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AMB Systems Short Course

In Cooperation with the International Symposium of

Magnetic Bearings (ISMB 17) - August 18-21, 2021

Industrial Applications Compressors, Turbines, Motors, Generators, Turbo Generators,

Refrigeration Compressors, Energy Storage Flywheels, Canned Pumps, Artificial Heart Pumps, Subsea Oil/Gas Production

Topics

Magnetic Bearing Operating Principles Amplifiers, Decoupled Tilt-Translate PID Controls

Flexible Rotor AMB Systems, Notch Filters, Unbalance Rejection Know Your AMB System, Model Verification

Digital Controller Specifications, Modern Controls Sensitivity Functions, API/ISO Standards

Auxiliary Bearing Design, Rotor Drop Modeling

Part 1: Dates: Mon/Tues/Wed August 2/3/4, 2021

Lecture Times: 1:00 – 4:00 GMT – Local Times 6:00 – 9:00 California, 9:00-12:00 Washington, 10:00-13:00 Rio de Janeiro,

14:00-17:00 London, 15:00-18:00 Central Europe, 21:00-24:00 Beijing, 22:00-1:00 Tokyo

Part 2: Additional Talks - Thursday August 5, 2021

Basic and Advanced Magnetic Bearing Systems – Design and Industrial Applications

Presented By: Rotor Bearing Solutions International August 2-5, 2021

− 2 per axis

− analog input ⚫ Selection depends on bearing design

− 2 per axis

− analog input ⚫ Selection depends on bearing design

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Course Description, Objectives, and Lecturers

The course will be presented online with Zoom, as set up by RBSI, at the times listed above. Questions can be asked of the lecturers

via the Zoom calls.

This magnetic bearing systems short course is intended for engineering staff

of companies interested in advanced understanding or using magnetic bearings. The

use of magnetic bearings is increasing in industrial applications but they are often not well

understood by mechanical engineers. This course will provide an introductory as well as

an advanced training program in magnetic bearing systems and controls. Details of several

industrial applications of magnetic bearings industrial machines are presented in the

course.

Part 1: A significant part of the course is the detailed controls design in rigid

rotor/AMB systems using the decoupled rotor center of gravity coordinates. Additional

topics on modern control for flexible shaft-AMB machines such as high pressure

compressors and surge control in compressors using magnetic bearings are presented.

API/ISO specifications for magnetic bearing supported rotating machines are presented.

The automated design of magnetic thrust and radial bearings is presented to design the

smallest bearing to supply the desired load capacity, while including the user’s desired

materials, coil wire, shaft diameter, and other parameters. The magnetic circuit

parameter design method is then automatically verified with a finite element model. Such

parameters as current gain, open loop stiffness, power loss and others are automatically

evaluated.

Part 2: The details of auxiliary bearing design using cageless, non-contact, ceramic

ball bearing design with spring and damping components is provided. A nonlinear time-

transient rotor dynamic analysis of method of AMB system rotor drops on auxiliary

bearings are presented. Several cases of industrial examples are provided and compared to

measured values for a few rotors. These three additional lectures are presented as an

option on Monday, August 5, as indicated below.

The use of mathematics in this short course is at a medium level for both electrical and mechanical engineers. It is assumed that the attendees have at least some minimum experience with magnetic bearings and controls but not at a high level.

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AMB Systems Short Course Detailed Talk

Descriptions – Part 1

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Day 1 Monday, August 2, 2021 - Lecture Times: 1:00 – 4:00 GMT

Session 1 – Overview/Design of Magnetic Bearings Talk 1: Introduction to Magnetic Bearings – Allaire’s Notes 5.1 - Parts 1&2 This talk presents the basic configuration and operating principles of magnetic bearings. The

magnetic bearing properties of supporting a single mass rotor in a non-contact manner is discussed.

The basics of magnetic circuits are presented – including airgaps, magnetic poles, coil windings,

coil/pole inductance, load capacity.

Talk 2: Introduction to Magnetic Bearing PID Control – Allaire’s Notes 5.2&Motor

Compressor This talk presents the concepts of magnetic bearing control gain and open loop stiffness.

Proportional, integral and derivative (PID) controls parameters as applied to a rigid rotor are

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developed with examples. An example rigid rotor motor compressor, illustrated below, on

magnetic bearings is discussed.

Break

Session 2 – Design/Build/Test of High Speed Turbo Aerator Talk 3: Design/Test/Build Magnetic Bearing for High Speed Turbo Aerator This talk presents the magnetic bearing suspension development for a 27,000 rpm centrifugal

turbine driving a generator for waste heat energy conversion, as illustrated below, for Kinetic

Traction in California. The magnetic bearing detailed design and installation in the turbo aerator

is discussed in detail.

Talk 4: Levitation Testing and AMB Control for High Speed Turbo Aerator The vertically oriented turbo aerator was levitated and extensively tested for minimum rotor

amplitude and control currents. The controls method is discussed and advanced unbalance

rejection control was successfully applied. The flexible machine substructure was tested and

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control notch filters used to avoid exciting the substructure natural frequencies. The detailed

control electronics, such as the control DSP shown below, and methodology is presented.

Day 2 Tuesday, August 3, 2021 - Lecture Times: 1:00 – 4:00 GMT

Session 3 – Control Standards and Sensitivity Functions

Talk 5: Control and Sensitivity Functions – ISO and API Standards Magnetic bearing control systems have standards for the best operating points based upon sensitivity

functions and system stability. These standards have been adopted by the International Standards

Organization (ISO) and the American Petroleum Institute (API). This talk presents the sensitivity function

standards now in common use in the AMB industry. Session 4 – Rigid Rotor AMB Modeling, Stability and Controls

Talk 6: Industry Standard Rigid Rotor Controls – Decoupled Tilt/Translate - PID Control The most common AMB controls method around the world is rigid rotor decoupled tilt-translate control for

rigid rotors – rotors operating below the rotor first critical speed. The method of decoupling the equations of

motion for a rotor center of gravity (CG) coordinate system, as illustrated below, is presented in detail. Issues

are the 1) non-collocation of the sensors and actuators, 2) decoupling the AMB open loop stiffness terms. 3) low

pass filters for the PID controller, amplifiers and sensors, as well as 4) rotor gyroscopic effects. Sensitivity

functions are employed to insure a well-designed control system. An example industrial AMB supported motor

is presented to illustrate the decoupling process.

ilt and ranslate

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Break

Talk 7: State Space, Notch Filter for Bending Mode and Unbalance Rejection Tracking

Notch Filter This talk extends Talk 6 and discusses the AMB feedback control loop, illustrated below, formulates the rigid

rotor uncoupled tilt/translate equations into state space form. One of the most important issues with the

simple decoupled PID control is the presence of a rotor bending mode just above the machine maximum

operating speed. The design of a notch filter, used to prevent excitation of that first bending mode, while

retaining overall control system stability, is presented. Another important issue concerns the reduction of

high 1X unbalance response in rotors. The reduction is carried out with the design of an unbalance rejection

notch filter which tracks the rotor operating speed. The unbalance rejection method is designed while

maintaining overall control system instability. An example industrial motor supported on magnetic bearings

is provided as an example industrial rotor.

Session 5 – Design and Finite Element Validation of Magnetic Bearing Designs Talk 8: Automated Design of Thrust and Radial Magnetic Bearings A difficult task is designing an optimum thrust and/or radial magnetic bearing configuration for a given load

capacity, shaft diameter, and other desired properties. The method of carrying out this optimum design is: 1)

using simplified magnetic circuit parameters and then 2) verifying validating the resulting design with a finite

element model. This talk presents an automated software package MagDes, developed by RBSI, which takes

inputs such as 1) load capacity, 2) existing shaft/housing dimensions, 3) desired magnetic material, 4) bias and

maximum control currents, 5) desired coil wire diameter and maximum current rating, 6) desired radial

bearing lamination thickness, 7) radial lamination thickness shrink fit, 8) necessary thrust disk axial length,

and many other parameters. MagDes produces the minimum thrust bearing volume or the minimum radial

bearing volume which meets the design objectives using the simplified magnetic circuit bearing parameters, as

illustrated for the radial bearing shown below. Following the development of the magnetic circuit parameter

based design, the MagDes code automatically produces an exact finite element model of the thrust or radial

bearing. It then uses the FEA open source free-ware FEMM and validates the design magnetic fluxes, wire

currents, pole forces, etc. Also, the FEMM model automatically increased the design control currents to

evaluate the AMB current gain and then moves the rotor magnetic component a small physical distance to

evaluate the open loop stiffness. MagDes outputs many properties of the bearings and detailed finite element

plots are provided to the user.

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Day 3 Wednesday, August 3, 2021 - Lecture Times: 1:00 – 4:00 GMT

Session 7 – Flexible Rotor AMB Stability and Controls Talk 9: Design and Characterization of Flexible, High Speed Rotor on Active Magnetic

Bearings This Talk presents the design and measured characterization of a large, high speed, flexible rotor test rig.

The purposes of the test rig were 1) modern control with s representation, 2) simulation of a multistage, high

pressure industrial centrifugal compressor with a balance piston seal, as illustrated below, introducing

unstable cross coupled stiffness near the center of the rotor, 3) operation of the test rig above the normal

instability initiation speed using the mu synthesis control to keep it stable. The test rig had two support

AMBs and two excitation AMBs. The electronic control system hardware used to implement the control is

presented In many multistage industrial compressors, the numerical value of the cross coupled stiffness is not

well known so it’s numerical value is considered to be uncertain in this test rig. The interior (between AMBs)

excitation AMB was used to input the simulated seal cross coupled stiffness instability source near the rotor

center. The other AMB was used to provide a sinusoidal excitation sweep of the operating rotor/AMB

system while operating at high speed. An important part of this talk is the comparison between the modeling

and measured properties of the operating rotor/AMB/control system to show that the modeling is accurate

prior to proceeding to the final testing, given the following talk.

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Talk 10: Mu Synthesis Control of Flexible, High Speed Rotor Operating Above First

Critical Speed This Talk presents the advanced Mu Synthesis AMB control approach used to control the large, flexible, high

speed rotor in the test rig, as illustrated below, described in the previous talk at operating speeds well above

the first rotor bending mode. One feature of Mu Synthesis is that it is designed to implement the control

with some system uncertainties – meaning that an approximate numerical value of the uncertain parameter is

known but that value may vary by as much as 50% to 100%. The Mu Synthesis controller requires the

control designer to establish the rotor location of the uncertain seal cross coupled stiffness and a suitable

performance weighting function for the controller to employ. Also, some other system uncertainties, such as

rotor gyroscopic effects, were taken into account in a similar manner. While the simulated seal cross coupled

stiffness numerical value was known, the Mu Synthesis control was not provided that information and had to

consider the unknown cross coupled stiffness, near the rotor center, as uncertainty. The rotor operated

through the rotor bending critical speed and up to the maximum system speed of 18,000 rpm. Quite a few

measurements were recorded for this test rig and discussed in this talk in detail.

Break

Session 8 – Centrifugal Compressor Surge Test Rig and Control Talk 11: Design, Construction and Initial Testing of Surge Control Test Rig This Talk, and Talk 12, are concerned with a test rig, as shown below, for a high speed motor driven industrial centrifugal compressor with axial magnetic bearing control used to eliminate surge. Surge, induced by closing the discharge flow control valve, creates transmission line acoustic gas flow waves which push flow back into the compressor impeller/shroud area and generate very high level pressure waves. The compressor impeller was moved back and forth but a sinusoidal reference input to the thrust AMB with the proper frequency to cancel the high pressure surge acoustic waves. The design of the testing system is presented, along with the initial motor magnetic radial bearings operating as a rigid rotor. The AMB system control properties are described in detail.

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Talk 12: Suppression of Centrifugal Compressor Surge with AMB Thrust Bearing Control This Talk is an extension of Talk 11. It describes the initiation of surge in the motor-compressor test rig upon closure of the discharge valve as pressure waves measured in both the compressor shroud and the downstream piping system. Normally, industrial compressors are not operated above the surge line (usually 10% off of the optimum performance point) on the compressor performance map to avoid the initiation of surge and possible major damage to the compressor. An advanced AMB control system was employed to move the compressor impeller, using the AMB thrust disk shown below, back and forth in it’s shroud to create local changes in compressor efficiency and resulting pressure waves to totally cancel the surge pressure waves and total suppress surge. This surge control allowed the compressor to operate on any point along the compressor performance map. This talk presents the complete description of how the cancellation was accomplished. It is expected that compressor performance will be increased by approximately 10% with the use of AMB surge control/cancellation.

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End of Basic and Advanced Magnetic Systems short Course ____________________________________________________________

Design and Performance Analysis of Auxiliary Bearings

Part 2 – Additional Talks

Day 4 Thursday, August 5

Talk 13: Design of Auxiliary Bearings for Rotor Drop This Talk provides an introduction to auxiliary bearing design for AMB systems. Magnetic bearing systems

are highly reliable. However, situations can occur when 1) electric power fails (in spite of the backup battery),

2) high loads enter the system and overload one or more AMBs, 3) non-rotating machine components may move

and provide strong rubs to the rotor, 4) other problems can occur. All high speed rotating machines on AMBs

are provided with auxiliary bearings to assist in keeping the rotor off of the non-rotating machine components.

The relatively low cost auxiliary bearings are normally designed to fail due to contact instead of the very

expensive rotor. Usually, the auxiliary bearings are designed to survive a minimum number of drops, such as

5 or 6, prior to replacement. The rotor drop analysis consists of a nonlinear rotor/auxiliary bearing dynamic

analysis. Rotors can be either horizontal (compressor or motor) or vertical (energy storage flywheel). A

schematic diagram of a rotor drop analysis is provided. Typical auxiliary bearing types include rolling element

bearings, plain bearings, planetary bearings, zero clearance auxiliary ball or roller bearings, permanent

magnets. By far, the most common auxiliary bearings are ball bearings. RBSI has worked with Cerobear, a

prominent German ball bearing manufacturing firm, to provide double row angular contact bearings with

silicon nitride ceramic balls and no cage, as shown in the following diagram. It has a one piece inner ring and

a preload on the separated outer races. The clearance between the shaft and the auxiliary bearing inner race

is set at ½ of the AMB radial clearance. The angular contact rolling element auxiliary bearings have a

compliant substructure, as described in this talk. This support structure provides stiffness and damping

properties, supplied by a stack of Bellville washers and a wavy spring.

Talk 14: Rotor Drop Analysis of a Vertical Axis Energy Storage Flywheel with Replacement

Aux Bearings

This Talk describes the nonlinear transient rotor drop of an industrial energy storage flywheel, as shown below,

on newly designed auxiliary bearings using the configuration described in Talk 13. The original auxiliary

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bearings, with 10 mm bore and steel balls, but without any flexible damped supports, failed on the first drop

each time and had to be replaced after each drop. The non-linear transient analysis presented here evaluates

all of the balls, including all 12 degrees of freedom, in the auxiliary bearings as they accept the rotor loads. A

flywheel finite element rotor model, involving axial and lateral displacements, was established and employed

in the drop analysis. A rotor undamped critical speed map was evaluated. The original auxiliary bearings

were 10 mm bore balls. The rotor/auxiliary bearing axial motions were evaluated and found to be relatively

small. However, the original aux bearing maximum compressive stresses during drop, without support stiffness

and damping components, were found to be approximately 5x10^9 Pa in inner race and 3x10^9 Pa in the outer

race. The maximum yield stress of the original steel balls was 2.0x10^9 Pa, which showed why they failed

during the first drop. The replacement Cerobear ceramic double row bearings used much larger bore balls at

40mm. Also, they had flexible damped supports, as described in Talk 13, such that the contact force during

drop reduced from 9,000n in the original bearings to 1,000N in the new bearings. The maximum stress in the

new aux bearings was reduced to 1.35x10^9 Pa in the inner race and 1.1x10^9 Pa in the outer race. The full,

nonlinear transient rotor drop displacements were evaluated and the results presented in this talk. The shaft

speed reduction and the aux bearing inner race increased rotating speeds were evaluated and shown in this

talk. The ball motions were evaluated. The final result, due to the auxiliary bearing redesign and the nonlinear

transient rotor drop modeling result produced a new rotor drop system in the energy storage flywheel that has

been very successful and provides an expected 5 to 6 rotor drops before the aux bearings need to be replaced.

Break

Talk 15: Rotor Drop of Example Horizontal Rotors and Comparison to Measurements

The previous Talk discussed a replacement auxiliary bearing system for a vertical axis energy storage flywheel.

This talk presents the auxiliary bearing design process and the rotor drop nonlinear analysis for an example

three stage compressor unit. The auxiliary bearing rotor displacements, inner race motions, ball maximum

stresses, contact angle, and other parameters. Comparisons of calculated vs measured data are presented for

a small test rotor, with relatively good agreement. In cooperation with a magnetic bearing manufacturer, a

series of comparisons were made between an industrial rotor and the RBSI rotor drop modeling code. A large

motor, two compressor train supported in magnetics bearings had several sets of auxiliary bearings using the

Cerobear auxiliary bearings. It was intentional dropped several times for testing purposes. Rotor

displacements were calculated, as show below in blue, and compared to the measured displacements shown in

red below, were compared. The calculated value compared relatively well with the measured results. The

results are presented in this Talk.

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Course Lecturers

1. Paul Allaire, Chief Technical Officer and Owner, Rotor Bearing Solutions International Also, ISMB Original Co-Founder (1 of 3), ISMB Lifetime Achievement Award, Chaired Professor, Mechanical

and Aerospace Engineering, University of Virginia, Retired – Long Time Director of Rotating Machinery and

Controls Laboratory, Ph. D. Northwestern University, ASME Life Fellow, Professor of Engineering, Wake

Forest University.

2. Pablo (Se Young) Yoon, Associate Professor of Electrical Engineering, University of New Hampshire,

Durham New Hampshire, USA Also – Post Doc and Ph. D., ROMAC Lab, University of Virginia (Co-Advisor: Paul Allaire), and Consultant

with RBSI

3. Saeid Dousti, RBSI Consultant Also - Ph. D., ROMAC Lab, University of Virginia (Advisor: Paul Allaire), and Former President of RBSI

The course lecturers and contributors have the combined experience and ability to explain rotor-AMB systems

making this training program unlike any other magnetic bearing training program found in today’s world.

Paul Allaire has 45 years of experience in research and teaching rotor dynamics and magnetic bearings. As noted

above, he was a Chaired Professor of Mechanical and Aerospace Engineering as well as the Founder/Director of

the Rotating Machinery Controls Industrial Research Lab from 1980 to 2013, when he retired. He has taught more

short courses on magnetic bearings to engineers in industry than anyone else. From 2012 to the present, he is the

founder and owner of Rotor Bearing Solutions International – the industrial consulting firm. He has refined the

basic lectures on magnetic bearings over the past 30 years as well as built the largest academic AMB laboratory in

existence from 1984 to 2013.

Pablo (Se Young) Yoon is an expert on magnetic bearing controls and electronics. He is an Associate Professor

of Electrical Engineering, University of New Hampshire, Durham New Hampshire. He is also affiliated with

RBSI and obtained his Ph. D. in the ROMAC Lab at the University of Virginia about 8 years ago with the

successful elimination of surge in a centrifugal compressor. He was a Post Doc in ROMAC for several years.

He is the lead author of the book Control of Surge in Centrifugal Compressors by Active Magnetic Bearings:

Theory and Implementation, by Se Young Yoon, Zongli Lin, Paul E. Allaire, Springer, 2013.

Saeid Dousti is an expert on bearings and rotor dynamics. He is currently working with a company on fluid film

bearing software but remains a consultant with RBSI. He was one of the primary developers of the MagDes

AMB design code and has worked with the rotor drop software as well.

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Cost and Registration for AMB Systems Short Course

The cost of the AMB Systems Short Course (Talks 1-12) is US$800 per

person/$300 for University participants.

The cost for the Auxiliary Bearings Additional Talks (Talks 13-15) is

an additional $100 per person/$50 for University participants

This registration amount is to be paid to Rotor Bearing Solutions

International in advance. RBSI Bank of America

payment information will be supplied upon registration.

Contact: Paul Allaire – paul.allaire@rotorsolution.com, 1-434-249-53132,

5211 Mountain View Road, Winston Salem, NC 27104, USA

Please provide your name, company/university affiliation, email address,

and mobile phone number. A full set of notes for all of the talks,

in electronic form will be sent to the attendee, by email,

prior to the start of the AMB Systems short course. Participants

will need to have the capability to receive Zoom.

Additional Short Course Program Talk Contributors

1. Simon Mushi, Currently Principal Electrical Engineer, Singular Genomics, Formerly: Director of

Magnetic Bearings/RBSI and Owner of SEM Controls, Ph. D. University of Virginia, Ph. D. ROMAC

Lab (Paul Allaire, Co-Advisor), University of Virginia.

2. Jianming Cao, Currently Finite Element Specialist, Nastran, Irvine, CA, Formerly: Vice President for

Rotor Dynamics RBSI, Ph. D. University of Virginia (Advisor: Paul Allaire), Ph. D. ROMAC Lab,

University of Virginia,

3. Tim Dimond, PE, Currently Senior Engineer, Solar Turbines, Ph. D. University of Virginia (Advisor:

Paul Allaire), Formerly – Principal Scientist, Rotating Machinery and Controls Laboratory, University

of Virginia, Co-Founder and President, RBSI

4. Brad Nichols, Currently: Assistant Professor, Mechanical Engineering, Virginia Commonwealth

University, Richmond, Virginia, Formerly Senior Fellow, RBSI, Ph. D. University of Virginia (Advisor:

Paul Allaire)