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O+P Fluidtechnik 3/2016

O+P Fluidtechnik 3/2016


MEASUREMENT FORSCHUNG UND ENTWICKLUNG PEER REVIEWED contribute to the volumetric change of oil ∆Q according to equation 5. ACCURACY ANALYSIS AND DISCUSSION Although the higher accuracy of sensors the better, the influence degree of pressure sensors and flow meters still needs to be calculated according to equation 13 and then demonstrated. Except for the default settings in assumption 2, the pressure drop is 250 bar here for a convenient observation. Figure 05 clearly shows that the accuracy of pressure sensors has almost no influence compared to flow meters on the experimental accuracy of effective bulk modulus determination in this method. When the sensor’s accuracy is 1 %, the pressure sensor and the flow meter causes 1.01 % and 83.04 % error of effective bulk modulus, respectively. The reason can be seen in the fact that the value of pressure change in this system is much larger than the absolute accuracy of pressure sensors, but the value of flow rate change is close to the absolute accuracy of flow meters. In order to simulate more specifically, the datasheets from various commercial companies have been referenced. The average accuracy data of following sensors are employed to evaluate this method here [25]: the pressure sensor, from Bosch Rexroth AG, WIKA and Baumer, has 0.5 % accuracy and 0.1 % non-repeatability; the gear flow meter, from KEM Küppers, KRACHT and VSE Volumentechnik, has 0.1 % linearity, 0.3 % accuracy and 0.1 % reproducibility. For the three situations discussed above, the corresponding simulations for errors are revealed in figure 6. Several conclusions can be obtained: Firstly, it is seen from figure 06a that the enlargements of flow rate will not improve the accuracy of effective bulk modulus in this method. Hence, the desired flow rate mainly depends on the measuring range of the flow meter. It is necessary to notice that the flow rate through this setup of effective bulk modulus online measurement is a bypass flow from a test point in an operating hydraulic system. For the real application, a smaller bypassed flow rate can cause smaller influence to the operating hydraulic system and is more energy efficient. Secondly, as in figure 06b, the increasing percentage of the entrained air can enlarge the ∆Q and thus improve the accuracy at the chosen 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 ), 10. Long hose with a directional control valve. 07 The structure of the online measurement method of effective bulk modulus with the additional parts ∆p, however, as mentioned above, this parameter is unforeseeable in a real system, and the effect only appears at low pressure. Thirdly, according to figure 06c, effective bulk modulus changes caused by the oil characteristic can influence the accuracy, but the amplitude between the curves is relatively small (around 1.7 % error per 1 000 bar). Lastly, it is noticed from figure 06b that even with 5 % entrained air in oil, this method still provides ± 10 % error of effective bulk modulus. According to the equation 13 and the accuracy analysis part, if the final purpose is applying this method to normal oil (0.1 % entrained air) in hydraulic system, the flow meter accuracy should reach 0.5 ‰ to obtain the error of effective bulk modulus of ± 5 %. DISCUSSION FOR FURTHER RESEARCH For future research, one interesting objective is about discovering the influence from the entrained air and dissolved air in the hydraulic oil. In this paper, according to the assumption 3, the percentage of entrained air in the oil is constant and there is no transformation between the entrained air and the dissolved air. If there is enough time to let the dissolved air transform to the entrained air at low pressure, it will obtain a larger flow rate than before. Hence, a long hose with a directional control valve (10) in figure 07 is introduced here. A long hose can create a long time for releasing the dissolved air after the pressure drop. A directional control valve can provide a comparison between two different situations. However, this idea works only when the pressure p c , which is controlled by the pressure relief valve (8), is much lower than 50 bar. This is because the entrained air has no influence on the volumetric flow rate change ∆Q when the pressure is above 50 bar as shown in figure 02 and figure 03. CONCLUSION The present research was an attempt to provide an approach of online measurement of bulk modulus in hydraulic systems. Briefly, in this system, the data of pressure drops and flow rate changes were collected to calculate the effective bulk modulus by mathematical models. The accuracy tolerance of this method was also analyzed and testified carefully. As a result of this study – for the volumetric changes of flow rate in this method are so close to the limitation of 80 O+P – Ölhydraulik und Pneumatik 3/2016

MEASUREMENT flow meters’ accuracy – the accuracy tolerance of effective bulk modulus here is higher than expected. It is still reasonable to employ this method in an operating system to obtain the effective bulk modulus online in case suitable sensors are used. Besides, when the flow meter with extremely high accuracy would be available on the market, this method would be very helpful and convenient knowing state of the fluid condition in a hydraulic system. ACKNOWLEDGEMENT During this research, the author is financed by the fellowship „Sino- German (CSC-DAAD) Postdoc Scholarship Program“, which is funded by both the Chinese government and the German federal and state government. The author thanks for the support of the work. Authors: Dr. Chuan Ding, research associate at the Institute for Fluid Power Drives and Controls (IFAS), RWTH Aachen University; Univ.-Prof. Dr.-Ing. Hubertus Murrenhoff is head of the Institute TABLE OF FORMULAE Symbols Units Descriptions E [bar] Bulk modulus E eff [bar] Effective bulk modulus E oil [bar] Bulk modulus of hydraulic oil E 0 [bar] Bulk modulus of hydraulic oil at atmosphere pressure and room temperature m n [ - ] [ - ] p [bar] Pressure Pressure related term in equation to express bulk modulus Temperature related term in equation to express bulk Modulus p a , p b , p c , p s [bar] Measured pressure at each points p 0 [bar] Pressure of atmosphere, considered as 1 Bar Q [l/min] Flow rate Q air [l/min] Flow rate of entrained air Q oil [l/min] Flow rate of hydraulic oil Q a , Q b [l/min] Measured flow rate at each points S pa , S pb , S Qa , S Qb , S E [ - ] Sensitivity coefficients of each error of sensors T [K] Temperature T c , T s [K] Measured temperature at each points T 0 [K] Room temperature, considered as 293.15K V [m 3 ] Volume V air [m 3 ] The volume of entrained air V oil [m 3 ] The volume of hydraulic oil α α [ - ] [ - ] ε [ - ] Error ε ε [ - ] κK [ - ] Polytropic constant Volumetric content of entrained air at initial pressure Volumetric thermal expansion coefficient for mineral oils, considered as 7 10 -4 K -1 [1] Errors occurring in measurements by using sensors References: [1] Murrenhoff, H., 2005. Grundlagen der Fluidtechnik, 4 th ed., Shaker Verlag, Aachen. [2] Walters, R. B., 1991. Hydraulic and electro-hydraulic control systems, Elsevier Applied Science, London. [3] Niezrecki, C., Schueller, J. K., and Balasubramanian K., 2004, “Piezoelectricbased Fluid Bulk Modulus Sensor” Journal of Intelligent Material Systems and Structures, 15 (12), pp. 893–899. [4] Merrit, H. E., 1967. Hydraulic control systems, Wiley, New York. [5] Manring, N. D., 1997, “The Effective Fluid Bulk-Modulus Within a Hydrostatic Transmission,” J. Dyn. Sys., Meas., Control, 119(3), p. 462. [6] Schrank, K., Stammen, C., and Murrenhoff ,H., 2014, “A New Approach to Model a Multip-hase Hydraulic Capacity and its Experimental Validation,” The 9 th International Fluid Power Conference. [7] Schrank, K., Stammen, C., and Murrenhoff ,H., 2013, “Measurements of Air Absorption and Air Release Characteristics in Hydraulic Oils at Low Pressure,” Proceedings of the ASME/BATH 2013 Symposium on Fluid Power & Montion Control. [8] Schrank, K., Murrenhoff, H., and Stammen, C., 2014, “Investigation of Different Methods to Measure the Entrained Air Content in Hydraulic Oils,” Proceedings of the ASME/BATH 2014 Symposium on Fluid Power & Montion Control. [9] Wylie, E. B., Streeter ,V. L., and Suo, L., 1993. Fluid transients in systems, Prentice Hall, Englewood Cliffs, NJ. [10] Yang, H., Feng, B., and Gong, G., 2011,“Measurement of Effective Fluid Bulk Modulus in Hydraulic System,” J. Dyn. Sys., Meas., Control, 133 (6), p. 061021. [11] Yu J., Chen, Z., and Lu, Y., 1994,“The Variation of Oil Effective Bulk Modulus With Pressure in Hydraulic Systems,” J. Dyn. Sys., Meas., Control, 116 (1), p. 146. [12] Kim, S., and Murrenhoff H., 2012, “Measurement of Effective Bulk Modulus for Hydraulic Oil at Low Pressure,” J. Fluids Eng., 134 (2), p. 021201. [13] Kim, S., 2012, “Measurement of Effective Bulk Modulus and its use in CFD Simulations,” Dissertation, IFAS, RWTH Aachen, Aachen, German. [14] Kajaste, J., 2005, “Experimental Validation of Different Models for Effective Bulk Modulus of Hydraulic Fluid,” Proceedings of the 9 th Scandinavian International Conference on Fluid Power. [15] Feng, B., 2011, “Study on Effective Fluid Bulk Modulus and Measurement in Hydraulic Systems,” Dissertation, SKLoFPTC, Zhejiang University, Hangzhou, China. [16] Kim, G. W., and Wang, K.-W., 2009, “On-line Estimation of Effective Bulk Modulus in Fluid Power Systems Using Piezoelectric Transducer Impedance,” Journal of Intelligent Material Systems and Structures, 20 (17), pp. 2101–2106. [17] Ruan, J., and Burton, R., “Bulk Modulus of Air Content Oil in a Hydraulic Cylinder,” ASME 2006 International Mechanical Engineering Congress and Exposition, pp. 259–269. [18] Cho B.-H., Lee H.-W., and Oh J.-S., 2002,“Estimation Technique of Air Content in Automatic Transmission Fluid by Measuring Effective Bulk Modulus,” International Journal of Automotive Technology, 3 (2), pp. 57–61. [19] Vähäoja, P., and Kela, L., 2009, “Measuring Pressure Wave Velocity in a Hydraulic System,” World Congress on Science, Engineering and Technology, pp. 501–507. [20] Li ,S., and Ge, S., 1989, “Online measurement of oil bulk modulus Be (in Chinese),” Journal of Mechanical Engineering, 3(1), pp. 88–93. [21] Karjalainen, J.-P., and Karjalainen, R., 2005, “The dynamics of hydraulic fluids-significance, differences and measuring,” PTMC 2005. [22] Theissen, H., 1983, “Die Berücksichtigung instationärer Rohrströmung bei der Simulation hydraulischer Anlagen,” Dissertation, IFAS, RWTH Aachen, Aachen, German. [23] Eriscon, L., and Palmberg, J.-O., 2009, “Measurement of Free Air in the Oil Close to a Hydraulic Pump,” JFPS International Journal of Fluid Power System, 2(2), pp. 39–44. [24] Drumm, S., Wohlers, A., Fatemi, A., and Murrenhoff, H., 2010, “Viscosity and Bulk Modulus Measurements under High Pressure Conditions,” 2010 STLE Annual Meeting & Exhibition. [25] Homepages for datasheets of companies visited on 22, Jan., 2015. – Bosch Rexroth AG: – WIKA: – Baumer: – KEM Küpper: – KRACHT: – VSE Volumentechnik: O+P – Ölhydraulik und Pneumatik 3/2016 81


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