A Strategy for Identifying Static Deviations in

International Conference on Leading Edge Manufacturing in 21st Century Oct. 19-22, 2005, Nagoya, Japan Copyright 2005

A Strategy for Identifying Static Deviations in Universal Spindle Head Type Multi-axis Machining Centers 1

Muditha Dassanayake K.M.1, Masaomi TSUTSUMI2, and Akinori SAITO3 Postgraduate, Tokyo University of Agriculture and Technology, 2-24-16 Nakacho, Koganei, Tokyo 184-8588，Phone: 042-388-7086, Fax: 042-388-7219 [email protected] 2 Professor, Tokyo University of Agriculture and Technology, 3 Associate Professor, Nippon University, Koriyama, Fukushima

Summary A number of test methods for checking the geometric inaccuracy of the RRTTT type five-axis machining centers have been specified in ISO standards. However such procedures are relatively involved in terms of equipments and operator expertise and simpler means are thus sought. This paper presents a new calibration method to check the geometric inaccuracy of the RRTTT type machining centers which is based on the modified motion of the basic motion described by the spherical interpolation of five axes as specified in clause K6 of ISO 10791- part 6. In addition, a methodology for identifying the static deviations is proposed. This methodology consists of three steps. In the steps 1 and 2, six of ten deviations were identified by means of observation equation. The rest of the ten deviations were identified in the step 3 by means of link geometry of the machining center. The simulations are carried out to verify the proposed calibration method and the results are confirmed that the proposed method gives good results for deviations. Key words; Multi-axis machining center, Observation equation, Geometric deviation, Spherical motion 1. Introduction In many minds, five-axis machining is synonymous with subtle curves. Feed with two rotary axes in addition to the standard three linear axes, make the machine capable to reorient the tool and /or workpiece in numerous compound angles(1), with only one setup required. This feature significantly reduces the cycle time and the cost of preparing fixtures through the elimination of manual repositioning and as a result the repositioning errors are eliminated. In addition, the five axis machining centers enable to use shorter cutting tools since the head can be lowered towards the work and the cutter oriented towards the surface. As a result higher cutting speeds can be achieved without putting excessive load on the cutter and it significantly reduces the vibration of the tool which effect to the surface finish of the workpiece. The manufactures of aircraft structural components, automobile parts etc. have been demonstrating these benefits for years. Even though the five-axis machining centers are very versatile, the users of these machining centers have to answer to the accuracy of the machined components which mainly depends on the geometric accuracy(2) of the machining centers. In past decades, a number of research works carried out on the geometric errors in five-axis machining centers. Two of authors(3),(4) reported two different identification methods for systematic deviations inherent to ZX/YAC (TTTRR) type machining centers by using simultaneous 3- and 4-axis control motions. The experimental data are gathered by using telescoping magnetic ball bar(5). Sakamoto and Inasaki(6),(7),(8) developed the identification methods of alignment errors of universal spindle head (RRTTT) type machining centers. Furthermore, in ISO 10791-1(9) specified seven clauses (BG1to BG7) to check the static deviations in universal spindle head of five-axis machining centers. However such procedures are relatively involved in terms of equipments and operator expertise and simpler means are thus sought. ISO 10791-6(10) specified a method for RRTTT type machining centers to check the accuracy of the path described by spherical interpolation of five axes and this method only gives the maximum or minimum deviation of the path. However, the tolerance of the error is not specified in the standard. Although a number of methods have been specified in ISO standards on the measurement and improvement of motion accuracy of RRTTT type machining centers, all the deviations cannot be identified. The necessity of an identification method is pointed out at the meeting of ISO TC39/SC2(11). This paper newly proposes a measurement method to check the geometric inaccuracy of the RRTTT type five-axis machining centers. The motion used in this method is a modified version of the basic motion specified in the ISO standard(10). Furthermore, in particular, a methodology for identifying the static deviations is proposed. This methodology consists of three steps. In the first and second steps, six of ten deviations were identified by means of observation equation based on least square method. The rest of the ten deviations were identified in the third step by means of link geometry of the machining center. The simulations are carried out to verify the proposed method and it is confirmed from the simulation that the proposed method gives good resolutions for deviations. - 121 -

Relative motion Spindle motion

Spindle head

Saddle

A-axis motion

C Table

Y

A

C -axis motion Y-axis motion

X

Positional deviations

Angular deviations

δ xSA δ ySA δ zSA

α SA β SA

δ yAC

β AC α CY β CY γ CY α

Z Bed

Z -axis motion X-axis motion

Fig. 1 Configuration of universal spindle head type five-axis machining center

YZ

β ZX γ ZX Where, αZX=αYZ , βCY=βCX

Fig.2 Determination process of inherent deviations

Spindle 2. Spherical Motion Specified in ISO 10791 side b 2.1 Configuration of 5-axis machining center and its a,d,g e inherent deviations The five-axis machining center used in this study is a universal spindle head type as illustrated in Fig. 1. The machine consists of basic linear axes, X, Y and Z c L SA R LS and two controllable rotary axes A and C which Ball bar Y provide two degrees of freedom to the spindle head. X Z Table side f The deviations inherent to this type of machining (a) Spherical path (b) Set-up of ball bar centers were determined by considering the A C X Y Z axis-rot． configuration of the machine(12). a 0º 0º 0 0 R 0º Fig.2 shows the inherent deviations determined by b -90º 0º 0 R 0 90º Inasaki et. al. It can be seen from the figure that there c -90º 90º R 0 0 180º are thirteen deviations(12) including four positional d 0º 90º 0 0 R 270º deviations and nine angular deviations. Among them e 90º 90º -R 0 0 360º three deviations, αYZ, βZX and γZX are related only f 90º 0º 0 -R 0 450º with basic translational axes which can be checked g 0º 0º 0 0 R 540º by conventional ways using dial gages and precision (c) Coordinates of starting and passing points levels. Only ten deviations which are highlighted in the Fig.3 Setup and motion specified in ISO10791-6 figure can be identified as the inherent deviations to RRTTT type machining centers. Among these ten deviations, γCY, αSA and δzSA are adjustable. 2.2 Spherical motion specified by ISO 10791-6 The basic motion specified in the clause 6 of ISO 10791-6 is a spherical interpolation motion as shown in Fig.3. The motion is described by the trajectory of the center of the ball on the spindle side which moves along the path shown in Fig.3(a) by passing through the points (a) to (g) as specified in Fig.3(c) respectively. These points are specified according to the coordinate system at the center of the ball on table side. 2.3 Effectiveness of the measurement defined by ISO 10791-6 2.3.1 Simulation procedure The influence of the 10 deviations on the shape of motion trajectory was simulated under the specified motion by means of the software called Dynamic Analysis and Design System (DADS). The deviations are applied one by one to the model under the same initial conditions and the data which represents the effect of each deviation to the motion trajectory are extracted. 0.01° and 0.01 mm were given as angular and positional deviations for the simulation, respectively. The setup of the ball bar is illustrated in Fig.3(b). The ball on the spindle side is set on the projected arm (length LS=100mm) from the spindle as in the figure. 2.3.2 Simulation results The simulated trajectories which are plotted against axis rotation are shown in Fig. 4. αCY, αSA and δySA are described same sine curves from 0°to 180°and from 360°to 540°of axis rotation. When considering the cumulative result these three entities act together. If one, two or all entities are negative or positive, the cumulative result can be even zero, very small value or very high negative or positive value from which we cannot understand anything. As well, the four deviations of βCY, βAC, βSA and δxSA are described same sine curves from 90°to 450°of axis rotation as shown in Fig.4(b). These deviations also act as explained above.

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αSA

δxSA

0.02

βCY

0.04 0.02

δxSA

0.015

βAC βSA

0 -0.02 -0.04

0 -0.02 -0.04 -0.06

Deviation (mm)

0.08 0.06

αCY

Deviation (mm)

Deviation (mm)

0.08 0.06 0.04

0

90

180 270 360 Axis rotation (0)

450

540

γCY

0.005 0

-0.005

δyAC

-0.01

-0.06 -0.08

-0.08

δzSA

0.01

-0.015 0

90

180 270 360 Axis rotation (0)

450

540

0

90

180 270 360 Axis rotation (0)

450

540

(b) δxSA, βCY, βAC and βSA (c) δzSA, γCY and δzSA (a) αCY, αSA and δySA Fig.4 Influence of deviations for the motion specified in ISO 10791-6

Therefore, the above two groups can be considered as two unique patterns. As shown in the Fig.4(c) the δyAC shows a strange behavior within 90ο to 450ο range of axis rotation and identified as a unique pattern. γCY is the initial angular position of C axis which can be adjusted at the calibration level of the assembling process of the machine. However it can be a very small angular deviation remains at the C axis. As according to Fig.4(c), when γCY is considered as 0.01ο the shown effect is very small as 0.0018mm compared to other influences. Therefore we can neglect the effect of γCY for above motion. Thus we can also consider the effect of δzSA as a unique pattern. As the projected length is influenced to the effect of angular deviations, the deviations αCY, αSA, βCY, βAC and βSA give comparatively larger values. Among them, αCY and βCY which are applied at the furthest point from center of the ball on spindle side give the maximum deviations of 0.06mm. As the effects of linear deviations are independent from the projected length, the deviations δxSA, δySA, δzSA and δyAC give maximum deviations of 0.01mm. Since the five moveable axes are involved three at a time to achieve the spherical interpolation motion all or most of the inherent deviations influence to the motion trajectory. Thus the potentiality of the motion to use for identifying the deviations is very high. But as this motion is carried out with the setup specified in the clause 6 of ISO 10791-6, only two deviations δyAC and δzSA show the unique patterns. Therefore, it may be said that some alternative motions are needed to evaluate the ten deviations inherent to the RRTTT b type machining center, because two deviations can a,d,g,h e only be identified by considering the shapes of the trajectories. 3. Newly proposed setup and motion c 3.1 Newly proposed setup to achieve the spherical LB motion L SA LS The setup which is illustrated in Fig.5 is newly R X YZ f Ball bar Spindle side proposed to use the spherical motion effectively for Table side (a) Spherical path (b) Set-up of ball bar identifying the deviations. The jig is prepared such that distance LB and LS have 200mm and 100mm Z Y A axis-rot． X C respectively. The offset arm is set in the negative X a R 0 0º 0º 0 0º direction. The axes are moved to achieve the motion b 0 -90º R 90º 0 0º illustrated in Fig.5(a). The motion of the center of the c 0 -90º 180º 0 90º R ball on spindle side is same as the motion shown in d 0º R 270º 0 90º 0 Fig.3. Only difference is that in this motion the center e 90º 0 360º 0 90º -R of the ball on spindle side passes through eight points as specified in Fig.5(c) as according to coordinate 90º f 450º 0 0º -R 0 system at the center of ball on table side. That is the 0º g 540º R 0º 0 0 range of the angle of axis rotation is expanded by 90ο 0º 630º R 90º 0 0 h without changing the spherical motion. (c) Coordinate of starting and passing points 3.2 influence of deviations to motion trajectory Fig.5 Newly proposed setup and motion Simulations are carried out by following the same procedure mentioned in Chapter 2 and the motion explained above. The deviation δzSA is an adjustable deviation which can be adjusted by adjusting the tool offset parameter easily. Since this is considered as possible to identify by using the first motion, only the 9 deviations except δzSA are considered here. The simulation trajectories which are plotted against to axis rotation are shown in Fig.6. It can be seen from the figure that there are six unique patterns. βAC and βxSA are described sine curves in between 90ο to 450ο of axis rotation and show the same behavior which explained in the previous section. αSA and δySA are also described sine curves in between 0ο to 180ο and 360ο to 540ο of axis rotation. As the

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δxSA

0.02 0 -0.02

βAC

-0.04 -0.06 0

90

180 270 360 450 540 630 Axis rotation (0)

(a) βAC and δxSA

0.04 0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04

γCY δyAC

δySA

Deviation(mm)

0.04

Deviation (mm)

Deviation (mm)

0.06

αSA 0

90

180 270 360 450 540 630 Axis rotation (0)

0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08

αCY

βSA

βCY 0

(b) αSA, δySA, δyAC and γCY Fig.6 Influence of deviations for newly proposed motion

90

180 270 360 450 540 630 Axis rotation (0)

(c) βSA, βCY and αCY

Deviation(mm)

above deviations are acting together, the four deviations 0.1 cannot be identified by using these motions. 0.08 Since δyAC is considered as possible to identify by using the New motion 0.06 previous motion, it can be considered as an ineffective 0.04 deviation. Therefore, the effect of γCY can be identified as a 0.02 unique pattern. As shown in Fig.6(c), αCY, βCY and βSA give 0 unique curves. When consider the influences between the -0.02 ο ο ISO 10791-6 range from 0 to 540 of axis rotation, the proportionate -0.04 cumulative figure of the influences of δySA, αCY and βAC gives -0.06 the equal result as the influence of βCY and thus cannot be 0 90 180 270 360 450 540 630 Axis rotation ( ) identified. However the newly proposed additional movement Fig.7 Ball bar outputs for the spherical in the range 540ο to 630ο of axis rotation gives a unique identity motions for the influences of αCY and βCY which emphasize the Table 2 Random and identified values importance of that motion to separate the two influences. for deviations According to these figures, it can be said that at least four of DeviRandom Identified values nine deviations can be identified by considering the shapes of ations values Step 1 Step 2 Step ３ the trajectories. This is emphasized that the newly proposed jig α CY /(º ) --0.0065 --0.00016 --0.00652 is considerably affected to the motion mentioned above. 0

βCY /(º )

-0.0084 -

0.00176

--0.00837

_ 0.00699 γ CY /(º ) 0.0070 4. Methodology for identifying deviations 4.1 Estimation of deviations using observation equation β AC /(º ) 0.0039 _ _ 0.00390 The deviations are estimated by using the method based on α SA /(º ) 0.0090 _ _ 0.00899 observation equation proposed by two of authors(4). For the β SA /(º ) 0.0120 _ 0.01200 whole process, it is assumed that the absolute distance δ xSA/(mm) -0.0051 _ -0.03198 -0.00510 between the two balls of the ball bar is accurately calibrated _ 0.03083 0.00725 δ ySA/(mm) 0.0073 prior to measurement, the translation axes are also -0.01801 δ zSA/(mm) -0.0180 perpendicular to each other, and the circular motions specified by ISO 10791-8(13) have no deviations. As mentioned above δ yAC/(mm) --0.0077 --0.00770 the ten deviations are considered and assumed that the angular and linear deviations effect to the motion trajectory linearly within the range of -0.1 to 0.1 degrees or millimeters respectively. The maximum permissible deviations for the machining centers with horizontal Z axis and universal spindle head(9) are 0.04/500=0.0045° and 0.03mm for the squareness and the shift between the two moving axes respectively. It can be said that the ranges of angular and positional deviations considered in the study are sufficient to carryout the simulations in order to check the deviations, because they are large enough to compare with the permissible deviations specified in the test conditions for the machining centers. Therefore all the deviations are assumed to be in this range. 4.1.1 Estimation of δyAC and δzSA : Step 1 The data for the observation equation are extracted by using the motion specified in ISO 10791-6. 1) Simulation results which explained in section 2.3.2 are used to prepare the matrix X. In this step the effects of αCY, βCY, δyAC and δzSA are selected as representatives for the four groups of deviations. 2) The matrix Y which represents the ball bar measurement is extracted from the simulation by applying 10 random values to the model as shown in Fig.7. The selected random values are given in Table 2. By means of the observation equation, four coefficients can be identified as given in Table 2. It can be seen that the two deviations δyAC and δzSA can be identified. The output figures of αCY and βCY give the cumulative effect of deviations in each group to the motion trajectory respectively. In this step, δzSA is adjusted by means of tool offset parameter. 4.1.2 Estimation of αCY, βCY, γCY and βSA : Step 2 Same as above, the matrix X and Y are prepared by using the newly proposed motion.

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C axis rotation(0)

C =0º to180º

0

90

180

Deviation(mm)

0.0000

A

LS=150mm

Z

ο

only the C axis is rotated around its axis from 0 to 180 . LSA is assumed as 150mm. The measurements are shown in Fig.9. If the actual difference in Y direction is positive value, the ball bar reads it as negative value and vise versa. Thus we have to consider the negative value as positive value. 4.2 Link geometry related to the identification Fig.10(a) and (b) show the relationship of deviations with the links in ZX and XY planes respectively. Fig.10(c) shows the link geometry of C axis, A axis and Spindle with whole machine structure in YZ plane. By considering Fig.10(a) and (c), the distance a1 can be written as in Eq.(1). (1) a =δ + δ + ( L + L ) cos( β + β ) sin α S

SA

150

90 = L150

L180 150 = 0.09342

Fig.9 Ball bar reading in Y direction

SA

AC

(LS+LSA)sin(βSA+βAC )-δxSA

βSA+βAC

LS+LSA

A

(a) Links in ZX plane

(LS+LSA)sin(βSA+βAC )-δxSA

C

b1

a1

C axis at 0º

Y γCY

X

B

(b) Links in XY plane Position 1 C ( L C axis=0º , L S+ L S+ L SA ) A axis=0º co SA s

(β SA +

ySA

αSA a1

zSA

LA

C

β AC )

δ

yAC

δ

B

A

Joint of A and C Joint of C and Y

Center line of C axis αCY

Position 2 C axis=180º , A axis=0º

For the two different lengths of LS (100mm and 150mm) two equations a11 and a12 are derived from the above, respectively. Since the rotation of C axis is symmetry about its own axis as illustrated in the figure the difference between the heights L1 and L2 can be express as in Eq.(2).

y1 L1 L2

L1 − L2 = L180 = 2{a1 cos γ CY − (( LS + LSA ) sin( β SA + β AC ) (2)

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X Z

-δxSA

SA

− δ xSA ) sin γ CY } cos α CY

(LS+LSA) cos(βSA+βAC)

C

δ

ο

ySA

= L180 100 0.07772

-0.2500

1) By using the results explained in section 3.2, the matrix X is prepared. The effects of αCY, βCY, γCY, βSA, δxSA and δySA are selected as representatives for the six groups of deviations. 2) Since δzSA is adjusted, the cumulative influence of nine deviations which represent the ball bar measurement to the motion trajectory is simulated. The simulated trajectory is given in Fig.7. As δyAC is identified in step1, the withdrawal of the influence of δyAC from the cumulative influence of nine deviations gives the cumulative influence of eight deviations to the motion trajectory. This result is used as matrix Y. Then, as above, six coefficients can be identified as given in Table 2. From the results it can be seen that the four deviations αCY, βCY, γCY and βSA can be identified in step2. The figures of δxSA and δySA give the cumulative influence of βAC, αSA, δxSA and δySA. By considering all above, it can be said that 6 of 10 deviations can be identified by using the spherical motion with two setups. βAC and δxSA are acting on ZX plane. At the same time αSA and δySA are acting on YZ plane. Since the both groups include an angular deviation and these angular deviations have direct relationship with the length of the projected arm (LS), we think about the link geometry of the machine to separate these deviations. 4.1.3 Estimation of βAC ,δxSA,αSA and δySA : Step 3 Additional motion is proposed to estimate the rest of the 10 deviations. As illustrated in Fig.8, the ball bar is applied in Y direction at two different lengths (LS=100mm and 150mm) and

yAC

90 = L100 0.11334

0.13507

Fig.8 Additional motion

1

100

-0.2000

L SA L S+

=1

Y

X

At 1800

((LS+LSA)sin(βSA+βAC )-δxSA)cosγCY +a1sinγCY

L

,15 mm 00

-0.1500

C axis at 90º

Ball bar

m 0m

LS=100mm

-0.1000

At 900

Length of extension bar/(mm)

-0.0500

L3

(c) Link geometry in YZ plane Fig.10 Link geometry of the machine in YZ plane

Y Z

180

180

Thus for the two positions shown in Fig.8 two equations L100 and L150 can be derived from the above by substituting 100mm and 150mm for LS. 180 180 Hence by deducting L150 from L100 and manipulating the result we can express sinαSA as below. 180 180 (3) ( L − L ) − 100 sin( β SA + β AC ) sin γ CY cos α CY sin α SA = 100 150 − 100 cos( β SA + β AC ) cos γ CY cos α CY As same before, for the rotation 0ο to 90ο of C axis, we can express the relationship as given in Eq.(4). ( L1 − L3 ) = L90 = {a1 cos γ CY − (( LS + LSA ) sin( β SA + β AC ) − δ xSA ) sin γ CY } (4)

cos α CY + {(( LS + LSA ) sin( β SA + β AC ) − δ xSA ) cos γ CY + a1 sin γ CY } cos α CY 90 90 Then for the two settings, two equations L100 and L150 can be derived by substituting 100mm and 150mm 90 90 for LS. Thus by deducting L150 from L100 and substituting the value of sinαSA, we can extract a relationship for sin(βSA +βAC) as given below.

sin( β SA + β AC ) =

90 180 180 2 cos γ CY ( L90 100 − L150 ) − ( L100 − L150 )(cos γ CY + sin γ CY ) − 100 cos α CY

(5)

Hence βAC and αSA can be identified. Then from the equations L100 and L100 , δxSA and δySA can be identified. The estimated deviations are shown in Table 2. 180

90

5. Conclusions In this paper, effectiveness of the spherical motion specified in Clause 6 of ISO 10791-6 is discussed and its application for identifying the inherent deviations of universal spindle head type five axis machining centers with horizontal Z axis is newly proposed. The identification procedure consists of three steps and the measurements should have to carryout four times. In the steps 1 and 2, spherical interpolation motion is used to measurements and 6 of 10 deviations were estimated by means of observation equation for which observed data are measured by using ball bar and the reference data are extracted by simulations. In the step 3, rests of the 10 deviations were identified by considering the link geometry of the machine. Only 0ο to 180ο of C axis rotation is carried out twice at 100mm and 150mm of LS and the measurements are extracted by means of the ball bar which is applied in Y direction. The validity of the proposed method has been confirmed by simulations. References (1) J.A. Baughman, Multi-axis machining with APT, in: W.H.P. Leslie(Ed.), Numerical control user’s Handbook, McGrow-Hill, New york, (1970),271-298 (2) D.N. Reshetov and V.T. Portman, Accuracy of machine tools, ASME Press, Newyork, (1988). (3) M.Tsutsumi and A.Saito, Identification and compensation of systematic deviations particular to 5-axis machining centers, International Journal of Machine Tool and Manufacture 43(2003) 771-780. (4) M.Tsutsumi and A.Saito, Identification of angular and positional deviations inherent to 5-axis machining centers with a tilting-rotary table by simultaneous four-axis control movements, International Journal of Machine Tool and Manufacture 44(2004) 1333-1342. (5) ISO 230-1: Test code for machine tools-Part 1-Geometric accuracy of machines operating under no-load or finishing conditions, second edition, (1996). (6) S.Sakamoto, I. Inasaki, H. Tsukamoto and T. Ichikizaki, Identification of alignment errors in five axis machining centers using telescoping ball bar, Trans. Jpn. Soc. Mech. Eng., Series C, 63 (605) (1997) 262-267, (in Japanese). (7) S.Sakamoto, I. Insaki, Identification of alignment errors in five-axis machining centers, Trans. Jpn. Soc. Mech. Eng., Series C. 60 (575) (1994) 2475-2483, (in Japanese). (8) S.Sakamoto, I. Insaki, Evaluation of alignment accuracy for five-axis machining centers errors using telescoping ball bar, Trans. Jpn. Soc. Mech. Eng., Series C 63 (605) (1997) 268-272, (in Japanese). (9) ISO 10791-1 Test conditions for machining centers-Part 1-Geometric test for machines with horizontal spindle and with accessory head (horizontal Z-axis), (1998). (10) ISO 10791-6: Test conditions for machining centers- Part 6- Accuracy of feeds, speeds and interpolations, (1998). (11) ISO/TC39/SC2/WG3, N104, Test codes for machining centers, Draft addendum D, Geometric tests for tilting tables (2001) (12) I.Inasaki, K,Kishinami, S. Sakamoto, N. Sugimura, Y. Takeuchi, F. Tanaka, Shape Generation Theory of Machine Tools-Its Basics and Applications, Yokendo, Tokyo, (1997), 95-103 (in Japanese) (13) ISO 10791-8: Test conditions for machining centers- part 8- Evaluation of the contouring performance in the three coordinate planes, (2001).

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