Design and Performance Evaluation of a Miniature Integrated Single Stage Centrifugal Compressor and Permanent Magnet Synchronous Motor Presented by Dipjyoti Acharya M.S.M.E Thesis Defense May 30, 2006, 11: 00 Dept. of Mechanical, Materials and Aerospace Engineering University of Central Florida, Orlando

Project Requirements Reverse Turbo Brayton Cycle Cryocooler Single Stage Centrifugal CompressorPermanent Magnet Synchronous Motor Specifications Working fluidAir Stages1 Compression ratio (total to total) 1.58 Inlet condition1 atm, 300K Impeller rev. speed108,000 RPM Mass flow rate7.3 g/s Efficiency0.65 Output Power2000 W Operational Speed200,000 rpm 77 K89.9 % RotorTitanium StatorSlot less Laminated MagnetSamarium Cobalt WireMulti-strand Litz Wire Winding6 turns/phase/pole

Single Stage Centrifugal Compressor

Components of the Centrifugal Compressor Impeller Diffuser Inlet Guide Vane Top plateCollector Koford Electric Motor Controller Coupler Courtesy : Ray Zhou, Kevin Finney

Compressor Experimental Setup P1, T1P2, T2 P3, T3 P4, T4

Experimental Initial Results

Issues to be resolved Resolve misalignment issues Design of new coupler to handle high speeds Design a new electric motor to handle the power required by compressor

Problems with Rimitec Coupler Servo-insert coupling allowed a restricted amount of misalignment Elastic material in the middle began to plastically deform Stainless steel retaining ring was slip fit Coupler more rigid and prevented it from handling any misalignment Disc couplings style –WM Berg Coupler

Coupler Selection Guide Coupler TypeBacklash Allo wed Torque Transmit tal Mis-alignment allowedSpeed Capab ility Overall ra ti ng AxialAngularParallelTorsional Importance Rating Scale RigidNoneLargeNone Large30 FlexibleJawMedium Small NoneSmall32 Servo-insert/ Disc NoneMedium SmallMedium51 Gear and Spline SmallLargeMedium Small 38 Helical and bello ws SmallLargeMediumSmall 49 Universal joint Medium SmallLargeNoneSmall 37

Design of the Helical Coupler 1)Why use a flexible shaft coupling ? 2) Helical Flexure 3) Multiple Starts 4) Flexure Creation Process 5) Material  Martensitic stainless steel CC455 H900 per AMS 5617  Wire EDM, Dynamically balanced while in production  Best for high speed application  Double Start, Ansys Analysis Heli-cal Inc. Rigid couplings would have been always used if it were possible to perfectly align these shafts

Helical Coupler Courtesy: Heli-cal Products Company Inc.

Alignment Issues and translational stages 1)Straight Edge 2)Laser Alignment Systems - Laser systems 3) Dial indicator methods are A)RIM FACE METHOD B)REVERSE RIM METHOD

Reverse Rim Alignment Method SCHEMATIC DIAGRAM OF COMPRESSOR – MOTOR SYSTEM FOR REVERSE RIM ALIGNMENT METHOD  M = the offset in the plane of the movable indicator.  S = the offset in the plane of the stationary indicator.  A = the distance between the stationary and movable dial indicator plungers.  B = the distance from the movable dial indicator plunger to the movable machine’s front feet bolt center.  C= the distance between the movable machines’ front and rear feet bolt centers.

Verification of Components With FARO ARM

Experimental Results – Translational Stages

Experiment Helical Coupler –Fixed Base

Compressor Characteristics Curve

Available Drivers for Centrifugal Compressor Required speed  108,000 rpm. Achieved Speed  90,000 rpm Electric Motor Air-TurbineTurbocharger Speeds 158,000 rpm250,000 rpm200,000 rpm Accessories ControllerTC-Control System Mist Lubricator Speed Controlling Unit Coupling Flexible Coupler Spline Shaft Cost $ 2500$ 30,000$35,000

Design of Permanent Magnet Synchronous Motor

Material Selection for Shaft

Shear Stress Analysis Maximum Shear Stress Theory Power being transmitted = P = 2000 W Speed of rotation of the shaft = N = rpm Angular velocity of rotation = ω = 2* π *N/60 Torque developed = T = P/ ω = N.m Maximum allowable shear stress = τ max Factor of Safety = F = 3 a = ASME factor for shaft design for shear = ¾ No vertical shear stress Rigidity modulus of the shaft m/l = γ = 117 GPa Angle of shaft twist because of torsion = α (maximum for the outer layer) For a τmax value of psi (for a Titanium), d = mm Thickness of the hollow shaft = t = [D – d]/2 = mm << 0.5 mm So, the shaft would not fail under pure shear. Also, Angle of Twist 

Bending Stress The values considered for the bending stress are as follows, Elastic modulus of shaft = 116,000 MPa Poisson’s ratio for shaft = υ = 0.34 Ultimate tensile strength of the shaft = 220 MPa Elastic modulus of permanent magnet = 150,000 MPa Poisson’s ratio for permanent magnet(ν) = 0.3 Ultimate tensile strength of the permanent magnet = 82.7 MPa Bending moment due to impeller weight = M = 3.74 N-mm Shaft cross-section – Hollow Shaft Permanent magnet cross-section – Solid Shaft Density of the shaft m/l (ρshaft) = 4500 kg/m3 Density of the permanent magnet (ρmagnet) = 7500 kg/m3 Maximum bending stress (σmax) = M/Z, where Z = section modulus. σmax,Titanium = MPa << Ultimate tensile strength of shaft. σmax, Permanent Magnet = MPa << Ultimate tensile strength of permanent magnet. So the shaft would not fail under pure bending.

Fracture Toughness Fracture Toughness is an issue at cryogenic temperatures. It is defined k = cs(√ π*c)α, where ‘k’ is the ‘Critical Stress Intensity’, Cs – Critical Stress, c – crack length, α – geometry factor (depends on the cross-section of the member) ‘k’ depends on the Bending Stress developed.

Centrifugal Stress Analysis Centrifugal stress developed in shaft at 200K rpm = 728 MPa. Centrifugal stress developed in magnet at 200K rpm = MPa

Thermal Analysis Thermal stress developed in the shaft at 77 K = 329 MPa Thermal stress developed in the magnet at 77 K = 130 MPa Stress due to centrifugal force in shaft rotating at 200,000 rpm = 728 MPa Stress due to centrifugal force in magnet rotating at 200,000 rpm = MPa Thermal stress developed in shaft due to operating at 77 K = 329 MPa The Total Stress = MPa < Titanium Grade Yield Strength 1420 MPa So the titanium shaft would not fail. Also, Thermal Stress developed in magnet = 130 MPa < Compressive Strength = 833 MPa. So, the magnet would not crack or crumble to powder.

Rotordynamic Analysis of Rotor Courtesy: Dr. Nagraj Arakere, UF, Gainsville

Assembly of the Rotor

Fabrication of PMSM

Results PMSM

Motor-Generator Set

Design of the Integrated Compressor –Motor System Elimination of the coupler Reduction of number of bearings in the system Usage of fewer components on the rotor to increase the stiffness

Rotordynamic Analysis of Integrated System

Fabrication of Integrated Rotor

Test Rig Structure

Features

Test Accessories – Electrical Code ComposerEmulator, DSP and Motor ControllerLow Pass FilterPower Meter Courtesy: Liping Zheng and Limei Zhou

Test Accessories – Flow P-Transducers Mass Flow Meter

Bearing mounting, fit and pre-load Roarke’s Handbook of Stress and Strain Courtesy : Krishna

Alignment of Bearings

Integrated Compressor – Motor Test Set-up Motor Jacket Stator inside Gas enclosure with adjustable IGV to control tip clearance

Two Piece Rotor Free spin test results were successful only to 42,000 rpm Wobbling near the aluminum impeller plug by inches Hair crack was visible at the joint Externally Threaded Shaft Internally Threaded Impeller Fabricated Two Piece Rotor

Compressor Performance Chart

Problems and Future Work in Test Setup Vibrations experienced around – rpm range. - leading to stoppage Bearings cooling method to be determined.

Conclusion Initial Compressor-Motor Test Setup developed and tested -Helical Coupler was designed and tested -Alignment method was improved by Reverse Rim Method and Translational Stages -Components were verified with FARO Arm and re-fabricated 2 KW Permanent Magnet Synchronous Motor designed and tested -Shaft Material Selection, Stress Analysis Performed and Optimized by Rotordynamic Analysis. Bearing Selection -Fabrication, Assembly Performed and Tested -Motor-Generator set developed to determine motor performance Integrated Compressor – Motor Structure Designed and Tested - Versions of Integrated Rotor was designed and tested -Bearing Fit determined, Pre-load structure designed -Innovative procedure for alignment developed -Adjustable IGV developed for control over tip clearance

Thank you