Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools

Influence of rotary axis on tool-workpiece loop compliance for five-axis machine tools

Accepted Manuscript Title: Influence of Rotary Axis on Tool-Workpiece Loop Compliance for Five-Axis Machine Tools Author: Daisuke Kono Yuki Moriya Ats...

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Accepted Manuscript Title: Influence of Rotary Axis on Tool-Workpiece Loop Compliance for Five-Axis Machine Tools Author: Daisuke Kono Yuki Moriya Atsushi Matsubara PII: DOI: Reference:

S0141-6359(17)30095-8 http://dx.doi.org/doi:10.1016/j.precisioneng.2017.02.016 PRE 6542

To appear in:

Precision Engineering

Received date: Accepted date:

15-2-2017 27-2-2017

Please cite this article as: http://dx.doi.org/10.1016/j.precisioneng.2017.02.016 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights

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> A method was described to calculate the tool-workpiece compliance in an arbitrary direction from compliances measured using orthogonal triaxial excitations. > The tool-workpiece compliance of a five-axis machine tool was evaluated comprehensively using the compliance map. > The influence of the rotation angle and clamping condition of the tilt axis on the tool-workpiece compliance was clarified.

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Type of contribution: Original paper Title: Influence of Rotary Axis on Tool-Workpiece Loop Compliance for Five-Axis Machine Tools

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Full names of authors: Daisuke Kono1, Yuki Moriya1, and Atsushi Matsubara1

Affiliation and address Department of Micro Engineering, Graduate School of Engineering, Kyoto University, c1S09, C3,Kyotodaigaku Katsura, Nisikyo-ku, Kyoto 615-8540, Japan

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Corresponding author Name: Daisuke Kono Tel.: +81-75-383-3677 Fax: +81-75-383-3677 E-mail address: [email protected]

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Influence of Rotary Axis on Tool-Workpiece Loop Compliance for Five-Axis Machine Tools Daisuke Kono1, Yuki Moriya1, and Atsushi Matsubara1

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Corresponding author: Daisuke Kono Department of Micro Engineering, Graduate School of Engineering, Kyoto University, c1S09, C3,Kyotodaigaku Katsura, Nisikyo-ku, Kyoto 615-8540, Japan Email: [email protected] Phone: +81-75-383-3677 Fax: +81-75-383-3677

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Abstract This study investigated the influence of the rotary axis of a 5-axis machine tool on the tool-workpiece compliance. The evaluation focused on the influence of the rotation angle and clamping condition of the B axis on the compliance variation. A method was determined to calculate the tool-workpiece compliance in an arbitrary direction from compliances measured using orthogonal triaxial excitations. Then, the tool-workpiece compliance of a 5-axis machine tool was evaluated and displayed using a color map. The compliance map showed that the magnitude of the compliance varied by up to 40 % with changes in the B axis rotation angle and its clamping condition. A drastic change in the negative real part of the compliance was also detected in the compliance map. The results of an experimental modal analysis are used to discuss the cause of the compliance variation. The bending mode of the B axis is an important mode because the change in the bending direction due to B axis rotation has a great influence on the direction dependency of the compliance magnitude and the stability limit. A cutting experiment was conducted to verify the correspondence between the evaluated compliance and the vibrational amplitude in a real cutting process. The compliance variation in the compliance map corresponded to the amplitude variation of the vibration in an end milling process. The compliance map revealed that the vibration synchronized with the passing cycle of cutters was decreased by 80 % by unclamping the B axis. Keywords: machine tool, vibration, evaluation, tool-workpiece compliance, direction dependency

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1. Introduction The relative vibration between the tool and workpiece is a significant issue in machining processes because it limits their productivity and accuracy [1–3]. The vibrational characteristics of a machining process can be evaluated by examining the tool-workpiece compliance, which is the frequency response of the relative displacement between the tool and workiece to the cutting force. The tool-workpiece compliance depends on the direction of the force and the displacement. It also depends on the position of feed drives. The direction and position dependencies of general use machine tools should be small because a large compliance for a specific condition in a machining process limits the productivity of the entire process. To design such machines, a method for comprehensive evaluation of the compliance in three dimensions is required. A design based on such an evaluation is also needed. Experimental evaluation of the compliance can be performed using excitation systems. They impose an artificial cutting force to the machine [4, 5]. A sensorless system for monitoring tool stiffness has also been developed [6]. The main goal of these systems is to measure the stiffness of spindles and tools. Modal analysis and frequency response identification of machine tools in real machining processes have been conducted [7–10]. In particular, Tounsi et.al. measured a 3×3 compliance matrix that represented the tool-workpiece compliance in three dimensions [10]. However, the direction and position dependencies of the compliance were not discussed in their paper. Design and computational evaluation methods for machine tools have also been studied. Although many design methods, including one for optimization, have been proposed [11–16], the direction and position dependencies of the compliance were not discussed in these studies. Luo et.al. predicted the position dependency of the natural frequency [17]. The direction dependency of the chatter stability limit has been evaluated in studies during the past five years [18–20]. The evaluation in these studies was limited to a two-dimensional plane. Moreover, the influence of the cutting force frequency was not clearly evaluated because they focused on the critical depth of cut. An experimental method for the comprehensive evaluation of tool-workpiece compliance has been developed in our previous studies [21]. A color map that illustrates the variation of frequency response with direction was used to evaluate three-dimensional compliance of a 3-axis machine tool. For a 5-axis machine tool, it can be easily estimated that the angle of the rotary axis greatly affects the three-dimensional compliance. However, the influence of the rotary axis on the three-dimensional compliance has not been quantitatively considered in the design of machines. This paper investigates the influence of the rotary axis of a 5-axis machine tool on the tool-workpiece compliance. The magnitude of the compliance depending on the tilt angle and clamping condition of the rotary axis is evaluated. The following section describes a method to calculate the compliance for an arbitrary three-dimensional direction from the compliances measured using three orthogonal excitations. The magnitude and the negative real part of the compliance are evaluated using a color map. The results of an experimental modal analysis are used to discuss the cause of the compliance variation. An end milling experiment is conducted to verify the correspondence between the evaluated compliance and the vibration amplitude in a real cutting.

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2. Method for measuring compliance 2.1 Measurement method A 5-axis machine tool was used in the experiment. A color map of the compliance (hereafter referred to as a compliance map) was obtained to investigate the influence of the tilt angle and clamping of a rotary axis on the direction dependency of the machine’s dynamic response. The configuration of the machine is shown in Fig. 1. The major specifications of the machine are listed in Table 1. A ball screw drive and linear ball guideway are used on translational axes. Figure 2 is a photograph of rotary B and C axes. Each of the two rotary axes is held by a cross roller bearing and driven by a direct drive motor. The rotary axes have a clamping system using hydraulic brake to fix the

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Fig. 1 Configuration of the machine tool used in the experiment Table 1 Specifications of machine

rotation.

Travel

X: 500 mm Y: 350 mm Z: 510 mm B: -180°–160° C: 360°

Size

Width: 3.8 m Length: 2.3 m Height: 3.3 m

Mass

9,400 kg

Drive

Translational axis: Ball screw Rotary axis: Direct drive

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Z Y

X Spindle head

Swept sine signal

Amplifier

Driven body of B-axis Amplifier

C axis rotary table

Signal generator

Excitation force Data logger

Acceleration Steel block

300 mm

Tool holder Force sensor Piezo electric actuator

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B axis driven body

Dummy tool

Z

X

Fig. 2 Photograph of rotary axes

Dummy workpiece

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Rotary table Accelerometer of C-axis Collet chuck

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Fig. 3 Schematic of experimental setup

Table 2 Specifications of experimental equipment

Measurement range

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Force sensor

Translational axis: Linear ball guideway Rotary axis: Cross roller bearing

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Guideway and bearing

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Sensitivity Accelerometer

fast Fourier transform (FFT) analyzer

Piezoelectric actuator

X and Y: ±4 kN, Z: ±8 kN

X and Y: -7.8 pC/N, Z:-3.8 pC/N

Measurement range

±100 m/s2

Sensitivity

50 mV/(m/s2)

Measurement range

10 mVrms – 10 Vrms

Resolution of A/D converter

24 bit

Size

5 mm×5 mm×10 mm

Maximum displacement

About 10 µm

The experimental setup with the B axis angle at 0° is shown in Fig. 3. A dummy tool is attached to the tool holder. A dummy workpiece is held in the collet chuck fixed on the table. The dummy tool and workpiece are almost cylindrical with 20 mm diameter. Two parallel surfaces are machined on their tip to attach a piezoelectric actuator and an accelerometer. The dummy tool and workpiece are carbon steel S45C. The dummy workpiece and dummy tool are simultaneously excited using the piezoelectric actuator.

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Dummy workpiec

Tool holder

X

Force sensor

Z

Dummy workpiec

Tool holder

X

Force sensor

Y

Y

Accelerometer

Accelerometer Accelerometer

Dummy tool

Accelerometer

Dummy tool Piezoelectric actuator

Steel block

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Piezoelectric actuator

Steel block

Collet chuck

Collet chuck Table

Table

(b) B = 90°

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(a) B = 0°

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Fig. 4 Experimental setups for B = 0° and B = 90° Sensor cables are omitted for clarity. Table 3 Measurement conditions

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The excitation force is measured with a force sensor (Kistler). The response of both the tool and workpiece is measured with three-dimensional accelerometers (PCB Piezotronics). The frequency response of the relative acceleration to the excitation force Condition Angle of B Clamp of B axis number axis B 1 0° With clamping 2 0° Without clamping 3 90° With clamping 4 90° Without clamping

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is calculated using a fast Fourier transform (FFT) analyzer (Ono Sokki). Then, the tool-workpiece compliance is obtained by integration. The specifications of the experimental equipment are summarized in Table 2. The compliance is measured by applying excitations in the X, Y, and Z directions. A compliance matrix consisting of nine separate compliance values is obtained. Then, the compliance matrix for a coordinate system tilted at an arbitrary angle is calculated to enable a comprehensive evaluation. The method used for the calculation is described in detail in the section 2.2. To investigate the influence of the tilt angle and clamping of the rotary axis on compliance, measurements are made for the four different conditions summarized in Table 3. The angle B is the tilt angle of the B axis. The table is nominally horizontal when B = 0°. Figure 4 shows photographs of the experimental setup for B = 0° and B = 90°. A preload is given to the piezoelectric actuator using the feed drive to keep the contact between the actuator, dummy tool and dummy workpiece. A 50 N preload is applied in this experiment. Then, a sinusoidal signal with swept frequency range of 1–250 Hz is applied to the actuator for 60 s. 2.2 Calculation of compliance in an arbitrary direction The direct compliance in an arbitrary three-dimensional direction is calculated to enable the evaluation of the direction dependency of the compliance. The compliance is assumed to be a second order tensor. The compliance matrix Ge in a coordinates system

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tilted with respect to the XYZ coordinate system is calculated using the following equation: (1) where Gm is the compliance matrix measured with excitations in the X, Y, and Z directions; Qφ and Qθ are transformation matrices; and θ and φ are the rotation angles shown in Fig. 5. The angle θ is negative in the right-handed coordinate system. Each matrix is represented in terms of its components as follows:

(2)

(3)

(4)

(5)

where, for example, Gxy represents the compliance about the Y displacement as a result of an X excitation force. The compliance Guu is the direct compliance in an arbitrary direction. 3. Measurement result 3.1. Evaluation of the compliance magnitude Figure 6 shows the compliance maps measured under the 4 different conditions in

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(d) Condition 4 B=90°without clamping

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Magnitude µm/N

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Fig. 6 Compliance maps

Table 3. The compliance magnitude is represented by the color scale. The excitation direction in the machine coordinate system is represented by the axes X, Y, and Z in the plots. The frequency is displayed along the radial direction of the maps. The maps are used in the discussion of the direction dependency of the compliance magnitude. In all results shown in Fig. 6, the compliance magnitude in the Z direction is smaller than those in the XY plane. This is because the compliance is greatly influenced by the response of the tool and the axial stiffness of the Z-axis drive is larger than the radial stiffness. A comparison of Fig. 6(a) with Fig. 6(b) shows that the compliance magnitude is decreased when the B axis is unclamped. The lines in sky blue at approximately 186 Hz in the XY plane and at approximately 110 Hz in the Z direction in Fig. 6(a) seemed to have disappeared in Fig. 6(b), which means that the magnitude is decreased when the axis is unclamped. The influence of the tilt angle is seen by a comparison between Fig. 6(a) and Fig. 6(c). The compliance is decreased at approximately 186 Hz in the X direction when B = 90°. However, the magnitude is slightly increased at approximately 75 Hz in the X direction. When the B axis is both tilted and unclamped, the magnitude change can be explained by a combination of the previous observations. A plot of the maximum value of the compliance magnitude is shown in Fig. 7 for a quantitative investigation. In Fig. 7, the excitation direction is represented in the same

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B=0 deg. with clamping B=0 deg. without clamping B=90 deg. with clamping B=90 deg. without clamping

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Fig. 7 Comparison of the maximum value of the compliance magnitude

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manner as in Fig. 6. The maximum value of the compliance magnitude is displayed along the radial direction. When B = 0°, the magnitude in the Z direction is decreased by a factor of 2 by unclamping the B axis. On the other hand, the magnitude does not change in the XY plane because the maximum value in this case is determined by the tool response. By tilting the B axis to 90°, the compliance magnitude in the XY plane is increased by 10–20 %. When B = 90° and the B axis is unclamped, the magnitude in the X direction is increased by approximately 40 % compared to the result with B = 0° and clamping.

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3.2. Evaluation of the negative real part of the compliance In regenerative chatter vibration, the stability limit is determined by the negative real part of the tool-workpiece compliance. Figure 8 shows the real part of the tool-workpiece compliance in similar manner to Fig. 6. Figures 8(a–c) show that the real part is negative at approximately 110 Hz in the Z direction. In Fig. 8(d), however, the real part is negative at approximately 80 Hz in the X direction. This result shows that the direction in which the stability limit is small can be greatly influenced by the tilt angle and clamping. The maximum of the absolute value of the negative real part is shown in Fig. 9 in similar manner to Fig. 7. Compared to the value with B = 0° and clamping, the maximum value is decreased by 50 % by tilting the B axis or unclamping it. In contrast, the maximum value is increased by approximately 240 % by unclamping the B axis when B = 90°. These variations correspond to a 100 % increase and 60 % decrease in the stability limit, respectively. 4. Discussion The overall vibration characteristics were described in the previous section. The cause of the compliance variation is investigated in this section. The compliance about the absolute displacement of the tool and workpiece measured in the excitation experiment described in section 2.1 is analyzed to investigate their contribution to the relative displacement. The results of an experimental modal analysis are used to discuss the cause of the compliance variation. The following sections discuss three cases. The first case is the compliance decrease

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at approximately 186 Hz in the X direction seen when tilting and unclamping the B axis. The second case is the compliance increase at approximately 75 Hz in the X direction seen when tilting and unclamping the B axis. The third case is the change in the direction in which the stability limit is small.

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50 Hz

-0.04

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(a) Condition 1 B=0°with clamping

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150 Hz 250 Hz

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(d) Condition 4 B=90°without clamping

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(c) Condition 3 B=90°with clamping

Fig. 8 Maps of the real part of the compliance

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B=0 deg. with clamping B=0 deg. without clamping B=90 deg. with clamping B=90 deg. without clamping

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X 0.05µm/N 0.1 µm/N 0.15 µm/N X

Fig. 9 Comparison of the maximum absolute value of the negative real part of the compliance

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B=0 deg. Clamp B=0 deg. Unclamp B=90 deg. Clamp B=90 deg. Unclamp

0.2 0.1 0

0

50

100 150 Frequency Hz

200

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100 150 Frequency Hz

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Fig. 10 Comparison of compliances about the absolute displacement of the tool in the X direction

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Fig. 11 Comparison of compliances about the absolute displacement of the workpiece in the X direction

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4.1 Compliance decrease at approximately 186 Hz in the X direction seen when tilting and unclamping the B axis Figure 10 shows the comparison of compliances about the absolute displacement of the tool. The result shows that the response of the tool is not changed at 186 Hz by tilting and unclamping the B axis. The comparison of compliances about the absolute displacement of the workpiece is shown in Fig. 11. The vibration modes obtained from an experimental modal analysis are also presented in the figure. The magnitude with B = 0° and clamping has a broad peak around 186 Hz, which results in the magnitude increase shown in Fig. 6(a). The magnitude peak in the workpiece response in Fig. 11 is caused by the rotation mode of the B axis. When B = 90°, the vibration direction of the workpiece due to this mode is in the Z direction. When the B axis is unclamped, the natural frequency of this mode shifts to the low frequency range. Therefore, the magnitude has no peak at 186 Hz under the other three conditions. 4.2 Compliance increase at approximately 75 Hz in the X direction by tilting and unclamping the B axis In Fig. 10, when B = 90° and the B axis is unclamped, the magnitude of the tool response at approximately 75 Hz is increased by 18–60 % compared to the results for the other conditions. Similarly in Fig. 11, the magnitude of the workpiece response has a peak and the magnitude is increased by 215 % only when B = 90° and the B axis is unclamped. Furthermore, the phase of the tool response is almost opposite to the workpiece. Thus, the magnitude increase shown in Fig. 6(d) is caused by the magnitude increase in both the tool and workpiece responses. The magnitude peak in the workpiece response in Fig. 11 is caused by the bending mode of the B axis. The magnitude peak in the tool response in Fig. 10 can be caused by the bending mode of the Z axis. The position dependency of the compliance is believed to be the reason for the magnitude increase in the tool response. The Z position was shifted by -45 mm and the length of the Z axis ram is longer when B = 90°.

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B=0 deg. Clamp B=0 deg. Unclamp B=90 deg. Clamp B=90 deg. Unclamp

0.2 0.1 0

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100 150 Frequency Hz

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Fig. 13 Comparison of compliances about the absolute displacement of the workpiece in the Z direction

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Fig. 12 Comparison of compliances about the absolute displacement of the tool in the Z direction

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4.3 Change in the direction in which the stability limit is small When B = 0° and the B axis is clamped, the negative real part of the compliance has a peak in the Z direction as shown in Fig. 8(a). Figures 12 and 13 show the responses of the tool and the workpiece, respectively. Because the magnitude of the workpiece response is larger than the tool response, the workpiece response dominates the relative response. Thus, the peak in Fig. 8(a) is caused by the same mechanism as the peak at approximately 105 Hz in Fig. 13. This peak results from the bending mode of the B axis. On the other hand, when B = 90° and the B axis is not clamped, the negative real part of the compliance has a peak near 75 Hz in the X direction as shown in Fig. 8(d). This peak is caused by the compliance increase described in section 4.2. When B = 90° and the B axis is clamped, the negative real part is in an intermediate condition between the two conditions described in this section. The previous discussion shows that the vibration modes of the Z axis and the B axis of the machine have an influence on the compliance magnitude. In particular, the bending mode of the B axis is an important mode because the change in the bending direction due to the B axis rotation has a great influence on the direction dependency of the compliance magnitude and the stability limit. 5. Cutting experiment 5.1 Experimental method A cutting experiment was conducted to verify the compliance variation discussed in section 3.1. For B = 0°, vibrations of the spindle head and the table are measured in an end milling process with and without the B axis clamp. The experimental setup is shown in Fig. 14. A radius end mill with 6 mm diameter was used for the tool. The workpiece material was a titanium alloy Ti-6Al-4V. The workpiece was fixed on a 3-axis dynamometer (Kistler) to measure the cutting force. The accelerations of the spindle head and the table were measured using 3-axis

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Table 4 Experimental conditions

Feed direction Tool

Workpiece

Accelerometer

1 mm WC TiAlN/AlCrN Ti-6Al-4V 2790 rpm 0.03 mm/tooth 0.45 mm 3 mm Down cut Dry

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Radius end mill 6 mm

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Type Diameter Corner Tool radius Material Coating Workpiece material Spindle speed Feed per tooth Radial depth of cut Axial depth of cut Cutting direction Lubricant

Tool holder

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Fig. 14 Experimental setup for cutting

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100 0 0

10

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100 0

Z force N

-100

30 Time s

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X force N

With clamping Without clamping

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30 Time s

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100

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Fig. 15 Comparison of cutting forces

accelerometers. The cutting force and acceleration data were recorded by a data logger with a 21 bit A/D converter. The cutting conditions are summarized in Table 4. The sampling frequency was set to 3 kHz. 5.2 Experimental result Figure 15 shows a comparison between the measured cutting forces with the B axis clamped and unclamped. The force fluctuation caused by three different cuttings is shown in Fig. 15. This force fluctuation is synchronized with the passing cycle of cutters. The amplitude of the X force fluctuation is approximately 81 N with clamping the B axis. The amplitude of the X force fluctuation is approximately 67 N without clamping the B axis. Therefore, the result shows that the amplitude of the X force without clamping the B axis is approximately 17 % smaller than that with clamping.

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30 Time s

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Fig. 18 Comparison of the amplitude spectra of the table acceleration

Comparisons of the measured accelerations are shown in Figs. 16 and 17. These figures show that only the X acceleration of the table is decreased by 40–50 % when the B axis is not clamped. The amplitude spectra of the X acceleration of the table are compared in Fig. 18. The comparison shows that the amplitude at 186 Hz is decreased by 80 % when the B axis is not clamped. This amplitude decrease is the one discussed in section 4.1.Because the dominant component of the vibration can be decreased, the improvement of the tool life is promising. The accuracy deterioration of the machine can be also prevented. Figure 19 shows the surface roughness profiles of the machined surface measured by a contact-type surface roughness measuring machine. The surface roughnesses are 0.18 µmRa with clamping and 0.19 µmRa without clamping. The surface roughness is not influenced by the clamping condition. This is because the component with 0.12 mm wavelength dominates the surface roughness. This component was caused by the radial run-out of the tool because its wavelength corresponds to the period of the spindle rotation. Thus, the vibration reduction shown in Fig.16 did not improve the surface roughness.

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3 Profile with clamping Profile without clamping

2 m µ el fi or P

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4 6 Distance mm (a) Roughness profile

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Fig. 19 Comparison of the roughness profiles of the machined surface The profile is filtered using a high-pass filter with 0.8 mm cut off.

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Generally, the rotational axis is clamped when the simultaneous 5-axis machining is not required. The forementioned experimental result shows that the cutting vibration can be decreased by unclamping the rotary axis. In determination of cutting conditions for end milling, the cutter cycle should be different from the natural frequency of the mechanical system. If the cutter cycle is near the natural frequency because of any limitation in cutting speed, one possible solution for vibration reduction is to decrease the compliance by changing the clamping condition and angle of the rotational axis. The compliance map is useful for conducting such counter measures. 6. Conclusions The tool-workpiece compliance of a 5-axis machine tool was evaluated using a compliance map. The evaluation focused on the influence of the rotation angle and the clamping condition of the B axis on the compliance variation. A cutting experiment was conducted to verify the correspondence between the evaluated compliance and the vibration amplitude in a real cutting. In this study, the following conclusions were drawn. ・A method was described to calculate the tool-workpiece compliance in an arbitrary direction from compliances measured using orthogonal triaxial excitations. ・The tool-workpiece compliance was evaluated comprehensively using the compliance map. The compliance map showed that the magnitude of the compliance varies by up to 40 % with changes in the rotation angle and clamping condition for the B axis. A drastic change in the negative real part of the compliance was also detected in the compliance map. ・If the rotation axis has an important vibration mode that dominates the dynamic characteristics, the direction in which the stiffness is small is strongly influenced by the angle of the rotation axis. In the machine used in this study, the bending mode of the B axis was the important mode. The influence of such a mode should be minimized in the design stage of the machine based on an evaluation of the

Page 17 of 43

compliance in three dimensions.

ip t

・The compliance variation in the compliance map corresponded to the amplitude variation of the vibration in a real end milling process. From the compliance map, it was seen that the vibration that was synchronized with the passing cycle of cutters was decreased by 80 % by unclamping the B axis.

cr

Acknowledgement This work was supported by KAKENHI (26820021) and Mazak Foundation.

Ac ce pt e

d

M

an

us

References [1] T. Mori, T. Hiramatsu, E. Shamoto, Simultaneous double-sided milling of flexible plates with high accuracy and high efficiency—Suppression of forced chatter vibration with synchronized single-tooth cutters, Precision Engineering 35 (2011) 416-423. [2] E. Shamoto, T. Mori, B. Sencer, N. Suzuki, R. Hino, Suppression of regenerative chatter vibration in multiple milling utilizing speed difference method – Analysis of double-sided milling and its generalization to multiple milling operations, Precision Engineering 37 (2013) 580-589. [3] D. S. Kim, I. C. Chang, S. W. Kim, Microscopic topographical analysis of tool vibration effects on diamond turned optical surfaces, Precision Engineering 26 (2002) 168-174. [4] M. Rantatalo, J. O. Aidanpäpä, B. Göransson and P. Norman, V Milling machine spindle analysis using FEM and non-contact spindle excitation and response measurement, International Journal of Machine Tools & Manufacture 47 (2007) 1034-1045. [5] A. Matsubara, S. Tsujimoto, D. Kono, Evaluation of dynamic stiffness of machine tool spindle by non-contact excitation tests, CIRP Annals Manufacturing Technology 64 (2015) 365-368. [6] R. Koike, R. Kumakura, T. Arai, E. Uchishiba, M. Murakami, T. Sagara and Y. Kakinuma, Sensorless tool stiffness monitoring in buffing, International Journal of Automation Technology 4 (2010) 303-311. [7] N. Suzuki, Y. Kurata, T. Kato, R. Hino, E. Shamoto, Identification of transfer function by inverse analysis of self-excited chatter vibration in milling operations, Precision Engineering 36 (2012) 568-575. [8] I. Zaghbani and V. Songmene, Estimation of machine-tool dynamic parameters during machining operation through operational modal analysis, International Journal of Machine Tools & Manufacture 49 (2009) 947-957. [9] B. Lia, H. Cai, X. Mao, J. Huang and B. Luo, Estimation of CNC machine–tool dynamic parameters based on random cutting excitation through operational modal analysis, International Journal of Machine Tools & Manufacture 71 (2013) 26-40. [10] N. Tounsi and A. Otho, Identification of machine–tool–workpiece system dynamics, International Journal of Machine Tools & Manufacture 40 (2000) 1367–1384. [11] Z. Yu, K. Nakamoto, T. Ishida and Y. Takeuchi, Interactive design-assistance

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[17]

[18]

[19]

[20]

[21]

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[16]

an

[15]

M

[14]

d

[13]

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[12]

system of machine tool structure in conceptual and Fundamental design stage, International Journal of Automation Technology 4 (2010) 303-311. D. Huo, K. Cheng and F. Wardle, A holistic integrated dynamic design and modelling approach applied to the development of ultraprecision micro-milling machines, International Journal of Machine Tools & Manufacture 50 (2010) 335–343. C. Brecher, P. Utsch, R. Klar and C. Wenzel, Compact design for high precision machine tools, International Journal of Machine Tools & Manufacture 50 (2010) 328-334. B. C. Wu, G. S. Young and T. Y. Huang, Application of a two-level optimization process to conceptual structural design of a machine tool, International Journal of Machine Tools & Manufacture 40 (2000) 783-794. R. Neugebauer, W.-G. Drossel, S. Ihlenfeldt and Ch. Harzbecker, Design method for machine tools with bionic inspired kinematics, CIRP Annals Manufacturing Technology 58 (2009) 371-374. B. Li, J. Honga and Z. Liu, Stiffness design of machine tool structures by a biologically inspired topology optimization method, International Journal of Machine Tools & Manufacture 84 (2014) 33-44. B. Luo, D. Pan, H. Cai, X. Mao, F. Peng, K. Mao and B. Li, A method to predict position-dependent structural natural frequencies of machine tool, International Journal of Machine Tools & Manufacture 92 (2015) 72-84. M. Leonesio, L. M. Tosatti, S. Pellegrinelli and A. Valente, An integrated approach to support the joint design of machine tools and process planning, CIRP Journal of Manufacturing Science and Technology 6 (2013) 181-186. M. Law, Y. Altintas and A. S. Phani, Rapid evaluation and optimization of machine tools with position-dependent stability, International Journal of Machine Tools & Manufacture 68 (2013) 81-90. J. J. Zulaika, F. J. Campa, L. N. Lopez de Lacalle, An integrated process–machine approach for designing productive and light weight milling machines. International Journal of Machine Tools & Manufacture 51 (2011) 591-604. D. Kono and A. Matsubara, Investigation of direction dependency of tool-workpiece compliance of machine tool, Procedia CIRP 46 (2016) 529-532, open access.

Page 19 of 43

Ac ce pt e

d

M

an

us

cr

ip t

List of Figure Captions Fig. 1 Configuration of the machine tool used in the experiment Fig. 2 Photograph of rotary axes Fig. 3 Schematic of experimental setup Fig. 4 Experimental setup for B = 0° and B = 90° (a) B = 0° (b) B = 90° Fig. 5 Rotation of coordinate system Fig. 6 Compliance maps (a) Condition 1 B = 0° with clamping (b) Condition 2 B = 90° without clamping (c) Condition 3 B = 0° with clamping (d) Condition 4 B = 90° without clamping Fig. 7 Comparison of the maximum value of the compliance magnitude Fig. 8 Maps of the real part of the compliance (a) Condition 1 B = 0° with clamping (b) Condition 2 B = 90° without clamping (c) Condition 3 B = 0° with clamping (d) Condition 4 B = 90° without clamping Fig. 9 Comparison of the maximum absolute value of the negative real part of the compliance Fig. 10 Comparison of compliances about the absolute displacement of the tool in the X direction Fig. 11 Comparison of compliances about the absolute displacement of the workpiece in the X direction Fig. 12 Comparison of compliances about the absolute displacement of the tool in the Z direction Fig. 13 Comparison of compliances about the absolute displacement of the workpiece in the Z direction Fig. 14 Experimental setup for cutting Fig. 15 Comparison of cutting forces Fig. 16 Comparison of table accelerations Fig. 17 Comparison of spindle accelerations Fig. 18 Comparison of the amplitude spectra of the table acceleration Fig. 19 Comparison of the roughness profiles of the machined surface

Page 20 of 43

ip t X: 500 mm Y: 350 mm Z: 510 mm B: -180°–160° C: 360°

M

9,400 kg

Translational axis: Ball screw Rotary axis: Direct drive

Ac ce pt e

Drive

Width: 3.8 m Length: 2.3 m Height: 3.3 m

d

Mass

an

Travel

Size

cr

us

Table 1 Specifications of machine

Guideway and bearing

Translational axis: Linear ball guideway Rotary axis: Cross roller bearing

Page 21 of 43

ip t cr

±100 m/s2

Sensitivity

50 mV/(m/s2)

Measurement range

10 mVrms – 10 Vrms

Resolution of A/D converter

24 bit

Size

5 mm×5 mm×10 mm

Maximum displacement

About 10 µm

Ac ce pt e

fast Fourier transform (FFT) analyzer

Measurement range

d

Accelerometer

Piezoelectric actuator

X and Y: -7.8 pC/N, Z:-3.8 pC/N

M

Sensitivity

X and Y: ±4 kN, Z: ±8 kN

an

Force sensor

Measurement range

us

Table 2 Specifications of experimental equipment

Page 22 of 43

ip t cr us

Clamp of B axis

d

M

Angle of B axis B 0° 0° 90° 90°

With clamping Without clamping With clamping Without clamping

Ac ce pt e

Condition number 1 2 3 4

an

Table 3 Measurement conditions

Page 23 of 43

ip t cr us

Radius end mill 6 mm 1 mm

Ac ce pt e

d

M

Type Diameter Corner Tool radius Material Coating Workpiece material Spindle speed Feed per tooth Radial depth of cut Axial depth of cut Cutting direction Lubricant

an

Table 4 Experimental conditions

WC TiAlN/AlCrN Ti-6Al-4V 2790 rpm 0.03 mm/tooth 0.45 mm 3 mm Down cut Dry

Page 24 of 43

ip t cr

Z

Z

X

us

Y

an

X

Y

B

Ac ce pt e

d

M

C

Fig. 1 Configuration of the machine tool used in the experiment

Page 25 of 43

ip t cr

us

B axis driven body

Ac ce pt e

300 mm

d

M

C axis rotary table

X

an

Y

Z

Fig. 2 Photograph of rotary axes

Page 26 of 43

ip t

Spindle head

Swept sine signal

Amplifier

Moving body of B-axis Amplifier

Excitation force

Signal generator

cr

Rotation direction of B-axis

an

Steel block

us

Data logger

Acceleration

M

Dummy tool

Rotary table of C-axis

Z

Force sensor Piezo electric actuator

Dummy workpiece

Collet chuck

Ac ce pt e

d

Y

Accelerometer

Tool holder

X

Fig. 3 Schematic of experimental setup

Page 27 of 43

ip t cr us

Z

Tool holder X

Force sensor Y Accelerometer

Z

Dummy workpiece

X

Force sensor

an

Dummy workpiece

Tool holder

Y

Accelerometer

Accelerometer

Accelerometer

Dummy tool

M

Dummy tool Piezoelectric actuator

Piezoelectric actuator

d

Steel block Collet chuck

Steel block Collet chuck

Ac ce pt e

Table

(a) B = 0°

Table (b) B = 90°

Fig. 4 Experimental setups for B = 0° and B = 90° Sensor cables are omitted for clarity.

Page 28 of 43

ip t

Guu W

Y

Ac ce pt e

X

d

M

φ

an

θ V

us

U

cr

Z

Fig. 5 Rotation of coordinate system

Page 29 of 43

ip t Y

250 Hz

X

Y

0

(a) Condition 1 B=0°with clamping

0.15

X

0.08

250 Hz

0

(b) Condition 2 B=0°without clamping

d

0.39

Y

0.39

Y

0.31

X

50 Hz

0.23

Y

X

X

250 Hz

(c) Condition 3 B=90°with clamping

Z

X 50 Hz

0.15

150 Hz

Z

Magnitude µm/N

Ac ce pt e

0.31

Z

0.08

0.23

150 Hz

Z

M

X

X

Y

0.08

X

50 Hz

0.15

150 Hz Z

Z

0.31

Magnitude µm/N

50 Hz

0.23

us

X

an

Z

Magnitude µm/N

0.31

0.39

Magnitude µm/N

cr

0.39

Y

0.23 0.15

150 Hz Z Y

X

X

250 Hz

0

0.08 0

(d) Condition 4 B=90°without clamping

Fig. 6 Compliance maps

Page 30 of 43

ip t cr

us

B=0 deg. with clamping B=0 deg. without clamping B=90 deg. with clamping B=90 deg. without clamping

Z

M

an

Y

X

0.1 µm/N

Ac ce pt e

d

0.2 µm/N 0.3 µm/N X

Fig. 7 Comparison of the maximum value of the compliance magnitude

Page 31 of 43

-0

-0

Y -0.02

50 Hz

-0.04

50 Hz

cr

Z

X

X

Y

-0.1

(a) Condition 1 B=0°with clamping

Z Y

X

Real part µm/N

-0.04

X

250 Hz

-0.08

-0 -0.02

Z

X 50 Hz

-0.06

Ac ce pt e

150 Hz

-0.04 -0.06

150 Hz Z Y

X

X

250 Hz

-0.1

(c) Condition 3 B=90°with clamping

-0.08 -0.1

Y

d

X

M

-0.02

an

-0

50 Hz

250 Hz

(b) Condition 2 B=0°without clamping

Y

Z

-0.06

150 Hz

-0.08

250 Hz

-0.04

Real part µm/N

X

Y

X

us

X

Z

-0.06

150 Hz Z

ip t

X

Real part µm/N

Z

-0.02 Real part µm/N

Y

-0.08 -0.1

(d) Condition 4 B=90°without clamping

Fig. 8 Maps of the real part of the compliance

Page 32 of 43

ip t cr

us

B=0 deg. with clamping B=0 deg. without clamping B=90 deg. with clamping B=90 deg. without clamping

Z

M

an

Y

X

0.05µm/N

Ac ce pt e

d

0.1 µm/N 0.15 µm/N

X

Fig. 9 Comparison of the maximum absolute value of the negative real part of the compliance

Page 33 of 43

0.2 0.1 0

0

50

0

50

100 150 Frequency Hz

ip t 200

250

200

250

M

0

d

Phase deg.

200

100 150 Frequency Hz

Ac ce pt e

-200

cr us

0.3

an

Magnitudeµm/N

B=0 deg. Clamp B=0 deg. Unclamp B=90 deg. Clamp B=90 deg. Unclamp

Fig. 10 Comparison of compliances about the absolute displacement of the tool in the X direction

Page 34 of 43

ip t Z

Z

X

B

X

0.1 0

0

50

0

50

100 150 Frequency Hz

B

200

250

200

250

M

0

100 150 Frequency Hz

Ac ce pt e

d

Phase deg.

200

-200

us

Y

Y

0.2

cr

0.3

an

Magnitudeµm/N

B=0 deg. Clamp B=0 deg. Unclamp B=90 deg. Clamp B=90 deg. Unclamp

Fig. 11 Comparison of compliances about the absolute displacement of the workpiece in the X direction

Page 35 of 43

0.2 0.1 0

0

50

0

50

100 150 Frequency Hz

ip t 200

250

200

250

M

0

100 150 Frequency Hz

Ac ce pt e

d

Phase deg.

200

-200

cr

us

0.3

an

Magnitudeµm/N

B=0 deg. Clamp B=0 deg. Unclamp B=90 deg. Clamp B=90 deg. Unclamp

Fig. 12 Comparison of compliances about the absolute displacement of the tool in the Z direction

Page 36 of 43

0.2 Z

0.1

Y

0

50

0

50

100 150 Frequency Hz

d

0

ip t cr 250

100 150 Frequency Hz

200

250

Ac ce pt e

-200

200

M

200 Phase deg.

B

X

0

us

0.3

an

Magnitudeµm/N

B=0 deg. Clamp B=0 deg. Unclamp B=90 deg. Clamp B=90 deg. Unclamp

Fig. 13 Comparison of compliances about the absolute displacement of the workpiece in the Z direction

Page 37 of 43

ip t cr

us

Z

Y

Tool holder

an

X

Feed direction

Tool

Workpiece

d

M

Dynamometer

Ac ce pt e

Accelerometer

Table

Fig. 14 Experimental setup for cutting

Page 38 of 43

0 0

10

20

30 Time s

0

10

20

30 Time s

0

10

100

-100 100

-100

d

0 20

30 Time s

ip t cr 50

60

40

50

60

40

50

60

M

0

40

an

-100

us

100

Ac ce pt e

Z force N

Y force N

X force N

With clamping Without clamping

Fig. 15 Comparison of cutting forces

Page 39 of 43

0

10

20

30 Time s

0

10

20

30 Time s

10

20

40

5

2

an

0 -5

0

30 Time s

d

0 -5

60

40

50

60

40

50

60

M

5

50

us

-5

Ac ce pt e

Z acceleration m/s

ip t

0

cr

5

2

Y acceleration m/s X acceleration m/s

2

With clamping Without clamping

Fig. 16 Comparison of table accelerations

Page 40 of 43

0

10

20

30 Time s

0

10

20

30 Time s

0

10

20

40

5

an

0 -5

60

40

50

60

40

50

60

M

5 0

30 Time s

d

-5

50

us

-5

cr

0

2

Z acceleration m/s

ip t

5

2

Y acceleration m/s X acceleration m/s

2

With clamping Without clamping

Ac ce pt e

Fig. 17 Comparison of spindle accelerations

Page 41 of 43

ip t cr

2.5

With clamping Without clamping

us

186 Hz

an

1.5

1

744 Hz

M

Amplitude spectrum

2

0.5

0

d

500

1000

1500

Frequency

Ac ce pt e

0

Fig. 18 Comparison of the amplitude spectra of the table acceleration

Page 42 of 43

Profile with clamping Profile without clamping

2

0 -1 -2

0

2

4 6 Distance mm (a) Roughness profile

3

an

1

-1 1.2

1.4 1.6 Distance mm (b) Magnified view

1.8

2

d

1

M

0

-2

10

Profile with clamping Profile without clamping

2 m µ el fi or P

8

cr

1

us

m µ el fi or P

ip t

3

Ac ce pt e

Fig. 19 Comparison of the roughness profiles of machined surface The profile is filtered using a high-pass filter with 0.8 mm cut off.

Page 43 of 43