Non-contact measurements and modelling of milling machine tool vibrations

Transcription

1 6:5 LICENTIATE T H E S I S Non-contact measurements and modeing of miing machine too vibrations Matti Rantatao Lueå University of Technoogy Department of Human Work Sciences Division of Sound & Vibration 6:5 ISSN: ISRN: LTU-ic SE

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3 Non-contact measurements and modeing of miing machine too vibrations Matti Rantatao Division of Sound & Vibration Lueå University of Technoogy SE Lueå Sweden Key words: machine too spinde, centrifuga, gyroscopic, non-contact measurement, anguar contact ba bearings, machine too chatter, aser Dopper Vibrometry, specke noise, rotor bearing systems, FEM, magnetic excitation, inductive dispacement sensors.

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5 ACKNOWLEDGEMENTS First of a I woud ike to thank my oving and encouraging famiy; Christina, Uno, Kerstin and Marianne, my parents Magda and Hugo and my parents in-aws Mona and Bengt - you a made it possibe for me to combine a oving famiy ife with the effort that must be invested in writing the thesis. Secondy, I woud ike to thank my supervisor, Professor Anders Ågren, for giving me this once in a ifetime opportunity to participate in a PhD study. A his hep during my studies and his being a great boss made a the difference. I woud aso ike to express my gratitude to Dr. Per Gren and Dr. Jan-Oof Aidanpää of Lueå University of Technoogy (LTU) and Bo Göransson of SKF for their hep, dedication and genuine interest in my work. I woud aso ike to thank my coeagues Peter Norman and Kourosh Tatar for their work and for making the beginning of my PhD studies a joyfu and memorabe time in my ife. I woud aso ike to express my gratitude to the rest of the peope invoved in LTU s research project in this genera area for interesting discussions, ideas and their interest: Tore Siver, Dr. Aes Svoboda, Prof. Inge Svennigson, Tommy Gunnarsson and Dr. Mikae Bäckström. Finay I woud ike to thank my current and previous coeagues at the Department of Sound and Vibration for sharing their knowedge and being great friends. The work conducted was financed by the Swedish Agency for Innovation Systems (Vinnova). The funds to pay for the aser Dopper Vibrometer (LDV) used in this research came from the Kempe Foundation.

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7 ABSTRACT This thesis concerns the deveopment of non-contact measurement methods and anaysis of rotors. The methods have been verified and appied to miing machine spindes in order to investigate the speed dependency in the miing machine spinde dynamic. The research was financed by the Swedish Agency for Innovation Systems (Vinnova). Turning operations ike miing are common in the automotive and aerospace industries where arge meta work pieces are reduced to a fraction of their origina weight when creating compex thin structures. During these operations it is important that unwanted behaviours such as excessive too vibrations be avoided (this is normay caed chatter ). Chatter causes poor surface finish and/or materia damage and can expose machine operators to annoying and/or dangerous noise eves. In order to predict processes parameters for a chatter free miing operation, knowedge of the properties of the dynamic system are essentia. Normay the system dynamics are measured during no rotation; in order to incude the infuence of the spin speed the system must be anaysed for a spinde speeds intended for the miing operation. This can be done either by measurement or modeing. Non-contact measurement techniques are however, often based on dispacement sensors which do not have the same sensitivity as veocity or acceeration based methods. To improve the sensitivity in non-contact measurements of rotors a aser Dopper Vibrometry (LDV) based method has been deveoped. The deveoped LDV method is based on the reduction of the rotor surface structure and makes it possibe to use singe beam LDV measurements of rotors. These types of measurements were previousy considered inaccurate but now have become feasibe through the use of the method described in this research. Furthermore the dynamic properties of a high-speed-miing machine spinde were studied by a contactess dynamic spinde tester (CDST) deveoped by SKF. The measurements were substantiated by simuations using a finite eement mode (FEM) which confirmed the measurement resuts. The CDST measurements coud be performed without vioating safety reguations regarding human interaction with high speed spindes through the use of a magnetic excitation method. In the measurements conducted by the CDST a speed dependency in the spinde dynamic coud be detected. By performing FEM simuations the major source of this dependency coud be identified. The centrifuga force of the bas in the anguar contact ba bearings was shown to have the argest infuence on the overa dynamics compared to the gyroscopic moment of the rotor. The study performed indicates that predictions of high-speed-miing stabiity must incude consideration of the speed dependency in the dynamic.

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9 CONTENTS 1 THESIS 1 INTRODUCTION 5 3 LDV MEASUREMENT METHOD 8 4 SPINDLE MEASUREMENTS 16 5 MODELLING 6 DISCUSSION 8 7 CONCLUSIONS 3 8 FUTURE WORK 33 9 NOMENCLATURE 33 1 REFERENCES 34 APPENDIX A: SPINDLE DRAWING APPENDED PAPERS PAPER I PAPER II PAPER III PAPER IV

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11 1 THESIS This thesis begins by introducing readers to the research probems of miing machine vibrations and spinde measurements. It then continues on by describing different non-contact measurement methods and, in particuar, the theoretica background and probems associated with aser Dopper Vibrometry (LDV) when appied to rotating targets such as miing machine spindes. A method for soving these LDV probems is presented together with a method for miing machine spinde anaysis using inductive dispacement sensors and eectromagnetic excitation substantiated by FEM simuations. Lasty, the findings are discussed aong with suggestions to future work. This thesis covers work described in greater detai in the four attached papers. 1.1 Paper I M. Rantatao, P. Norman, K. Tatar, Non-contact measurements of too vibrations in a miing machine, SVIB vibrations Nytt, () (4) -9 This paper presents a pre-study of two types of non-contact measurement methods for miing machine spinde vibrations. LDV on a rotating spinde and the use of an active magnetic bearing (AMB) for spinde dynamic measurements were tested. The AMB study was conducted on a ow speed (-7 rpm) miing machine spinde. The methods and findings in this work were further studied in Papers II, III and IV. Matti Rantatao prepared the too, outined the work and performed the AMB measurements with the assistance of Peter Norman. The LDV measurements were performed by Kourosh Tatar and Matti Rantatao and the miing machine was operated by Peter Norman. Matti Rantatao performed the post processing and anaysis of the data. Matti Rantatao wrote the paper with the assistance of Peter Norman and presented the work at the SVIB 4 Conference in Stockhom. Pubished in SVIB s member journa 4-. The paper was not subject to a review procedure. 1. Paper II M. Rantatao, K. Tatar, P. Norman, Laser Dopper Vibrometry measurements of a rotating miing machine spinde, in: Proc of the Eighth Internationa Conference on Vibrations in Rotating Machinery, Swansea UK, (4) () The paper describes a method for specke noise remova in LDV on rotating targets. The study is an extension of the LDV study presented in Paper I. The tite of the paper is a bit miseading in that a more genera work is suggested than was actuay 1

12 presented. A more representative tite woud be. A method for specke noise remova by surface structure reduction - an LDV appication to rotating targets. Matti Rantatao, Kourosh Tatar and Peter Norman outined the work. Matti Rantatao performed the post processing and anaysis of the data with the assistance of Kourosh Tatar. Measurement data ogged in Paper I was used in this paper. Matti Rantatao wrote most of the paper with the assistance of Kourosh Tatar and Peter Norman. Correspondence with the editor of the conference proceedings and the reviewers was conducted by Matti Rantatao Pubished in conference proceedings. The paper was subjected to a review procedure. 1.3 Paper III K. Tatar, M. Rantatao, P. Gren, Laser vibrometry measurements of an opticay smooth rotating spinde, submitted to: Mechanica Systems and Signa Processing, (6). The work incudes an investigation in the presence of crosstak between radia vibration components after using the method for specke noise remova presented in Papers I and II. Kourosh Tatar and Matti Rantatao outined the work with the assistance of Per Gren. Kourosh Tatar prepared and verified the dummy too quaity and performed together with Matti Rantatao the experiments. Matti Rantatao conducted the AMB measurements and Kourosh Tatar the LDV measurements. Kourosh Tatar performed the post processing of the data and together with Matti Rantatao and Per Gren the data was anaysed. Kourosh Tatar and Matti Rantatao wrote most of the paper with the assistance of Per Gren. Kourosh Tatar was the corresponding author. The paper has been accepted for pubication by Mechanica Systems and Signa Processing. 1.4 Paper IV M. Rantatao, J-O. Aidanpää, B. Göransson, P. Norman, Miing machine spinde anaysis using FEM and contactess spinde excitation and response measurement. Manuscript submitted for pubication. This paper demonstrates a method for spinde anaysis incuding FEM, contactess excitation and response measurement. The method was appied to a high-speedmiing machine with a spinde speed capacity of up to 4 rpm. The experimenta part in this paper, regarding the inductive measurement method, is a seque to the study presented in Paper I where a ow speed spinde was studied.

13 Matti Rantatao outined the work and performed the CDST measurements and tap tests with the assistance of Peter Norman. Matti Rantatao performed the post processing and the anaysis of data. Matti Rantatao impemented a FEM representation of the rotor bearing system and performed the simuations with the assistance of Jan-Oov Aidanpää. Measurement of the physica spinde dimensions was performed by the SKF spinde service and Bo Göransson at SKF performed the bearing stiffness cacuations and wrote parts about the physics behind the speed dependent bearings. Peter Norman outined the pre-oad test together with Bo Göransson and wrote about procedure and performed the measurements with the assistance of Matti Rantatao. Matti Rantatao performed the LDV measurements of the mode shapes. Matti Rantatao wrote most of the paper with the assistance of Jan- Oov Aidanpää and Bo Göransson. The paper has been submitted for pubication. 3

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15 INTRODUCTION Turning operations ike miing are common in the automotive and aerospace industries where arge meta work pieces are reduced to a fraction of their origina weight in the creation of compex thin structures. In Fig 1 a picture of the high speed (4 rpm) state-of-the-art 5-axes research miing machine used in this thesis can be seen. As with most operations, the deveopment of more efficient processes resuts in increased productivity. This is the case in miing where the process can be made more efficient by optimizing performance in such a way that it better fufis various demands such as fexibiity, machine too endurance, production time, operator work environment and production quaity. Fig 1. Photo of the Liechti Turbomi ST1 miing machine used in studies described in this thesis. A property highy associated with these optimization parameters is machine too vibration. Vibration can expose machine operators to annoying and/or dangerous noise eves. Regenerative machine too vibration (chatter) wi reduce the quaity of a surface finish and can damage a workpiece (down to the moecuar eve). Chatter can aso resut in increased too wear/faiure and/or compex and costy machine too faiures. Therefore it is important that the vibration eve be kept under contro. Chatter is sef-excited machine too vibration which can be caused by various physica parameters [1]. Chatter caused by friction, thermodynamics or mode couping in the cutting process is caed primary chatter. Secondary chatter is caused 5

16 by the waviness of a machined surface and is considered to be one of the most important causes of instabiity in the cutting process. The secondary chatter phenomenon is a significant issue and has been addressed and modeed by numerous authors over the past decades e.g. [-5]. The deveoped modes predict a specific chatter free depth of cut for a specific spinde speed. The predictions are based on the spinde speed and the frequency response function (FRF) of the too tip; assuming a rigid workpiece. The chatter free depth of cut is cacuated for different spinde speeds which can be potted as stabiity obe charts. Fig shows a typica stabiity obe chart where the area above the curve represents production parameters which wi resut in an instabe process. The area beow represents a stabe process. Increasing the depth of cut to the wrong side of the curve wi generate chatter Stabiity obes Depth of cut [mm] Instabe zone Stabe zone Spinde speed [rpm] Fig. Stabiity obes: The area above the stabiity obe curve represents a depth of cut which wi generate chatter vibrations. Vaues beow the curve wi render in a stabie miing process..1 Research probems The FRF of the too tip, which is used in the stabiity obe cacuations, is normay measured manuay by tap-tests of a non-rotating (rpm=) spinde/hoder/too system where the too tip is excited by an impuse hammer and the response is measured by a vibration transducer. Stabiity obes based on FRF measurements made at rpm are cacuated for a spinde speeds. The assumption in this procedure is that the dynamics of the spinde/hoder/too system is independent of the spin speed. This is 6

17 however not true for the case of high-speed-miing operations where the effect of gyroscopic moments and centrifuga forces wi change the FRF. [6-8]. The vaue of the depth of cut, in the rpm based stabiity obes, is ony vaid for the speed rpm and not for other spinde speeds uness the FRF is speed independent. In order to achieve spinde speed dependent stabiity obes the FRF s for each spinde speed must be inserted into the cacuations. Tap-tests to measure the high speed FRF woud add an extra risk to work environments of the operator or engineers who conducts such measurements. An aternative, safer excitation method for spinde anaysis is therefore desirabe. Knowedge of the origin of the speed dependency in the system dynamics can aso give vauabe information for spinde design. The physica properties of a fuy operating miing machine can either be anaysed by various measurement methods or by modeing. To accuratey mode spinde dynamics speed dependency the modes must incude a parts which can contribute significanty. Present measurement methods use dispacement based response sensors and various types of excitation methods which are a in some way in contact with the rotor during the measurement procedure. Dispacement sensors have a ower sensitivity to higher vibration frequencies than acceeration and veocity based methods. No substantia research using dispacement sensors for measurement of high frequencies was found during a survey of major databases. As an aternative, a veocity based measurement method woud increase the sensitivity to higher frequencies. LDV is such a method and it is aready a common instrument for vibration measurement. However, the method possesses imitations when appied to rotating targets because specke noise and crosstak between radia vibration components occurs. A method for LDV measurement of rotating rotors has been deveoped [9] but is based on a mutipe set of continuousy measuring LDV s. The possibiity of using a singe beam aser woud reduce the investment in measurement equipment and make it possibe to measure spinning rotors in, for exampe, situations where measurement from two directions is not practica.. Research questions In the previous section the research probems, which are the subject of this thesis, were outined. When anaysing the presented research probem the foowing research questions emerged: Is it possibe to measure radia vibrations of a spinning rotor using a singe beam LDV? How can a spinde be measured without vioating safety reguations regarding human interaction with high-speed-miing machines? What contributes the most to the speed dependent spinde dynamic? 7

18 3 LDV MEASUREMENT METHOD Vibration measurements of spinning rotors can be carried out using inductive/capacitive dispacement sensors or aser sensors based on trianguation. These methods are however, imited regarding detectabe frequency and ampitude and must be positioned reativey cose to the measurement surface. Laser Dopper Vibrometry (LDV) offers a more sensitive veocity based vibration measurement technique than other non-contact measurements methods. A 64 Hz B Frame mode 1,8 m String mode 1 Snowmobie frame,6 m C R = 18 mm D b = 4 mm String mode Speakers Tennis racket Fig 3. Exampe of scanning LDV measurements on vibrating objects. A: Large area LDV scan of a snowmobie frame. B: An LDV scan of the frame and strings of a tennis racket. C: LDV scan of a sma thin speaker membrane. D: LDV scan of a sma computer component. LDV is now a commony used method for vibration measurements. This technique has many advantages compared to traditiona vibration measurements. For exampe, it is easier to use than acceerometers pus it is often faster to use. Fig 3 shows an exampe of LDV measurements of four objects of different size and shape. The exampe shows a scan of the supporting frame of a scooter reveaing an eigen-mode at 64 Hz ocated at the bet tunne. The other scans show a racket, a speaker membrane and a sma computer component which demonstrates measurement of sma, thin and ightweight structures. The nature of the LDV system permits measurement without additiona mass oading and aows a wide range of distances between the sensor head and the object (from miimetres up to severa meters). Vibration measurement of hot objects can be performed as we as measurements of sma and ight weight structures as e.g. the tympanic membrane in a human ear [1]. 8

19 The LDV technoogy can aso be appied in other medica appications e.g. for teeth vibration measurements during driing [11]. Another appication of aser Dopper Vibrometry is the measurement of sound wave propagation in transparent medias ike gases [1, 13]. When a sound wave is propagating through a medium it changes the pressure. The changing pressure wi affect the refraction index of the medium and hence moduate the aser frequency. This moduation is then interpreted as a vibration veocity by the LDV system. 3.1 LDV principa A Poytech 1 PSV 3 scanning LDV system was used in this thesis. The LDV was equipped with a scanning aser head with a scanning ange of about ±. The LDV used for this work has a heium neon (He-Ne) aser with a waveength of 63.8 nm. The LDV measures the veocity component of the object aong the direction of the aser beam and is based on the detection of the Dopper shift in the aser ight refected from the surface. (f B =4 MHz) Mirror Osciator Object ωb = πf B Ω Ω + ω B Laser Bragg-ce Ω v v(t) Veocity decoder Beam spitter x(t) Dispacement decoder Detector x(t) Fig 4. Sketch of an LDV. In an LDV the emitted ight with the frequency Ω + ωb is aowed to interfere with the ight refected from the measured object. 1 Poytec GmbH 9

20 To determine the target s veocity the aser ight is demoduated by an interferometer where the refected ight is aowed to interfere with the origina transmitted ight (reference ight) on a photodetector. To be abe to determine the direction of the target veocity a virtua constant veocity is added by a Bragg-ce which frequency moduates the reference ight with a 4 MHz signa ( ω B Bragg-ce frequency), see Fig 4. The registered Dopper shift is then used to cacuate the veocity of the object by using the foowing equation; λ v = f D (1) where f D is the Dopper frequency and λ is the aser waveength. 3. Specke When iuminating an opticay rough surface with a aser, a phenomenon caed specke wi occur. Speckes are bright and dark spots that can be seen in a refected aser ight (see Fig 5). These spots are the resut of superimposing ight waveets which are caused by differences in traveed path ength, from ight source to detector, due to the rough surface. A surface is considered opticay rough if the surface structure exceeds the eve of approximatey haf the waveength of the ight source, in this case 316 nm. The specke phenomena is sometimes considered a disturbing noise but in other cases, ike in TV hoography [14], the speckes are used as the information carrier. Fig 5. Speckes on a detector. Speckes are formed at a detector due to superimposing refected ight waveets with different traveed path engths. 1

21 For a non moving target the summarized waveets are ony seen as an added DC eve to the detector signa. If the target starts to move this DC eve wi start to vary according to the specke popuation present on the detector. This resuts in specke noise. The noise wi moduate the phase of the aser ight and add a noise to the detected Dopper signa. This noise eve can be reduced by averaging due to its random behaviour. 3.3 Specke noise on rotating targets When measuring mutipe revoutions of a rotor using LDV the specke noise can not be averaged out from the signa and must be considered separatey. In a static LDV measurement of a rotor the same specke noise occurs each revoution. If the measurement spans a number of rotor revoutions the specke noise wi be apparent as peaks in the frequency domain at mutipe integers of the rotationa speed. If the rotor speed is constant and the measurement sequence contains many revoutions the specke peaks can easiy be distinguished from ordinary structura vibrations due to their narrow appearance. The specke noise has a simiar appearance to ordinary outof-roundness components which aso are ocated in the frequency spectra at mutipe integers of the rotationa speed. The main difference between specke peaks in the frequency domain and typica peaks originating from the out-of-roundness components is the decaying appearance with increasing frequency that the out-ofroundness components show (see Fig 6). Magnitude A Structura vibrations B Miss aignment & Roundess C x Specke noise f n = f n = f D n=1 n= n=3 n=4 x Fig 6. Spectra components from LDV measurements. A: Structura vibrations. B: Rotor centre miss aignment (n=1) roundness components (n=, n=3, ). C: Repeated specke noise. D: n=1 iustrates the rotor miss aignment and n=, n=3, iustrate the out-of-roundness components of the rotor surface structure. 11

22 3.4 Specke noise remova As described here, it has been shown by others that the specke noise eve in LDV can be reduced or removed by different methods. By optimizing the detector size and position within a vibrometer the noise eve can be reduced but not competey removed [15]. It has aso been shown that the specke noise in aser torsiona vibrometry measurements can be removed by randomising the path that the aser ight is undertaking during the revoutions. This is by either by moving the aser aong the shaft [16] or simpy by adding a new surface structure. The atter strategy can be achieved by continuousy appying oi or some other substances to the surface during measurement [17]. In theory, these techniques shoud aso work for LDV measurements. Another approach to specke noise remova is by reducing the target surface structure to beow haf the aser waveength [18, 19] (Papers I and II). Fig 7 shows a comparison between LDV measurements performed on a rotor with a rough (ower graph) and a smooth surface structure (upper graph). The ower graph shows specke peaks at mutipe integers of the rotationa speed (1 Hz). The upper graph shows a spectra with no peaks due to specke. The out-of-roundness components in the upper eft graph coud be extracted with no disturbing specke noise and the resut was verified by a mechanica roundness tester (see Fig 8). Magnitude [mm/s] Veocity FFT, 6 [rpm] n=1 Poished n=5 n=3 n= n=6 n=8 n=4 n=7 n=9 Rough Frequency [Hz] Veocity FFT, 6 [rpm] n=14 n=16.4 n11 n=1 n= Frequency [Hz] Fig 7. Spectra of the poished and the rough surface at a spinde speed of 6 rpm. The spectrum of the rough rotor has been mirrored aong the frequency axis down to the negative side to simpify comparison between the two. Mutipe harmonics of n*1 Hz (marked by back dots) can be seen in the spectrum of the sprayed surface (n = 1,,3 ). 1

23 Dummy too circumference profie [μm] 1º 9º 6 6º Mechanica LDV 15º 4 3º 18º º 1º 33º 4º 7º 3º Fig 8. Out-of-roundness. Out-of-roundness components extracted from the LDV measurements compared to a separate mechanica roundness measurement. 3.5 Crosstak When appying LDV to rotating opticay rough targets two probems occur; the presence of specke noise which has been described in the previous section and crosstak between vibration veocity components. The crosstak probem is caused by different veocity components which affect the Dopper shift in the refected ight. In this thesis (from Paper III) the crosstak between the two radia vibration components are studied. Due to an opticay rough surface, backscattered ight from the tangentia veocity component moduated by the in-pane dispacement wi be added to the outof-pane veocity. [9, -]. The measured veocities of a rotating opticay rough shaft in the two orthogona directions, v x, v y, can be expressed as [9]: v y and v x = y& + Ω( x x ) () = x& Ω( y y ), (3) where x& and y& are vibration veocities, x and y are the vibration dispacements, x and y are the distances to the spin axis due to aignment errors and Ω is the tota anguar veocity incuding torsiona vibrations. x& and y& are the desired veocity components for each direction. The methods for specke noise reduction/remova 13

24 described by previous authors cope with the specific specke noise probem but are not abe to neutraize the effect of crosstak in a singe beam LDV measurement. Consequenty; the signa obtained during measurements under these circumstances wi be a mix of the vibration components in both directions. A method for resoving the true vibrations in the two x- and y-directions using a setup of two simutaneousy measuring asers in both directions and an accurate measurement of the rotationa anguar veocity has been deveoped by Hakon and Rothberg [9]. The method does require a setup of two simutaneousy measuring LDV systems in an orthogona arrangement. In Paper III the cross sensitivity in the deveoped method presented in Papers I and II is investigate experimentay. The crosstak in LDV appied to a poished rotor is compared with the crosstak present when measuring an opticay rough rotor. As a reference, a set of inductive dispacement sensors (DS) measured the position of the rotor in the x and y-direction (see Fig 9). The excitation of the rotor was carried out by eectromagnets. y (t) DS x y x (t) DS Ω F (4 Hz) v& y (t) LDV Fig 9. Crosstak test. Sketch of setup used to examine the crosstak in LDV on rotating targets. 14

25 Simuated crosstak based on vaues from the reference sensors y and x (DS) LDV on a rough surface LDV on a smooth surface Dispacement sensors (y) for a smooth and rough surface Fig 1. Effect of crosstak in LDV: Veocities at 4 Hz for different spinde speeds 7, 14, 8, 56 and 7 rpm. Fig 1 iustrates the effect of crosstak on LDV measurements of a rotating rough surface for different spinde speeds and an excitation of 4 Hz orthogona to the aser beam. The measured vibration veocity of the dummy too after being sprayed with paint (triange up) shows a spinde speed dependent crosstak as expected from Eq. ( and 3), whie the same measurements on the smooth surface (trianges down) do not. The outputs from the dispacement sensor (DS) in the y-direction for both sets of measurements (smooth and rough measurement surfaces - square and pentagram) showed no physica crosstak during the excitation. Inserting the signas from the dispacement sensors y and x into Eq. () gave the same veocity (circes) as from the vibrometer when the surface was rough (triange up). This cacuation confirms the measured crosstak detected by the LDV when measuring the rough surface. 15

26 4 SPINDLE MEASUREMENTS During a miing process the cutting force and the frequency response function (FRF) at the too tip are two important parameters. The cutting force can be measured indirecty by the use of a force pate. The force pate measures the force on the work piece by measuring the force transferred by the work piece to the machine tabe. This procedure assumes that the work piece is rigid with no interfering moda properties. A Response Response Ba Bearings B Command votage response Too F Rotor F AMB 1 Rotor AMB AMB 3 Response Radia Bearings Axia Bearing C Response D Response Actuator Rotor Rotor F F Sensor Fig 11. Force and FRF measurement methods. A: Indirect cutting force measurement using inductive/capacitive dispacement sensors. B: Indirect cutting force measurement using the AMB command votage response. C and D: Speed dependent FRF measurement methods. An aternate approach is to measure the force that the work piece has on the too. In order to do this, non-contact sensors measuring the rotor vibrations are used. Noncontact measurement of rotating miing machine spindes customariy use inductive and capacitive dispacement sensors together with aser based dispacements probes [1]. Abrecht et a. [3] describe an indirect method of force measurement when miing that uses capacitive or inductive dispacement sensors. In this method, the transfer function between the force appied on the too tip and the dispacement from capacitive sensors mounted on the spinde cose to the housing is measured for different spinde speeds. Different Kaman fiters were then cacuated for each speed and appied to the dispacement sensor signa to produce rea time cutting force measurement data. Tap tests on a ba bearing mounted on the too tip were used to excite the structure (see Fig 11A). Spiewak [4] presented an aternative acceerometer based cutting force measurement method where a miing cutter was 16

27 instrumented with a 3-axia acceerometer inside the too cose to the tip. This method requires speciay manufactured toos. For spindes equipped with active magnetic bearings (AMB), Auchet et a. [5] have outined a another method for indirect cutting force measurement based on command votage of the AMB. The method used the reationship between cutting force and an increasing command votage in the magnetic bearings in order to keep the rotor in pace (see Fig 11B). The reationship was estabished by measuring the FRF between a force (tap test) appied to the too tip and the command votage of the AMB. The FRF measured at rpm as a predictor of the cutting force at high speed machining wi, in the view of this author, be a source of error. Using AMB s for measurement and chatter contro purposes has been investigated. Knospe [6] ooked at active chatter suppression through the use of AMB. Chen and Knospe [7] estimated cutting dynamics by both exciting the system and increasing the damping of the athe too using an AMB. Simiar to expoiting the reationship between the AMB command votage and the cutting force, methods which use the current in motorised spindes have been studied. For exampe, Jeong and Cho [8] deveoped a method where they improved the frequency rage from earier methods by a factor of two up to 13 Hz. 4.1 Speed dependent stabiity obes Knowedge about the too tip FRF is important when cacuating the stabiity obes and optimizing the maximum depth of cut. When deaing with rotating dynamic systems ike a miing machine spinde, especiay during high speed machining, the FRF depends on the spinde speed. To achieve the spinde speed dependent FRF, the machine too must be anaysed in a rotating state that spans the whoe range of spinde speeds intended for the operation. An experimenta method for the prediction of stabe cutting regions was presented by Schmitz et a. [9] which took into account the dynamic change that a rotating spinde undergoes. The method is based on impuse hammer excitation and capacitive probe response measurement of a too rotating during different spinde speeds (see Fig 11C). Stabiity obes for a discrete number of spinde speeds are cacuated and the imit vaue corresponding to the actua spinde speed used during the measurement is picked out to form a spinde speed dependent stabiity obe chart. Experimenta tests found that there is a changing stabe imit of cut above 16 rpm. Sims et a. [3] demonstrated a method for too tip FRF prediction based on piezoeectric actuators and sensors mounted near the base of the too (see Fig 11D). The predicted FRF was compared with ordinary impuse hammer tap tests at the too tip. 4. Spinde measurements For this thesis, a contactess dynamic spinde testing (CDST) instrument for measuring the speed dependency was used. The CDST uses inductive response measurement and eectromagnetic excitation of the tip of a dummy too (Papers I and 17

28 IV) for spinde testing. The too tip FRF can be measured in the radia directions x and y without vioating safety reguations regarding human interaction with high speed rotating spindes. Fig 1. Setup of the CDST measurement performed on the high-speed-miing machine. The rotor excitation was caused by eectromagnets which were fed by a frequency step vice sine sweep coi current which generated a magnetic force that acted on the rotor. The rotor consisted of a speciay manufactured dummy too with a aminated rotor part designed to reduce the energy osses caused by eddy current effects. In each radia direction two eectromagnets (on opposite sides of the rotor) worked together in attracting the rotor to cause the excitation. Two types of miing machine spindes were tested using this measurement method. Fig 1 shows the measurement setup of the CDST measurement of the high speed spinde. During the measurement procedure the spinde was owered, thereby inserting the dummy too into the CDST measurement unit. 4.3 Low speed spinde testing In an initia study presented in Paper I a 3-axes Dynamite miing machine with a spinde speed capacity up to 7 rpm was measured (see Fig 13). 18

29 7 Ex W13, Magnitude W13 Magnitude Position Position response Response [µm/a] [µm/a] 56 Spinde speed [rpm] 4 8 Rotor unbaance Mode Mode 3 14 Mode Frequency Log(Hz) [Hz] Fig 13. Measured FRF s for different spinde speeds. Bright coours correspond to high magnitudes. Arrows point out detected structura modes and the rotor unbaance. In Fig 13 the infuence of the rotor unbaance can be seen in the upper eft corner of the figure. Three structura modes of the rotating spinde can be seen in the figure between and 6 Hz. These modes do not seem to posses any visibe speed dependency except for the step between and 35 rpm. This change coud be due to the different dynamic properties of non-rotating and rotating bearings. 4.4 High speed spinde testing In a more extensive study presented in Paper IV, a Liechti Turbomi ST1 stateof-the-art machining centre (capabe of mutipe movement up to 5-axes) equipped with a Fischer spinde (MFWS-35/4/8) capabe of speeds of up to 4 rpm was studied. The FRF measured in this study were recacuated from [m/a] to [m/f] and the measurements were preformed in the intervas,, 4,,4 rpm. The detected eigen-modes in the measurements showed a cear speed dependency especiay above 1 rpm (see Fig 13). 19

30 Hyy [og(m/n)] Mode Frequency [Hz] Mode 3 8 Mode Mode Spinde speed [rpm] Fig 14. Measured FRF s for different spinde speeds. Bright coours represent arger magnitudes. 4.5 Stabiity obes for different spinde speeds By using the speed dependent FRFs, stabiity obes coud be cacuated for each spinde speed. When appying the method presented by [9] the depth of cut of a certain spinde speed can be picked out. Fig 15 shows stabiity obe cacuations 3 based on different FRFs measured during different spinde speeds. The thick red curve represents the stabiity imit cacuated when based on the FRF measured at rpm. Back thin curves are based on FRFs measured during speeds in the intervas,, 4,,4 rpm. Green dots mark the speed dependent depth of cut for the speeds 1, 1, 14,,4 rpm which were picked out from each curve. For miing, based on rpm stabiity oad predictions, green dots ocated above the red curve indicate that the depth of cut coud be increased for that speed whie dots beow indicate that chatter vibrations wi occur at that speed. The exampe in Fig 15 iustrates the importance of investigating the speed dependency in FRFs when performing predictions of high-speed-miing machine stabiity. Correct predictions can mean avoidance of chatter vibrations or identification of speeds where the depth of cut can be increased. 3 The stabiity obes were cacuated by Sandvik Coromant using CutPro.

31 16 Stabiity obes 14 1 Depth of cut [mm] Spinde speed [rpm] Fig 15. Stabiity obes cacuated for different spinde speeds. The red curve is based on rpm FRF. Back curves are based on FRFs measured at the speed intervas of, 4, 6,,4. Green dots represent the speed dependent depth of cut picked out from stabiity obes based on FRFs measured at that specific speed. 1

32 5 MODELLING The speed dependency shown in the high speed spinde measurements wi ater the stabiity obe predictor criterion. Paper IV describes investigations into the spinde speed dependency described in the previous section through the use of numerica simuations. The simuation examined the infuence of the gyroscopic moment of the rotor and the centrifuga effects in the ba bearings on the eigen-frequencies of the spinde. In their anaysis of a miing machine spinde, Wang and Chang [31] presented a modeing method based on FEM. The mode did not incude rotation and therefore centrifuga forces and gyroscopic moments were not considered. In 1976 Neson and McVaugh [3] presented a FEM formuation of a rotor bearing system based on the Euer Bernoui beam theory where the effect of gyroscopic moments and centrifuga forces is incuded. Zorzi and Neson [33] ater added interna damping and in 198 Neson [34] presented another formuation based on the Timoshenko beam theory which factored in shear deformation effects. Xiong et a. [7] presented a way of combining this FEM representation and the miing cutting force mode formuated by Atintas [3]. The mode, which ony consisted of the rotor, predicted that the gyroscopic moment woud not affect the stabiity regions in miing but woud increase the rea part of the eigen-frequency and thus reduce the axia depth of cut. The mode aso predicted a change in spinde resonance frequencies of about ± 1 Hz. Chi-Wei Lin et a. [35] integrated a thermo-mechanica-mode into the Timoshenko FEM description. Numerica and practica experiments verified an increase in bearing stiffness with increasing bearing preoad. The work aso predicted a softening of the spinde shaft with increasing spinde speed. It was suggested that the softening of the bearing radia stiffness due to speed coud be compensated for by the thermay-induced preoad. Cao and Atintas [8] presented a genera method for the modeing of a spinde bearing system which incuded the axia coordinate pus a corresponding spinde speed and preoad dependent five degree of freedom bearing stiffness matrix. In the spinde mode a rotor reated centrifuga force was modeed by subtracting a Ω term 4 from the stiffness matrix. The numerica simuations presented in Paper IV were based on the FEM formuation described by Neson [34] and were extended by incuding a separate mass and stiffness radius together with a stiffness radius dependent shear deformation factor [36]. A second order homogenous differentia equation was used to describe the dynamica system; [ M ] q& + Ω[ G] q& + [ K ] q = {} (4) 4 Ω mutipied by a radia version of the transationa mass matrix.

33 where [ M ], [ G ], and [ K ] are the system matrixes of a shaft eement (see the Appendix in Paper IV). q is the generaized coordinates of the FEM assemby. The assembed second order homogenous differentia equation was transformed into a first order differentia equation, using the state vector notation described in [37]. The equation of motion coud then be rewritten as: Ω[ G] [ M ] [ ] [ ] {} [ K ] [ ] {} = {} h& + [] [ ] h M M, (5) where {} h {} { &} = q q (6) 5.1 Spinde mode In the simuation of the miing machine spinde a reduced mode without the machine foundation and spinde housing was used. The mode was based on the drawings shown in Appendix A. The mode consisted of the rotor and a pair of supporting ba bearings. +y +z +x Front bearing Motor Back bearing Dummy too Fig 16. Spinde mode incuding the rotor and the bearings. The rotor incuded the spinde shaft, motor package, inner bearing rings, too hoder and dummy too. The rotor was divided into FEM eements and speed dependent 3

34 bearing stiffness was added to nodes corresponding to the bearing positions. Fig 16 shows the rotor and the bearings modeed as springs. The figure is a simpified iustration of modeed bearing stiffness. Apart from the iustrated radia stiffness of the bearings, an anguar stiffness component and a cross couping term are incuded in the mode. 5. Preoad measurement To be abe to cacuate the bearing stiffness the preoad force of the bearings needs to be known. However, when deaing with a rea miing machine spinde the bearing preoad is normay not known to the operator and must be measured. On-ine measurements which give continuous information about the preoad status woud be preferabe. Studies of on-ine measurements and contro of the bearing oad have been described by Chen and Chen [38]. Most spindes now used for production work do not have and can not be retrofitted for on-ine measuring. The preoad must therefore be measured or be provided by the spinde designers. The spinde used in this study was designed to use spring-oaded bearings as shown in Fig 17. It consists of a rotor with two hybrid ange-contact bearings paced back to back. The preoad is measured by puing the spinde towards z whie the dispacement is measured using a dia indicator. The force needed to unoad the front bearing, hence the preoad, was estimated as 145N. Front bearing F Motor Preoad spring Housing Rotor Z+ Dia indicator Front bearing Back bearing Fig 17. Sketch of spinde showing the preoad measurement setup 5.3 Bearing stiffness cacuations Using the resut from the preoad measurement the bearing stiffness within the speed interva,, 4,, 4 rpm were cacuated. The bearing stiffness cacuations were performed by SKF with their in-house deveoped software Bearing Beacon. The bearing stiffness for different spinde speeds in reation to the stiffness at rpm are potted in Fig 18. The pot shows that the stiffness in the radia direction of the back bearing decreased to a eve of 6% of its origina ( rpm) vaue 4

35 when the speed increased to 4 rpm. The corresponding vaue for the front bearing was 38%. This bearing softening was caused by the centrifuga force which acted on the bas by dispacing them axiay and radiay. In doing this, an extra spring is added in series with the norma Hertzian contact spring. The shape of the stiffness variation of the bearings can be seen in the eigen-frequency variation of the bearing reated modes measured by the CDST (see Fig 14) Bearing stiffness 4 rpm (Preoad 145 N) Back bearing Fx/x Percentage of stiffness at rpm [%] Front bearing Spinde speed [rpm] x 1 4 Fig 18. Changes in bearing stiffness in the x direction with increasing spinde speed. 1% represents the bearing stiffness at rpm. 5.4 Simuations The eigen-frequencies of the modeed spinde can be seen in Fig 19. In Graph A the gyroscopic effect of the rotor can be seen; each mode spits up into a backward and a forward mode. Graph B, shows the same simuation with speed dependent bearing stiffness. The speed dependency in the bearing stiffness originates from the centrifuga force that acts on the bas in the bearing. In this case, the effect of the centrifuga force acting on the bas in the bearings had a more significant infuence on the eigen-frequencies than the gyroscopic moment. With the speed dependent bearing stiffness a reduction of the eigen-frequencies of the first and second modes of about 4% and 37% coud be detected. In comparison, the reduction was approximatey 1% when ony the gyroscopic effect was present. When incuding the speed dependent bearing stiffness, the same shape - as seen in the bearing stiffness variation (Fig 18) - coud be seen in the variation of the eigen-frequencies of bearing reated modes. 5

36 A Mode 4 Frequency [Hz] Mode Mode Mode Spinde speed [rpm] B Mode 4 Frequency [Hz] Mode Mode Mode 1 Intersection area Spinde speed [rpm] Fig 19. Simuated eigen-frequency for different spinde speeds. A: Infuence of the gyroscopic moment of the rotor. B: Infuence of both the gyroscopic moment of the rotor and the centrifuga effect in the bearings. 6

37 5.5 Mode shape and eigen-frequency identification The rigid body modes of the rotor are governed by the mass distribution and the bearing stiffness [39]. The rigid body mode governed by the front bearing has a node point at the back bearing position which causes a arger dispacement at the front bearing position. This mode wi form a conica shape and vice versa for the back bearing. The radia bearing stiffness mainy contributes to the rigid body modes whie the stiffness of the rotor shaft dictates the fexura modes. In reaity, the modes often appear as a mix of rigid body modes and fexura modes. The mode shape anaysis of the simuation reveaed that the first mode shape was governed by the back bearing and the second mode by the front bearing. The third mode was a pure fexura mode and the forth was a mix of a fexura mode and the front bearing. Due to the reduced bearing stiffness, the first and second mode shapes intersected (see Fig 19B) at approximatey 14 rpm. The simuated mode shapes were verified by an LDV ine scan of the visibe part of the rotor at rpm (see Fig ). Mode Simuation LDV LDV measured mode shapes Simuated mode shape Bearing position Fig. Mode shapes of the spinde at rpm. Simuations compared to LDV measurements. 7

38 6 DISCUSSION In this thesis a method for singe beam LDV measurements on rotating spindes has been presented together with a spinde anaysis method based on inductive dispacement measurement, eectromagnetic excitation and FEM. The LDV method removed the specke noise and the cross sensitivity in the measurements and the miss aignment and out-of-roundness components coud be extracted from the measurements signa. By appying this method, singe beam LDV measurements can be conducted on rotating spindes. The second method for spinde anaysis identified the bearing stiffness as the weakest ink in the spinde design regarding the speed dependent spinde dynamics. A simpified mode of the spinde system showed good agreement with the measurements. 6.1 LDV on rotating targets The deveoped singe beam LDV method for radia rotor vibration measurements requires that the measurement surface be poished. When using this method the measurement surface must be kept smooth and cean during the measurement procedure. When choosing materia for the dummy too, stainess stee is preferabe. This type of materia is non-corrosive and thus avoids surface probems which woud ead to inaccurate measurement. The aignment of the aser is aso a parameter that must be considered when using this method. The aignment was however, found to be an easy procedure. The biggest issue in aignment is that too arge a dispacement during the measurement coud refect the returning ight away from the path of the emitted ight. This effect was however, not detected in the measurements performed on the miing machines studied. 6. Modeing Excuded parts: The mode, used in Paper IV, is a reduced miing machine mode. The machine foundation, spinde housing and parts beonging to the pre-oad mechanism were not incuded. Consequenty the bearing support was modeed as a rigid support. Asymmetry in the spinde housing or in the mounting of the spinde was not incuded in the mode. Rotor unbaance was aso not incuded in the simuation. Couping: The couping between the hoder and the spinde shaft and the couping between the hoder and the too was not considered. The couping was simpy modeed as a rigid connection. This simpification resuted in a sighty stiffer spinde being simuated. Drawbar and springs: Inside the spinde shaft, mechanica components ike the drawbar and springs are mounted. These parts are used to pu the too and connect it to the spinde shaft. The content of the hoow spinde shaft coud not be determined 8

39 with a high degree of confidence and therefore the inner mass radius of the hoow spinde shaft was set to zero. The eigen-frequencies and gyroscopic moments coud be affected by an inaccurate mode of the mass distribution inside the spinde. Motor: The part of the integrated motor which is mounted on the spinde shaft was modeed as a mass without any stiffness properties. In reaity, it may be that the motor part adds some stiffness to the shaft; meaning that this assumption woud resut in a softer mode rotor. FEM description: A FEM formuation based on the Euer Bernoui beam theory presented by Neson and Mc Vaugh [3] was compared to the formuation based on the Timoshenko beam theory [34]. Eigen-vaues simuated by the use of the Timoshenko formuation are marked by circes and simuations made by the Euer Bernoui formuations are marked by asterisks in Fig 1. The absence of the shear deformation in the Euer Bernoui formuation means that a stiffer spinde with higher eigen-frequencies is depicted. The difference is greater when the frequency increases. Mode 1-6 showed a change in eigen-frequency at rpm of about 4%, 3%, 4%, 4%, 8% and 13%. It can be argued that the impact of the difference between the two beam theories coud be ignored and that the shear deformation is of itte importance. In this case, the difference for the 1 st and 6 th mode corresponded to 7 Hz and 419 Hz respectivey. The amount of difference is dependent on the actua geometry of the rotor and must be considered for each case. Damping, gravity and the centrifuga effects of the rotor described by [8] were not incuded in the mode. The axia oad during free run was considered negigibe and therefore excuded from the simuation. Shear deformation factor: The shear deformation factor incuded in the shear effect in the Timoshenko beam theory is normay determined experimentay and a typica vaue of this variabe is.9 for a soid circuar shaft. In the study presented in Paper IV an anaytica method [36] to achieve the shear deformation factor of a circuar hoow shaft was used. The use of the anaytica vaue resuted in ower eigenfrequencies of the modes (see Fig ). The difference between the two methods increased for higher frequencies but the infuence of the shear deformation factor was not as evident as the infuence of the actua shear deformation effect. Mode 1-6 shows a change in eigen-frequency at rpm of about 1%, 1%, 1%, 1%, % and 3%. For modes 1 and 6 the percentage corresponds to 8 Hz and 15 Hz respectivey. 9