SERBIATRIB th International Conference on Tribology. Kragujevac, Serbia, May 2011

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1 erbian ribology oiety ERBIARIB th International Conferene on ribology ragujea, erbia, May 2011 Faulty of Mehanial Engineering in ragujea ANALYI OF CHANGE OF BUL MODULU OF MINERAL OIL EFFEC ON HE DYNAMIC BEHAVIOR OF HYDRAULIC ACUAOR Darko nežei, Aleksandar Milašinoi, Zdrako Miloanoi, Vladimir ai 1 Faulty of Mehanial Engineering Banja Luka, BiH R, darkokn@bli.net 2 Faulty of Mehanial Engineering Banja Luka, BiH R, aom@bli.net 3 Faulty of Mehanial Engineering Banja Luka, BiH R, mzdrako@ur.rs.ba 4 Faulty of ehnial iene Noi ad, erbia, sai@uns.a.rs Abstrat: When setting up the equations that desribe the dynami behaior of hydrauli atuators, it is important to know the physial properties of working fluid and the mathematial desription of hange of these properties with hanging pressure and temperature. Although the ompressibility of liquids in the pratial analysis of the flow an usually be ignored, in dynami analysis of work of hydrauli omponents fluid must be iewed as an elasti medium whih is deformed at rest with hanging pressure and temperature. In addition to the dynami behaior of hydrauli atuators largely influened by the presene undissoled air in the hydrauli fluid. Een in ery small quantities, whih an not be aoided in hydrauli systems, usdissoled air in the hydrauli fluid signifiantly hanges the elasti properties of the working fluid, affets the transmission speed of pulses of hange of pressure, leading to delay response of atuators and others. In this paper, hange of alue of effetie bulk modulus of mixture of mineral oil and dissoled air is gien on the basis of data obtained from manufaturers and experimental data obtained in the analysis of deompression of oil in the hydrauli ylinders. eywords: bulk modulus, pressure, temperature, undissoled air, deompression, dynami behaiour 1. INRODUCION Besides the basi funtions that transmit energy in the hydrauli system from the plae of transformation of mehanial into hydrauli energy (pump) to a plae of transformation hydrauli into mehanial energy (ylinder, rotary or osillating motor), hydrauli oils and fluids, perform a few extra features suh as lubriation of all plaes ontats within the hydrauli omponents, orrosion protetion, download the generated heat and, later, its transmission to the enironment, and others. In aordane with the requirements for hydrauli fluid that sets omponents, system, enironment and onditions of exploitation has formulated a series of strutural and quality different hydrauli fluids. In pratie, as hydrauli fluids are ommonly used mineral oils. hey are 370 lassified into six qualitatie leels (HH, HL, HM, HR, HV and HG), but now in the hydrauli systems used exlusiely oils lasses HM and HV. his is essentially the same quality lass of oil, noting that in oil lass HV alue of isosity index inreased relatie to oil HM. he alue of the bulk modulus of mineral oils for hydrauli systems depends primarily on the hemial omposition of base oil. [1] Mineral base oils are omposed of omplex moleules of arbon-hydrogen. Aording to the domination of the representation of ertain arbonhydrogen in oil, mineral oil an be diided into paraffini, naphtheni and mixed. Hydrauli oil is almost ompletely deried from base oil of paraffini struture, and the naphtheni oil, beause of redued aailability, used only in speial onditions of appliation. [1] 12 th International Conferene on ribology erbiatrib 11

2 Paraffin arbon-hydrogens an be straight (nparaffins) and branhy (iso-paraffins) and hae the general formula C n H 2n+2. Moleular struture and weight arbonhydrogens affet the physial and hemial behaior of mineral oil. Moleules of arbonhydrogens in paraffin oil ontain arbon atoms and hae the aerage moleular weight of [2] 2. COMPREIBILIY HE ELAICIY OF HYDRAULIC FLUID Compressibility of fluid are quantitatiely expressed in differential form, dv dp V, (1) where is a bulk modulus (olumetri elasti modulus) and for the hydrauli oil without undissoled air its alue depends on the pressure, temperature and thermodynami method of proess. Figure 1. N-paraffins In Figure 2.1 are gien the distane between atoms, in nanometers, into paraffin moleules of arbon-hydrogen. Gien the number of arbon atoms in a moleules an be alulated that the length of the moleules n-paraffin nm ( m). In iso-paraffin moleules length is smaller (beause a ertain number of atoms of arbon and hydrogen form lateral hains), but the width is higher than the n-paraffins. Figure 2. Iso-paraffins he alue of bulk modulus in this paper is gien for mineral hydrauli oil HM 46. As the alue of the bulk modulus depends almost exlusiely on the hemial struture of liquids, this oil an sere as a representatie for a wide range of mineral hydrauli oils used in pratie. [3] he auray of this statement is onfirmed by experimental data obtained by measurements in the analysis proess deompression of mineral oils in the ylinders of hydrauli presses. [4] Figure 3. Compressibility of fluid Elasti properties of liquids an be expressed by the oeffiient of elastiity whih an be generally gien pattern, dv A df Adp A F V dh dh dh h hp, (2) h height of olumn of fluid in the ylinder (a ylindrial ontainer), p pressure, F pa pressure fore. 3. IOHERMAL BUL MODULU OF MINERAL OIL Isothermal bulk modulus haraterizes a hange of density (olume) of fluid at onstant temperature p p V V. (3) 12 th International Conferene on ribology erbiatrib

3 Figure 4. Isothermal bulk modulus of mineral oil Change the isothermal bulk modulus as funtion of pressure and temperature, in Figure 4, is gien for mineral hydrauli oil isosity lass HM 46, based on data obtained from the manufaturer. [3] 4. ADIABAIC BUL MODULU OF MINERAL OIL Adiabati bulk modulus haraterizes a hange of density (olume) of fluid in thermodynami proesses without exhange of heat. Unlike the isothermal or stati bulk modulus, whih is signifiant for relatiely slow proesses of ompression, adiabati bulk modulus is important for analysis of the speed of propagation of the pulses of pressure, sudden relief of hambers under pressure, and other proesses where a hange in oil ondition ours relatiely quikly p p V V, (4) Figure 5. Adiabati bulk modulus of mineral oil 5. PEED OF PROPAGAION OF MALL DIURBANCE (PEED OF OUND) IN MINERAL OIL peed of response on the hange of pressure in the hydrauli system is ery important in a ery dynami proess, where signifiant speed and auray of the positioning of hydrauli atuators. peed of propagation of the pulses of pressure through a fluid is equal to the speed of sound through the fluid and depends on adiabati bulk modulus and fluid density z. (6) Based on data for the adiabati bulk modulus and density were alulated data for the eloity of sound for mineral oil HM 46 and gie the following diagram. p, (5) p speifi heat at onstant pressure, and speifi heat at onstant olume. Change the adiabati bulk modulus as funtion of pressure and temperature, in Figure 5, is gien for mineral hydrauli oil isosity lass HM 46, based on data obtained from the manufaturer. [3] Figure 6. peed of sound in mineral oil th International Conferene on ribology erbiatrib 11

4 6. EFFECIVE BUL MODULU OF HE MIXURE OF MINERAL OIL AND UNDIOLVED AIR Inreased flexibility of working fluid due to the presene undissoled air in the oil will be greater beause of the higher olume undissoled air, regardless of the size of air bubbles. he analysis will be done on the example of a hydrauli ylinder, noting that the results obtained for equialent ompression module does not depend on the type hamber under pressure. Effetie bulk modulus of the mixture of oil and air, at a gien pressure, an be determined using the analogy of the mehanial model, diiding the total spae of the ylinder pressure hamber to the part that meets the oil and the part that meets the undiluted air. As an effetie bulk modulus seres to desribe the elasti properties of the working fluid, in the ase of a mixture of oil and undissoled air, the equialent stiffness of the working fluid an be defined as the equialent stiffness of two serially onneted springs. h height of the ylinder hamber that is filled by air. he equialent stiffness is gien by 1 e 1 1. (9) u As E A e, (10) h substituting expressions (2.23) (2.24) and (2.27) into (2.25), we get E u, (11) V Vu u V V E effetie bulk modulus (mixture of oil and air), V u part of the olume of the ylinder hamber that is filled by oil, V part of the olume of the ylinder hamber that is filled by air and V total olume hamber ylinder. 7. AN EXAMPLE OF EFFECIVE BUL MODULU OF MIXURE OF HYDRAULIC OIL AND UDIOLVED AIR UNDER ADIABAIC CHANGE OF AE OIL AND IOHERMAL CHANGE OF AE UNDIOLVED AIR Figure 7. Mehanial model for alulating the equialent stiffness of the mixture of oil and air he stiffness (oeffiient of elastiity) oil is gien by pattern A u u, (7) hu u bulk modulus of oil, A the ross-setion of the ylinder and h height of the ylinder hamber that is filled by oil, while the stiffness (elastiity oeffiient) air is gien by bulk modulus of air and A, (8) h Experiments arried out to analyze the proess of deompression mineral hydrauli oil in hydrauli presses hae shown that due to relatiely rapid hanges in the onditions of proess, hange of state of oil an be onsidered adiabati. Regardless of the adiabati hange of state, beause of the signifiant heat apaity, oil temperature is slightly hanged, so that the hange of state of dispersed undissoled air bubbles in oil an be onsidered isothermal. [4] If the hange of state of undissoled air is isothermal, then the olume of undissoled air in oil, depending on the pressure, gien by V pa V a. (12) p he effetie bulk modulus of the mixture of oil and undissoled air, by inserting the expression (12) into (11), is 12 th International Conferene on ribology erbiatrib

5 E p pa Va p Vu p p a pa Vu Va Vu V p p a. (13) pressure in the hydrauli systems (up to 350 bar) and standard operating temperature (from 15 to 70 o C). Experimental erifiation of the theoretial model, in whih the alue of the effetie bulk modulus was alulated by the formula (13), was shown that the proess of deompression of mineral hydrauli oil an mathematially be desribed with great auray, een for small pressure when the impat undissoled air in the elastiity working fluid ery large. Although during the ompression and deompression of oil in the hydrauli ylinders are ourred omplex proesses of gradual dissolution undissoled air in the oil during ompression and extration of dissoled air from the oil during deompression, the experimental data showed that the analytial desription an be ounted with the presene undissoled air in the hydrauli oil from a to 3% of the total olume of the ylinder at atmospheri pressure. Figure 8. Effetie bulk modulus at oil temperature of 30 C: a) the absene of undissoled air, b) 0.5% undissoled air, ) 1% undissoled air, d) 3% undissoled air; e) 5% undissoled air 374 Figure 9. Effetie bulk modulus depending on the pressure and temperature in the presene of 1% undissoled air in mineral oil 8. APPLICAION OF VALUE EFFECIVE BUL MODULU IN HE ANALYI PROCE DECOMPREION (UNLOADING) OF OIL IN HE HYDRAULIC CYLINDER heoretially analyzes the proess of unloading of hydrauli ylinders ontrolled by draining the oil that is released through the relief nozzle-shaped openings with sharp edges. In parallel experimental study was arried out of the proess. Experiments were arried out with mineral hydrauli oil HM 22, 32, 46 and 64 and HV 46, the ommon alues of Figure 10. Change of pressure during the proess of deompression of mineral oil whih ontent 3% undissoled air at atmospheri pressure (oil temperature is 30 C) Figure 10 is an example of omparing experimental results with theoretial model desription of the proess of deompression, in whih the alue of the effetie bulk modulus alulated by the formula (13). he experimental results in Figure 10 are proided for hydrauli ylinder diameter of 140 mm and length of stroke of 1000 mm. [4] Controlled load shedding is done by draining the oil through a nozzle with a sharp edge diameter 2 mm. he theoretial model was alulated with undissoled air ontent of 3% in oil, at atmospheri pressure. 12 th International Conferene on ribology erbiatrib 11

6 9. CONCLUION he alue of the bulk modulus of hydrauli fluid has a large impat on the effiieny of the hydrauli system. It affets: peed of propagation of the pulse pressure hange in the system, Positioning auray of hydrauli atuators, Volumetri effiieny of pumps, he stability of the system aording to its own flutuations, he intensity of the hydrauli shok. his paper gies the alues of bulk modulus whih are representatie for mineral oil for hydrauli systems. he data are presented in the form of a diagram as a funtion of temperature and pressure. Data were heked indiretly, experimental measurements hange of pressure during proess deompression of mineral oil in the hydrauli ylinders. Experimental results show that it is not possible to aoid the presene of undissoled air in the work of hydrauli systems. Comparing experimental data with theoretial model shows that in determining the effetie bulk modulus an be ount ontent of undissoled air in mineral oil in quantities of 1 to 3% at atmospheri pressure. REFERENCE [1] JUGOMA Group of Authors, Lubriants and Lubriation, he Union of Yugosla oieties for Appliation of Fuels and Lubriants, Zagreb, [2] eith P., Hodges B., Hydrauli Fluids, Arnold, London, [3] Frauenstein M., Guide for Fluid Under Pressure for Construtors, Mobil Oil, [4] nežei D., Analysis of Deompression of Hydrauli Oil in Cylinders of Hydrauli Presses, M.. hesis, Faulty of ehnial ienes Noi ad, th International Conferene on ribology erbiatrib