improvement of machining accuracy for 3d surface machining

Bulletin of the JSME

Journal of Advanced Mechanical Design, Systems, and ManufacturingVol.12, No.4, 2018

Paper No.18-00034© 2018 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2018jamdsm0089]

Abstract The present paper describes a new non-axisymmetric curved surface turning (NACS-Turning) method. Fast tool servo (FTS) technology has been widely researched and developed. However, the movable range of the FTS is limited to a few millimeters owing to its mechanism. Therefore, in the present study, we describe the development of a new NACS-Turning method that can realize long stroke and high bandwidth in the cutting direction (X-axis) of the turning tool by using a linear motor. We confirmed that NACS-Turning could machine a non-axisymmetric workpiece while the X-axis slide was synchronized at an acceleration of 4.5 ɡ with a spindle rotation of 750 min-1. However, in this machining method, the machining accuracy deteriorates depending on the acceleration and cutting reaction force of the X-axis slide. In particular, excess from the designed allowable acceleration threatens to cause a serious machining error. Therefore, the present paper describes the possibility of machining considering the acceleration and improvement of machining accuracy in NACS-Turning. We examine the relationships between machining parameters and the accelerations as well as the tool path generation method considering these relationships. Moreover, machining accuracy is improved by on-machine measurement. We constructed a system whereby a re-machining tool path is generated by measuring the profile of the machined workpiece and feeding the measurement results back to the CAM. As a result, we obtained a theorem for the possibility of machining via NACS-Turning and confirmed the improvement in accuracy.

Keywords : Non-axisymmetric surface, Turning, CAM, On-machine measurement, Rotary tool

1. Introduction

The fast tool servo (FTS) (Okazaki, 1990; Dow, 1991; Rasmussen et al., 1994; Zhu et al., 2001; Rakuff and

Cuttino, 2009; Zhou et al., 2016) was developed in order to achieve high-efficiency machining for workpieces with non-circular or non-axisymmetric surfaces, such as optical components. The FTS allows machining of non-axisymmetric surfaces by controlling the cutting tool to synchronize the cutting direction with the rotation of the workpiece at high speed using a piezoelectric actuator or a voice coil actuator. However, a minute stroke is inevitable owing to its mechanism. The stroke of the piezoelectric actuator is only tens of micrometers, and even the voice coil actuator has a stroke of only several millimeters. Therefore, the production target for the FTS is limited.

On the other hand, in practice, workpieces with a non-axisymmetric surface that require a long stroke movement in the cutting direction, such as cam profiles for an internal combustion engine, are machined by a dedicated grinding

1

Improvement of machining accuracy for 3D surface machining with CNC lathe

* Institute of Science and Engineering, Kanazawa University

Kakuma, Kanazawa-shi, Ishikawa 920-1192, Japan

E-mail: [email protected]

** Department of Mechanical Engineering, Kanazawa Institute of Technology

3-1 Yatsukaho, Hakusan, Ishikawa 924-0838, Japan

*** Technical Division, Takamatsu Machinery Co., Ltd.

1-8 Asahigaoka, Hakusan, Ishikawa 924-8558, Japan

Received: 18 January 2018; Revised: 25 May 2018; Accepted: 19 August 2018

Keigo TAKASUGI*, Yoshitaka MORIMOTO**, Yoshiyuki KANEKO***, Naohiko SUZUKI*** and Naoki ASAKAWA*

2© 2018 The Japan Society of Mechanical Engineers[DOI: 10.1299/jamdsm.2018jamdsm0089]

Takasugi, Morimoto, Kaneko, Suzuki and Asakawa,Journal of Advanced Mechanical Design, Systems, and Manufacturing, Vol.12, No.4 (2018)

machine (Yoneda et al., 1990; Tsai and Lee, 1999). Although this machining method is efficient, its versatility is low. Recently, it has become possible to use a multi-tasking machine tool, although such a tool has very low efficiency. Since the machining process is a milling-centric process, the machining time to achieve sufficient surface roughness remains long.

In order to solve these problems, we have developed a new lathe for non-axisymmetric curved surface turning (NACS-Turning) (Morimoto et al., 2014). In this lathe, a linear motor is adopted for the positioning mechanism in the cutting direction (X-axis), and CNC is designed so that several interpolation processes, such as position and velocity feedback control, are not executed in order to shorten the control period. Thus, it is possible to provide fast simultaneous control between the X-axis and the rotation spindle (C-axis) with a long stroke. An overview of the newly developed NACS-Turning method and its specifications are shown in Fig. 1 and Table 1, respectively. The NACS-Turning system is approximately the same as a general CNC lathe. However, the X-axis slide is designed to be driven until 10 ɡ and can be synchronized with the C-axis at 720 points per rotation. The C-axis then rotates at 375 min-1 while synchronized with the X-axis, which means that the CNC lathe can be controlled at a period of 0.222 ms. In the present study, since we focused on difficult-to-cut materials such as SKD11 (HRC 60) for the cam of an internal combustion engine, a cylindrical rotary tool has been implemented, and high cutting performance has been confirmed. Furthermore, since the NACS-Turning system is a machine tool that has a novel machining mechanism, there is no commercially available CAM system. Therefore, an original CAM system (Takasugi et al., 2014a) for NACS-Turning has been developed using our CAM kernel (Takasugi et al., 2014b). In the present paper, the method of generating the tool path for NACS-Turning is explained and the relationship between machining accuracy and the interval of machining points are researched. Using this CAM system, several workpieces with non-axisymmetric curved surfaces can generally be machined.

NACS-Turning has achieved high stroke and high efficiency turning for non-axisymmetric curved surfaces. However, the machining accuracy of NACS-Turning is insufficient because of the high accelerations involved in the

Fig. 1 Overview of the NACS-Turing system

C-axis

X-axis

Z-axis

Rotary tool

Workpiece

Table 1: Specifications of NACS-Turning

Specification Value

Head stock

Max. spindle speed 10,000 rpm Power of main motor 1.0/2.64 kW Stroke in the Z-direction 200 mm Max. acceleration in the Z-direction 12.1 m/s2

Carriage Stroke of X-direction 90 mm Max. acceleration in the X-direction 98.0 m/s2 Mass 36.4 kg

Total size 720 mm × 498 mm × 1,300 mm CNC Control period 0.222 ms

2



machining and the followability of the CNC, for example. If NACS-Turning was performed without compensation, the machining error would exceed 100 micrometers. Therefore, in the present paper, we describe the improvement in accuracy of NACS-Turning. Specifically, the goal is to achieve an accuracy capable of providing a general fit tolerance such as the h7/H7 tolerance for mechanical parts specified in ISO 286.

The errors in NACS-Turning can be assigned to three basic factors: (1) control delay of the linear motor in the X-direction, (2) insufficient servo stiffness due to the linear motor drive, and (3) tool deflection due to the cutting reaction force. Unlike a FTS, the X-axis linear motor is driven by a general CNC servo controller. As mentioned above, the controller is designed such that several interpolation and acceleration/deceleration processes are skipped in order to realize fast simultaneous control. This means that the synchronizing delay of the X-axis slide and the C-axis rotation cannot be controlled completely, which causes a synchronizing error. However, this error is constant. This error differs only slightly according to the machining. Therefore, in the present study, this error can be ignored by determining the delay of the C- and X-axes in advance by real cutting. The second factor, i.e., insufficient servo stiffness, is a disadvantage of the linear motor drive and causes deterioration of the machining accuracy. Since this error is derived from acceleration, the error distribution changes depending on the workpiece profile, i.e., the tool path. Moreover, since NACS-Turning is driven at high acceleration, this error is large compared with the other error factors. The last factor depends on the dynamic stiffness of the structure and does not occur only in NACS-Turning, although the instantaneous cutting depth differs point-by-point in this method. Therefore, it is difficult to estimate the error compared with general turning.

Therefore, in the present study, the mechanism of acceleration generation based on the machining principle of NACS-Turning is first described, and a tool path generation method that can minimize the acceleration is proposed. However, since it is impossible to set the acceleration to zero, errors on the machine tool side must also be considered. Here, two methods were implemented. One is to compensate for position deviations of the X-axis between the command position values and real-position values from servo feedback measured by the linear scale during real movement. The improved tool path is generated by adding the measured deviations to the original tool path. Then, since performing compensation only once cannot sufficiently improve the accuracy, this process is repeated until the deviations saturate.

The above compensation method is applied to compensate for factor (2) without real cutting. Therefore, another compensation method is needed for factors (2) and (3) on the machine tool. The second compensation method involves on-machine measurement in order to compensate for factors (2) and (3) considering real cutting. We constructed a system of on-machine measurement using a line laser sensor and a feedback system of the measurement data. The measured data are fed back to the CAM, and a re-machining tool path is generated.

In the present paper, we first explain the machining principle of NACS-Turning, and the relationship between the machining conditions and acceleration is clarified. Thus, a basic technic for suppressing acceleration when a tool path is generated on the CAM is presented. Next, two compensation methods, namely, repeated compensation of servo delay and compensation by on-machine measurement, are proposed for the machine tool. Finally, the effectiveness of the compensation is verified.

2. Machining principle in NACS-Turning 2.1 Geometric machinable condition

As described above, since, in the present study, a cylindrical rotary tool is used instead of a general turning tool, interference between the workpiece and the tool must be considered, as shown in Fig. 2. An idea for preventing interference is to prepare a tool offset in the Y-axis direction (Fig. 2(b)). In the following, we describe the derivation of the tool offset.

As shown in Fig. 3, the relationship between a workpiece with a non-axisymmetric surface and the rotary tool is similar to the relationship between a cam and a cam follower. In other words, the cam slides in the X-direction while maintaining contact with the cam follower. Then, the necessary tool offset value d is obtained by deriving the maximum value of the Y-coordinate (yd)max at the contact point P = {xd, yd} during one rotation of the cam. When the cam profile is defined as a parametric curve C(t) represented by a curve parameter t ∈ [0, 1] and a unit vertical vector L = {0, 1}, the following two equations are obtained:

=

=′

)(

)(

t

t

RCP

LCR (1)

3



where C' is the first-order differential of t, and R is the two-dimensional rotation matrix at the angle θ between L and C'.

−=

θθ

θθ

cossin

sincosR (2)

By deleting θ in Eq. (1), the following x-y coordinates about d are obtained.

′−′

′−′=

yyxx

xyyx

d

d

y

x

CCCC

CCCC (3)

where subscripts x and y represent the X- and Y-coordinate values, respectively. From Eq. (3), the necessary minimum tool offset value can be obtained by calculating (yd)max with an appropriate numerical method, and the machinable condition is cleared by selecting a value greater than (yd)max. Then, a method by which to determine the value of d that is greater than (yd)max is clarified by investigating the relationship between the tool offset and acceleration.

2.2 Relationship between tool offset and acceleration

Although preparing the tool offset is the necessary machining condition for this method, the tool offset causes deterioration of the acceleration of the X-axis slide. In this section, the relationship between the tool offset and acceleration is clarified in terms of the form shaping theory (Portman, 1981; Reshetov and Portman, 1988). The acceleration in the X-direction can be approximated by the discrete second-order differential of the travel distance between adjacent machining points on the X-axis slide. Namely, clarifying the relationship between the x coordinate value of the X-axis slide at each machining point and d can provide the relationship between acceleration and d.

The form shaping function of NACS-Turning is expressed as follows: tXZCw rAAAr = (4)

where AC, AZ, and AX are homogeneous transformation matrices that express the travel distance along each axis indicated by the subscript. Here, rw = [xw yw zw 1]T and rt = [xt yt zt 1]T are the position vectors in the workpiece and the

Rotary tool

Interference

x

y

x

y

Workpiece

Turning toolRotation center

Offset d

Fig. 2 Machining mechanism of NACS-Turing and required tool offset

(a) General turning tool (b) Rotary tool

x

y

yd

Workpiece profile

θ

C(t)

C (t0) t0

Tangential vector

xd

P

Fig. 3 Derivation of the required tool offset

4



tool coordinate systems, respectively. Then, when the origin of the tool coordinate system is set at the bottom face of the rotary tool, rt yields [0 d 0 1]T. Moreover, we simply need to discuss the form shaping function on the x-y plane. Therefore, Eq. (4) is simplified as follows:

+

+−

=

−

=

1

sincos

cossin

1

0

100

010

01

100

0cossin

0sincos

1

θθ

θθ

θθ

θθ

xd

xd

d

x

y

x

w

w

(5)

From Eq. (5), the travel distance in the X-direction expressed as 222 dyxx ww −+= (6)

Equation (6) is described geometrically as shown in Fig. 4(a). When a base circle of radius d from the rotation center of the C-axis is described, travel distance x is the length of a tangential vector from the circle to the workpiece profile. Then, since the rotation speed is constant and there are 720 machining points per rotation, if the workpiece profile is axisymmetric, the arc lengths between continuous machining points are constant. However, in the case of non-axisymmetry, the arc lengths are not constant. Therefore, movement of the X-axis, i.e., acceleration, is generated.

Figure 4(b) shows the case in which d is larger than in Fig. 4(a). The tool is shifted to the +Y-direction. The change in the distribution of the arc lengths can be confirmed. Then, the arc lengths increase, and the acceleration is also believed to increase. In order to confirm the relationship between acceleration and d, we defined the workpiece as shown in Fig. 5 and simulated the acceleration distribution. The cross sections of this workpiece are composed of an arc part and a free curve part. In addition, non-axisymmetry increases in the –Z direction from the edge face, and the

Fig. 4 Geometric relationship between acceleration, tool offset, and rotation direction

(a) Geometric deviation of tool travel distance on the X-axis

(b) With changing tool offset (c) With changing rotation direction

d

|rw|d

Rotary tool

Machining point rw

Workpiece curve C(t)

x

Base circle (radius: d)

Tangential line

Arc length s(t)

P

O

Q

xy

z27mm

Cross section A

x

y

33 m

m

30 mm

Cross section B

5o

x

y

39 m

m

30 mm

Free curve part

Fig. 5 Workpiece used in the verification of acceleration reduction with changing rotation direction

5



maximum twist of the cross section profile is 5 degrees. The X-axis does not travel along the arc part because of axisymmetry, although the acceleration along the free curve part is based on Eq. (6). Figure 6 shows the simulation results for acceleration along the X-axis on cross section B during one rotation as d is changed. Acceleration is confirmed to increase due to the increase of d.

For the above reasons, d must ensure the machinable condition, although d must be minimized in order to suppress acceleration. Therefore, ideally, d = (yd)max. However, in practice, d is determined to be greater than (yd)max for safety considerations. Therefore, the value obtained by adding 0.5 mm to (yd)max is adopted as d in the present study.

3. Acceleration reduction by changing the rotation direction

In NACS-Turning, another method of reducing acceleration along the X-axis can be achieved geometrically.

Figure 4(c) shows this method, which indicates that the tool is shifted to the counter side of the workpiece. By doing so, the rotation direction of the C-axis is inversed, and acceleration is changed dramatically, as compared with the case of Fig. 4(a), even if the offset amount is the same. Figure 7 shows an example of excess acceleration calculated on the CAM to the workpiece shown in Fig. 5. In this section, 4 ɡ is set as the limit of acceleration for instance. It can be confirmed that the change in the tool position causes a change in the acceleration area. Therefore, it is possible to perform machining considering acceleration reduction by adopting the following acceleration. First, an initial tool path is calculated, and the theoretical acceleration is calculated simultaneously. If an area of excess acceleration is detected, the tool path is modified so that the excess area is not cut, i.e., air-cut, as shown in Fig. 8. After that, the tool is positioned at the inverse side, and a new tool path is calculated. Then, although a different area will experience excess acceleration, this is not a problem because the area was already cut at the initial tool position.

0 90 180 270 360

0

-2

-4

2

4

6

Acc

eler

atio

n of

X-a

xis s

lide

[ɡ]

Rotation angle [deg.]

d = 8

d = 5

d = 2

Fig. 6 Change in acceleration for each tool offset

Fig. 7 Generated tool path in CW and CCW rotation (excess acceleration area is shown in red)

Tool path

Area of excess acceleration

CCW CW

6



When a tool path with air-cuts is generated, it is important to consider the continuity of the connection points Ps and Pe from an air-cut to a real-cut, as well as that from a real-cut to an air-cut. If acceleration is discontinuous, the continuity of acceleration, namely jerk, must be considered because an instantaneous change in acceleration causes

Fig. 8 Schematic diagram of air-cut path generation

Tool pathwith air-cut x

y

Area of excessAcceleration

Ps

Pe

Initial tool path Tool

0

-30

-20

-10

0

10

20

30

-30 -20 -10 0 10 20 30

Path modified by air-cut

Original path

0

0 0

15

20

25

30

-0.2

-0.1

0

0.1

0.2

0.3

0

4

2

6

-2

-4

0

-2000

-4000

-6000

2000

4000

6000

Posit

ion

ofX

[mm

]V

eloc

ity [m

/s]

Acc

eler

atio

n [ɡ

]Je

rk [m

/s3 ]

Rotation angle [deg.]90 180 270 360




Fig. 9 Tool path modified by air-cut (position, velocity, acceleration, and jerk for the original and modified tool paths)

7



cutter marks. In this report, the following equation, referred to as the Ferguson interpolation curve (Ferguson, 1964), is adopted for the air-cut path:

∑=

=7

0

)(i

iiair bC ττ (7)

where τ ∈ [0, 1] is the curve parameter, τ = 0 at Ps, and τ = 1 at Pe. The curve order is set at eight considering the position vector to the jerk vector, and bi are coefficients. When all bi are found, Cair is uniquely determined. Here, bi can be found as follows. When the positions, velocity, acceleration, and jerk of the X-axis at Ps and Pe are defined as xs, xe, vs, ve, as, ae, js, and je, these values are determined from the tool path and correspond to the first- through third-order differentials of Cair. Therefore, the following equation is obtained:

=

′′′

′′′

′′

′′

′

′

=

e

s

e

s

e

s

e

s

j

j

a

a

v

v

x

x

C

C

C

C

C

C

C

C

b

b

b

b

b

b

b

b

3

3

2

2

0

1

2

3

4

5

6

7

)1(

)0(

)1(

)0(

)1(

)0(

)1(

)0(

00062460120210

00060000

002612203042

00200000

01234567

01000000

11111111

10000000

τ

τ

τ

τ

τ

τ

(8)

Equation (7) is determined by solving for bi in Eq. (8). Figure 9 shows graphs that express the status of the tool path at cross section B after applying air-cut paths. The acceleration is confirmed to be reduced to less than 4 ɡ, and continuity at connecting points is ensured from the position vectors to the jerk vectors. Moreover, Fig. 10 shows the overall re-calculated tool path. The excess acceleration areas shown in Fig. 7 have disappeared, and the addition of partial air-cut paths can be confirmed in each rotation. Finally, Fig. 11 shows the accelerations for real movement for the cases with air-cut and without air-cut. The accelerations for the real movement and the simulation are in

CCW CWFig. 10 Re-generated tool path considering excess acceleration

0 10 20 30Time [s]

5 15 25

0

-2

2

Acc

eler

atio

n of

X sl

ide

[ɡ] 4

-4

0

-2

2

Acc

eler

atio

n of

X sl

ide

[ɡ]

0 10 20 30Time [s]

5 15 25

4

-4

Fig. 11 Acceleration for the nominal tool path and the tool path with air-cuts (a) Without air-cut (Original tool path) (b) With air-cut (Proposed tool path)

8



approximate agreement, as shown in Fig. 9, and the reduction of acceleration can also be confirmed by the simulated values.

4. Compensation of position deviation through repeated compensation

As mentioned in the introduction, in NACS-Turning, multiple feedback control of the servo motors is not executed in order to realize the fast synchronous control. This means that the X-axis can move to the next command point before it reaches the current command point. Figure 12 shows the step response to the step command of 100 µm on the X-axis. Approximately 40 ms is required in order to achieve the command value. Since the control period in NACS-Turning is 0.222 ms, as shown in Table 1, the X-axis moves to the next position before the X-axis slide reaches the command value. In other words, real positioning of the X-axis is expressed in a manner similar to the convolution of a digital filter. However, it is difficult to derive the filter coefficients analytically because an enormous number of filter coefficients will be required. Therefore, the present study uses a simpler pre-compensation method, which can be conducted on the machine tool before real cutting, as follows.

First, the original tool path without compensation is expressed as CL0, and the NACS-Turing is actuated by air-cut using the CL0. Then, real positioning values FB0 from the servo motor are recorded. The difference between CL0 and FB0 is defined as follows:

000 FBCLdiff −= (9) and the next tool path CL1 including the compensation value is calculated as follows:

001 diffwCLCL ⋅+= (10) where w ∈ (0, 1] is the weight of compensation. From Eq. (10), a new tool path considering deviations between the command and real positions is obtained. However, sufficient accuracy cannot be ensured by one compensation. Therefore, this compensation cycle is executed repeatedly until the deviations converge to an appropriate value. Then, this compensation cycle is expressed as follows:

ii FBCLdiff −= 0 (11)

-120

-100

-80

-60

-40

-20

0

20

0 0.01 0.02 0.03 0.04 0.05

Posit

ion

of X

slid

e [ ∝

m]

Time [s]

Output (Step response)

Input (Step command)

Fig. 12 Step response on the X-axis

Fig. 13 Verification of compensation

(a) Defined workpiece profile (b) Relationship between number of compensations and deviation

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 2 3 4 5 6 7Number of compensations

Posit

ion

devi

atio

nof

X sl

ide

[mm

]2 µm

4mm

38mm

x

y

Center of rotation

0

9



)10(1 ≤<⋅+=+ wdiffwCLCL iii (12) where i is the counter parameter. In Eq. (11), when diffi is calculated, the calculation has to be executed for the original tool path (CL0) and the ith positioning values (FBi).

In order to verify the effectiveness of the proposed method, the relationship between the number of compensations and the change in the position deviation was examined for the workpiece defined in Fig. 13(a). The defined workpiece is circular with a diameter of 38 mm, where the center of the circle is shifted by 4 mm from the rotation center of the C-axis. Then, the maximum acceleration of the X-axis is approximately 1 ɡ for the simulation. Here, w is set at 0.9. Figure 13(b) shows the history of the position deviations for each compensation. The original tool path has a deviation of over 120 µm. However, the deviation is confirmed to have been reduced substantially as the compensation was repeated, and the deviation became less than 2 µm after the seventh compensation. In this case, although the deviation was greatly improved because the defined workpiece had a primitive profile, the deviation was confirmed to have been suppressed to within ±10 µm, even for a more complex workpiece and a higher required acceleration.

Therefore, a simple compensation method for the error derived from the servo stiffness before real cutting was developed, and its effectiveness was demonstrated. In the next section, we consider the compensation method for factors (2) and (3) for real cutting. Since the errors are derived from the cutting reaction force, it is difficult to predict the required compensation before cutting. Therefore, we improve the accuracy by measuring the workpiece profile obtained by real cutting.

5. Improvement of machining accuracy by on-machine measurement 5.1 Configuration

Figure 14 shows the system developed for on-machine measurement. A machined workpiece is measured using a laser displacement sensor (LJ-V7020, KEYENCE) mounted on the tool holder in NACS-Turning. The repeatability of the sensor is 0.2 µm, and the measurable region is shown in Fig. 15. The measured data, which constitute a point cloud, are fed back to the CAM and reconstructed using a 3D model. Next, by considering the differences between the measured and defined 3D models, a new tool path having an appropriate cutting depth is obtained, and re-machining is performed.

When a measurement device is mounted to a machine, setting errors must be recognized and adjusted beforehand. In the case of this line laser sensor, the system includes Y-direction, pitch, roll, and yaw errors. Identification of these rotation errors or the position error described above can be converted into the problem of identifying volumetric errors in machining tools. For example, Umetsu et al. (2005) investigated a calibration method for a coordinate measuring machine (CMM) that uses a laser tracker system. In this method, by solving simultaneous equations for the overcomplete system consisting of the light path length and the positions of the laser sensor, volumetric errors are identified. Therefore, we applied an error identification method, as described in the next section, based on this identification method for volumetric errors for a CMM. Figure 16 shows the developed jig for adjustment of the laser sensor. The jig has adjusting bolts for the yaw, pitch, and Y-direction errors. The roll error is adjusted by grinding the

3D measurement device

Workpiece

NACS-Turning

CAM

Measured data

Re-machiningpath

Fig. 14 System configuration of on-machine measurement

Measurable region

Reference line

7 mm(Length)

5.2 mm(Depth)

Laser sensor

20 mm

Fig. 15 Measurable region of the implemented line sensor

10



surface where the jig and bottom surface of the tool holder are attached.

5.2 Calibration of sensor position In the present study, these setting errors are adjusted using a cylindrical artifact, as shown in Fig. 17. Then,

adjusting the roll and yaw error is easy. If there are no roll and yaw errors, the obtained displacement data should be constant in the length direction of the line laser. In contrast, when roll and yaw errors exist, different distances are detected in the length direction. Therefore, we can adjust the angles to a certain level of repeatability of the sensor. However, it is impossible to separate the Y-direction error and the pitch error, because the difference between the errors does not appear as the difference between the displacement data for one measurement. Accordingly, it is necessary to adjust the Y-direction and the pitch errors. Specifically, we used geometric relationships and a convergence calculation with the Newton method to separate these two errors, as shown in Fig. 18. First, the sensor is set at the coordinate values B(x, y) where the laser length l1 is the shortest. This operation is performed manually using positioning on the Y-axis of the machine tool. Then, B(x, y) includes both errors, and the coordinates of point A irradiated with the laser will be (r, 0), where r is the radius of the artifact. Next, the sensor is shifted in the X-direction by ∆x. Let us regard the positioning accuracy of the machine tool as sufficiently small compared to the position errors of the sensor; the coordinate values of the sensor change to (x+∆x, y) according to only the setting errors. Then, the position on the artifact indicated by the laser is dislocated from A(r, 0) because of the error ∆x. Therefore, as in the above manual method, point A(r, 0) is searched again. When the movement in the Y-direction and the laser length for this case are ∆y and l2, respectively, the sensor is located at C(x+∆x, y+∆y), and following equations are obtained from the above geometric relationships:

Adjuster for Y dir.

Adjuster for rollAdjuster for yaw

x zy

Fig. 16 Adjustment jig for setting the errors of the laser sensor

Laser sensor

Artifact(Cylinder)

xz

y

y

x

y

x

y

z

z

x

Fig. 17 Variation including setting errors of the laser sensor

(a) Isometric view (b) Y-direction error (c) Pitch error

(d) Roll error (e) Yaw error

11



∆++−∆+=

+−=

2222

2221

)()(

)(

yyrxxl

yrxl (13)

Since the variables without x and y are known, Eq. (13) can be solved by numerical calculation, for example, using the Newton method, and B(x, y), i.e., the pitch and Y-direction errors are revealed.

5.3 Verification

We attempted to verify the improvement in accuracy by real cutting of the workpiece defined in Fig. 19. The workpiece is composed of circles on an x-y cross section. Although the center of the circle corresponds to the rotation axis at the edge face of the workpiece, the degree of non-axisymmetry increases gradually. The center of the circle is

A(r, 0)

l1l2

y

B(x, y)

Artifact

Sensor

r C(x+ , y+ )

x x

y

x y

Fig. 18 Geometric relationship for separating the Y-direction and yaw errors

Fig. 19 Defined workpiece for verification of the on-machine measurement system

21

35 29x

y

z

y

Unit: mm

Position in z direction0 3 96 12 15 18 21

-60

-40

-20

0

20

40

60

80

100

Fig. 20 Analysis results for the CAM of on-machine measurement

(a) Reconstructed model (b) Deviation between defined workpiece profile and measured data

12



shifted approximately 4.5 mm in the +Y-direction at Z = -21 mm. Therefore, the X-axis does not move at the beginning part of the workpiece. However, the movement of the X-axis gradually becomes faster as the machining advances. The workpiece is machined by NACS-Turning beforehand until the remaining finishing depth becomes approximately 0.3 mm. The cutting conditions are shown in Table 2.

Next, Fig. 20(a) shows the reconstructed workpiece shape on the CAM from on-machine measurement data. This point cloud contains a total of 5,160 points. Moreover, Fig. 20(b) shows the deviation between the measurement data and the defined surface. The maximum deviation is 76 µm. Finally, an overview of the machined workpiece based on the error distribution is shown in Fig. 21. At the beginning of machining (Z = 0), since the workpiece is approximately axisymmetric, turning can be performed in a few strokes in the X-axis direction, and the deviation also can be suppressed. However, as machining progresses, the degree of non-axisymmetry and the load due to rapid driving in the X-axis direction increase. Therefore, the deviation also gradually increases. The measurement results for the diameters and circularities at sections (a) and (b) in Fig. 21 are listed in Table 3. The objective was to achieve the general fit tolerance for mechanical parts. This confirmed that high accuracy, i.e., 8 μm at (a) and 2 μm at (b), is obtained for the target tolerance. In particular, since the tolerance at (b) is less than that at (a), where the X-axis does not move, the effectiveness of the compensations was confirmed to be sufficient. However, unlike the circularities at (a), those at (b) are not satisfactory. The following are assumed to be the reasons for this.

i. Deformation of the workpiece by chucking pressure ii. Effect of machining load

First, it is assumed that the workpiece is attached with little deformation due to the high chucking pressure. In this case, since the machining induces some deformation, when the workpiece is detached, i.e., the pressure is released, after machining, the deformation remains. Next, the X-axis in NACS-Turning is assumed to have different machining loads between the direction approaching the workpiece and the direction of retraction from the workpiece. If the latter is the main reason for the insufficient circularity, another compensation method must be considered. However, we intend to improve this method in future studies.

6. Conclusion

The present paper described the development of a novel machining method for non-axisymmetric curved surface

turning, called NACS-Turning, and its machining accuracy. In NACS-Turning, without compensation, machining errors of several hundred micrometers may occur; therefore, in the present study, we attempted to suppress errors of less than several micrometers. Specifically, the relationship between acceleration, which has an adverse influence on the machining accuracy, and this machining method is revealed, and we proposed a method for reducing acceleration

Fig. 21 Re-machined workpiece

5mm

(b)(a)

Table 3: Machining accuracy after the proposed compensation Place Diameter [mm] Circularity [mm]

(a) 29.008 (error: 0.008) 0.0152 (b) 34.9983 (error: -0.002) 0.0544

Table 2: Cutting conditions Cutting parameter Value Spindle speed [rpm] 375

Feed [mm/rev] 0.2 Depth of cut [mm] 0.3 Tool offset [mm] 7.5

Workpiece material SKD11

(HRC60)

13



on the CAM based on the acceleration characteristics. Moreover, a repeated compensation for the delay of the linear motor on the X-axis and a compensation using on-machine measurement for the cutting reaction force were proposed. As the result of these compensations, we obtained sufficient machining accuracy, which can generate mechanical parts capable of achieving the general fit tolerance.

Therefore, we presented a method by which to make practical use of the machining method for non-axisymmetric curved surfaces with unprecedented high versatility and efficiency.

Acknowledgment

The present study was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Number JP15554114).

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improvement of machining accuracy for 3d surface machining

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