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 Compressor
Permanent Magnet Synchronous Motor
Specifications
Specifications
Working fluid
Air
Output Power
2000 W
Stages
1
Operational Speed
200,000 rpm
Compression ratio
(total to total)
1.58
Efficiency @ 77 K
89.9 %
Inlet condition
1 atm, 300K
Rotor
Titanium
Impeller rev. speed
108,000 RPM
Stator
Slot less Laminated
Mass flow rate
7.3 g/s
Magnet
Samarium Cobalt
Efficiency
0.65
Wire
Multi-strand Litz
Wire
Winding
6 turns/phase/pole
Single Stage Centrifugal Compressor
Components of the Centrifugal Compressor
Coupler
Impeller Controller
Koford Electric Motor
Collector
Top plate
Inlet
Guide Vane
Diffuser
Courtesy : Ray Zhou, Kevin Finney
Compressor Experimental Setup
P1, T1
P2, T2
P3, T3
P4, T4
Experimental Initial Results
Cast Impeller
Pow er versus Speed
1400.0
Straight
Blade
Impeller Test
1
1200.0
Power (Watts)
1000.0
800.0
Straight
Blade
Impeller Test
2
600.0
400.0
Straight
Blade
Impeller w/
Data
Acquisition
200.0
0.0
0
20000
40000
60000
Speed (rpm )
80000
100000
120000
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 Type
Importance
Rating
Torque
2
Mis-alignment allowed
Transmit
tal
Speed
Overall
Capab
ility
ra
ti
ng
Axial
Angular
Parallel
Torsional
3
4
5
6
1
7
None
Large
None
None
None
None
Large
30
Jaw
Medium
Medium
Small
Small
Small
None
Small
32
Servo-insert/
Disc
None
Medium
Medium
Medium
Medium
Small
Medium
51
Gear
and Spline
Small
Large
Medium
Medium
Medium
Small
Small
38
Helical and
bello
ws
Small
Large
Medium
Small
Small
Small
Small
49
Universal
joint
Medium
Medium
Small
Large
None
Small
Small
37
Scale
Rigid
Flexible
Backlash
Allo
wed
Design of the Helical Coupler
1) Why use a flexible shaft coupling ?
Rigid couplings would have been always used if it
were possible to perfectly align these shafts
2)
Helical Flexure
3)
Multiple Starts
Best for high speed application
Double Start, Ansys Analysis Heli-cal Inc.
4)
Flexure Creation Process
5)
Material
 Wire EDM, Dynamically
balanced while in production
 Martensitic stainless steel
CC455 H900 per AMS 5617
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-Turbine
Turbocharger
Speeds
158,000 rpm
250,000 rpm
200,000 rpm
Accessories
Controller
TC-Control System
Mist Lubricator
Speed Controlling
Unit
Coupling
Flexible
Coupler
Spline Shaft
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
1
[ D 4  a * F * 32 * T * D]  4
d 

 * max


Power being transmitted = P = 2000 W
Speed of rotation of the shaft = N = 200000 rpm
Angular velocity of rotation = ω = 2* π *N/60
Torque developed = T = P/ ω = 0.095 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 20305 psi (for a Titanium), d = 15.846 mm
Thickness of the hollow shaft = t = [D – d]/2 = 0.077 mm << 0.5 mm
So, the shaft would not fail under pure shear.
Also, Angle of Twist    584 * Torque * 1
D4 *
  1.847 *10 4
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 = 0.037 MPa << Ultimate tensile strength of shaft.
σmax, Permanent Magnet = 0.048 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 = 261.2 MPa
Thermal Analysis
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 = 251.2 MPa
Thermal stress developed in shaft due to operating at 77 K = 329 MPa
The Total Stress = 1308.2 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.
•Thermal stress developed in the shaft at 77 K = 329 MPa
•Thermal stress developed in the magnet at 77 K = 130 MPa
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
Emulator,Low
DSP
Power
Code
Pass
and
Composer
Meter
Filter
Motor Controller
Courtesy: Liping Zheng and Limei Zhou
Test Accessories – Flow
P-Transducers
Mass Flow Meter
Bearing mounting, fit and pre-load
      100000 2 
3
s
  1    R   3   
deltaRCF  

 


2
2

1800s Es





deltaRS  50R K  s
Roarke’s Handbook of Stress and Strain
Courtesy : Krishna


2
R
R0
2




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 0.008 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 34000 – 37000 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