Development of dynamic gas thrust bearings: design and first experimental results

Transcription

1 Development of dynamic gas thrust bearings: design and first experimental results Rodrigo Villavicencio, Federico Colombo, Terenziano Raparelli, Vladimir Viktorov Department of Mechanical Engineering, Politecnico di Torino, Italy Keywords: Air thrust bearings, high speed rotors. SUMMARY. This article is focused on the experimental test and validation of axial dynamic thrust bearings. The application of this kind of bearings is the sustentation of a high speed compressor for generation of electricity in a vehicle using a fuel cell system. As explained in [1], the rotational speed of the compressor is rpm. The use of dynamic gas bearings is a good solution for this kind of applications, due to the absence of pressurized air supply. The experimental study was carried out with a test bench, designed to make the rotor rotate in stable conditions up to rpm. The dynamic bearings tested are a spiral groove thrust bearing and a taper land thrust bearing. The results of the tests were compared with simulations and they show good relation with them. In numerical models the deformation of the thrust disk due to centrifugal forces was taken into account to correct the axial air gap. 1 INTRODUCTION Fuel cells are used in electrical cars to convert the energy stored in hydrogen tanks into electric energy. Fuel cell systems require auxiliary components e.g. air and hydrogen compressors more and more wieldy. The IBIS laboratory in Politecnico di Torino in collaboration with CRF and other industrial partners is developing high speed compressors for hydrogen recirculation and air. By downsizing the scale of the compressor, it is necessary to rotate at high speeds. Gas bearings are employed to support the compressor shaft. For the radial bearings, externally pressurized bearings are used. For the axial bearings it was decided to use dynamic gas bearings. Among these type of bearings, were investigate the taper land bearings and the spiral thrust. It was seen [2] the thrust load was of about 300 N. The taper land bearings have been longly studied as the case of infinite long bearings by Constantinescu [9] and others. Some tests of taper land bearings can be found in [2]. Anyway, in this paper we decided not to use chart diagrams or other results from literature but to develop dedicated numerical programs as will be show in paragraph [2]. The spiral thrust bearings have been studied since 1951 [3]. The calculations of the pressure distribution, load carrying capacity and the dynamic stability was studied by V. N. Constantinescu ([4], [5]). An important study for the correct dimensioning of spiral groove thrust bearings was performed by Y. Xue and T. A. Stolarski [6]. These articles show information about spiral thrust bearings with and without internal chamber and hybrid bearings, that use external air supply. In the paper[7] different geometries of spiral groove bearings are numerically analyzed in terms of load capacity and stability. Some experimental results about dynamic groove thrust bearings were published by Hashimoto and Ochiai [8]. Their work is about geometry optimization and experimental tests with a high speed test bench. The test bench described in paper [8] could operate with a force in the range 0-50 N. In present work the thrust bearings are designed by means of numerical models and design procedures found in literature. Then the numerical results are compared with experimental tests. Both the load capacity and the force applied by 1

2 the compressor increase with the rotational speed. For the spiral groove as the numerical model is complicated to be developed, design charts from paper [4] were used. 2 MATHEMATICAL MODEL 2.1 Taper land bearings The Reynolds equation in cylindric coordinates is solved to calculate the pressure distribution on the air dynamic surface [9] [10]. r ) (h 3 p2 + r r 2 θ ) (h 3 p2 = 12µω (ph) + 24µ (ph) θ θ t where p is the pressure, r the radial coordinate, h is the clearance, θ the angular distance coordinate, µ the viscosity of the fluid and ω the rotational speed. Eq.1 is discretized with finite difference technique using central derivatives: 2 p 2 r 2 = p2 (i + 1, j) 2p 2 (i, j) + p 2 (i 1, j) r 2 2 p 2 θ 2 = p2 (i, j + 1) 2p 2 (i, j) + p 2 (i 1, j) θ 2 p 2 r = p2 (i + 1, j) p 2 (i 1, j) 2 r p p(i + 1, j) p(i 1, j) = θ 2 θ The differential equation problem reduces to an algebraic equation problem. Fig.1a shows the taper land bearing one sector of which is numerically simulated. The integration domain is specified by: (1) 0 < θ < 2π N Where N is the number of the thrust sections r i < r < r e Atmospheric pressure is considered on the border of the pad under analysis (see Fig.1b). The air clearance is specified by Eq.2, see a representation in Fig.1c h = h g + h b (2) The load capacity was calculated integrating the pressure on the surface of the bearing, using Eq.(3). F = N re ri 2π N 0 (p p a ) dr dθ (3) 2

3 θf (a) sketch and mesh grid (b) boundary conditions (c) radial section of the air gap Figure 1: Taper land bearing 2.2 Spiral bearings The film thickness h is the sum of distance h b and the groove depth h g as indicated in Fig.2b. The bounder of the spirals are expressed by: r = r 0 e ctg(α(θg θ L)) where α is the spiral angle, θ g the angle of groove, θ b the angle of land, r i the inner radius, r o the outer radius, r g the radius to the grove 3 NUMERICAL RESULTS The pressure distribution and the carrying force were calculated for the thrust bearings represented in Fig.1 and 2. The geometric parameters used are reported in Tab.1. Fig.3 shows an example of the pressure distribution under the sector of the taper land bearing. The load capacity of the taper land bearing is shown in Tab.2 as a function of the rotational speed. In Fig.9b is reported a numeric calculation of non-dimensional load capacity extrapolated from paper [6] with (θ g + θ L = 30 0 ).This graph was used to design the spiral groove bearing. 4 EXPERIMENTAL ACTIVITIES A test bench was designed and realized to measure the load carrying capacity of dynamic gas bearings at high speeds of rotation. In Fig.4 are represented the rotor and the thrust bearings under test. The load capacity of the thrust bearing at different axial air gaps is obtained indirectly by imposing the pressure on a chamber situated on the opposite side of the thrust (see item 4 in Fig.5) and measuring the axial displacement from the zero position. 3

4 θg θl α θ (a) sketch (b) radial section of the air gap Figure 2: Spiral groove bearing Table 1: Geometric parameters of the thrust bearings analyzed (a) Taper land bearing h b 5 µm h g 20 µm r i 16 mm r e 33 mm θ 1 20 o θ 2 40 o N 6 (b) Spiral groove bearing h b 5 µm h g 35 µm r i 16 mm r o 33 mm r g 20 mm 10 o θ g θ L 20 o N 12 α 135 o The shaft deformation due to centrifugal forces must be considered to correct the axial air gap along radial direction in numerical calculations. 4.1 Test bench description Fig.5 shows the principal components of the test bench: the rotor (1) is rotated by an air turbine (2) and faces the thrust disk (3) under test. An external axial force is imposed on the rotor by means of a pressured chamber (4). The axial rotor displacement is measured by means of a capacitive sensor (5), while other 4 sensors are placed in radial direction (6) on two measuring planes detect the rotor runout. The static gas journal bearing were designed to be to be stable up to rpm with supply pressure on the radial bearings of 6 bar. The test bench is depicted in Fig.6. 5 COMPARISON OF NUMERICAL AND EXPERIMENTAL RESULTS The deformation of the shaft due to centrifugal forces was taken into account to correct the air gap along the radial direction. Fig.7 shows the FEM results on the thrust disk. The shaft disk is 4

5 Figure 3: Calculated pressure distribution of the taper land bearing at rpm. Table 2: Load capacity of the taper land bearing; numerical results with h b = 5 µm and h g = 20 µm Speed of Rotation(rpm) Force(N) deformed axially towards the shaft. At rpm the air gap increases of 4 µm at the r e radius in relation to the air gap at r i radius. Tab.3 shows how the air gap changes with the rotational speed. The shaft deformation introduces important modifications in the load capacity respect to considering constant air gap. The dimensionless load carrying capacity (Eq.4) of the taper land bearing and the spiral thrust bearing are shown in Fig.8a and Fig.8b respectively. They are represented as a function of the bearing 5

6 Figure 4: Measurement of the load capacity of the thrust gas bearings. Figure 5: Section of the test bench. number (see Eq.5) for different rotational speeds and gaps. W = F p a (r 2 e r 2 i )π (4) Λ = 3.µ.ω.(r2 e r 2 i ) p a.h 2 (5) Fig.9 compares the numerical and the experimental load capacity. The maximum dimensionless load of the spiral thrust bearing is W = 0.78 and it correspond to 210 N at rpm and 5.5 µm. The taper land bearing has a lower load capacity than the spiral bearing but this last suffers of hammer instability for bearing numbers greater than 70. Taper land bearing has a maximum dimensionless load of W = 0.48 and it correspond to 130 N at rpm and 5 µm. 6

7 Figure 6: Views of the test bench. Figure 7: Shaft deformation due to centrifugal forces obtained with FEM software. Table 3: Difference between the shaft axial deformation at internal radius ri and external radius re at different rotational speeds. Speed of rotation(rpm) Deformation by centrifugal force(µm)

8 W Bearing number Λ 10000rpm 15000rpm 20000rpm 25000rpm 30000rpm 35000rpm 40000rpm 45000rpm 50000rpm 55000rpm 60000rpm 65000rpm 70000rpm W Bearing number Λ rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm rpm (a) Taper land bearing (b) Spiral thrust bearing Figure 8: Experimental dimensionless load capacity vs bearing number W experimental numerical model W experimental numerical model Bearing number Λ Bearing number Λ (a) the taper land thrust bearing. (b) Spiral thrust bearing. Figure 9: Comparison between numerical and experimental load capacity. 6 CONCLUSIONS A test bench for dynamic air thrust bearings was designed and realized. A taper land and a spiral grooved thrust bearings were tested on the bench at different rotational speeds and air gaps. The first one presents a lower load capacity but do not suffers of hammer instability. The shaft deformation due to centrifugal forces must be considered to correct the axial air gap along radial direction in numerical calculations. References [1] Colombo, F., Raparelli, T. Viktorov, V., and Villavicencio, R., SVILUPPO DI UN REG- GISPINTA ASSIALE DINAMICO AD ARIA, Coordinamento della Meccanica Italiana. Rev.,108, (2012). 8

9 [2] Masayoshi O., Self-acting Air-lubricated Bearings without Oil Lubrication, R & D Review of Toyota CRDL, 41(1), (2005). [3] Whipple R.T.P., Therory of the spiral groove thrust bearings with liquid or gas lubricant, Ministry of Spupply Harwell, (1951) [4] Constantinescu V. N. and Galetuse S., On the Dynamic stability of the spiral-grooved gaslubricated thrust bearing, Journal of Tribology, 109, (1987). [5] Constantinescu V. N., Galetuse S., Stability criterion for spiral grooved thrust gas bearings, Journal of Tribology, 112, (1990) [6] Xue, Y. and Stolarki, T. A., Numerical prediction of the performance of gas-lubricated spiral groove thrust bearings, in Proc. of the institution of Mechanical Engineers, Part J, 211, (1997). [7] Yoshimoto S., Miyatake M,. Iwasa T. and Takahashi A., A method of reducing the windage power loss in a laser scanner motor using spiral-groove aerodynamic thrust bearings functioning as a viscous vacuum pump, Microsyst Technnol, 41 (13), (2007). [8] Hashimoto H.and Ochiai M., Optimization of Groove Geometry for Thrust Air Beating to Maximize Bearing Stiffness, Journal of Tribology, 130 (2008) [9] Constantinescu V.N., Gas Lubrication, ASME United Engineering Center, (1969). [10] Grassam N. S. and Powell J. W., Gas Lubricated Bearings, Butterworths, London, pp (1964). 9