Fabrication of Turboexpander with Gas Foil Bearings
6.1 The rotor
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Chapter 6
Fabrication of Turboexpander with Gas
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possible to use aerodynamic journal bearings with low load carrying capacity with a low bearing surface area. The dimension of the shaft depend on the position of bearings, deformation, natural frequencies and heat transfer rate. Major features of the shaft, which control dimension of the rotor are described below:
Bending and torque on the rotor at the designed speed.
Location of shaft collar.
Stress at the root of the collar.
Bending critical speed of the rotor.
Heat conduction between warm and the cold ends.
Overall compactness of the system.
The diameter of the rotor is determined by the bending load and torque to be transmitted. For a small cryogenic turboexpander rotor, the torque, as well as the bending load, is small [2]. However, the operating speeds are very high, which demands a consideration of stress distribution, deformation, critical speed and stability, so the diameter is fixed by the stress, deformation and rotodynamic analysis of the rotor. The position of the collar is chosen to be in the middle as it reduces the unbalanced response at the bearings at high rotational speed. Steps at the both the ends of the shaft which provides a seat for the turbine and brake compressor and these steps also serve to locate the brake compressor and the turbine wheel in the radial direction. A step some distance away from the turbine wheel, reduces the cross section of the shaft and, consequently, reduces the heat transfer rate from the lower bearing area to the cold end.
The outer diameter of the collar, which provides as thrust bearings area is fixed from the consideration of centrifugal stress at its root and total deformation at the journal area. The stress and deformations analysis of the rotor is carried out using ANSYS (Figs.
6.1(a) and 6.1(b)). The yield strength (0.2% offset) for age hardened monel K-500 is 790 MPa. The design stress is calculated as 395 MPa with a factor of safety of order 2, accounting cyclic fatigue and other unknown effects. The maximum stress at the root of the collar is 189.6 MPa and this value is under the design stress of the rotor. The shaft material Monel K-500 is a nickel-copper alloy that combines the excellent corrosion resistance characteristic with the added advantage of greater strength and hardness. They maintain excellent mechanical properties at sub-zero temperatures. The radial deformation of the journal area is nearly 20 m at its designed speed( Fig. 6.1(b)), so the radial clearance for both the journals should be higher than 20 m. The radial clearance on both
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the journal bearings are 25 m as described in Chapter 3. The major dimensions and the fabricated rotor are shown in Figs. 6.2(a) and 6.2(b).The detailed fabrication drawing of the shaft is shown in Appendix (Drawing. No: TEX-01).
(a) (b)
Figure 6.1: FEM analysis of rotor at designed speed: (a) Stress and (b) Deformation.
(a) (b)
Figure 6.2: The prototype rotor: (a) with dimension (b) Assembled rotor.
6.1.1 Balancing
The most common source of vibration in a turboexpander is rotor imbalance [85]. The imbalance in a rotor arises because the center of mass does not fall on the geometric axis, which is also the axis of rotation. The imbalance occurs from machining inaccuracies and inherent inhomogeneity in the material. An additional imbalance is created, when a
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turbine or a compressor is attached to a shaft, due to inherent asymmetry in the mass distribution of the blades. The rotating imbalance forces produce a whirling motion of the rotor known as synchronous whirl [85], which can be reduced only by balancing the rotor.
The critical speed and unbalance response study in chapter 5 prevails that, the limit of unbalance at journal bearings of the rotor has to be 100 mg.mm.
Balancing is a method of removing material from different planes in the rotor, such that the mass center and the geometric center coincide. Although in practice real rotors can never be fully balanced owing to errors in measurement, However, the amplitude of vibration can be reduced significantly by dynamic balancing. Since the prototype rotor is designed to run at speed 66% below the first bending critical speed (described in Chapter 5), it would suffice to balance the rotors dynamically using two planes without taking account of shaft flexibility. For the trouble-free operation of cryogenic turboexpanders, a rotor imbalance of 600 mg.mm/kg is considered tolerable [2].
Figure 6.3: Schematic showing the planes and bearing support for balancing the prototype rotor.
The dynamic balancing of the rotor is done using Schenck Ro Tec GmBH make hard bearing type precision balancing machine at BARC, Mumbai. The balancing machine is meant for small rotors and able to balance less than 10 mg per plane. It is a dynamic balancing machine, with the following specifications:
Bearing type: Hard bearing
Make: Schenck, RoTec GmBH D-64273 Darmstadt Type: HT08
Weight limit: 2 Kg
The entire rotor, consisting of the shaft, the turbine wheel, the brake compressor and the fixing screws at both ends, is taken together for balancing. A pair of rollers, which make
Planes selected for removal of balancing mass
Expansion Turbine Brake Compressor
Balancing machine’s hard bearing support.
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up the hard bearing, supports the journal at the bearing locations. The planes for balancing are shown in Fig. 6.3. A small color tape attached to the shaft acts as a reference or key phasor for phase measurements with a stroboscopic sensor. The rollers directly measure the force transmitted to the hard bearing. The rotor is balanced to within a limit of 100 mg.mm (within 10 mg at 6.5mm radius) of unbalance at both the planes at speed of nearly 2000 rpm. The balancing report for two prototype rotors is mentioned in Table 6.1 and the removed mass is shown in Fig. 6.4. After successful design, fabrication and balancing of rotor, next objective is to fabricate bearings for the rotor as described in subsequent sub- chapters.
Table 6.1: Balancing report of the prototype rotor
Rotor No Location of balancing plane Before balancing After balancing
01 Turbine Side 31.5 mg @ 920 6.45 mg @ 1410
Brake Compressor side 37.8 mg @3460 7.31 mg @ 2290
02 Turbine Side 82.6 mg @ 2280 7.43 mg @ 170
Brake Compressor side 71.8 mg @2150 6.51 mg @ 880
Figure 6.4: Rotor with removed unbalance mass.