The dynamic properties of the bearings are determined to be used in the rotor dynamics analysis. The last part includes a performance study of the fabricated turbo expander with gas foil tap and thrust bearing.
Nomenclature
Vn = Shear forces at the right faces of the nth disk Wt = Weight of the rotor. GFJB: Gas cylinder journal bearing GFTB: Gas cylinder thrust bearing RPM: Rotation per minute TW: Turbine wheel.
Introduction
- Anatomy of cryogenic turboexpander
- Bearing for cryogenic turboexpander
- Gas foil bearings
- Objectives and organization of the thesis
A turboexpander designer focuses on the points given below for the design and manufacturing process of the turboexpander [2]. This chapter also provides a brief overview of various technological issues related to the design, manufacture and testing of the gas foil bearing in the past.
Literature Review
- Gas bearings for high-speed rotor
- Gas bearings for cryogenic turboexpanders
- Gas foil bearings state of the art
- Aerodynamic analysis of gas foil journal bearings
- Aerodynamic analysis of gas foil thrust bearings
- Development of gas foil bearings
- Development of bump gas foil journal bearings
- Development of gas foil thrust bearings
- Gaps in literature
Gas foil bearings to increase dynamic properties such as stiffness and damping coefficients of the bearings. Development of gas foil bearings is always a bottleneck for manufacturers due to the tight tolerance in manufacturing.
Bump Type Gas Foil Journal Bearing
The working principle
The aerodynamic pressure film developed between the smooth top foil and the pin is responsible for carrying the radial load of the pin. This bias between the top foil and the pin remains in contact until the lift speed is achieved.
Bearing geometry
The bearing base houses a series of corrugated bumps made from a thin strip of foil and a smooth sheet above it. In the deformation action, there is friction between the upper sheet - the collapsing sheet and the supporting base of the collapsing sheet.
Performance analysis of gas foil journal bearings
- The governing equations
- Boundary conditions
- Load carrying capacity
- Frictional torque
- Dynamic coefficients
The values of the geometric parameters taken to predict the stiffness of the bumps are shown in Table 3.2. The predicted hardness value is compared with the actual static stiffness of the manufactured gas.
Numerical procedure
- Discretization of equation
- Convergence criteria
- Flow chart and grid refinement study
- Validation of computational program
- Feasibility of GFB for current application from literature data
Static property analysis determines the possibility of foil bearing and they are pressure profile, film thickness and bearing capacity. A three-dimensional bearing pressure distribution, gas film thickness, and load-carrying capacity of the GFB is shown in Fig.
Results and discussion
- Effect of bump foil materials on the static performances
- Effect of bump foil thickness on the static performances
- Effect of bump length and pitch on the static performances
- Analysis with final dimensions of bump foil
So an analysis was done to find the effect of bump length and pitch on the bearing capacity. The bearing capacity can be improved with less radial clearance, but this increases the cost of the bearing.
Detail design procedure for gas foil journal bearing
Bump Type Gas Foil Thrust Bearing
Thrust load calculation
- Axial force at the compressor wheel
- Axial force at the turbine wheel
The Ftotal is the result of the total forces acting on the compressor wheel (FCW), the turbine wheel (FTW) and the weight of the rotor (Wt), as shown in figure. The four different axial forces acting on the brake compressor side can be calculated. using equations. The algebraic sum of all four different forces acting on TW is given in Eq. Compressive force acting on the exhaust surface.
The resultant forces acting on the rotor are calculated by summing forces acting on CW, TW and weight of the rotor (Wt).
Working principle and bearings geometry of GFTB
Axial forces are calculated at design rotational speed and mass flow rates to study rotor thrust loading. This information is essential for designing a thrust bearing with the desired lower thrust bearing capacity. In order to avoid any possible change in load, the upper thrust bearing is also designed in current use.
Performance analysis of gas foil thrust bearing
- The governing equations
- Method of solution
- Double gas foil thrust bearing
- Result and discussion
The total thickness of the carrier film is the sum of the thickness of the upper and lower thrust bearing layers, and their ratio is given in Eq. His extensive studies show that a ramp volume of b = 0.5 gives a higher load capacity. Thus, the film thickness for the upper bearing at the designed rotor speed will be 45 m.
The pressure profile and film thickness on the bearing surface for an individual sector and the pressure profile for the entire bearing surface are shown in fig.
Axial passive magnetic bearings
- Mathematical modelling of active magnetic thrust bearings
- Calculation of magnetic forces
The basic configuration of the permanent magnet bearings with concentric polarized magnetic rings is shown in Fig. The dipolar method is very popular and accurate for the magnetic bearings where the air gap is larger than the dimensions of the magnets[83]. These parameters are used to calculate magnetic forces between four surfaces A, B, C and D. The elementary magnetic force on discrete surface element 'A1' of the rotor magnet surface 'A' due to the surface element 'B1' on the stator magnet surface 'B' is expressed in Eq. J1 : Magnetic polarization of the rotor magnetic ring J2 : Magnetic polarization of stator magnetic ring.
The repulsive forces between the ring magnets are slightly above the dead weight of the rotor (0.998 N), when the distance between the ring magnets is kept at 7 mm.
Detail design procedure of gas foil thrust bearings
The distance to be maintained between the upper and lower ring magnet for both configuration pairs can be determined from Fig. Crankcase materials and crankcase dimensions such as thickness, pitch, length and bump height. Determine the load carrying capacity equal to the thrust load of the rotor at the design speed.
Rotordynamics of the Prototype Rotor
- Transfer matrix method with gyroscopic effect
- Critical speed and mode shapes analysis
- Unbalance response analysis
- The lumped inertia model of the prototype rotor
- Computation of critical speeds
- Simulation results and discussion
- Computation of unbalance response
- Simulation results and discussion
The critical speed and mode states of the system are determined by calculating the overall transfer matrix. Vn : Shear forces on the right side of the nth disc ln : Shaft element length. The unbalance response of the rotor of the prototype turboexpander is simulated using the above explained theory presented in section 5.1.2.
The analysis of critical speed and unbalance response of the rotor bearing system for current application is safe to work at its designed speed of 140,000 rpm.
Fabrication of Turboexpander with Gas Foil Bearings
The rotor
- Balancing
The dimension of the shaft depends on the position of bearings, deformation, natural frequencies and heat transfer rate. The diameter of the rotor is determined by the bending load and torque to be transmitted. The maximum stress at the root of the collar is 189.6 MPa and this value is below the design stress of the rotor.
The dynamic balancing of the rotor is done using Schenck Ro Tec GmBH make precision hard bearing balancing machine at BARC, Mumbai.
Fabrication of gas foil journal bearings
- Fabrication of bearing base
- Foil Materials
- Fabrication of smooth top foil for journal bearings
- Fabrication of journal pre-form bump foil
- Journal bump foil using rigid bottom and flexible top die
- Journal bump foil using rigid top and bottom die
- Assembly of gas foil journal bearings
This chapter discusses the production of thrust foil for journal bearings using two different sets of dies. The PTFE sheet available in the domestic market is harder than silicon sheet, and during the molding process, the stamping foil is found to be distorted and inaccurate. The schematic of the lower and upper die with the workpiece is shown in Fig.
The detailed profile of the hump for the die is shown in attachment (DIE-04 and DIE-05).
Fabrication of gas foil thrust bearings
- Fabrication of thrust bearing base
- Fabrication of smooth top foil for thrust bearing
- Fabrication of thrust pre-form bump foil
- Thrust bump foil using flexible top die
- Thrust bump foil using rigid top and bottom dies
- Assembly of gas foil thrust bearings
This arrangement reduces the tooling cost, so an attempt is made to fabricate pressure bump film using a flexible rubber sheet as the top die. A similar approach as described in subsection 6.2.6 is followed to fabricate pressure burst foil with rigid top and bottom dies. Installing a gas foil thrust bearing involves attaching bump foil and smooth foil to the thrust bearing base.
The leading edge of the bump foil is rolled and placed in the radial holes in the bearing base.
Fabrication of other parts of turboexpander
- Bearing housings
A pair of flanges (A and G) are provided at the top and bottom of the housing to attach the hot and cold side housing. ii) A groove (B) is made on the upper flange for the O-ring seal. Space for lock nuts (C and G) is provided to adjust the position of the turbine and axial clearance of the rotor. iv) Holes (D) are made for the insertion of proximity probes for vibration analysis. The bearing housing is the central component of the structural system, which accommodates all the precision components.
The extreme faces of the housing are taken as datum surfaces and must be straight with a flatness specification of 2 m.
This seal prevents high pressure gas from leaking from the hot end to the outside. iii). An arrangement is also made to study the vibrations of the machine using the accelerator, so a pair of flat faces (E) is made near the journal bearings. In general, the manufacturing tolerance is kept as close as possible for a large component such as a bearing.
Slot for O-ring
Threads for upper locknut
Holes for inserting proximity probes
Flat seat for accelerometer
Threads for lower locknut
- Dynamic seal
- Spacers and locknut
- Passive magnetic ring bearings
The basic principle of a labyrinth seal is based on the difficult path of the labyrinth seals that causes a gradual loss of pressure, thereby minimizing leakage. The width of the spacer I depends on the design clearance between the thrust bearings and the shaft collar, as described in Chapter 4. In the first test phase, the rotor is tested without any coating or passive ring magnets to study the performance of the rotor.
The next phase of the test is with passive magnetic bearings, where one ring magnet is inserted into the rotor and the other onto the dynamic seal.
Shaft with circular slot B:Ring magnet fixed
Circlip
Dynamic seal with ring magnets (E1 and
- Coating
- Assembly of turboexpander components
- Analysis of the axial length fit of the prototype assembly
- The assembly sequence
- Precautions during fabrication and assembly
The bottom turbo expander locknut is bolted to the bearing base from the bottom. The direction of rotation of the rotor must coincide with the direction of the top foil from fixed to free end. The upper foil of the upper thrust bearing from fixed to free end should coincide with the direction of the rotor.
Similar to the lower journal bearings, the direction of the upper foil from fixed to free side coincides with the direction of rotation of the rotor.
Performance of Turboexpander with Gas Foil Bearings
Turboexpander test set-up
The nozzle and expansion turbine are designed for an inlet pressure of 0.7 MPa inlet pressure to the nozzle. The pressure in the pressure vessel is maintained above 0.5 MPa for consistent supply of process gas at a pressure of 0.5 MPa to drive the expansion turbine. A high-pressure line connects the vessel to the turbine inlet through fine filters and an air purification unit (APU).
The accelerometers are mounted on the bearing housing close to the upper and lower axle bearings.
Speed and vibration measuring equipment
The high frequency accelerometer (B&K 4508) is mounted close to the turbine as the numerical analysis estimated higher vibration mark near the turbine as described in Chapter 5. The specification of the digital oscilloscope used to display the vibration signals is given in Table 7.2.
The experiments
- Tribology Issues
- Vibrational studies
During the start and stop of the machine, the runner comes into contact with the smooth top sheet. A solid lubricant coating or the use of active ring magnets is preferred to handle wear problems during rotor start and stop. No comparison could be made with the vibration level near the lower journal holder due to the lack of data in the previous development program.
Rotor swirl is self-excited instability caused by gas swirling in bearing clearance.
Conclusions
Overview
Contributions
The detailed analysis steps can help as a useful technical resource for future gas leaf bearing programs. The design procedure is not only for gas leaf bearings, but also for associated turbocharger components such as the shaft, spacers, dynamic seal, lock nuts and bearings. A test rig has been modified to study the performance of a gas leaf bearing turboexpander rotor bearing.
The prototype turboexpander is tested on this rig, where the turbine rotates stably at about 81,000 rpm at room temperature with limited radial vibration of the rotor.
Future research scope
39] Iordanoff I., "Analysis of an aerodynamic foil-compliant thrust bearing: methods for a rapid design", Journal of Tribology, vol. 42] San Andrés L., Ryu K. and Diemer P., "Performance prediction of gas thrust bearings for oil-free automotive turbochargers", Journal of Engineering for Gas Turbines and Power, vol. 45] Conboy T., "Real gas effects on thrust sheet bearings operating in the turbulent regime", Journal of Tribology, vol.
74] Balducchi F., Arghir M., Gauthier R. and Renard E., "Experimental analysis of the start-up torque of a lightly loaded foil thrust bearing", Journal of Tribology, vol.
Production drawing of fabricated parts
BASE 01
TWO sets of Base01 and Base02 to be produced. One set for the bottomDie and another set for the Top Die.
Assembly of Rings and Base
Allignment Pin1(06)
All dimensions must be concentric with datum C by in 0.005 mm All dimensions are in mm.
![Table 2.1: Summary of cryogenic turboexpander and their bearings from open literature [2, 5].](https://thumb-ap.123doks.com/thumbv2/azpdfnet/10557257.0/30.892.116.832.544.1118/table-2-summary-cryogenic-turboexpander-bearings-open-literature.webp)
