Design and construction of a contactless excitation and response measurement system

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IN

DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

,

STOCKHOLM SWEDEN 2019

Design and construction of a

contactless excitation and

response measurement system

JOHAN WESTLUND

KTH ROYAL INSTITUTE OF TECHNOLOGY

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Design and construction of a contactless excitation and

response measurement system

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Keywords— Rotor dynamic, Electromagnet, Contactless excitation, LabVIEW,

Mea-surement instruments, Force control, CERS

Abstract

Manufacturing industry works on Overall Equipment Effectiveness (OEE) to increase the yield and speed of machining. A good knowledge of the machine properties is important to increase the speed while still maintaining stable cutting with low tool usage.

To make models of the machine is therefore important and in machining a common way to extract the dynamic properties is frequency response measurement. One way is to use an impact hammer to excite the machine tool and measure the response. The prob-lem is that a hammer can only be used on a non running machine. At Manufacturing and Metrology Systems division at KTH (MMS) a test method for contact less excitation has been developed that uses electromagnets to excite the machine tool. By using contact less testing it can be used on rotating machine tools without real cutting in materials.

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Nyckelord— Rotordynamik, Elektromagnet, Kontaktlös exitaion, LabVIEW,

Kraftkon-troll, CERS

Sammanfattning

Dagens tillverkningsindustri arbetar för att utrsutningens totala effiktivitet ska höjas ge-nom att öka hastigheten och minska material- och verktygsanvändningen vid bearbet-ningen utan att minska kvalitén på slutprodukten. För att öka hastigheten krävs en god kännedom om maskinens egenskaper för att maskinen ska arbeta under stabila förhållan-den där också verktygets slitage minskas.

Att ta fram modeller över maskinen är därför viktigt och inom skärande bearbetning är frekvensresponsmätning ett sätt att få ut de dynamiska egenskaperna av det skärande verktyget. En vanlig testmetod är att med en hammare exitera verktyget och mäta re-sponsen. Problemet är dock att hammaren bara kan mäta vid stillastående maskin. Vid MMS har en testmetod för kontaktlös exitering tagits fram där elektromagneter används för exiteringen. På så sätt kan testet utföras på roterande verktyg utan att man behöver förbruka material.

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Acknowledgements

This master thesis is a result of my work at Manufacturing and Metrology Systems divi-sion at KTH, but it wouldn’t have been possible without the support from and previous work by PhD Tomas Österlind and Professor Andreas Archenti. Thanks to Tomas for the practical and theoretical help in understanding and building the system. To Andreas for his unlimited trust and support as a supervisor in the ups and downs of this work.

A big thanks to the personnel and PhD students helping out with making parts, sug-gesting solution, overall contribution to this work and for the Wednesday fika. Especially a thank to technician Jan Stamer and Anton Kviberg and to PhD student Nikolas Theis-sen for their contribution to this work moving forward.

I would also like to express my appreciation to Sofia Pedersén, Johan Nygren, Ylvali Sjögren, Erik Nilsson and Alexander Magnusson for their support in motivation, studies and discussions.

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Abbreviations

ADC Analog Digital Converter. 1, 23

AMB Active Magnetic Bearing. 1, 6, 10, 12, 14, 17

CERS Contacless Exitaction and Response System. 1, 17, 33

FRF Frequency Response Function. 1, 12, 15

MMS Manufacturing and Metrology Systems division at KTH. 1, 2, 3, 8

OEE Overall Equipment Effectiveness. 1, 2, 9

PWM Pulse Width Modulation. 1, 22, 23

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Introduction

A big part of today’s world are all the rotating machinery in manufacturing industry and products. In this industry the need to measure dynamic properties increase to improve efficiency, quality and lower the cost of maintenance.

1.1 Background

Rotors are common elements in engineering applications such as: turbo machinery, ma-chine tools, spindle units, compressors in rocket and automotive applications. One com-mon characteristic is that rotor behaviour is strongly dependent on rotational speed. In order to characterize this behaviour, contactless excitation and response measurements is needed. At the MMS current research is developing new measurement instruments and methodologies to capture rotor dynamic behaviour applied on high speed machine tool spindles.

Ongoing research has shown that electromagnetic excitation is a useful way for cap-turing rotor dynamic behaviour.

1.2 Problem

Research at MMS [1] have made hardware and software for contactless rotor dynamic testing. Current systems have limits that does not fulfill the wanted requirements for the purpose of the system in terms of force and frequency bandwidth, it is not flexible to different rotor sizes and there is no complete integrated testing system. Those limitation and how to overcome those have to be studied.

1.3 Purpose

The purpose is to describe, discuss the thesis work and explain the results of the work. To investigate and to identify limitations in existing system to set up the goals for ways of implementation to overcome the limitations of the existing system. To build a proto-type to identify limits of a new system.

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CHAPTER 1. INTRODUCTION 9

1.4 Goal

Suggest ways of increasing force levels at higher frequencies compared to existing hard-ware. Enable flexibility in applications by a modular design.

Design and construct an embedded system for contactless excitation, including: • Electromagnets

• Amplifiers • Cabling • Sensors

• Software (based on National Instrument, NI, LabVIEW)

Evaluate performance on a test bench to find limits and opportunities of the con-structed system. The work will support development of new evaluation methods for ro-tor systems.

1.4.1 Benefits, Ethics and Sustainability

The testing will be conducted in industry environment with the associated risk for work-ing in that environment. An insufficient verification of the performance could have con-sequences in the use of the results for application in future projects.

The system may help in reducing waste from machine calibration, increase the per-cent of approved parts from production and give a higher resource utilization of the ma-chine park with a higher OEE.

1.5 Methodology / Methods

Conduct a literature study of previous and similar work by others to identify limits and opportunities in solutions.

Analytically method [2] to the design the system for the purpose of including uncer-tainty in the equations and improve understanding of the system components.

Verifying the design through experimental method [2] to prove the design is working according to specification.

1.6 Delimitation

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10 CHAPTER 1. INTRODUCTION

1.7 Outline

Chapters:

• Background describes the background on how AMB works

• Methods goes through the equations and methods that will be used in this thesis • Work, the design and constructions of the concept system

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Chapter 2

Background

2.1 Machining

Even with the emerging additive manufacturing methods, a major part of the manu-facturing sector is still machining methods. The economic and environmental impact of machining based manufacturing system depends on their energy efficiency and mate-rial utilization. The limits of those machines lies in their physical characteristics and not knowing those properties puts limits on the fully exploiting the machines capabilities. Using the machine system’s capability requires characterization of the interaction be-tween the machine tool structure and the cutting process and the disturbance affect on it. The disturbance errors can come form: positioning and kinematic errors, temperature errors, static errors and dynamic errors.

A common limiting factor in machining has always been the vibration when the ma-terial removal rate has been pushed to it is limit. This often leads to excessive tool wear, damaged work piece and shortened machine tool life. This has been studied and meth-ods of preventing it has been developed over time. [3]

2.2 Rotor dynamics

Machine tool spindle units in a manufacturing machine can consist of many parts. The tool is usually connected to the shaft of the spindle through a tool holder. The tool holder is then attached to the shaft and the shaft is attached to the machine though bearings to the machine, the machine can be assumed to be rigid for the purpose of this thesis.

For the purpose of metal cutting, the spindle dynamic plays a critical role in machin-ing. Requirements of a spindle are accuracy, speed range capability, high rigidity, high damping capacity and stable operating temperature. An important phenomenon at high rotation speeds are the centrifugal forces and gyroscopic moments acting on the spindle. The centrifugal forces together with the externally applied forces from cutting affect the ball bearings and thus reduces stiffness of the spindle. [4]

One important stability affecting problem is the self-excited vibrations (Chatter) in machining. It has been identified as the main problem in increasing the productivity. It is a problem induced by the forces in the dynamic process itself and thus it can only be studied under operational condition. [1]

Knowing the modal parameters of the spindle can help in identifying chatter free cutting conditions based on natural frequencies, damping ratios and stiffness values at

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12 CHAPTER 2. BACKGROUND

different working conditions. This helps to know where the spindle structure does not induce unwanted vibrations due to the dynamics of bearings and other parts of the spin-dle.

To match a model to the physical system, one way can be to solve the eigenvalue problem of the undamped system and then fit the analytic solution to experimental data by adding empirical modal damping ratios. This can be obtained by measure the spin-dles Frequency Response Function (FRF) between force and displacement at the tooltip. Having this in the model is important for the stability prediction of the machine tool.

FRF can be measured using impact hammers or shakers at standstill or as the system described in this thesis is intended to be measured at different rotor speeds using contact less electromagnetic force actuators. [5]

Using contact less testing methods enables testing at high-speed regimes.

2.3 Active Magnetic Bearing (AMB)

In mechanical systems you have a lot of different bearings to stop the parts from mov-ing in all directions except the desired one and to reduce the friction between movmov-ing parts. [5] A lot of different type of bearings exist, but to enable high speed the solid to solid contact need to be eliminated to reduce the friction compared to the rolling bear-ing. Bearings exist with liquids or gas to instead of balls or cylinders and one type that’s used is AMB, which is basically magnetic actuators, position sensors and a control sys-tem that tries to keep the rotor in the center of the clearance space of the spindle, despite external forces. The benefits are less friction compared to a ball bearing as it is floating in air, thus enable higher rotation speeds. [6] As the AMB use magnetic force to hold the rotor in place. The force can also be used the other way around to displace the rotor. This is useful in testing spindles for their FRF and for prediction of chatter in cutting. This method of using AMB has been shown in the following papers: Electromechanical actuator development for integrated chatter prediction on high speed machining centers [7], Milling machine spindle analysis using FEM and non-contact spindle [8] and System identification during milling via active magnetic bearing [9].

2.3.1 Electromagnets

Electromagnets are used to produce the force in AMB. The force produced is propor-tional to the magnetic flux flowing in the material. Magnetic flux can be controlled with voltage or current as shown in the equations below. Figure 2.1 shows a common setup and magnetic flux flow in an AMB.

Where the normal bearing uses physical contact, AMB uses electromagnetic force without direct physical contact on the ferromagnetic rotor. The force that is acting on the ferromagnetic body (µr >> 1), (relative permeability), is generated by a change of field

energy (Wa) in the air gap (lair) between the rotor and the electromagnet. [10, Page 5]

See equation (2.1).

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CHAPTER 2. BACKGROUND 13

Figure 2.1: Example of a test setup with two axis force and position. The orange color is the copper coil and yellow the magnetic flux flowing in the magnetic material. (Top View)

F = −∂Wa ∂lair

(2.1) As described in paper [11], the force of the electromagnet is proportional to the cur-rent as shown in equation (2.2) for a curcur-rent-controlled amplifier.

F = Af e· µ0· (N I)

2

4l2 air

(2.2) Where F is the electromotive force, Af e is the cross sectional area of the iron core in

the electromagnet, µ0 the vacuum permeability, φ magnetic flux, N the number of turns

of the coil and I the current.

Paper [11] also describes how we can get how the force is proportional to voltage for a voltage controlled amplifier. This is shown in equation (2.5), with some equations (2.3), (2.4), leading up to it. F = Φ 2 µ0· Af e (2.3) Φ = 1 N · Z V dt (2.4)

The voltage required to generate the force: Vw = N ·pµ0· Af e·

d dt

√

F (2.5)

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14 CHAPTER 2. BACKGROUND Q1 L1 V+ V-Q2 L2 Q3 D1 D2

Two-level

Three-level

Figure 2.2: Two- and three-level schematics

2.3.2 Power supply

A power supply is needed to deliver a stable voltage at a wide range of frequencies and amplitudes so that this does not impact the control strategy. There are two type of power supply, direct and alternating current.

2.3.3 Output stage

The output stage, often called amplifier, can be designed using several different tech-niques depending on efficiency, accuracy, noise and complexity.

There is two major power drivers in AMB systems. The classic analog linear circuits and modern switching amplifiers. The classic analog circuits is know for their poor ef-ficiency while a switching have been proven to be efficient and yet have an acceptable noise level. Switching amplifiers has the advantage of enabling the user to move more of the complexity from classic analog circuits to computer code. Thus enable more ad-vanced and complex digital controllers and the possibility to add checks for out of speci-fication operation. The dynamic range is often better. [12]

Even in switching amplifiers there are different ways to design the system. Two com-monly used techniques are and three-level switching using half h-bridges. A two-level amplifier use only one transistor to switch on and off. Three-two-level amplifier use two transistors to add a middle state. [13] This can be seen in figure 2.2.

One key difference between two- and three-level switching amplifiers is that the cur-rent ripple in a two-level amplifier is proportional to DC voltage. Where as in the three-level amplifier the current ripple it is not affected by the DC voltage. [14]

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CHAPTER 2. BACKGROUND 15

(a) Two-level control signal (b) Three-level control signal

Figure 2.3: Two- and three-level schematics

v(t) = Ldi

dt (2.6)

Control strategy for three-level control to work the same way as two-level control can be seen in figure 2.3b.

(1) Current is flowing from from the positive rail to through Q3, L2 and Q2 to the negative rail.

(2) Q2 switches off and due to the current in equation (2.6) decreasing. The voltage over L2 will change polarity and rise proportional to the current as it is decreasing. This means that the potential over D2 will be so that it conducts and we will have a upper loop that is unloading the energy from the coil.

(3) Now the Q2 switches on again and the current runs as in (1).

(4) Q3 switches off. The same process as in (2) happens but this time D1 conducts and we will have the lower loop unloading the energy from the coil.

2.3.4 Transducers

The test method for FRF on a spindle proposed in this thesis rely on an applied forced vibration and a displacement response in the spindle. Given this the force applied and the displacement in the spindle needs to either be measured or estimated. Also the con-troller for the system needs to have additional transducers for improved controlability and calibration.

The voltage out should be measured for initial calibration of parameters to get an ac-curate model of the system before testing so that the given voltage reference is close to the true voltage out.

Because the proposed force controller can work outside the linear region of the elec-tromagnet, a force estimation from the observed current might be hard to realize. There-fore a force transducer could be implemented to accurately measure the force.

Current and magnetic flux transducer could be good to have in the observer vector for implementing feedback, but cannot be used in a pure feed-forward controller.

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16 CHAPTER 2. BACKGROUND

for the resistive losses in the system. It could also be used together with voltage and a model to estimate the magnetic flux for a feedback controller.

2.3.5 Force controller

Two different approaches to control the force acting on the rotor are:

Control through current

Current can be approximated to be linear to the force under small changes with applied bias to move away form the virgin curve.

Disadvantage with using current controlled force are such as unstable zero, hidden information such as stray flux, eddy currents or hysteresis and more. And the non-linearity with the force and airgap. [11]

Control through voltage

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Chapter 3

Methods

3.1 Rotor dynamics

In a previous work detailed in those papers [4], [1], a method of analysis of dynamic properties is the use of experimental modal analysis and the use of recursive estimation of modal parameters from the data. The proposed method for extracting data is to apply a white noise force on the rotor and measure the displacement. The work in this thesis is to design and test a concept of the system for a high power data extracting using a contact-less excitation and response system. In the paper a first version of a Contacless Exitaction and Response System (CERS) have been used.

3.2 Electromagnets and AMB

The design will be using the same technique as the previous system using an AMB based design. To make it more modular and easier to build the system after parameters, each force producing magnet and sensor will be mounted on it is own support structure with it is own dedicated electronic module. The placement of the magnet are so that to are parallel but opposite to produce the positive and negative direction forces in one axis and two orthogonal for the other axis. The sum of the forces will be the force direction on the rotor.

3.2.1 Design parameter equations

The equations for design parameters for the magnet can be attained by rearranging the equations from section 2.

Using equation (2.5) and equation (2.2) to calculate the design parameters. Rearranging equation (2.2): Af e· µ0= F · 4l2_air (N I)2 (3.1) And equation (2.5): Af e· µ0= V2· d2_t N2_{· F} (3.2)

Now we can put equation (3.1) and equation (3.2) together and rearrange which gives:

F2· 4l2_air= V2· I2· d2t (3.3)

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18 CHAPTER 3. METHODS

Given that the power, P = V · I, and say that dt is 1_f(inverse frequency), we end up with:

P = f · F · 2lair (3.4)

Rearranging equation (2.2) for the last two unknown parameters:

N · I = s

F · 4l2_air Af e· µ0

(3.5) Af e and lair is dependent on the mechanical design and can be decided on separately

from the electrical design as long as it can handle the magnetic flux. The maximum mag-netic flux can be found in data sheets for the iron core material.

To estimate the size of the magnet to the required force, equation (3.7) was used from paper [15]. F = B 2_{· A} f e µ0 (3.6) The area of the magnet core needed is then:

Af e =

Fmax· µ0

B_sat2 (3.7)

3.3 Power supply and output stage

3.3.1 Power Supply

A DC power supply is chosen as it is easier to control and the losses in the magnetic core is less.

3.3.2 Output stage

As section 3.2.1 shows, we can tweak V, I and N freely as long as the product V · I and N · I are the same. This means that we aren’t constrained by a particular voltage or mag-net, but can choose based on market and design constrains for the parts.

3.4 Force controller

For the force controller in this concept a voltage based feed forward controller as scribed in section 2 is chosen based on the insight from paper [11]. In the paper it is de-scribed that a feed forward controller is a faster than a closed with flux feedback and that the force is easier to accurately control through voltage. An option to add an ob-server model for more accuracy is another point in using this control method.

3.5 Testing framework

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CHAPTER 3. METHODS 19

Figure 3.1: Simple block diagram of the test system

3.5.1 Steady state testing

Testing the system with the rotor at standstill will be used to test the concept system as it will be enough to see the stability and accuracy of the concept system. A voltage sup-ply with variable voltage output will be used to step up the voltage in small increments and verify the concept system function in each step. This will prevent expensive compo-nents from breaking in case of a fault in the system that can be found through verifica-tion of the funcverifica-tion of the system in each step. As long as the testing is conducted in the allowed range of the magnet and electronic components the functionality as described in the equations in section 2 and 3 can be verified.

3.5.2 Dynamic testing

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Chapter 4

Development and construction

4.1 Design parametrization

Some assumptions of possible parameters in the concept system from previous systems and the constrains on size of components:

lair 0.6 mm

Af e 9 cm2

µ0 4π · 10−7 N_A2

Table 4.1: Predetermined design parameters

A mentioned goal of the final system is given in table 4.2. Those values will be used in the design parametrization to set a size of the concept system to work from. This will be tested after the concept has been verified to work to verify if the method is too con-servative or if the losses are bigger than anticipated and that the concept needs to be reparametrisized in the next iteration to meet the goals.

F 500 N

f 5000 Hz

Table 4.2: Desired maximum force and frequency possible to test with this system Now we have all parameters in table 4.1 and table 4.2 and can put them in equation (3.4) and equation (3.5).

As seen in figure 4.1a. The relation between frequency and power at a force of 500 N is linear and for the goal in table 4.2 a power of at least 3 kW is needed.

From the force given in table 4.2 the amp-turns (product of current and number of turns of the coil) can be calculated.

And the magnet field is calculated to make sure that the maximum field strength is under the saturation of the magnetic material Hi-lite NO20 that we have chosen to this concept test. This material is made in thin sheets of 0.2 mm so that the eddy currents can be limited and the material has a relatively high magnetic saturation point well outside the operating field strength under 800 amp − turns in figure 4.1c.

The result from the code in appendix A.2 is this: P = 3 kW and N · I = 798 At (ampere-turn).

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CHAPTER 4. DEVELOPMENT AND CONSTRUCTION 21

(a) Power need for 500 N at different frequencies

(b) Maximum force at different amp-turns (c) Power need for 500 N at different frequencies

Figure 4.1: The relation between different parameters in the system

4.2 Concept construction

To prevent losses in the system from the actuation to the sensor, reducing torque and side loads is essential to be sure that the sensor is measuring what is actually applied on the tool. There might still be losses in the material connecting the sensor to the load but this is easier to model by taking reference measurements and comparing.

Therefore a rigid holder of the magnet has been built as seen in figure 4.2. The holder consist of:

a) The sensor mount fixed to the fixture g).

b) C formed iron core made by sheets of 0.2 mm magnetic material. c) Coil pair, 50 turns in each for a total off 100 turns.

d) Tool under test.

e) Low friction guide rails to limit the degrees of freedom of the magnet to only one direction.

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22 CHAPTER 4. DEVELOPMENT AND CONSTRUCTION

g) Fixture

Figure 4.2: The machine setup with the magnet holder

4.2.1 Electric circuit design Isolation

After the first testing showed problem with instability that disappeared when a grounded oscilloscope was attached it was determined that additional components to isolate the power part from the control part from each other was needed. A supply, U1, was added to isolate the power supply to the MOSFET driver, U4, and a fast optocoupler, U2, to isolate the control signal. Fast optocoupler is needed to be able to have small discrete steps(that corresponds to small voltage steps on the output ie more fine control) and a high Pulse Width Modulation (PWM) frequency so that the low frequency response of the coil system will smooth out the voltage from the PWM on off to a more fine voltage level.

Given that a PWM frequency of more than two times the signal frequency of 5kHz is needed to meet the Nyquist rate. A frequency of 20kHz was chosen to have a margin. As mentioned in the article [16], the equation (4.1) is used to calculate the frequency of the PWM signal. With a 10-bit resolution to be able to have at least 1V resolution at 380V and the frequency chosen earlier we can see that the rise and fall time of the optocoupler needs to be about 50 ns.

F requencyP W M =

2 n(tr+ tf)

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Fault protection

As seen in the schematic in appendix A.1. The fuse, F1, is to protect the system from the coil unloading it is energy in the system in case of a fault. Together with the diode, D5, it protects against negative voltage generated by the coil. And the two varsitors, RV1 and RV2 protects against voltage spikes. RV1 conducts electricity at 450V to blow the fuse to protect the system from a big energy spike coming back from the coil. In case the fuse blows and the coil still has a lot of energy to produce large voltage spikes, RV2 is supposed to unload the energy if the voltage rise above 900V to prevent arc-over in the fuse or on the PCB trace. Another fuse, F2, located between the HV in connector and the powerstage is used to protect the power stage from the control stage in case the diodes, D4 and D6 or transistors Q1 and Q2 fails short.

Power supply

A Artensyn AIT02ZPFC-01NL 1600 W was chosen as it can be put in parallel to get more power out to meet the needs of voltage and current in this work.

4.2.2 Block diagram

The system design with the electric connection is shown in figure 4.3. It consist of a high power, high voltage part and a low voltage control signal part. All wall plugged connec-tions are fused on the input in case of any fault in the power supplies. In the high volt-age part it starts with a power supply that converts AC to DC for the reason explained in section 3.3.1. The increase in voltage is to decrease the current as much as possible to be able to run smaller cables and overall smaller components in the system. After the power supply there is a capacitor bank that takes care of the fast transients that the power supply cannot handle. The discharge resistor is implemented to discharge the ca-pacitor bank when turning of the system. They are constantly discharging but the resis-tance is too big that it does not affect the system when turned on. A fuse is protecting the power supply from the PWM and the coil stage. The power electronics part in the PWM consist of the transistors for controlling the power supplied to the coil as shown in figure 2.2. A hall effect current transducer and hall effect voltage transducer takes the output voltage and current and galvanic isolated transfers the measurements to the Ana-log Digital Converter (ADC) module in the cRIO unit. A diode over the output protects the electronics from the back-emf of the coil and a fuse from high currents like a short of the output or high power back-emf.

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4.2.3 Algorithm implementation Force to Voltage

The force to voltage part of the algorithm is implemented using the equation (2.5) with the designed parameters.

Voltage to Duty-Cycle

To control the voltage over the magnet, UL, the transistors are on for a duty-cycle of the

input voltage, Ui, that are wanted on the output. But the transistors has an on resistance,

Ron, and diodes has the forward voltage drop and this is taken into account in equation

(4.2) when calculating the duty-cycle, D.

D = UL− RonI − Uon Ui− 3RonI − Uon

(4.2)

4.3 Testing

All graphs and data are from the file "test_70-200Hz_+-15N.tdms"

4.3.1 Electric circuit testing Duty to voltage testing

Tests show that the voltage output is corresponding to the voltage variable that the duty cycle it is calculated from. The figure 4.4b shows that the voltage follows the reference voltage, figure 4.4b up to the limit of the power supply used under test.

(a) Voltage variable in LabVIEW (b) Voltage measured

Figure 4.4: Testing of voltage accuracy

Voltage to force testing

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than described in the ideal case in figure 4.5 may decrease the measured force. Also er-ror in the model and parametrization of the constants in the equations might affect the results.

Figure 4.5: The ideal case of the force on the current setup.

To test the ideal case we need a framework for testing that can be verified to be the actual force on the tool. A proposed way of testing is to place a force sensor on the ta-ble attached to the tool to measure the force in steady state. In this work however the force transducer holding the magnet was the only sensor used in testing. From it the fre-quency can be extracted for verification but the amplitude cannot be verified without an external separate sensor attached to the tool.

4.3.2 Magnet core design

The magnet has been placed standing in an axial configuration to maximize the effective area between the core and the tool. It will also isolate the force to one direction. A ra-dial configuration could also be used if there is a limit in height, but the force would be acting in two directions normal to the two surface of the iron core facing the tool.

4.3.3 Steady state testing

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Chapter 5

Result

5.1 Filter

To be able to extract frequency from the data, a filter to remove the high frequency noise called Savitzky-Golay filter has been used in MATLAB with the input K = 3 and F = 41.

Figure 5.1: Zoomed in section of before applying Savitzky-Golay filter to measured force data.

Figure 5.2: Zoomed in section of after applying Savitzky-Golay filter to force data.

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28 CHAPTER 5. RESULT

After running a script, a part of appendix A.3, to detect peaks on the filtered data shown in figure 5.2. The time between peaks could be used to calculate the frequency. This was done to generate figure 5.4.

5.2 Steady state testing

Analyzing the data, script in appendix A.3, from a few test by calculating Af e in

equa-tion (2.5) from the measured data shows that the iron core area of the magnet should be 23 cm2_{. This corresponds close to the two time the area of the core design and it could}

be explained from that there are two areas where the force is acting on the rotor, the up-per part of the magnet and the lower part.

Figure 5.3 show the measured force of a 15 N , 70 - 200 Hz test.

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CHAPTER 5. RESULT 29

Figure 5.4: Frequency of the force.

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Figure 5.5: Electrical power used

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CHAPTER 5. RESULT 31

Figure 5.6: Calculation of the power from force and frequency.

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Figure 5.7: Force amplitude at different frequencies

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Chapter 6

Conclusions

6.1 Conclusions

In this work a system for CERS has been designed, constructed and tested for verifying an control approach for higher force and frequency in testing. The testing at 30W shows that the system can be used to generate a 15 N force at a specific frequency of 70 Hz to 200 Hz.

6.2 Discussions

The testing shows that the frequency and force are controllable with the proposed method and instrumentation used in this work. This indicates that a scaled up system with more refined testing and a bigger power supply that is needed for more accurate control of force and for generating a bigger amplitude. For future testing the force also needs more accurate verification by the use of separate sensor on the tool itself to calibrate the pa-rameters of the system.

6.3 Future work

The implementation can be harder than expected with too may untested dependencies in the design to get an accurate control over the whole expected working range. Time to specify requirements, test and verify each component separately so that the force control approach and testing method is verifiable to work independent of problems in untested sub-components.

In paper [11] an observer is proposed for including effects that might be missed in the idealized model.

Another thing to look at is if the force can be separated into a low frequency, high amplitude amplifier part and a high frequency, low amplitude part in case that the pro-posed concept cannot handle a high dynamic range.

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Bibliography

[1] Andreas Archenti. A Computational Framework for Control of Machining System Capa-bility: From Formulation to Implementation. PhD dissertation, KTH Royal Institute of Technology, Stockholm, 2011.

[2] Anne Håkansson. Portal of research methods and methodologies for research projects and degree projects. WOLRDCOMP’13, 2013.

[3] Tomas Österlind. Estimation of Machining System Dynamic Properties - Measurement and Modelling. PhD dissertation, KTH Royal Institute of Technology, Stockholm, 2017. [4] Andreas Archenti, Lorenzo Daghini, and Cornel Mihai Nicolescu. Recursive esti-mation of machine tool structures dynamic properties. In Proceedings of 4th CIRP International Conference on High Performance Cutting, 2010, pages 365–370, 2010. [5] Eberhard Abele, Yusuf Altintas, and Christian Brecher. Machine tool spindle units.

CIRP Annals - Manufacturing Technology, 59:781–802, 2010.

[6] Eric H. Maslen and Guoxin Li. Rotordynamic design audits of amb supported ma-chinery. 2008.

[7] F. Donald Caulfield. Electromechanical actuator development for integrated chatter prediction on high speed machining centers. Master’s thesis, North Carolina State University, 4 2003.

[8] Matti Rantatalo, Jan-Olov Aidanpää, Bo Göransson, and Peter Norman. Milling ma-chine spindle analysis using fem and non-contact spindle excitation and response measurement. International Journal of Machine Tools and Manufacture, 47(7):1034 – 1045, 2007. ISSN 0890-6955.

[9] Eberhard Abele, Andreas Schiffler, and Stefan Rothenbücher. System identification during milling via active magnetic bearing. Production Engineering, 1(3):309–314, Nov 2007. ISSN 1863-7353.

[10] Hannes Bleuler, Matthew Cole, Patrick Keogh, R Larsonneur, E Maslen, Y Okada, G Schweitzer, A Traxler, Gerhard Schweitzer, Eric H Maslen, et al. Magnetic bearings : theory, design, and application to rotating machinery. Springer Science & Business Media, Dordrecht New York, 2009. ISBN 978-3-642-00496-4.

[11] Claudius M Zingerli and Johann W Kolar. Novel observer based force control for active magnetic bearings. In Power Electronics Conference (IPEC), 2010 International, pages 2189–2196. IEEE, 2010.

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BIBLIOGRAPHY 35

[12] Mor Mordechai Peretz Shai Arogeti Tomer Ben-Moha, Sergei Basovich and Ziv Brand. Digitally controlled switch-mode power driver for active magnetic bear-ings. In 2014 IEEE Energy Conversion Congress and Exposition (ECCE), pages 3030–3035. IEEE, 2014.

[13] Jun Wang and Longxiang Xu. System model of three-level switching power ampli-fier for magnetic bearing. In 2009 International Conference on Measuring Technology and Mechatronics Automation, pages 708–711. IEEE, 2009.

[14] Liu Shuqin Yu Wentao, Li Hongwei. The development of power amplifier for the high-power magnetic. In International Power, Electronics and Materials Engineering Con-ference (IPEMEC 2015), pages 774–711. IEEE, 2015.

[15] Gerhard Schweitzer. Active magnetic bearings – chances and limitations. In Proc. of 6th International IFToMM Conf. on Rotor Dynamics.

[16] Janet Heath. Selecting an optocoupler to isolate a pwm.

https://www.analogictips.com/selecting-optocoupler-isolate-pwm/.

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Appendix A

Electronics design

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APPENDIX A. ELECTRONICS DESIGN 37

A.1 Control stage

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38 APPENDIX A. ELECTRONICS DESIGN

A.2 Parameterization scipt

1 % 2 % Design s c r i p t 3 % 4 5 % v a r a b l e s 6 7 x = 6e −4; % a i r g a p 8 A_fe = ( 3 e −2) ^ 2 ; % a r e a o f magnet c o r e 9 my_0 = p i∗4 e −7; 10 F_max = 1 0 : 1 0 : 1 0 0 0 ; % newton 11 B = 0 . 1 : 0 . 1 : 2 ; 12 my_r = 5 0 0 0 ; 13 rho_cu = 1 . 6 7 8 e −8; %copper 14 15 f = @( p , F ) ( p . / ( 2 ∗ x . ∗ F ) ) ; 16 NI = @( F ) (s q r t( F . ∗ ( ( 4 ∗ x ^2) /( A_fe ∗my_0 ) ) ) ) ; 17 18 N I _ a i r = @( b ) ( b . ∗ ( 2 ∗ x/my_0 ) ) ; 19

20 V_m = @( turns , new ) t u r n s . ∗s q r t( my_0∗ A_fe ) ∗ f ( 3 0 0 0 , 5 0 0 ) . ∗s q r t( new ) ; 21

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APPENDIX A. ELECTRONICS DESIGN 39 46 N = NI ( 5 0 0 ) / I 47 48 I 2 =s q r t( 1 0 0 0 ) 49 V2=3000/ I 2 50 N2 = 1000/ I 51 52 f i g u r e( 3 ) 53 b = N I _ a i r ( B ) ; 54 p l o t( B , b ) 55 t i t l e( ’ Magnetic f i e l d ’) 56 x l a b e l( ’ F i e l d ( T ) ’) 57 y l a b e l( ’ Ampturns ( NI ) ’) 58 NI_max = N I _ a i r ( 1 . 5 ) 59 60 N∗ I /1000 61 62 ( ( 8 0 / ( 3 5 ∗ my_0∗ A_fe ) ) ^2) ∗ ( ( ( 1 / 5 0 0 0 ) ^2) /2) 63

64 V_max=N∗s q r t( my_0∗ A_fe ) ∗ f ( 3 0 0 0 , 5 0 0 ) ∗s q r t( 5 0 0 ) 65

66 V3 = 3 8 0 ; 67 I 3 = 3 0 0 0 / 3 8 0 ; 68 N3 = NI ( 5 0 0 ) / I 3 ; 69

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A.3 Analyse scipt

1 % Analyse s c r i p t 2 %

3 % I n c l u d e f u n c t i o n from Humphreysb t o import TDMS l o g f i l e t o Matlab 4 % h t t p s :// se . mathworks . com/ m a t l a b c e n t r a l / f i l e e x c h a n g e /44206− converttdms−v10 5 % 6 7 f i l e n a m e = ’ logged_data . tdms ’;

8 t d m s _ s t r u c t = convertTDMS ( 0 , f i l e n a m e ) ; % Convert t o matlab using Humphreysb ’ s s c r i p t

9

10 % Take a look i n s i d e t h e t d m s _ s t r u c t t o s e t t h e c o r r e c t row f o r each s i g n a l

11 time = t d m s _ s t r u c t . Data . MeasuredData ( 1 1 ) . Data ; 12 Force = t d m s _ s t r u c t . Data . MeasuredData ( 7 ) . Data ; 13 Force = Force − min( Force ) ;

14 v o l t a g e = t d m s _ s t r u c t . Data . MeasuredData ( 1 0 ) . Data ;

15 l a b v i e w _ v o l t a g e = t d m s _ s t r u c t . Data . MeasuredData ( 1 0 ) . Data ; 16 c u r r e n t = t d m s _ s t r u c t . Data . MeasuredData ( 5 ) . Data ;

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APPENDIX A. ELECTRONICS DESIGN 41 42 43 44 N= 1 0 0 ; 45 my_0 = 4∗p i∗1 e −7; % H/m 46 47 sqF = s q r t( Force ) ; 48 df = sqF ( 2 :end) − sqF ( 1 :end−1) ; 49 dt = time ( 2 :end) − time ( 1 :end−1) ; 50 d f o r c e = df . / dt ;

51 sq_my0_Afe = v o l t a g e ( 2 :end) . / (N. ∗ d f o r c e ) ; 52 %f i g u r e ( 1 0 )

53 %p l o t ( time ( 2 : end ) , sq_my0_Afe ) 54 Afe = ( sq_my0_Afe . ^ 2 ) . / my_0 ;

55 Afe = Afe ( ~any( i s n a n( Afe ) | i s i n f ( Afe ) , 2 ) , : ) ; 56 f i g u r e( 1 0 )

57 p l o t( Afe ) 58 legend( ’ Afe ’) 59 m_AFE = mean( Afe ) ; 60 M_AFE = median( Afe ) ; 61 std_AFE = s t d( Afe ) ; 62

63 dtime = time ( 2 :end)−time ( 1 :end−1) ; 64 Fs = 1/mean( dtime ) ;

65

66 %

67 % Smooth s i g n a l s with Savitzky −Golay F i l t e r i n g 68 % 69 70 s c u r r e n t = s g o l a y f i l t ( c u r r e n t , 3 , 4 1 ) ; 71 f i g u r e( 1 0 ) ; 72 p l o t ( time , s c u r r e n t ) 73 legend( ’ c u r r e n t smooth ’) ; 74 75 s F o r c e = s g o l a y f i l t ( Force , 3 , 4 1 ) ; 76 f i g u r e( 1 1 ) ; 77 p l o t ( time , s F o r c e ) 78 legend( ’ f o r c e smooth ’) ; 79 80 s v o l t a g e = s g o l a y f i l t ( v o l t a g e , 3 , 4 1 ) ; 81 f i g u r e( 1 2 ) ; 82 p l o t ( time , s v o l t a g e ) 83 legend( ’ v o l t a g e smooth ’) ; 84 85 spower = s g o l a y f i l t ( power , 3 , 4 1 ) ; 86 f i g u r e( 1 3 ) ; 87 p l o t ( time , s v o l t a g e )

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89 x l a b e l( ’ s ’) 90 y l a b e l( ’W’) 91

92 % Try A_fe again but with smooth s i g n a l s 93 sqF = s q r t( s F o r c e ) ;

94 df = sqF ( 2 :end) − sqF ( 1 :end−1) ; 95 dt = time ( 2 :end) − time ( 1 :end−1) ; 96 d f o r c e = df . / dt ;

97 sq_my0_Afe = s v o l t a g e ( 2 :end) . / (N. ∗ d f o r c e ) ; 98 %f i g u r e ( 1 0 )

99 %p l o t ( time ( 2 : end ) , sq_my0_Afe ) 100 Afe = ( sq_my0_Afe . ^ 2 ) . / my_0 ;

101 Afe = Afe ( ~any( i s n a n( Afe ) | i s i n f( Afe ) , 2 ) , : ) ; 102 f i g u r e( 1 4 )

103 p l o t( Afe ) 104 legend( ’ Afe ’) 105 m_AFE2 = mean( Afe ) 106 M_AFE2 = median( Afe ) 107 std_AFE2 = s t d( Afe ) 108

109 %

110 % Analyse t h e f r e q and amplitude 111 % 112 113 f_max = 2 0 0 0 ; % f Hz period 114 115 f i g u r e( 6 5 ) 116 c l f ; 117 p l o t( sForce , ’ b ’) 118 legend( ’ T e s t o f d i f f ’) 119 hold on

120 I = f i n d(abs(d i f f( s F o r c e ) ) < 0 . 0 5 ) ; % Find p o i n t s c l o s e t o t h e top and bottom

121 i n d i c e s = f i n d( d i f f( I ) <(1/(mean( dt ) ∗f_max ) ) ) ; % removes c l o s e p o i n t s

122 I ( i n d i c e s ) = [ ] ;

123 p l o t( I , s F o r c e ( I ) , ’ r ∗ ’) 124

125 f i g u r e( 6 6 )

126 freq _chan ge = 1 . / (d i f f( I ) ∗mean( dt ) ∗ 2 ) ; % 2 t o put t h e two h a l f p e r i o d s t o g e t h e r

127 x = l i n s p a c e( 1 ,l e n g t h( fr eq_cha nge ) ,l e n g t h( f req_ch ange ) ) ; 128 x i = l i n s p a c e( 1 ,l e n g t h( fr eq_cha nge ) ,l e n g t h( time ) ) ;

129 f r e q _ c h a n g e _ t i m e = i n t e r p 1( x , freq_change , x i ) ; 130 p l o t( time , f r e q _ c h a n g e _ t i m e )

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APPENDIX A. ELECTRONICS DESIGN 43 133 x l a b e l( ’ s ’) 134 135 f i g u r e( 6 7 ) 136 peaktopeak = abs( d i f f( s F o r c e ( I ) ) ) ; 137 p l o t( peaktopeak ) 138 legend( ’ p2p ’) 139 y l a b e l( ’N’) 140 141 f i g u r e( 6 8 ) 142 o f f s e t = ( s F o r c e ( I , 1 ) + s F o r c e ( I + 1 , 1 ) ) . / 2 ; 143 p l o t( o f f s e t ) 144 legend( ’ O f f s e t ’) 145 y l a b e l( ’N’) 146 147 f i g u r e( 6 9 ) 148 n o t s t r e t c h e d = l i n s p a c e( 1 ,l e n g t h( o f f s e t ) ,l e n g t h( o f f s e t ) ) ; 149 s t r e t c h = l i n s p a c e( 1 ,l e n g t h( o f f s e t ) ,l e n g t h( peaktopeak ) ) ; 150 o f f s e t i = i n t e r p 1( n o t s t r e t c h e d , o f f s e t , s t r e t c h ) ; 151 peak = o f f s e t i ’ +( peaktopeak . / 2 ) ; 152 p l o t( peak ) 153 legend( ’ Peak ’) 154 y l a b e l( ’N’) 155 156 f r e q _ c h a n g e _ f i l t = s g o l a y f i l t ( freq_change , 3 , 4 1 ) ;

157 x = l i n s p a c e( 1 ,l e n g t h( fr eq_ch ange ) ,l e n g t h( f req_ch ange ) ) ; 158 x i = l i n s p a c e( 1 ,l e n g t h( fr eq_ch ange ) ,l e n g t h( s F o r c e ) ) ; 159 f r e q _ c h a n g e i = i n t e r p 1( x , freq_change , x i ) ; 160 P_mech = f r e q _ c h a n g e i ’ . ∗ s F o r c e . ∗ (N. ∗ s c u r r e n t . ∗s q r t( 0 . 0 0 2 ∗ my_0 . / s F o r c e ) ) ; 161 f i g u r e( 7 0 ) ; 162 p l o t( time , P_mech )

163 legend( ’ Power Mechanical ’) 164 x l a b e l( ’ s ’)

165 y l a b e l( ’W’) 166

167

168 %

169 % sForce , power and f r e q _ c h a n g e i have a l l t h e same time s p a c i n g so t h a t can

170 % be used i n t h a t index f o r a l l o f them a r e t h e same . 171 %

172 norm_Force = s F o r c e ;%. / power ; % Norm f o r c e t o power 173 %f i g u r e ( 7 5 ) ;

174 %p l o t ( time , norm_Force ) 175 %legend ( ’Norm f o r c e ’ ) 176 %x l a b e l ( ’ s ’ )

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TRITA -ITM-EX 2019:91

Design and construction of a contactless excitation and response measurement system

Design and construction of a

contactless excitation and

response measurement system

JOHAN WESTLUND

Design and construction of a contactless excitation and

response measurement system

Abstract

Sammanfattning

Acknowledgements

Abbreviations

Contents

Chapter 1

Introduction

1.1

Background

1.2

Problem

1.3

Purpose

1.4

Goal

1.5

Methodology / Methods

1.6

Delimitation

1.7

Outline

Chapter 2

Background

2.1

Machining

2.2

Rotor dynamics

2.3

Active Magnetic Bearing (AMB)

Two-level

Three-level

Chapter 3

Methods

3.1

Rotor dynamics

3.2

Electromagnets and AMB

3.3

Power supply and output stage

3.4

Force controller

3.5

Testing framework

Chapter 4

Development and construction

4.1

Design parametrization

4.2

Concept construction

4.3

Testing

Chapter 5

Result

5.1

Filter

5.2

Steady state testing

Chapter 6

Conclusions

6.1

Conclusions

6.2

Discussions

6.3

Future work

Bibliography

Appendix A

Electronics design

A.1

Control stage

A.2

Parameterization scipt

A.3