air in the fluid [6]. DESCRIPTIONS OF THE EFFECTIVE BULK MODULUS A hydraulic system can’t be completely isolated from air. During the manufacturing or transportation process of hydraulic oil, assembling process of the hydraulic system and its operating process, air can enter into the fluid by any chance, especially in a mobile hydraulic system. Since the existence of air in a hydraulic system is undesirable but inevitable [7], it is necessary to study its influence on fluid bulk modulus. This air existence can be divided into two forms: dissolved air and entrained air. The solvable quantity of dissolved air depends on the kind of fluid, temperature and pressure, and follows the Henry-Dalton’s law with temperature modification. However, dissolved air itself doesn’t change the characteristics of hydraulic oil, including viscosity and bulk modulus [1] and thus it can’t be monitored directly. The volumetric percentage of entrained air can influence the bulk modulus of a fluid dramatically at low pressure [5]. According to Merritt’s exploratory research as early as 1967, one percent entrained air can dramatically reduce the bulk modulus of hydraulic oil as much as 75 % of its original value [4]. Hence, a conception called effective bulk modulus has been introduced to take the entrained air into consideration. eq. 1 Although the equation of effective bulk modulus is simple and straight forward, it has to be recognized that the determination of the volumetric percentage of air is as hard as the determination of the bulk modulus of air-oil mixture through any practical application [8]. There are quite a lot of different models available to explain the effective bulk modulus in an either isothermal or adiabatic process specifically [9, 10, 11]. However, for more common applications, models derived under a polytropic process are preferred. IFAS has developed the following complex model and validated it through experiments [1, 12, 13]. eq. 2 The relationship between pressure and fluid bulk modulus of hydraulic oil E_oil is considered as linear with the coefficient m, and is expanded by Kim with the influence of temperature [12, 13]. eq. 3 The above model is based on the assumption that, according to Henry’s law, the release of dissolved air or absorption of entrained air in oil can be ignored with rapid pressure changes, within a few minutes, in pumps, valves and actuators. Hence, it is reasonable to carefully demonstrate the relationship among effective bulk modulus, temperature and pressure in a real application. MEASURING METHODS OF THE EFFECTIVE BULK MODULUS Various methods are employed by researchers to obtain the effective bulk modulus from hydraulic systems. All measuring methods can be roughly divided into three main categories. The first one called volume-change method [13], is widely recognized by many scientists [6, 13, 14, 15]. In this method, the basic requirement is to build a sealed chamber containing a specific constant volume of air-oil mixture under the initial conditions. Once the chamber of air-oil mixture is formed, the inflow and outflow is commonly cut off to avoid the influence of continuing flow or leakage. Then, the effective bulk modulus can be easily calculated by changing volume purposefully and measuring pressure changes with pressure sensors. Advantages of this method are the relatively high accuracy and it can easily be used to build the one-dimensional mathematical model. In recent decades, the development of new materials, especially piezoelectic materials has been extremely improving the accuracy of this measuring method [3, 16]. However, the primary problem of this new material lies in the way to arrange piezoelectric pieces in the path of tension always lowering the effective mechanical stiffness. This is independent of the advance of currently available piezoelectric materials having high mechanical stiffness monolithically. The flow-change method, as the second kind of method, is also named as mass-change method [1]. In this method, a constant volume is required and the main observed or monitored object is the flow rate. Like the architecture introduced in Ruan’s research [17], it embodies an adjustable piston-cylinder to form a constant volume under designed experimental temperature and atmosphere pressure. An injector is used to press the countable quantities oil into the cylinder. By calculating the quantities of oil and reading the pressure, the effective bulk modulus can be obtained. Kim also O+P – Ölhydraulik und Pneumatik 3/2016 75


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