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O+P Fluidtechnik 3/2016

O+P Fluidtechnik 3/2016

MEASUREMENT FORSCHUNG

MEASUREMENT FORSCHUNG UND ENTWICKLUNG PEER REVIEWED used this method as one part of his dissertation, but a flow meter is used to account the oil [13]. In a hydrostatic transmission, Manring figured out a closed hydraulic circuit to measure the effective bulk modulus online [5]. In his research, the flow rates and pressures of inlet, outlet and leakage are monitored by flow meters and pressure sensors respectively. Although a detailed study about error was conducted, Manring’s method still exhibits almost ± 41 % uncertainty range and the influence of temperature and entrained air in his research was not considered. In the third kind of method, the hydraulic oil itself is taken as the medium to transport the test signals like step pressure wave or sound wave. The latencies of the signals between two or more test points are measured in the transporting line. The speed of this signal propagated in the hydraulic oil can be calculated from the measurement results and then used to obtain the effective bulk modulus of hydraulic oil. In order to get the velocity of the pressure wave, many scientists have designed various architectures, but there is one common structure: a long pipe with some test points on it [11, 18, 19]. Furthermore, for pressure wave signal, Li used a hydraulic RC network to form a low pass filter to reduce the system noise and to enhance the accuracy [20]. Karjalainen improved the structure with series of throttles to avoid cavitation and a heat controller to maintain the temperature [21]. For sound signal, Theissen [22] and Ericson [23] utilized a RALA for the determination of effective bulk modulus. The RALA is a low-reflecting line termination, which can be used to avoid the influence from the reflection of pressure ripple. Ultrasonic sensors have also been introduced to monitor the transport speed of sound in oil [24]. Although in this kind of method a real effective bulk modulus can be obtained by measuring and calculating, it faces two main problems. One is the long pipe structure. A real hydraulic system usually doesn’t allow enough space to utilize this structure. Another aspect lies in the accuracy problem. The oil density 1. Test point with pressure sensor S (p s ) and temperature sensor S (T s ), 2. Flow meter A (Q a ), 3. Conjunction point with pressure sensor A (p a ), 4. Flow control valve, 5. Conjunction point with pressure sensor B (p b ), 6. Flow meter B (Q b ), 7. Conjunction point with pressure sensor C (p c ) and temperature sensor C (T c ), 8. Pressure relief valve, 9. Tank (p 0 ). 01 The online measurement method of effective bulk modulus a) the structure of the online measurement, b) the pressure change through the structure, c) the flow rate change through the structure 76 O+P – Ölhydraulik und Pneumatik 3/2016

MEASUREMENT plays a key role in the calculation here, which is hard to be defined precisely because of the unknown quantity of the entrained air. In this paper, an approach based on the flow-change method will be presented utilizing two or three flow meters to obtain the effective bulk modulus of the hydraulic oil in the system online. The main idea is to use a large pressure drop to create different volumetric flows in one flow channel and then, though monitoring the flow rate change and the pressure change, the effective bulk modulus can be calculated by its basic expression. STRUCTURE DESCRIPTION OF THE METHOD The structure of the online measurement method of bulk modulus was generally presented in Figure 01a. Here, a measured flow, normally supposed to be a small bypass flow from the test point of an operating hydraulic system, passes through several components, flow meter A (2), flow control valve (4), flow meter B (6) and pressure relief valve (8) successively flowing to the tank (9). Ob viously, two flow meters are used to measure the volumetric flow rate change. The pressure of each conjunction points (1, 3, 5 and 7) and the temperatures of conjunction points 1 and 7 are monitored carefully by pressure and temperature sensors. The flow control valve controls the flow rate and is also responsible for the creation of a large pressure drop ∆p as shown in figure 01b. The value of p c depends on the pressure relief valve, which will also influence the flow rate and should be setup carefully considering the control ability of the flow control valve. The figure 01b and figure 01c shows the theoretical pressure and flow rate changes through the structure of the online measurement method. The reason which causes flow rate change ∆Q will be discussed in the chapter of simulation analysis. Besides, the flow rate change caused by the pressure drop at pressure relief valve (8) cannot be measured because of its negligible amount. It is necessary to point out that the percentage of entrained air in the hydraulic oil does not change through this method because the time to release the dissolved air is insufficient. MATHEMATICAL DERIVATION The bulk modulus is defined as the slope of a stress-strain curve and, for the fluid, is normally described by the following equation. eq. 4 The volumetric flow rate means the volume of the fluid passing one particular cross-sectional area per unit time. Hence, the equation 4 can also be expressed as eq. 5 As ∆Q and ∆p become zero in the limit, the differential expression of equation 5 is eq. 6 For such a measurement method discussed above, the initial condition is, Q = Q a when p = p a , the volumetric flow rate at Q b can be derived as eq. 7 Therefore, the relationship among bulk modulus, flow rates and pressures is described by the equation eq. 8 According to the physical definition of bulk modulus, which indicates the volumetric changeability of the fluid when the pressure is altering, equation 8 can be used to calculate the bulk modulus of the pure fluid, or the effective bulk modulus if entrained air exists in oil at the initial pressure p a , through collecting the pressure and flow rate data from sensors. ACCURACY DISCUSSION Since the method introduced in this paper is using several sensors, it is necessary to evaluate the accuracy or uncertainty of these calculations. The error of this method can be derived from equation 8 as follow eq. 9 In order to study influences from percent-error associated with measurement devices, a first order Taylor approximation is employed [5] here to obtain eq. 10 where ε pa , ε pb , ε Qa and ε Qb are the errors occurring in measurements by using sensors, which are calculated from the datasheets provided by device manufacturers. The other parameters S pa , S pb , S Qa and S Qb , are so-called sensitivity coefficients of each corresponding error, which all contribute to describe the sensitivity of ε from every sensor’s error and can be calculated by the following formula. eq. 11 in which x means the subscripts of each parameter and all the data used here to approach sensitivity coefficients have to be considered as true values. To calculate the error of bulk modulus during the measurement, equation 10 can be simply derived as eq. 12 where S E follows the routine of equation 11. Therefore, through combining equation 10 and 12, the expected error of bulk modulus in this method is expressed here eq. 13 Although it is supposed to use true values during the calculation of bulk modulus’ error, the utilization of measured actual O+P – Ölhydraulik und Pneumatik 3/2016 77

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