Vane geometry effect on lubrication conditions between vane tip and cam-ring in hydraulic vane machines

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1 Internatinal Jurnal f Mechanical Engineering and Applicatins 015; 3(1-): 1-10 Published nline Nvember 3, 014 ( di: /j.ijmea.s ISSN: X (Print); ISSN: (Online) Vane gemetry effect n lubricatin cnditins between vane tip and cam-ring in hydraulic vane machines Mhamed Elashmawy 1,, *, Abdulaziz Alghamdi 1 1 Mechanical Engineering Department, Engineering Cllege, University f Hail, Hail, Saudi Arabia Engineering Science Department, Faculty f Petrleum and Mining Engineering, Suez University, Suez, Egypt address: arafat_696@yah.cm (M. Elashmawy), a.alghamdi@uh.edu.sa (A. Alghamdi) T cite this article: Mhamed Elashmawy, Abdulaziz Alghamdi. Vane Gemetry Effect n Lubricatin Cnditins between Vane Tip and Cam-Ring in Hydraulic Vane Machines. Internatinal Jurnal f Mechanical Engineering and Applicatins. Special Issue: Advanced Fluid Pwer Sciences and Technlgy. Vl. 3, N. 1-, 015, pp di: /j.ijmea.s Abstract: Vane gemetry is an imprtant parameter affecting the lubricatin cnditins f hydraulic vane machines. A simple therm-elast-hydrdynamic lubricatin (TEHL) mdel was used t calculate the frictin between vane tip and cam-ring f the hydraulic vane machines. Effect f vane gemetry and its dimensins n hydraulic vane machines was theretically investigated. Navier-Stkes and energy equatins were numerically slved using finite difference technique. Viscsity and density distributins were cnsidered in the TEHL-mdel. Results shw that vane gemetry ptimizatin is quite imprtant t enhance lubricatin cnditins f hydraulic vane machines. The study shws that the straight vane gemetry is the best chice fr high pressure applicatins. At higher values, increasing f vane tip radius f curvature and vane thickness enhances lubricatin cnditins between vane tip and cam-ring. Vane tip radius f curvature and vane thickness shuld nt be less than mm and 1.5 mm respectively. Keywrds: Vane Gemetry, Frictin Cefficient, TEHL-Mdel, Vane Tip Radius, Vane Thickness 1. Intrductin Frictin frces between vane tip and cam-ring in hydraulic vane machines is essential parameter affecting its perfrmance. Trying t understand the nature and behavir f this parameter is very imprtant t minimize it. Decreasing vane tip frictin enhances hydraulic vane machines perfrmance which enhances its wear, life time and its fuel cnsumptin. Many parameters affecting the hydraulic vane machines perfrmance were studied by thers. The fllwing parameters were selected: 1.1. Oil Temperature Therm-elast-hydrdynamic lubricatin (TEHL) mdel was used. Navier- Stkes and energy equatins were numerically slved using finite difference technique. The effect f perating il temperature and il film thickness n frictin cefficient between van tip and cam-ring was studied fr 3 different il grups t predict the effect f il type n van pump perfrmance. Results shw that increasing f il film thickness alne des nt guarantee the imprvement f vane tip and cam-ring lubricatin cnditins. Operating il temperature strngly affects the frictin cefficient. Increasing perating il temperature increases cefficient f frictin in the lw temperature regins while decreases it at the high temperature regins. Fr vane pump that runs under different perating cnditins, mre than ne il type may be required t ptimize its perfrmance [1]. Temperature variatin is taken int cnsideratin fr thermal TEHL mdels, hwever it fixed and taken equal t pump il temperature in case f isthermal TEHL mdel. Results shw that isthermal analysis is highly nt recmmended fr the applicatins and parameters that depend n viscsity and/r velcity distributins []. Increasing il temperature decreases frictin frces and enhances vane pump efficiency in lw temperature regins, hwever increasing il temperature nt decreases frictin frce in high temperature regins [3]. Fr balanced vane pumps the regin f higher verall pump efficiency is at il temperature arund 80 C and decreases at extremely lw and high il temperatures [4]. 1.. Cam Surface Rughness and Vane Tip Catings Fr transfer pump lubricated with diesel fuel reducing surface rughness imprves film thickness-t-surface

2 Mhamed Elashmawy and Abdulaziz Alghamdi: Vane Gemetry Effect n Lubricatin Cnditins between Vane Tip and Cam-Ring in Hydraulic Vane Machines rughness rati [5]. Lessening cam cntur surface rughness reduces frictin trque, which imprves pump mechanical efficiency [6]. A cmparisn study was perfrmed between five different Physical Vapr Depsitin (PVD) cated vane tips in additin t the traditinal vane withut cating. The effect f the radial vane frce and the pressure difference between the tw sides f the vane were fund very small cmpared t ther parameters such as vane relative speed. Cating material shws insignificant effect fr the frictin cefficient between vane tip and cam-ring in il vane pumps [7] Vane Gemetry Fr transfer pump lubricated with diesel fuel, increasing blade surface radius imprves the lubricant film parameter and reduces the frictin by 80 % [5]. A theretical study using CAD and CFD mdeling was perfrmed fr three different vane tip gemetries, Fig. 1. Results shw that the vane tip ptimum gemetry was fund fr a prfile with radiused inlet and with NACA investigated prfile in the utlet [8]. Figure. Straight vane gemetry fr balanced hydraulic vane machine. Table 1. Vane Material Prperties. Prperty Value Unites Elastic Mdulus in X MPa Pissn's Ratin in XY Shear Mdulus in XY MPa Mass Density 7700 kg/m 3 Tensile Strength in X MPa Yield Strength 60.4 MPa Thermal Expansin Cefficient in X 1.3e-005 /K Thermal Cnductivity in X 50 W/(m K) Specific Heat 460 J/(kg K) Figure 1. The three deferent vane tip gemetries [4]. An experimental and theretical study abut the rati f vane pump lift t vane thickness (ε) effect n vane tip frictin trque was perfrmed fr balanced vane pumps. Results shw that ε is an imprtant parameter affecting the pump efficiency. Increasing f ε and reducing frictin cefficient increases pump efficiency. Increasing ε increases the variatin f the vane frictin trque [9]. Figure 3. Stress analysis and material deflectin f the straight vane gemetry fr balanced vane machine.. Vane Gemetry Analysis Vane gemetry is an effective parameter f hydraulic vane machines. The cmmn material used fr the vane is DIN S Cmmn vane gemetry is f straight shape. Fig. shws a straight vane belngs t a balanced hydraulic vane machine that cnsists f 10 vanes. SlidWrks was used fr 3D-CAD gemetry and stress analysis. Table 1 tabulated vane material prperties f steel ally. Simulatin-Xpress Analysis Wizard f SlidWrks sftware was used t simulate stress analysis and material deflectin f all vane gemetries used in this study. Fig. 3 shws stress analysis and material deflectin fr straight vane gemetry. Minimum factr f safety f 1.4 is used fr all vane shapes under pressure f 00 bar (radial vane frce was neglected fr all vane gemetries). The minimum vane thickness f straight vane gemetry is 1.3 mm with maximum vane deflectin f 1 µm. Figure 4. Frward curved vane gemetry fr balanced hydraulic vane machine. Fig. 4 shws balanced hydraulic vane machine f frward curved vane gemetry. Fig. 5 shws stress and gemetry analysis f frward curved vane gemetry. Analysis shws minimum vane thickness f.4 mm with maximum vane deflectin f 18.5 µm.

3 Internatinal Jurnal f Mechanical Engineering and Applicatins 015; 3(1-): x P ( x) = PH 1 (1) bh P u µ u = µ + x y y y () h =.69G U W R (3) Figure 5. Stress analysis and material deflectin f the frward curved vane gemetry fr balanced hydraulic vane machine. Figure 6. Backward curved vane gemetry fr balanced hydraulic vane machine. Fig. 6 shws balanced hydraulic vane machine f backward curved vane gemetry. Where G: material parameter ( parameter ( ' G = α p E ), U: speed µ u U = ' ), W: lad parameter E R F P ( = = H ' E E W π ' ', E =, υ = E, E = ) E R l E (1 υ ) E1 + E eff R1 R and R: reduced radius f curvature ( R = ). R1 + R Energy equatin (4) was used t calculate the temperature distributin fr lubricant il film. Using specific heat f il c p =000 J/kgK. Cnductin heat transfer cefficient fr il was taken accrding t Rdermund (5). T T u T ρ P _ ρ c p u + v x y ρ T x T u + k + µ = 0 y y (4) With bundary cnditins, T=T fr x - 4 P P k = k , k P = W/mK (5) Figure 7. Stress analysis and material deflectin f the backward curved vane gemetry fr balanced hydraulic vane machine. Fig. 7 shws that, fr backward curved vane gemetry, the minimum vane thickness f 3.0 mm with maximum vane deflectin f 18.1 µm. Stress and deflectin analysis shws that the best vane gemetry is the straight vane shape. 3. TEHL-Mdel Vane tip smth cntact with cam-ring is simulated and mdeled using therm-elast-hydrdynamic lubricatin mdel, TEHL-mdel []. Pressure distributin is simply replaced by Hertzian distributin elliptic curve (1). Theretical mdels slving Navier-Stke's equatin () with elastic defrmatin were used fr TEHL-mdel. Cntact gemetry area was simplified by tw parallel surfaces. Lubricant film thickness is calculated accrding t Hamrck-Dwsn frmula (3) [10]. Viscsity variatin (6) as a functin f pressure and temperature was used. Table 1 (appendix1) shws the cnstants f (6) at lw and high pressure regins. Tw mineral il types (FVA1 and FVA) were used accrding t the classificatin f reference il f the German research assciatin f drives technlgy r in German Frschungsvereinigung Antriebstechnik (FVA) [11]. Bp ln µ T,P = ln K p + + T + C B 1 1 P αt + P T + C T + C With C = 95 C, P = Patm, and T = 0 C Table (appendix1) shws the cnstants f (7) at lw and high pressure regins fr the il types used [11]. (6) α p P = ρ + TαT bar + Pα + PT (7),,,0 P, C T ρt 0 4. Results and Discussin Vane gemetry effect n vane tip lubricatin cnditins is

4 4 Mhamed Elashmawy and Abdulaziz Alghamdi: Vane Gemetry Effect n Lubricatin Cnditins between Vane Tip and Cam-Ring in Hydraulic Vane Machines the fcus f this study. Vane tip radius f curvature and vane thickness effects n frictin cefficient, il temperature and il film thickness were theretically investigated using the TEHL-mdel fr tw mineral il types (FVA1 and FVA) at different vane speeds, temperatures and pressures Effect f Vane Tip Radius n Frictin Cefficient Vane tip radius f curvature is quite imprtant parameter that shuld be designed with great attentin. Fig. 9 shws the effect f vane tip radius f curvature n frictin cefficient fr FVA mineral il at 1.5 mm vane thickness, 60 C and 150 bar perating temperature and pressure respectively. Cmparing curves f Fig. 9 with Fig. 8 shws that the curves at lw vane tip radius f curvature (belw mm) have different behaves (smetimes behave inversely). But bth il types have the same behavir at higher vane tip radius f curvatures. This shws the imprtance f prper il type selectin beside physical prperties f machine gemetry. Figure 8. Effect f vane tip radius f curvature n frictin cefficient fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 150 bar. Fig. 8 shws the effect f vane tip radius f curvature n frictin cefficient fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 150 bar perating temperature and pressure respectively. Curves shw that radius f curvature has significant effect n the frictin cefficient between vane tip and cam-ring. Increasing radius f curvature increases frictin cefficient at lw values f radius (almst mm) fr lw vane speeds, while it decreases at higher radius values fr all vane speeds. The effect f radius f curvature n frictin cefficient is significant at lw vane speeds. The radius effect significantly decreases by increasing vane speed. This behave indicates that vane speed is a key parameter fr hydraulic vane machines. The speed higher than 5000 rpm is recmmended. Fr lw speed hydraulic vane machines, great attentin f vane tip gemetry is quite imprtant fr gd lubricatin cnditins and lw energy cnsumptin. Figure 10. Effect f vane tip radius f curvature n frictin cefficient fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 3500 rpm. Fig. 10 shws the effect f vane tip radius f curvature n frictin cefficient fr FVA1 mineral il at 1.5 mm vane thickness, 60 C perating temperature, 3500 rpm. Curves shw that increasing perating pressure shifts the peak f curves t the right side. Increasing perating pressure increases the minimum accepted vane tip radius f curvature that starts t decrease the frictin cefficient between vane tip and cam-ring. Curves shw that the minimum value f vane tip radius f curvature shuld nt be less than 3 mm fr gd lubricatin cnditins between vane tip and came ring. Figure 11. Effect f vane tip radius f curvature n frictin cefficient fr FVA mineral il at 1.5 mm vane thickness, 60 C and 3500 rpm. Figure 9. Effect f vane tip radius f curvature n frictin cefficient fr FVA mineral il at 1.5 mm vane thickness, 60 C and 150 bar. Fig. 11 shws the effect f vane tip radius f curvature n frictin cefficient fr FVA mineral il at 1.5 mm vane thickness, 60 C perating temperature, 3500 rpm. Fr FVA grup, the minimum value f vane tip radius f curvature

5 Internatinal Jurnal f Mechanical Engineering and Applicatins 015; 3(1-): shuld nt be less than 3 mm fr gd lubricatin cnditins. 4.. Effect f Vane Tip Radius n Oil Film Thickness Fig. 1 shws the effect f vane tip radius f curvature n il film thickness fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 150 bar fr three different speeds. Curves shw that increasing f vane tip radius enhances il film thickness. Oil film thickness enhancement increases significantly by increasing f vane speed. Effect f vane tip radius is almst similar t effect f vane speed. Increasing perating pressure significantly wuld result in significant deviatin because f mixed frictin which is nt included in the mdel. The results drawn frm this theretical study is cnsidered as primary results and need mre investigatin fr accurate results. Figure 14. Effect f vane tip radius f curvature n il film thickness fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 3500 rpm. Figure 1. Effect f vane tip radius f curvature n il film thickness fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 150 bar. Figure 15. Effect f vane tip radius f curvature n il film thickness fr FVA mineral il at 1.5 mm vane thickness, 60 C and 3500 rpm. Figure 13. Effect f vane tip radius f curvature n il film thickness fr FVA mineral il at 1.5 mm vane thickness, 60 C and 150 bar. Fig. 13 shws the effect f vane tip radius f curvature n il film thickness fr FVA mineral il at 1.5 mm vane thickness, 60 C and 150 bar fr three different vane speeds. Curves shw that increasing f vane speed affects the FVA il film thickness much mre than FVA1 il type. Oil prperties plays great rule n hydraulic vane machines perfrmance. Fig. 14 shws the effect f vane tip radius f curvature n il film thickness fr FVA1 mineral il at 1.5 mm vane thickness, 60 C and 3500 rpm fr three different perating pressures. Curves shw that increasing f vane tip radius f curvature significantly enhances il film thickness. Increases f perating pressure have negative impact n il film thickness. It shuld be mentined that the TEHL-mdel is designed nly t deal with il film between vane tip and cam-ring assuming that came ring as a circular cntur. Fig. 15 shws the effect f vane tip radius f curvature n il film thickness fr FVA mineral il at 1.5 mm vane thickness, 60 C and 3500 rpm fr three different perating pressures. Curves shw that FVA il type has significant il film thickness than FVA1 il grup. While FVA1 has better frictin cefficient behavir than FVA grup as shwn in Fig. 10 and Fig. 11. Increasing il film thickness nt necessarily enhances lubricatin cnditins Effect f Vane Tip Radius n Oil Film Temperature Oil film temperature at cntact area is quite imprtant parameter affecting lubricatin cnditins. Fig. 16 shws the effect f vane tip radius f curvature n il maximum and average temperatures fr FVA1 mineral il at 1.5 mm vane thickness, and 150 bar at three different vane speeds. The maximum and average il temperatures were calculated in the middle f the cntact area in flw directin (x-axis) taking the maximum value and the average f the radial directin (y-axis). Curves shw that increasing radius f curvature

6 6 Mhamed Elashmawy and Abdulaziz Alghamdi: Vane Gemetry Effect n Lubricatin Cnditins between Vane Tip and Cam-Ring in Hydraulic Vane Machines decreases bth f maximum and average il temperature within cntact area. Increasing vane speed als increases il maximum and average temperatures. temperature has the same effect f vane speed. Fig. 18 shws the effect f vane tip radius f curvature n il maximum and average temperatures fr FVA mineral il at 1.5 mm vane thickness, and 150 bar at three different vane speeds. FVA has higher temperatures than FVA1 which gives little advantage fr FVA1 il grup. Figure 16. Effect f vane tip radius f curvature n il film temperature fr FVA1 mineral il at 1.5 mm vane thickness, and 150 bar. Figure 19. Effect f vane tip radius n il film temperature fr FVA mineral il at 1.5 mm vane thickness, and 3500 rpm. Fig. 19 shws the effect f vane tip radius f curvature n il maximum and average temperatures fr FVA mineral il at 1.5 mm vane thickness, and 3500 rpm at three different perating pressure values. Increasing perating pressure increases il temperature at vane tip cntact area Effect f Vane Thickness n Frictin Cefficient Figure 17. Effect f vane tip radius f curvature n il film temperature fr FVA1 mineral il at 1.5 mm vane thickness, and 3500 rpm. Vane thickness is an imprtant parameter fr vane hydraulic machines. Increasing f vane thickness wuld result n an increase f applied radial frce n vane tip. Figure 18. Effect f vane tip radius f curvature n il film temperature fr FVA mineral il at 1.5 mm vane thickness, and 150 bar. Fig. 17 shws the effect f vane tip radius f curvature n il maximum and average temperatures fr FVA1 mineral il at 1.5 mm vane thickness, and 3500 rpm at three different perating pressure values. Curves shw that increasing perating pressure increases il maximum and average temperatures. General effect f perating pressure n il Figure 0. Effect f vane thickness n vane tip frictin cefficient fr FVA1 mineral il at mm vane tip radius, 3500 rpm and 100 bar. Fig. 0 shws the effect f vane thickness n vane tip frictin cefficient fr FVA1 mineral il grup at mm vane tip radius, 3500 rpm and 100 bar. Curves were calculated at temperatures f 40, 60 and 80 C. FVA1 il grup at lw perating pressure (100 bar) shws an increase f frictin cefficient by increasing f il perating temperature fr higher vane thickness values. Increasing vane thickness

7 Internatinal Jurnal f Mechanical Engineering and Applicatins 015; 3(1-): decreases vane tip frictin cefficient at lw temperatures while increases it at higher temperatures. Increasing perating pressure frm 100 bar t 00 bar leads the peak f all curves t be shifted tward the right side, Fig. 1. Bth curves f Fig. 0 and Fig. 1 shw that vane thickness shuld be higher than 1.5 mm t satisfy lw vane tip frictin cefficient. temperatures. Curves shw that vane tip frictin cefficients are significantly high in the regin belw vane thickness value f 1.5 mm especially at higher perating temperatures. Fig. 3 shws that increasing perating pressure slightly increases the general value f frictin cefficient. The curve f FVA il grup at lw perating temperature (40 C) shws dramatic increase f vane tip frictin cefficient by increasing f vane thickness Effect f Vane Thickness n Oil Film Thickness Oil film thickness is a sensitive parameter that greatly depends n il type, il prperties, perating cnditins, and machine gemetry. Figure 1. Effect f vane thickness n vane tip frictin cefficient fr FVA1 mineral il at mm vane tip radius, 3500 rpm and 00 bar. Figure 4. Effect f vane thickness n il film thickness fr FVA1 mineral il at mm vane tip radius, 3500 rpm and 100 bar. Fig. 4 shws the effect f vane thickness n il film thickness fr FVA1 il grup at mm vane tip radius, 3500 rpm vane speed and 100 bar perating pressure. Curves f Fig. 4 shw that il film decreases by increasing vane thickness. Figure. Effect f vane thickness n vane tip frictin cefficient fr FVA mineral il at mm vane tip radius, 3500 rpm and 100 bar. Figure 5. Effect f vane thickness n il film thickness fr FVA1 mineral il at mm vane tip radius, 3500 rpm and 00 bar. Figure 3. Effect f vane thickness n vane tip frictin cefficient fr FVA mineral il at mm vane tip radius, 3500 rpm and 00 bar. Fig. shws the effect f vane thickness n vane tip frictin cefficient fr FVA mineral il grup at mm vane tip radius, 3500 rpm and 100 bar fr 40, 60 and 80 C perating Fig. 5 shws the effect f vane thickness n il film thickness fr FVA1 il grup at mm vane tip radius, 3500 rpm vane speed and 00 bar perating pressure. Increasing f vane thickness has the same effect f increasing the radial vane frce. Althugh increasing f vane thickness decreases il film thickness, it causes the vane tip frictin cefficient t decrease especially at vane thickness values greater than 1.5

8 8 Mhamed Elashmawy and Abdulaziz Alghamdi: Vane Gemetry Effect n Lubricatin Cnditins between Vane Tip and Cam-Ring in Hydraulic Vane Machines mm, Fig. 0. Figure 6. Effect f vane thickness n il film thickness fr FVA mineral il at mm vane tip radius, 3500 rpm and 100 bar. Fig. 6 shws the effect f vane thickness n il film thickness fr FVA il grup at mm vane tip radius, 3500 rpm vane speed and 100 bar perating pressure. Curves f Fig. 6 shw that the il film decreases by increasing f vane thickness. Increasing f perating temperature significantly decreases il film thickness. Increasing perating pressure decreases il film thickness, Fig. 7. Figure 8. Effect f vane thickness n vane radial frce at 100 bar and 00 bar perating pressures Effect f Vane Thickness n Vane Tip Defrmatin Length f Elast-Hydrdynamic Defrmatin Elast-hydrdynamic defrmatin due t very high pressure f lubricant between vane tip and cam-ring within cntact area was mdeled accrding t Hertzian distributin elliptic curve (1). Fig. 9 shws the effect f vane thickness n vane tip elast-hydrdynamic defrmatin length at 100 bar and 00 bar perating pressures. Curves f Fig. 9 shw that increasing f vane thickness increases vane tip elast-hydrdynamic defrmatin length. Increasing f the perating pressure causes the curve t be shifted upward and increases all values f vane tip defrmatin length. Figure 7. Effect f vane thickness n il film thickness fr FVA mineral il at mm vane tip radius, 3500 rpm and 00 bar Effect f Vane Thickness n Radial Vane Frce Vane thickness effect n radial vane frce has a linear behave. At cnstant vane width (16 mm) increasing f vane thickness wuld result f an increase f vane area subjected t machine perating pressure which increases radial vane frce linearly. Increasing radial vane frce increases vane tip cam-ring tightness which decreases il leakage between them. At the same time it may cause negative influence n frictin cefficient f vane tip sliding cntact with cam-ring. Fig. 8 shws the linear curves f vane radial frce as a functin f vane thickness at 100 bar and 00 bar perating pressures. Increasing f perating pressure magnifies the effect f vane thickness n vane radial frce. Figure 9. Effect f vane thickness n vane tip elast-hydrdynamic defrmatin length at 100 bar and 00 bar perating pressures. 5. Cnclusins This study cncentrates n vane gemetry effect n il van machines perfrmance. TEHL-mdel develped by Elashmawy [] was used fr theretical parametric study f vane gemetry and its impact n vane tip frictin cefficient, il film thickness, maximum and average il film temperatures. The study was perfrmed fr tw different mineral il type grups, FVA1 and FVA accrding t the German research assciatin f drives technlgy [11]. Results shw that increasing f vane tip radius f curvature enhances lubricatin cnditins between vane tip and

9 Internatinal Jurnal f Mechanical Engineering and Applicatins 015; 3(1-): cam-ring. Vane tip radius f curvature shuld nt be less than mm and recmmended t be higher than 3 mm. Effect f increasing vane tip radius f curvature is similar t the effect f increasing vane speed. Bth enhance lubricatin cnditins after sme certain values ( mm and 1000 rpm). Increasing vane thickness causes an increase f radial vane frce and as a result il film thickness decreases. In general increasing vane thickness decreases vane tip frictin cefficient at lw temperatures while increases it at higher temperatures. 1.5 mm vane thick r higher is recmmended. Straight vane design is the best chice fr high perating pressures applicatins. SlidWrks was used fr 3D-CAD gemetry and stress analysis. Steel ally was selected fr cmparisn between three vane gemetries (straight, frward and backward curved). Simulatin-Xpress Analysis Wizard f SlidWrks was used t simulate stress analysis and material deflectin f the three selected vane gemetries. Operating pressure f 00 bar and factr f safety f 1.4 were selected as a base f cmparisn. The minimum vane thickness f straight vane gemetry was 1.3 mm with maximum vane deflectin f 1 µm. While the minimum vane thickness value f.4 mm and 3.0 mm with maximum vane deflectin f 18.5 µm and 18.1 µm were btained fr frward and backward curved vane gemetries respectively at the same factr f safety (1.4). Nmenclature b H Hertzian defrmatin length [µm] E Mdulus f elasticity [Pa] G Material parameter [--] h Mean film thickness [µm] k Thermal cnductivity [W/mK] k Thermal cnductivity at atmsphere [W/mK] l eff Effective cntact length, vane width [m] P System pressure [bar] P H Hertzian pressure [bar] R Reduced radius f curvature [--] R V Vane tip radius f curvature [mm] T Oil temperature [ C] T Oil initial temperature [ C] U Speed parameter [--] u Oil velcity cmpnent, x-axis [m/s] v Oil velcity cmpnent, y-axis [m/s] W Lad parameter [--] Greek Symbls λ Frictin cefficient [--] µ Dynamic viscsity [Pa.s] υ Pissn s rati, 0.3 fr steel [--] ρ Density [kg/m 3 ] τ Shear stress [N/m ] Appendix 1 Tables f Data Used fr TEHL-Mdel Pressure Range K P [cp] Table 1. Cnstants f (6) at lw and high pressures fr the used il grups [11] B P [ C] α [10-3 /bar] B / P [ C/bar] Errrr [%] 11: FVA1 (p 10 3 ) : FVA1 (p>10 3 ) : FVA (p 10 3 ) : FVA (p>10 3 ) T Pressure Range ρ, Table. Cnstants f (7) at lw and high pressures fr the used il grups [11] α T,0bar [10-4 ] α [10-5 ] α p / T [10-7 ] Errr [%] 11: FVA1 (p 10 3 ) : FVA1 (p>10 3 ) : FVA (p 10 3 ) : FVA (p>10 3 ) P, 0 C References [1] Mhamed Elashmawy. Theretical Investigatin f Frictin Frces between Vane Tip and Cam-Ring in Oil Vane Pumps. Internatinal Jurnal f Science, Technlgy and Sciety. Vl., N. 5, 014, pp di: /j.ijsts [] M. Elashmawy. Study f Vane Tip Frictin in Oil Vane pump. Suez Canal University Dissertatin. Egypt, 009. [3] Y. Inaguma. Oil temperature influence n frictin trque characteristics in hydraulic pumps. Prc IMechE Part C: J Mechanical Engineering Science 6(9); pp , 011. [4] Y. Inaguma and N. Yshida. Mathematical Analysis f Influence f Oil Temperature n Efficiencies in Hydraulic Pumps fr Autmatic Transmissins. SAE Int. J. Passeng. Cars - Mech. Syst. 6(): , di:10.471/ , 013. [5] P. C. Sui. Predictin f film thickness and frictin at a rtary pump blade and liner interface. American Sciety f Mechanical Engineering (ASME). Vl. 7, ASME, New Yrk, pp.115-1, 1995.

10 10 Mhamed Elashmawy and Abdulaziz Alghamdi: Vane Gemetry Effect n Lubricatin Cnditins between Vane Tip and Cam-Ring in Hydraulic Vane Machines [6] Y. Inaguma, and A. Hibi. Reductin f frictin trque in vane pump by smthing cam ring surface. Prceedings f the Institutin f Mechanical Engineers Part C-Jurnal f Mechanical Engineering Science. 1 (5), pp , 007. [7] M. Elashmawy, and H. Murrenhff. Experimental Investigatin f frictin frce between vane tip and cam-ring in il vane pumps. Internatinal Jurnal f Fluid Pwer. Vl. 10, N. 1, pp 37-46, 009. [8] M. Panek. Vane pump cntrl in rder t maintain liquid frictin and leak tightness. Internatinal Capathian Cnference ICCC. Zakpane, Pland, 004. [9] Y. Inaguma, and N. Yshida. Variatin in Driving Trque and Vane Frictin Trque in a Balanced Vane Pump. SAE Technical Paper, , 014. [10] P. W. Gld. Triblgy. Umdruck zur Vrlesung. Trans-Aix-Press, Aachen, Germany, 003. [11] J. Blume, Druck und Temberatureinfluß auf Viscsität und Kmpressibilität vn flüssigen Schmierstffen, RWTH Aachen University Dissertatin, 1987

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