Cutting stability investigation on a complicated free surface machining

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1 o Achievements in Materials and Manuacturing Engineering VOLUME 31 ISSUE 2 December 2008 Cutting stability investigation on a complicated ree surace machining S.Y. Lin*, R.W. Chang, C.T. Chung, C.K. Chan Institute o Mechanical and Electro-Mechanical Engineering, National Formosa University, 64, Wunhua Rd., Huwei, Yunlin 632, Taiwan * Corresponding author: sylin@nu.edu.tw Received ; published in revised orm ABSTRACT Purpose: Both the results obtained previously relating to structure dynamics o a simultaneous ive-axis movement machine tool and to the investigations on dynamic cutting behavior are urther applied as a oundation to study the eect o the process parameters on the cutting stability in the process o a complicated ree surace machining. Design/methodology/approach: In the paper cutting stability investigation on a complicated ee surace machining are described. Findings: The experimental data obtained rom the cases with and without a real cutting process ind that a test under a speciied rotational speed can generate its own charcteristic 3-direction requencies. The paper specially select the characteristic requency with the most signiicant change on response amplitude to analyze. Practical implications: The investigation procedures and the results obtained may be used as a reerence and guidance or the analysis o cutting stability in the ive-axis machining o a complicated surace in industrially practical use. Originality/value: The results shown on requency domain or identiying characteristic requencies can be interpreted on time domain to observe amplitude variation respect to time and urther understand its changing pattern under the cutting process. Keywords: Five-axis machining; Frequency response; Vibration modes; Cutting stability; Spectrum analysis 1. Introduction Industry has been constantly pursuing a desirable cutting perormance o high precision, ast productivity as well as less maintenance. Conventionally, a three-axis machine tool is widely used to achieve a machining process on a workpiece. However, as or complicated surace, its lack o ive-axis reedom, that is required to ensure a secured range o collision-ree distance between tools and workpieces, results in an undesirable perormance either on precision or on processed suraces. This is requently amended by adopting massive post processing. Sometimes, the resulting precision and eiciency can not ulill the requirement o industry. Thereore, a ive-axis rather than three-axis machine tool is now avorably used to seek or higher precision and aster productivity. Under this trend, the vibration problem associated with annoying noise in processing may become more serious especially on quality, precision, tool lie, machine usage, and cutting eiciency. Furthermore, the aggravating tool wear may result in cutting tool racture and machine tool itsel damage. Hence, analyzing the resulting vibration generated rom a machining process can extend the application o experimental know-how o dynamic cutting to this area, and may be beneicial to design o process parameters and planning o a cutting process. As stated above, it is now clear that the vibration phenomenon in cutting processes has large impact on surace roughness, smoothness, and dimension accuracy o workpiece, as well as tool lie and machine. The emitted high-requency noise can urther cause environmental pollution and also low production rate. Thus, vibration has been a major issue in studying the cutting processing o machine tool. However, it is still ar beyond ully Copyright by International OCSCO World Press. All rights reserved Research paper 531

2 Journal o Achievements in Materials and Manuacturing Engineering Volume 31 Issue 2 December 2008 understanding since its behavior and characteristics is too complicated to build up an accurate model or analyzing. In the cutting processes o machine tools, vibration can be classiied as our types based on source and type o exciting orce: 1. Forced vibration by impact caused by the impact between tools and workpieces due to the existing material nonuniormity, such as granules and porous apertures, o the cut workpiece as the cutting process starts. This can be gradually dissipated owing to damping o mechanical structure. 2. Forced vibration rom sources other than cutting processes generated by the periodical excitation rom the unbalanced rotation o the machine components. 3. Forced vibration rom cutting processes induced by cutting discontinuity and accumulation o chip. This type o vibration is closely related to cutting situation, but is not a major actor or chatter. Normally, it is originated rom the unbalance o the rotational components o machine tools or impact during perorming intermittent cutting using multi-tooth tools. 4. Sel-excited vibration initiated rom negative damping phenomenon o cutting system as energy keeps surging in due to increased processing load. It is also called chatter in the application o machine tools. Toh [1] elucidated and compared the employment o up milling and down milling using static and dynamic cutting orce and analysis o variance analysis in order to gain an in-depth understanding on its eects on tool lie results obtained via the parametric study o alternative cutter path strategies when high speed milling hardened steel. The study urther evaluated the three-dynamometer cutting orce components in order to identiy which component is the most sensitive to tool wear and cutting conditions applied. Static and dynamic cutting orce analysis suggested that the static normal orce is the most sensitive to tool wear and cutting conditions imposed. Chiou and Liang [2] presented an analytical model or acoustic emission dynamics in orthogonal cutting with chip thickness variation. An analytical expression or acoustic emission generated in turning was established as an explicit unction o the cutting parameters and tool/work piece geometry. Based on the theoretical static cutting acoustic emission model, the generation o the RMS acoustic emission was ormulated as the unction o three process parameters, namely tool displacement, cutting speed, and rake angle. The incremental change o the RMS acoustic emission is related to the chip ormation process in an elemental cutting area and it is characterized by the dynamic variation o these process parameters. Li and Li [3] presented a predictive time domain chatter model or the simulation and analysis o chatter in milling processes. The model was developed using a predictive milling orce model, which represents the action o milling cutter by the simultaneous operations o a number o single-point cutting tools and predicts the milling orces rom the undamental workpiece material properties, tool geometry and cutting conditions. The instantaneous undeormed chip thickness was modeled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration eect is taken into account. A proposed method [4] was based on the interrupted cutting o a specially designed workpiece that provides a strong broadband excitation. A method was proposed to identiy the nine terms o the dynamometer transer matrix rom only one cutting coniguration under normal machining operation. The determined transer matrix was used or dynamic cutting orce compensation under some milling operations. Chiou and Liang [5] presented an analysis o the chatter behavior or a slender cutting tool in turning in the presence o wear lat on the rank. The mechanism o a sel-excited vibration development process with tool wear eect was studied. The components contributing to the orcing unction in the turning vibration dynamics were analyzed in the context o cutting orce and contact orce. Stability plots were presented to relate width o cut to cutting velocity in the determination o chatter stability. The use o an active dynamic absorber to suppress machine tool chatter in a boring bar was studied [6].The vibrations o the system are reduced by moving an absorber mass using an active device such as an piezoelectric actuator, to generate an inertia orce that counteracts the disturbance acting on the main system. A cutting process model that considers the dynamic variation o shear and riction angles, that causes sel-excited chatter during the cutting process, was applied to the lumped mass model. The theory o regenerative chatter was also applied to the model. Stability boundaries have been calculated or maximum permissible width o cut as a unction o cutting speed. Shi et al. [7] developed a uniied nonlinear time series analysis approach to the problem o eature extraction o machine tool chatter. Considering the mechanism o chatter development, the procedure proposes the limit cycle behavior o sel-excited random vibration to be the intrinsic index o chatter occurrence, and provides the exponential autoregressive model to extract the index rom on-line measured machining signal. Kondo et al. [8] introduced a new criterion or detecting regenerative chatter by application o spectral analysis. It can be seen that the vibration amplitude perpendicular to a workpiece surace comes equal to the amplitude o surace undulation at the stability limit. Validity o this criterion was examined by using numerical simulations assumed to be orthogonal, and then experiments or veriication o criterion validity were carried out using the regenerative chatter o a turning workpiece in orthogonal cutting. Altintas and Budak [9] presented a new method or the analytical prediction o stability lobes in milling. The stability model requires transer unction o the structure at the cutterworkpiece contact zone, static cutting orce coeicients, radial immersion and the number o teeth on the cutter. Analytically predicted stability lobes were compared with the lobes generated by time domain and other numerical methods available in the literature. Smith and Tlusty [10] described the theoretical basis behind a system or the elimination o chatter in milling through the automatic regulation o the spindle speed. This technique is most eective in milling operations where the tooth passing requency can approach the natural requency o the mode responsible Experimental data were quoted to illustrate typical improvements in metal removal rate. Schmitz [11] applied receptance coupling substructure analysis to the prediction o the tool point dynamic response, combining requency response measurements o individual components through appropriate connections to determine assembly dynamics using simple vector manipulations. 532 Research paper S.Y. Lin, R.W. Chang, C.T. Chung, C.K. Chan

3 Altintas and Engin [12] presented a generalized modeling o arbitrary end mills or inserted cutter geometry. The cutting edge along the helical lute or along the arbitrary inserts were modeled mathematically. The chip load at each point along the cutting edge is identiied by combining the rigid body kinematics o milling and structural dynamic deormations o cutter body and workpiece. The proposed approach allows the design and analysis o a variety o milling operations used in industry. Su et al. [13] introduced a new approach or predicting chatter in high-speed end milling by using a uzzy neural network. A milling experimental setup was built and a set o the valuable experimental data was acquired under dierent tool wear states and careully selected cutting parameters. Then, the experimental system was simpliied into a uzzy neural network model which is trained in the experimental date. Some simulation results were thus obtained on the basis o the trained model. Finally, the calculated results were compared with the experimental ones in order to check the eectiveness o the method described. Dynamic cutting processes and dynamic characteristics o the structure o machine tool determine cutting stability during cutting. The interrelation between the inluential actors and ive-axis cutting stability is shown in Fig.1, where the line with arrows at both ends indicates that the corresponding actor has interaction with the latter. These include structure deormation, dynamic cutting orce, and tool wear. The igure also shows that geometric characteristics o curve, material o workpiece, cutting condition, and ive-axis cutting strategy are all the inluential actors as well. The actors mentioned above all possess deterministic inluence on generating chatter and noise during cutting and thereby degrading surace roughness o the workpiece or producing various undesirable orms o chip. They can be compared and sorted out the most signiicant actor or urther analyzing and investigation. 2. Related theory theory 2.1. Types o o chatter chatter Basically, sel-excited chatter can be classiied as three types: 1. Regenerative chatter: It is due to wave on wave during successive cutting. As indicated in Fig. 2, i some hard spots existing in a workpiece or random luctuation occurring during cutting result in relative motion between the tool and workpiece, wave-like ripples remain on the surace o the workpiece ater cutting and subsequently change the amount o thickness to be cut. This will then generate dynamic cutting orce which drives the tool and workpiece to vibrate and again undesirably aect thickness o undeorm chip. Fig. 2. Chatter with Regenerative Eect 2. Mode coupling chatter: Since practical cutting system possesses more than one degree o reedom (DOF), there exists coupling phenomenon on motion characteristics in each direction. This type o chatter is ound in a cutting system with more than two degrees o reedom. A simple example is shown in Fig. 3. This system composes o two springs with dierent stiness connected to a mass. The direction X 1 and X 2 are mutually normal, and the stiness in direction X 1 is greater than that in direction X 2 (K 2 >K 1 ). Fig. 3. Chatter with Coupling Mode o 2 DOF Fig. 1. Interaction between ive-axis cutting stability and the corresponding inluential stability 3. Chatter due to alling characteristic o cutting orce: In cutting processes or most workpiceses, cutting orce will get higher as cutting speed gets lower. As shown in Fig. 4, when the tool moves toward right direction during vibration, the eective cutting speed relative to the workpiece decreases by an amount o, and vice versa. Thereore, the vibration toward right and let direction results in decrease and increase o Cutting stability investigation on a complicated ree surace machining 533

4 Journal o Achievements in Materials and Manuacturing Engineering cutting orce, respectively. This characteristic that variation o the cutting orce is dominated by vibration is a major cause or dynamic instability. Volume 31 Issue 2 December 2008 c. Sampled Function G( ) g (t )e n j 2St n n (5) g ( tn ) Fig. 4. Chatter due to Falling Characteristic o Cutting Force 1 s G ( )e j 2St n d ³ s 0 (6) Being periodic in requency domain and discrete in time domain d. Discrete Fourier Transorm 2.2. Fourier series transorm 2.2. Fourier series transorm Basically, there are our dierent orms or Fourier series transorm and are presented by ormula and graphical illustrations as ollows: G( k ) a. g ( tn ) 1 N N 1 Integral Transorm N 1 g ( tn ) e j 2Snk N (7) n 0 G ( k )e j 2Snk N (8) k 0 G( ) ³ g (t )e j 2St d (t ) (1) g (t ) ³ G ( )e j 2St d (2) Both o them being discrete and periodic in both requency and time domain 3. Experiment set-up and 3. Experiment executionset-up and execution Both o them being continuous in requency and time domains b. Fourier Series T G( k ) 1 g (t )e j 2S k t dt T ³0 g (t ) G( k k )e j 2S k t (3) (4) Being discrete in requency domain and periodic in time domain 534 Research paper The accelerometer with piezoelectric charge type was utilized in this experiment and it is connected to an accelerometer coupler to ampliy the acquired signal. Next, the sampled signal was processed via spectrum analyzer displaying some relevant unction transormation to investigate the properties and characteristics o the dynamic cutting behavior during a ree surace cutting. PowerMILL CAM sotware was utilized or ive-axis machining o a ree surace, which has a simultaneous 3~5 axes movement control unction in its commercial modulus. Dierent machining strategies based on a complicated geometrical theory may be lexibly selected and combined together on its user interace via graphical icon, user may learn and be amiliar with its operation easily during a short period. The main unction dierence between three-axis and ive-axis in it is only the setting o cutting tool orientation and projection direction. PowerMILL with multi-axis unction may ully be applied on ixed direction machining, multi-axis mill and simultaneous ive-axis continuous movement machining. The collision between workpiece and jig during the spindle head moving or change tool orientation may also be avoided deinitely. S.Y. Lin, R.W. Chang, C.T. Chung, C.K. Chan

5 The geometrical proile o a ree surace machining in experiment is shown in Fig. 5. This multiple ree surace may be machined successully through a simultaneous ive-axis movement machining strategy having a 5 degree-o-reedom path motion driven by the servomotor. It is based on a projection machining manner and this machining strategy or a prescribed amount o the tool-workpiece contact angle and the overhang length o the cutting tool maintenance may be ensured during a multiple ree surace machining process. The cutting tool path is automatically generated as shown in Fig. 5 or a ree surace machining based on this machining strategy, the moving orientation o the cutting tool pass and the square boundary o the ree surace may keep a 45 o inclination angle. parameters, 9 cutting condition sets can be constituted. To detect the acceleration along the three mutually perpendicular axes, xyz, at the most sensitive location and result data o 27 sets through the simultaneous ive-axis movement cutting experiment is thus obtained. Fig. 8 shows the low chart pertaining to execution procedures or a ive-axis cutting stability experiment. Ater undertook the analysis and comparison o the data sampled rom the experiment, the inluence o the variations o cutting parameter on the cutting stability perormance can thus be ascertained. Fig.5.Geometrical proile o a ree surace and its cutting tool path planning Figs. 6 and 7 show a schematic diagram or the measurement apparatus set-up, the accelerometer was adhered to the location where is most sensitive to cutting vibration during machining process. CNC-rotary-table is the weaker zone o this machine tool and that has detected rom the results o the modal analysis perormed previously. The cylindrical bar workpiece is mounted on the chuck along the c-axis, the cutting orce interacted between workpiece and tool has a large part concentrated around this area. Hence, the accelerometer was adhered at the back surace o the b-axis rotary element o the CNC-rotary-table, where is the most sensitive site to sensor the possible indirect vibration induced during a ree surace machining. Since the accelerometer is not able to adhere to cutting tool and work piece to detect the cutting vibration signal directly. This acquisition manner is adopted to detect the indirect vibration signal suitably. In this study, accelerometer is adhered to the location where is the intersection point between the bottom surace swing about the b-axis and the extension line o the c rotational axis as described in Fig. 7 in detail. This adhesion action accounted or the cutting behavior o the CNC-rotary-table with acting orce transmission natures. The selection o adhered site is not only or the vibration state o the swing action during the ree surace machining but also or that signal direct detection. Pure aluminum cylindrical bar and high-speed steel were used as workpiece and end mill, respectively in experiment. The diameter o end mill is 6 mm with three cutting edges. The depth o cut and rotational speed were selected as machining parameters, combinations o depth o cut and rotational speed o the cutter as the cutting parameter actors. Reer to workpiece properties, each three levels o cutting parameter were set as 0.1, 0.2, 0.3 mm or depth o cut and set as 4000, 5500, 7000 rpm or cutter rotational speed. Cutting path is automatically generated through CAM sotware based on the geometrical proile o the machined surace. Through the combinations o machining Fig. 6. Schematic illustration o a dual-axis CNC-rotary-table coniguration and the indication on that table or accelerometer adhesion in experiment Fig. 7. Schematic diagram or the adhesion location o an accelerometer or vibration detection (detailed indication) 4. Result and and discussion discussion The vibrational behavior o the CNC-rotary-table with various combinations o process parameters can be investigated in both requency and time domain through the spectrum analyses o the measured data. This can be indirectly utlilized to determine the relative cutting stabilities among these experimental cases. The spectrum analysis indicates that, as operated under no cutting action at a rotational speed o 4000, 5500, and 7000 rpm, considerable spikes o response amplitude can be detected at the three-direction requency o 60 Hz and 536 Hz, where the ormer is the natural requency o the table and the latter is that o the Cutting stability investigation on a complicated ree surace machining 535

6 Journal o Achievements in Materials and Manuacturing Engineering Volume 31 Issue 2 December 2008 CNC-rotary-table. Based on these data, the researchers can urther examine whether various combinations o the process parameters can stimulate larger response respect to the requency o 536 Hz o the CNC-rotary-table or the other requencies. a larger cutting orce to eectively remove chip. However, during the cutting process with ive axes moving simultaneously and the position o each axis changing constantly, the corresponding dynamic cutting orce may reveal an unstable phenomenon. A larger cutting orce can easily result in a more unstable state, and thus induce a larger vibration amplitude. In the region o high-requency spectrum, the signal pattern o vibration due to various depths o cut changes with dierent rotational speeds. It can be explained that racture on the cutting surace causes some chips rubbing each other in the cutting region. In the case o 4000 rpm rotational speed, relative low riction generated by low vibration energy is not suicient to excite response o the corresponding characteristic requency. As or 5500 rpm, increased orces accompanied by increased depth o cut enhance the amplitude response in high-requency region so that amplitude spikes can be observed in the case o depth o cut o 0.2 mm at 1.9 khz and 2.3 khz. Finally, in the case o 7000 rpm, the highest one compared with the other two, the correponding amplitude reponse is the most signiicant. However, variation on depth o cut does not notably change the values o characteristic requency. Fig. 8. Flow chart or a ive-axis cutting stability experiment The experimental data obtained rom the cases with and without a real cutting process ind that a test under a speciied rotational speed can generate its own characteristic 3-direction requencies. The paper specially select the characteristic requency with the most signiicant change on response amplitude to analyze. The chosen requencies corresponding to the rotational speed o 4000, 5500, and 7000 rpm are 132, 184, and 116 Hz, respectively. The results shown on requency domain or identiying characteristic requencies can be interpreted on time domain to observe amplitude variation respect to time and urther understand its changing pattern under the cutting process Spectrum analysis or the 4.1. Spectrum eect o analysis depth or o cut the eect on cutting o depth o cut stability on cutting stability The content shown in Fig. 9 is a typical vibration spectrum along x direction in requency domain under the cutting depth o 0.1 mm, 0.2 mm, and 0.3 mm at the rotational speed o 4000 rpm. The other vibration spectrums along y and z directions at the other rotational speeds o 5500 and 7000 rpm all have the same distribution pattern as shown in this igure. The trend o amplitude distribution agrees with the common vibration modes o a machine tool. It is clear that all the characteristic requencies lie within lower requency region (below 600 Hz). The vibrational energy in this region is relative higher than that in higher requency region. Comparison among in each igure (a), (b), and (c) conditions under a speciic rotational speed implies that a larger depth o cut causes a larger energy level o vibration. This is because depth o cut is one o the major actor in cutting processes. Increasing depth o cut can enlarge the contact area between tool and surace o workpiece. The tool must withstand Fig. 9. Frequency spectrum along x-direction or dierent depths o cut at 4000rpm rotational speed 4.2. Exhibition o time-domain signal 4.2. at Exhibition speciic o requency time-domain during signal at speciic cutting requency process during cutting process This section ocuses on the continuous time-varying pattern o the requency signal with maximum response at each rotational speed. Fig. 10 reveals the relationship between vibration amplitude o acceleration and elapse time corresponding to various depth o cut at a speciic rotational speed. Fig. 10. Relationship between vibration amplitude o acceleration and elapse time corresponding to The dynamic-behavior measured at time domain along x-direction under the rotational speed o 4000 rpm at three consecutive cutting stages 536 Research paper S.Y. Lin, R.W. Chang, C.T. Chung, C.K. Chan

7 4.3. Analysis relation between 4.3. Analysis o o relation between depth o cut and cutting and depth cuttingo cut stability along stability dierent along dierent directions directions Figs 11, 12, and 13 show the trends o vibration amplitude o acceleration and elapse time along each x, y, z direction or dierent depths o cut at the rotational speed o 4000, 5500, and 7000 rpm, respectively. Each igure contains nine subplots arranged in three columns which correspond to the three cutting stages o engagement, duration, and exit, respectively. It can be observed that the vibration levels or the case with depth o cut o 0.1 mm are the smallest among all, a larger depth o cut indicates a larger vibration level due to increased cutting orce. However, even though the dierence o amplitude between the conditions o depth o cut o 0.2 mm and 0.3 mm is not so obvious, we can still ind that the amplitude with the cases o 0.2 mm is generally smaller than those o 0.3 mm. Now, we continue to compare the results among the three cutting stages. In the stage o engagement, since the tool has not contacted with the workpiece yet, the vibration level along z direction is considerably large compared with that along x and y directions. As the tool initially engages the workpiece, the CNC-rotary-table mounted on the table starts to move, and then enhances the vibration amplitude along x and y directions. It should be also noted that the y direction coincides with that o center line o b axis. Hence, swinging the rotary-table back and orth about b axis does not stimulate vibration response along y direction. Then, it can be detected that the vibration level along x direction is comparably larger than that o y direction. When the cutting process is gradually stabilized, the varying trends o amplitude are all similar, as shown in the subplot (x2), (y2), and (z2) o Figs 11, 12, and 13. Moreover, the swinging movement about b axis generates a constantlyswinging coordinate o x and z on the diving plate relative to a stationary coordinate o x and z on the table. This results in correlation between the vibration amplitude along x direction and z directions. That is to say, a larger vibration amplitude along x direction is accompanied with a smaller one along z direction and vice versa. Additionally, the vibration amplitude along y direction also increases due to a rotational eect along c axis. As the process enters the inal stage o exit, the accelerometers along all ive axes start to return to their original reerence points, and the resulting displacements make the measured vibration levels along each direction naturally increased, as revealed in the corresponding subplots (x3), (y3), and (z3) o Figs 11, 12, and 13. The magnitude o vibration amplitude depends on the position swung about b axis and phase angle rotated relative to c axis during the transient state beore entering the stage o exit. Hence, a larger displacement relative to these two axes or returning their original points induces a larger measured vibration amplitude. Fig. 11. Relationship between vibration amplitude o acceleration and elapse time along each x, y, z directions or dierent depths o cut and 4000rpm rotational speed at three consecutive cutting stages. (Note: let to right graphs represent cutting at dierent stages: initial engagement, duration and exit moment) Fig. 12. Relationship between vibration amplitude o acceleration and elapse time along each x, y, z directions or dierent depths o cut and 5500 rpm rotational speed at three consecutive cutting stages Cutting stability investigation on a complicated ree surace machining 537

8 Journal o Achievements in Materials and Manuacturing Engineering Volume 31 Issue 2 December 2008 A larger depth o cut can generate a larger vibration level. However, varying the cutting orce does not signiicantly change the characteristic requencies. 2. Rotational speed o the spindle is the major actors or the response o the characteristic requencies. Dierent patterns o vibration signal can be observed or dierent rotational speeds and depths o cut. Due to the riction eect in the cutting zone, the vibration response in the spectrum region o high requency is moderate or lower rotational speed. As rotational speed increases, the global amplitude increases and the amplitude response in high-requency region enhances. 3. The actions o both the displacing axis and swinging axis have considerable impacts on cutting stability. Both the swinging motion about b axis and rotation about c axis can aect the corresponding vibration amplitudes. A larger movement o these two axes is ollowed by a larger measured vibration amplitude. 4. Since a variable ree-curve cutting path rather than a lat one is selected to process, the eed rate o cut can not keep as a constant and should be determined by considering the swinging angle o the tool and the calculated contact area between the tool and workpiece. Thereore, under a cutting condition or simultaneous movement o ive-axis, the eed rate o cut keeps changing with time and thereby causes a variation o characteristic requencies. Fig. 13. Relationship between vibration amplitude o acceleration and elapse time along each x, y, z directions or dierent depths o cut and 7000rpm rotational speed at three consecutive cutting stages 5. Conclusions In order to analyze the cutting stability in the ive-axis ree surace machining, a multi-dimensional ree geometric curve is specially designed and a CAM sotware or path planning o a tool is adopted to organize a processing program or simultaneous ive-axis movement. Depth o cut associated with rotational speed o tool is selected as the actor o process parameters. Considering the characteristics o the selected material o the workpiece and machine tool, Based on a ullactor experimental design with three selected values o depth o cut and rotational speed as inputs, totally nine processing paths o simultaneous ive-axis movement are deliberately planned. An accelerometer on bottom surace o b-axis o the dividing plate is utilized to monitor and acquire the vibration signal in the cutting processes o the engagement, duration, and exit stages. Through the spectrum analysis or each case, the maximum amplitude o requency response along three axes can be obtained so as to investigate and compare the relative cutting stabilities. Thereby, the ollowing conclusions can be drawn: 1. The vibration levels o the depth o cut o 0.1 mm are the smallest among all cases, no matter what direction is selected to measure. A larger depth o cut indicates a larger vibration level due to increased cutting orce. However, even though the dierence o amplitude between the conditions o depth o cut o 0.2 mm and 0.3 mm is not so distinguishable, we can still ind that the amplitude with the cases o 0.2 mm is generally smaller than those o 0.3 mm. Acknowledgements Acknowledgments The authors would like to extend their thanks to the National Science Council (Grant No. NSC E ) and National Center or High-Perormance Computing in Taiwan. Reerences [1] C.K. Toh, Static and Dynamic Cutting Force Analysis When High Speed Rough Milling Hardened Steel, Materials and Design 25 (2004) [2] R.Y. Chiou, S.Y. Liang, Dynamic Modeling o Cutting Acoustic Emission Via Piezo-electric Actuator Wave Control, International Journal o Machine Tools and Manuacture 40 (2000) [3] H. Li, X. Li, Modelling and Simulation o Chatter in Milling Using a Predictive Force Model, International Journal o Machine Tools Manuacture 40 (2000) [4] N. Tounsi, A. Otho, Dynamic Cutting Force Measuring, International Journal o Machine Tools and Manuacture 40 (2000) [5] R. Chiou, S.Y. Liang, Chatter Stability o A Slender Cutting Tool in Turning with Tool Wear Eect, International Journal o Machine Tools and Manuacture 38 (1998) [6] S.G. Tewani, K.E. Rouch, B.L. Walcott, A Study o Cutting Process Stability o A Boring Bar with Active Dynamic Absorber, International Journal o Machine Tools and Manuacture 35 (1995) [7] Z. Shi, Y. Tamura, T. Ozaki, A Study on Real-time Detecting o Machine Tool Chatter, International Journal o the Japan Society or Precision Engineering 32/3 (1998) Research paper S.Y. Lin, R.W. Chang, C.T. Chung, C.K. Chan

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