Measurement method for the identification of individual teeth in milling operations

CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

Contents lists available at SciVerse ScienceDirect

CIRP Journal of Manufacturing Science and Technology journal homepage: www.elsevier.com/locate/cirpj

Measurement method for the identification of individual teeth in milling operations§ J. Repo a,*, L. Pejryd a,b,c, T. Beno a,c a

Department of Engineering Science, University West, 461 86 Trollha¨ttan, Sweden Production Technology Centre, Innovatum AB, 461 29 Trollha¨ttan, Sweden c Volvo Aero Corporation, 461 81 Trollha¨ttan, Sweden b

A R T I C L E I N F O

A B S T R A C T

Article history: Available online 4 January 2012

Internal sensors already available in the machine tools may prove to be an interesting approach to monitor the machining process. Accurate determination of the position of the individual tooth on a milling cutter is important to be able to correlate the measured responses from the machine tool position encoders to the tooth or teeth that may be the cause of the response. The aim of the work presented in this paper is to develop a measurement method to identify the individual tooth on a milling cutter by their angular position relative to a specified 08-direction. If the lower and upper bounds of the cutting zone are known, together with the actual spindle position and the starting time of the cut, it will be possible to track and identify which teeth are within the cutting zone at a given time in the following off-line analysis of the responses. This may simplify the task of finding potential correlations between the state of individual teeth on the milling cutter with measured responses from various sensors during the milling process. The proposed method is based on a reflectance detector and uses accurate position information provided by the position encoders. A validation of the measurement method is also presented which shows that the error of the estimated angular position is approximately 0.158 for the validation setup used in this case. ß 2011 CIRP.

Keywords: Angular position measurement Milling tool Encoder signals Reflectance detector

1. Introduction Increasing commercial pressure stresses the need for machining process improvements. Some of the current activities to meet these needs are increased robustness and automation of the processes. A current focus of an on-going research project is to use internal sensors already available on machine tools as means of monitoring the robustness of machining processes. The results achieved so far indicate that operational frequencies, such as cutter and tooth passing frequencies, exist in the measured encoder signals [1]. The hypothesis that follows is that the process dynamics and the underlying phenomena, such as tool wear, give rise to the signal variations and can be further investigated by analyzing the response from the position encoders. A series of measurements obtained from a milling process have been used to detect various states of an individual cutting insert on the milling tool. Different cases are considered, i.e. worn, broken

§ This work has been supported by the Swedish Governmental Agency for Innovation Systems (VINNOVA). * Corresponding author. Tel.: þ46 520 223349. E-mail addresses: [email protected] (J. Repo), [email protected] (L. Pejryd), [email protected] (T. Beno).

1755-5817/$ – see front matter ß 2011 CIRP. doi:10.1016/j.cirpj.2011.11.002

and missing tooth. The preliminary results show that the position encoders give a characteristic response for the different cases studied. However, to carry out the remaining analysis of the encoder responses, the position of the individual cutting inserts must be determined. Detection of tool breakage by analysis of the output from the rotary encoder has been shown by Girardin et al. [2]. However, they did not detect which of the individual that was the cause of the response. Andersson et al. [3] measured the cutting forces acting on each individual tooth on a face mill using a special milling force sensor [4] based on strain gages in order to study cutting force variations. Mechanical measurement devices, such as the digital protractor [5], may give angular readings in steps of 1 arc minute, i.e. approximately 0.0178, but such devices are not practical in this situation. A proximity sensor mounted on the spindle head was used by Abele et al. [6] for in-process detection of the position of a single cutting tooth. The peak in the sensor output, which occurs once per spindle revolution, was aligned with the cutting edge. The peak was aligned with the angular measurement system of the spindle to obtain high accuracy angular values for the cutting edge. No other adequate measurement method to determine the angular positions of cutting teeth on a milling tool relative to a specified 08direction has been found in the literature.

J. Repo et al. / CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

27

This paper presents a systematic approach to carry out the angular position measurement and is organized as follows: In Section 2 the measurement method to determine the angular positions of the teeth on a milling tool is presented. A validation of the measurement method is carried out in Section 3. A practical application on using the extracted position information to track and identify a worn tooth on a milling cutter is presented in Section 4.

even for moderate spindle speeds. Various methods have been devised to estimate the spindle position w(t) from measured encoder signals, e.g. the direct arc tangent method, Hilbert transform (HT) used in, e.g. [2], Phase Locked Loop (PLL) method used in, e.g. [7]. In this work, the arc tangent method is used. Under the assumption that no machining is taking place, the two output signals from the rotary encoder are given as

2. Method for measurement of tooth position

(

Encoders are used internally by the machine tool for closed-loop control of the motion axes. In general, high-precision CNC machine tools are equipped with Sin/Cos encoders for both linear and angular motion axes. The output is continuous sinusoidal signals which allow interpolation to achieve the desired positioning accuracy. The differential output signals, A and B, which are 908 out of phase, are used internally by the machine tool drive modules to determine the position and the direction of motion. In the positive motion direction, A is ahead of B and vice versa when moving in the negative direction. The rotary encoder on the main spindle also outputs a differential reference mark signal R which contains a Gaussian-like pulse to indicate a full spindle revolution, see Fig. 1. The differentially measured signals are denoted uA(t), uB(t) and uR(t). The 5-axis machine tool used in this work (DECKEL MAHO DMU 160 FD) is equipped with linear encoders (HEIDENHAIN LC 481) for the X, Y, Z feed axes and a rotary encoder (WOELKE WG 05) for the main spindle S1. 2.1. Estimation of the initial spindle position

1. 2. 3. 4.

Rotate the spindle to zero position (NC code: SPOS=0). Start sampling. Start running the spindle. Stop the spindle (after that steady state speed has been reached). Step 5. Off-line signal analysis.

The carrier frequency fc in the measured signals is directly proportional to the actual spindle speed n and given as fc ¼

n MR 60

(1)

½Hz

uA , uB , uR [V]

where MR = 256 is the resolution of the rotary encoder (in cycles/ period). Note that the carrier frequency becomes relatively high

uA uB uR

1 0.5 0 −0.5 1.04

1.045

1.05

1.055

1.06

(2)

where A is the amplitude and f0 is the initial phase. Since uA(t) and uB(t) are orthogonal, the analytic signal z(t) is given directly by the generalized Euler’s formula which relates the complex exponential function with the trigonometric functions as e jfðtÞ ¼ cos fðtÞ þ j sin fðtÞ

(3)

The rotary encoder signals may therefore be expressed as the phasor (or phase vector) as zðtÞ ¼ uB ðtÞ þ juA ðtÞ ¼ jzje jð2p f c tþf0 Þ The instantaneous phase is defined as   u ðtÞ fðtÞ ¼ argzðtÞ ¼ tan1 A uB ðtÞ

(4)

(5)

The spindle position signal is given by scaling of the phase function as

When the spindle is rotating at a steady state speed, the spindle position is naturally periodic with a period of 2p radians. The output signals uA(t) and uB(t) from the rotary encoder are nearsinusoidal with 256 cycles per spindle revolution. The measurement procedure utilises the output signals from the rotary encoder and can be summarized in the following steps: Step Step Step Step

uA ðtÞ ¼ A sinð2p f c t þ f0 Þ uB ðtÞ ¼ A cosð2p f c t þ f0 Þ

1.065

1.07

1.075

t [s] Fig. 1. Output signals from the rotary encoder. Differentially measured quadrature signals uA(t), uB(t) and reference mark signal uR(t).

’ðtÞ ¼ ’0 þ

1 fðtÞ; MR

’0 ¼ 0

(6)

where w0 is the initial spindle position. The estimated position signal w(t) using the arc tangent method, corresponds to the incremental position change from an unknown initial spindle position w0. To ensure that w0 = 0, the spindle is first rotated to its zero position1 before the sampling is started. By doing so, an interesting relation between the pulses in the uR(t) signal and the spindle’s internal zero direction can be found. The choice of spindle speed is arbitrary. Here, a low spindle speed 60 rpm is used, which gives a carrier frequency fc = 256 Hz in the uA(t) and uB(t) signals. To avoid signal distortion, uA(t), uB(t) and uR(t) were sampled at 20 kHz using a 16-bit voltage input module.2 By keeping the spindle at steady state rotation at 60 rpm, a Gaussian-like pulse will appear in the uR(t) signal per second rotation. The analysis of the differentially measured output signals from the rotary encoder involves detection of the Gaussian-like pulses in the reference mark signal uR(t) and numerical calculation of the spindle position w(t) based on the quadrature signals uA(t) and uB(t). The pulses in uR(t) are detected by using a numerical peak detection algorithm. A threshold value is used to select valid peaks. The peak detection algorithm also evaluates the time separation between the pulses to eliminate all spurious pulses which may have passed the initial thresholding due to small amount of noise. Additional interpolation is involved to obtain pulse detection at subsample level. The center of the Gaussian pulse is taken as the pulse location. Fig. 2 shows the estimated spindle position signal for subsequent spindle revolutions. The spindle’s reference angle wR is defined as the angular value w(t) at the time of the detected pulses. The approach taken so far assumes that the initial spindle position is zero (SPOS=0). Sampling of the spindle position signal w(t) once per spindle revolution using the time indices of the 1 2

NC code: SPOS=0. NI 9215 4-Channel, 100 kS/s/ch, 16-bit, 10 V Analog Input Module.

J. Repo et al. / CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

28

ϕ(t) [rad]

2π

Workpiece ω

π

y

0º x

0 1

1.5

2

2.5

3

3.5

4

4.5

Feed

t [s] Fig. 2. Spindle position signal w(t) obtained from the encoder signals uA(t) and uB(t). The vertical lines indicate the times of the detected pulses in the reference mark signal uR(t).

Fig. 3. Geometry of the slot-milling process.

’1’ pulses, see Fig. 2, gives the spindle’s reference angle wR. This angle is directly related to the initial spindle position w0 as K ’ ¼ ’0 þ ’R

(7)

ω y

RD

0º u

The angular value wR, when w0 = 0, can therefore be regarded as a machine-specific constant Kw, allowing w0 to be estimated directly from the measured encoder signals. This is particularly useful when the initial spindle position is not known in advance. Note that the pulse in uR(t) repeats itself during the spindle rotation. Estimation of w0 therefore only requires detection of the first pulse in uR(t). This also explains why the sampling must be initiated before running the spindle to find its initial position. 2.2. Determination of the angular position of a cutting tooth To determine the angular position of a cutting tooth, a 08direction must first be defined. The teeth on the milling tool with nz teeth are indexed as 1, 2, . . ., nz. An arbitrary tooth on the milling tool is marked as tooth 1. The spindle will rotate the tool in the positive rotation direction. The teeth which follow are numbered 2, 3, . . ., nz in the negative rotation direction. Given that the angular gap between the teeth are known, it is sufficient to know the angular position of the first tooth to determine the angular positions of the remaining nz  1 teeth. Assumed that a milling operation is performed on the XY-plane and the workpiece is fed towards the rotating milling tool in the negative direction along the Y-axis, see Fig. 3. The aim is to relate the angular positions of the individual teeth to the specified 08direction, which may be an arbitrary direction on the XY-plane. Here, the 08-direction is set in the positive direction along the controlled feed axis (Y). The measurement method relies on the angular position information from the rotary encoder and the position information from the linear encoders. An additional reflectance detector3 (RD) is used to relate tooth 1 to the angular position information from the rotary encoder. The use of an optical instrument to obtain a synchronization signal was reported in, e.g. [8]. In this work however, the RD is used to define a reference direction as shown in Fig. 4. A thin strip of a reflective tape, which is properly aligned with the leading edge of tooth 1, is attached either to the tool shaft holder or the tool shaft as shown in Fig. 7. When the milling tool is rotated in front of the RD and crosses the mid section of the detector surface, the RD will output a pulse train (square wave form), under the assumption that sufficient amount of the ambient light is reflected back to the detector. By simultaneously measuring the output voltage (TTL-level) from the RD and the output signals from the rotary encoder, the position of tooth 1 can be related to the actual spindle position. The steps 3

OMRON EE-SY413, Light ON model, MAX. sensing distance 10 mm.

x

r

Fig. 4. Reflectance detector (RD) aligned with the specified 08-direction.

involved in the tooth position measurement are identical to the five-step procedure given in Section 2.1, but the intention now is to relate the RD pulse train to the spindle position. When combining the RD pulse train, encoder reference mark signal and the spindle position signal, information about the angular position of tooth 1 relative to the specified 08-direction is obtained. The first crossing between the RD pulse train and the spindle position signal gives wRD, which is the angle that the tool is rotated before tooth 1 passes the detector. The negative value of this angle is therefore the relative initial position of tooth 1 with respect to the 08-direction defined by the orientation of the RD, see Fig. 4. Thus, to obtain the position of tooth 1, the initial spindle position must also be taken into account.

’1 ¼ ’0  ’RD

(8)

The angular positions of the remaining teeth are obtained by considering the angular spacing between the teeth. In general, the angular position of tooth j on a milling cutter with nz teeth is

’ j ¼ ’1  ð j  1Þf p ;

j ¼ 1; 2; . . . ; nz

(9)

where fp denotes the cutter pitch angle [9], given here as 3608/nz. 2.3. Alignment of the reflectance detector with the spindle reference direction In general, alignment of the RD properly with the desired 08direction as illustrated in Fig. 4, is very difficult and gives no control of the accuracy in the estimated tooth position. A better alternative is to align the RD with the fixed reference direction of the spindle. This can be achieved by aligning the falling edge in the RD pulse train with the detected pulse in the reference mark signal uR(t) from the rotary encoder. The pulse alignment can be accomplished by on-line positioning and orientation of the RD until the falling edge in the RD pulse train almost coincides with the pulse in the uR(t) signal as illustrated in Fig. 5. The measurement resolution MRw, defined as the minimum detectable change in the measured quantity [10], corresponds to the angle covered by the rotating tool at spindle speed n during the sampling interval Ts. It strongly determines the accuracy in the

J. Repo et al. / CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

29

Pulse location in uR (t) Falling edge in RD out (t)

±T s Fig. 5. Alignment of the falling edge in the RD pulse train RDout(t) with the location of the pulse in the reference mark signal uR(t).

Fig. 7. A strip of reflective tape attached to the tool shaft holder and aligned with the leading edge of tooth 1 on the milling cutter.

pulse alignment and given as

MR’ ¼

2pn Ts 60

(10)

which implies that a low measurement resolution is obtained when using a low spindle speed and a short sampling interval. At best, the pulses can be aligned within an accuracy of Ts, see Fig. 5. If the initial spindle position w0 is known, the contribution from w0 to the total error in the estimated position can be neglected and the error due to the limited measurement resolution will be 0.0188, given that a spindle speed 60 rpm and sampling rate 20 kHz is used. Note that even if the pulses are aligned within an accuracy of, say 10Ts, the alignment error due to the measurement resolution will still be relatively small, i.e. in the order of 0.188. In general, the desired 08-direction, defined by the vector u, will not be in the direction of the spindle’s reference direction r due to the angular offset ar as can be seen in Fig. 6. Thus, to allow an arbitrary 08-direction to be specified, the offset angle ar must be known. This implies that the physical direction of the spindle’s reference direction r must be determined. The trick used to find the physical direction of r on the XY-plane is to perform a 2-point measurement with the RD, using accurate position information provided by the machine tool. Hence the name of the measurement method (RD2P), which is summarized in the following two steps:

The vector r, which defines the spindle’s reference direction in physical coordinates, is given as r ¼ ðp2  p1 Þ ¼ ðr x ; r y ; r z Þ ¼ ðx2  x1 ; y2  y1 ; 0Þ;

’1’ ω y

0º u x

αr r RD

Fig. 6. Reflectance detector (RD) aligned with the spindle’s reference direction r.

(11)

Note that Eq. (11) is only valid for stationary spindles, i.e. when the RD, which is mounted on the table, is travelled along the X- and Yaxes. In the case when the spindle is linked to the X-axis, the sign of the rx component must be changed to rx. In the case when the spindle is linked to the Y-axis, the sign of the ry component must be changed to ry. The angle ar between r and the desired 08-direction vector u, is given by their scalar product as

ar ¼ cos1 ðuˆ  rˆÞ

(12)

ˆ and ˆr denote the normalized direction vectors. Note that where u Eq. (12) is ambiguous in that it always yields a positive value for ar. The correct sign for ar is obtained by evaluating the vector product

v ¼ ðv1 ; v2 ; v3 Þ ¼ u  r

(13)

where the resulting vector v is perpendicular to both u and r and normal to the plane spanned by the vectors u and r. It turns out that if the sign of the 3rd component of v is negative, then ar will also become a negative angle. In general, ar is given by

ar ¼ signðv3 Þcos1 ðuˆ  rˆÞ Step 1. Manually position and orient the RD so that the falling edge in RDout(t) coincides with the pulse in uR(t), keeping the distance between the detector and the reflective tape to a minimum. Note the physical coordinates of the actual position p1 = (x1, y1, z1). The coordinates are read from the operator interface of the machine tool. Step 2. Move the RD a short distance away from the reflective tape by jogging along the feed axes X and Y by using the hand wheel of the machine tool. When the falling edge in RDout(t) once again coincides with the pulse in uR(t), note the coordinates of the actual position p2 = (x2, y2, z2 = z1).

jjrjj > 0

(14)

where 8 < 1; signðxÞ ¼ 0; : 1;

x<0 x¼0 x>0

(15)

The angular position of ‘tooth 1’ relative to the desired 08-direction is found by modifying Eq. (8) so that the offset angle ar in Fig. 6 is also taken into account.

’1 ¼ ’0  ’REF þ ar

(16)

Note that perfect alignment between the RD and the spindle’s reference direction r cannot be achieved in practise, why wR  wRD. The reference angle wREF is given as the average angular value

’REF u ’RD  ’R 

’RD þ ’R 2

(17)

Note that wRD and wR are scalar N-point sequences containing samples of the spindle position signal w(t) during N spindle revolutions. The angular values are triggered at the time of the detected negative flanks in the RD pulse train RDout(t) and at the time of the detected pulses in the spindle’s reference mark signal uR(t), respectively. The reference angle wREF represents the average of the observed pulse alignments.

J. Repo et al. / CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

30

3. Validation and discussion The aim of the validation is to find the total error in the angular position measurement. For a known initial spindle position, e.g. w0 = 0, the uncertainty in wREF and ar in Eq. (16) will contribute to the total error e in the estimated angular position w1. Under these assumptions, Eq. (16) may be rewritten as (

samples

2

1

0

’1 ¼ ð’0  ’REF þ ar Þ  e

(18)

e ¼ e’ þ ea

where ew and ea denote the uncertainty in wREF and ar, respectively. The reflective tape is attached to the tool shaft holder and properly aligned with the leading edge of ‘tooth 1’ as shown in Fig. 7. For the validation, a spindle speed 60 rpm and a sampling rate 20 kHz were used. A software tool to allow on-line monitoring of the pulse alignment was developed and used in the measurement procedure. A numeric value displayed on the user interface, indicated the sample separation between the falling edge in the RD pulse train and the pulse in the spindle’s reference signal. The positioning of the RD was terminated when the numeric value was close to zero, indicating that a good pulse alignment has been achieved. The spindle was then restarted from zero and the rotary encoder signals uA(t), uB(t), uR(t) and the pulse train from the RD output were acquired simultaneously during multiple spindle revolutions. The acquired signals were used in the validation. The validation is based on 36 observations of the first pulse alignment and 31 observations of the second pulse alignment. The off-line analysis of the signals revealed that the falling edges in the RD pulse train and the pulses in the reference mark signal were not perfectly aligned as can be seen in Fig. 8. In the ideal situation, the sample separation will be zero. However, a systematic error seems to occur in the pulse alignment, which in this case gives an underestimation of the location of the falling edge in the RD pulse train. Fig. 9 shows the misalignment as the number of samples for subsequent spindle revolutions. A trigger level 2.5 and a hysteresis 1.0 V were used to detect the falling edge in the RD pulse train. Cubic spline interpolation was used in the peak detection and interpolation to allow evaluation at subsample level. As can be seen, the misalignment is varying between 1 and 2 samples. The error in the pulse alignment was corrected by adding the average error to the location of the falling edge in the RD pulse train. After correction, the falling edges in the RD pulse train were aligned within 0.5 sampling intervals or MRw/2 with the pulses in the reference mark signal. Note that wR  wRD, why Eq. (17) was applied to the angular samples to obtain a sequence of wREF values.

5

10

15

20

25

30

35

Pulse number Fig. 9. Error in the first pulse alignment for subsequent spindle revolutions. The horizontal line indicates the error as the average number of samples.

The uncertainty in wREF at 99.7% confidence level (3s) is

e’ ¼ 0:01125

(19)

The maximum angular error in the second pulse alignment is given as 



e’;max ¼ max j’R  ’RD j  0:01591

(20)

The angle ew,max corresponds to a small displacement er from the position p2 as illustrated in Fig. 10. For small values of ew,max and a maximum radial distance rmax = 50 mm, i.e. the radius of the tool shaft holder plus the maximum sensing distance for the RD, away from the axis of rotation, the maximum displacement er from p2 is found by

er u rmax tanðe’;max Þ  r max e’; max

p 180

 0:014 mm

(21)

The interpretation of er is that it is possible to move p2 inside a circle with radius er, without actually observing any pulse misalignment, i.e. the sensitivity to detect (or observe) any pulse misalignment in this case is 14 mm. This was also verified experimentally by manually controlled m-incremental movements around p2 using the hand wheel of the machine tool. This ‘‘blind spot’’ cannot be neglected in the analysis since small movements around p2 affect the value of ar in Eq. (16). To estimate the uncertainty in ar, a circle with radius er is centered at p2 as shown in Fig. 10. Fig. 11 shows the possible values of ar evaluated for 1000 pseudo points p20 uniformly distributed over u 2 [0, 2p] for the circle with radius er. The uncertainty in ar is found as the maximum deviation from the measured value ar =  3.78038 and given as

ea ¼ maxfjar ðuÞ  ar jg  0:1332

(22)

5

0

uR (t) [V]

RDout (t) [V]

1

ω Tool shaft holder ε ϕ,max

0 1.056

1.057

1.058

1.059

rmax p1

εr p2

−1

t [s] Fig. 8. Alignment error between a falling edge in the RD pulse train RDout(t) and a Gaussian pulse in the spindle’s reference mark signal uR(t).

Fig. 10. Analysis of the uncertainty in ar. A circle with radius er is centered at p2.

J. Repo et al. / CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

31

π 2

−3.65

ϕ (t) [rad]

α r (θ )[º]

−3.7 −3.75 −3.8 −3.85

i

0

iii

ii

−3.9

2π

− π2

Fig. 11. Variation in ar around the measured value 3.78038 (horizontal line), reflecting the uncertainty in the second pulse alignment.

The numerical values used to determine the teeth positions in this particular case are given as

’0 ¼ 0’REF ¼ ð224:0925  0:01125Þ u ¼ ðux ; uy ; uz Þ ¼ ð0; 1; 0Þr ¼ ðr x ; r y ; r z Þ ¼ ð0:394; 5:963; 0Þar ¼ ð3:7803  0:1332Þ

(23)

Using Eq. (18), the angular position of tooth 1 in this case is

’1 ¼ ð’0  ’REF þ ar Þ  e ¼ ð227:8728  0:1444Þ

(24)

The positions of the teeth 2,3,. . .,nz can now be determined using Eq. (9). In general, when the spindle is rotating the cutting tool, the time-varying angular position of tooth j is given as

’ j ðtÞ ¼ ’0 þ ’ðtÞ þ ’1  ð j  1Þf p ;

j ¼ 1; 2; . . . ; nz

(25)

Note that perfect alignment of the reflective tape with the the leading edge of the tooth on the milling cutter in Fig. 7 is assumed. However, 100% perfection in the alignment is not possible to achieve, leading to a systematic error in the estimated angular position. This type of bias may however be corrected by adding an angular offset to the final angular values. The uncertainty in the estimated angular position of the leading edge of the reflective tape is 0.14448 under the aforementioned validation settings. The accuracy in the estimated tooth position may however be increased by modifying the above conditions, i.e. decreasing the spindle speed, using a higher sampling rate, and decreasing the radial distance to the RD. Again, the total error is always lower when the initial spindle position is known in advance. In milling, the number of teeth that are cutting material simultaneously depends on the number of teeth on the cutter and the radial width of the cut [9]. The response type from the milling process depends largely on these active teeth since they contribute to the periodic excitations of the machining system. In the simplest machining setting, the milling operation is performed such that the workpiece is fed towards the rotating milling cutter along a straight line. Fig. 12 shows the evolution of the lower and upper bound of the cutting zone from start to finish of the cut. It can be seen that the size of the cutting zone varies with the linear position of the milling tool along the feed axis (Y). Three different stages of the cut can be identified: (i) the entry stage when the cutting tool is not yet fully immersed, when the cutting zone grows from zero to 1808, (ii) stationary stage during full immersion milling, when the cutting zone is 1808, and (iii) the exit stage, when the cutting zone develops (or splits) into two separate cutting zones which decay from 908 to zero when the cutting tool finally exits the workpiece. Given an initial position y0 for the milling process, it will be possible with sufficient accuracy to virtually track each tooth through all stages of the cut simply by checking if the jth tooth is within the lower and upper bound of the cutting zone. Tooth

0

10

20

30

40

50

60

y(t) [mm] Fig. 12. Lower and upper bounds of the cutting zone during the (i) entry phase, (ii) stationary phase and (iii) exit phase of the milling process. The diameter of the milling cutter is 32 mm.

tracking can also be extented to curve-like tool paths on the XYplane. Let x(t) and y(t) define the tool path and let the vector u(t) be the tangent to the curve at time t. Hence, the time-varying 08direction is now given by u(t). The angle ar is then calculated using Eq. (14) and used in Eq. (16) which gives an estimation of w1. Eq. (25) then gives the angular positions of all teeth relative to the time-varying 08-direction specified by the tool path. 4. Application example – tooth tracking A series of milling tests were conducted to study the effect of tool wear on the responses from position encoders. The tooth marked as ‘1’ was replaced by a worn tooth. The cutting forces in three orthogonal directions were measured simultaneously with the responses from the position encoders. Fig. 13 shows the sequence diagram of the tooth engagement for each tooth. A HIGH state in this diagram indicates that a tooth is inside the cutting zone and a LOW state when outside the cutting zone. It also shows qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the resultant cutting force FðtÞ ¼ F x ðtÞ2 þ F y ðtÞ2 þ F z ðtÞ2 and the displacement x(t) transversal to the feed direction during three spindle revolutions during the initial stage of the cut. It can be seen Tooth engagement Tooth 5 Tooth 4 Tooth 3 Tooth 2 Tooth 1 0 400

F(t) [N]

π θ [rad]

0.5

1

1.5

1

1.5

Tooth ”1” cutting

300 200 100 0

0

0.5

Tooth ”2” cutting

2

x(t) [μm]

0

1 0 −1 −2

0

0.5

1

1.5

y(t) [mm] Fig. 13. Tooth engagement diagram, resultant cutting force F(t) and estimated micro-vibrations x(t) from the feed axis transversal to the feed direction during three spindle revolutions in the slot-milling operation.

32

J. Repo et al. / CIRP Journal of Manufacturing Science and Technology 5 (2012) 26–32

that F(t) decreases when the worn tooth 1 is inside the cutting zone and increases when the following tooth 2 enters the cutting zone. It can also be seen that the periodicity in x(t) is disrupted due to the fact that tooth 2 now makes a deeper cut. Note that the worn tooth itself does not seem to have any significant effect on the microvibration signature x(t) when inside the cutting zone. The vibrations generated by the leading cutting edges actually seem to die out when tooth 2 enters the cutting zone. This enables the identification of a worn tooth on the milling tool at an early stage in the cut by using encoder signals. 5. Conclusions A reliable and practical optical 2-point measurement method (RD2P) to estimate the angular positions of individual teeth on a milling cutter relative to a specified 08-direction, has been developed. The proposed method is based on accurate position information provided by the machine tool and gives a sufficiently high accuracy of the estimated angular positions, which is approximately 0.158 for the actual validation parameters. The method is useful in, e.g. tool condition monitoring research to obtain a renewed or better insight into the milling process during the off-line analysis of the measured signals from the machining process. The proposed measurement method gives the possibility to virtually track and identify all teeth on a milling cutter with sufficient accuracy in the off-line analysis of the measured process responses. This allows finding potential correlations between the measured responses and the condition of individual teeth on the milling cutter. The measurement method has been tested on a milling cutter with exchangable cutting edges but may also be used for other type of cutting tools.

Acknowledgement This work was financially supported by the Swedish Governmental Agency for Innovation Systems (VINNOVA), which is gratefully acknowledged.

References [1] Repo, J., 2010, Condition Monitoring of Machine Tools and Machining Processes Using Internal Sensor Signals, Licentiate Thesis, KTH Industrial Engineering and Management. [2] Girardin, F., Re´mond, D., Rigal, J.-F., 2010, Tool Wear Detection in Milling – An Original Approach With a Non-Dedicated Sensor, Mechanical Systems and Signal Processing, 24/6: 1907–1920. [3] Andersson, C., Andersson, M., Sta˚hl, J.E., 2011, Experimental Studies Of Cutting Force Variation in Face Milling, International Journal of Machine Tools and Manufacture, 51/1: 67–76. [4] Adolfsson, C., Sta˚hl, J.E., 1995, Cutting Force Model for Multi-Toothed Cutting Processes and Force Measuring Equipment for Face Milling, International Journal of Machine Tools and Manufacture, 35/12: 1715–1728. [5] To¨nshoff, H.K., Inasaki, I., 2001, Sensors in Manufacturing, Vol. 1 of Sensors Applications, Wiley-VCH, Weinheim. [6] Abele, E., Dietz, S., Schiffler, A., 2009, Analysis of Cutting Force During Milling With Regards to the Dependency on the Penetration Angle, Production Engineering, 3/4: 483–487. [7] Hung Van, H., Jae Wook, J., 2007, Signal compensation and extraction of high resolution position for sinusoidal magnetic encoders, International Conference on Control, Automation and Systems, 2007 – ICCAS’07, pp.1368–1373. [8] Davies, M.A., Dutterer, B., Pratt, J.R., Schaut, A.J., Bryan, J.B., 1998, On the Dynamics of High-Speed Milling With Long, Slender Endmills, CIRP Annals Manufacturing Technology, 47/1: 55–60. [9] Altintas, Y., 2000, Manufacturing Automation: Metal Cutting Mechanics, Ma.chine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge [10] Beckwith, T.G., Marangoni, R.D., Lienhard, J.H., 2008, Mechanical Measurements, 6th ed. Pearson Education International, Upper Saddle River.