Motion Characteristics of High Performance Rotary ... - Semantic Scholar

Proceedings of IMECE2008 2008 ASME International Mechanical Engineering Congress and Exposition October 31−November 6, 2008, Boston, Massachusetts, USA

IMECE2008−66108

Motion Characteristics of high performance rotary tables for cnc machines K.M.Muditha Dassanayake Sankyo Seisakusho Co., 2290, Honjo, Kikugawa Shizuoka , 439−0018 [email protected]−seisakusho.co.jp

Masaomi TSUTSUMI Tokyo University of Agriculture and Technology 2−24−16 Nakacho,Koganei, Tokyo 184−8588 [email protected]

Ryuta SATO Tokyo University of Agriculture and Technology 2−24−16 Nakacho,Koganei, Tokyo 184−8588 [email protected]

ABSTRACT In this paper, the characteristics of two rotary tables driven by worm gear and roller gear cam are measured and compared. The positioning accuracy and repeatability as specified in ISO 230-2 are measured together with the rotational fluctuation, backlash, friction torque, frequency response of the systems and also the influence of unbalance mass on rotational motion. Two rotary encoders which were attached to motor and output axis were used for measurements. The motor, controller, and the rotary encoders were kept the same for both tables to ignore the effects of these units on results. Furthermore, the simulations were carried out by mathematical models which were proposed by two of the authors and the results were compared with measured results. From the simulation results, the torsional stiffness and friction torque were identified and also compared. The results show that the measured and simulated data have a good agreement and therefore it can be said that the identified parameters from simulations are accurate. The result shows that the performances of the rotary table driven by roller gear cam is better than that of rotary table driven by worm gear. 1. INTRODUCTION In the present day, because of the complexity of the products, the five-axis CNC machines are becoming popular in the shop floors. Most of these machines consist of three linear and two rotary axes (1, 2). The rotary axes reduce expenses just

Hisayoshi ITO Sankyo Seisakusho Co., 2290, Honjo, Kikugawa Shizuoka , 439−0018 ito_h@ szk.sankyo−seisakusho.co.jp

by reorienting the tool and/or workpiece outside the cut. This rotary movement saves setup time by letting the spindle reach opposing faces of the part in a single setup. It also saves tooling costs by letting a standard milling cutter, held at an angle, machine an angled surface that would otherwise require a custom tool. The rotary axis can be a rotary table which supports the work or a rotary head which supports the tool. Therefore to build the most of the five-axis machines as well to convert the conventional three-axis machines to four or fiveaxis machines, the rotary table is an immense necessary part. And also accuracy of these machines determines the dimensional accuracy and surface finish of the parts produced by the machine. Therefore to keep the accuracy level of the machine high, the motion performances of the rotary tables also have to be in a high degree. These rotary tables are driven by various means such as worm gears, roller gear cams (3) and direct drive motors. The characteristics of the driven mechanisms such as rotational fluctuation, backlash, rigidity, etc. directly affect the motion performance of the rotary tables. S.-H. Suh et.al. (4) proposed a comprehensive procedure for calibration of rotary tables and compensation the errors. However in their method they only accounted geometric deviations. There are number of research papers on geometric deviations of the rotary axes of 5-axis machines. M. TSUTSUMI et.al (5, 6)

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Copyright © 2008 by ASME

Worm gear mechanism

Roller gear cam mechanism

Moment of Inertia of motor

13.9*10-4

4.8*10-3

Moment of Inertia of spur gears and driving part of driving mechanism

4.3*10-4

Parameters

Symbols

Units

Jm

kgm2

Jw

kgm2

Jt

kgm2

Moment of Inertia of Table and driven part of driving mechanism

Mw

kg

Weight of driving unit of driving mechanism

0.108

5.0*10-2

1.2

5.3 0.17

Cm

Nm/(rad/s)

Viscous damping coefficient of motor axis

8.0*10-3

Cw

Nm/(rad/s)

Viscous damping coefficient of driving mechanism axis

1.0*10-2

Cb

Ns/m

Viscous damping coefficient in driving mechanism’s axial direction

1.2*10-3

0.1

Ct

Nm/(rad/s)

Viscous damping coefficient of table

1.2*10-2

1.4*10-2

Cig

Nm/(rad/s)

Internal damping coefficient in between motor and driving mechanism axis

5.0*10-2

Ciw

Nm/(rad/s)

Internal damping coefficient in between table and driving mechanism axis

0.1

2.0

fm

Nm

Coulomb’s friction torque of motor axis

0.14

0.14

fw

Nm

Coulomb’s friction torque of driving mechanism

0.24

ft

Nm

Coulomb’s friction torque of Table

0.26

Kg

Nm/rad

Torsional stiffness in between motor axis and driving mechanism axis

850

Kw

Nm/rad

Torsional stiffness in between table and driving mechanism axis

3.1*105

1.11*106

Kb

N/m

Stiffness of bearing of driving mechanism in axial direction

5.8*107

9.0*106

Rg

-

Reduction gear ratio of spur gears

4/5

0.0

Rw

-

Reduction gear ratio of driving mechanism

1/72

1/24

r

m

Radius of driven part of driving mechanism

8.0*10-2

0.135

θbg

rad

Backlash of spur gears

θbw

rad

Backlash of driving mechanism

θm

rad

Rotating angle of motor axis

θw

rad

Rotating angle of driving mechanism

θt

rad

Rotating angle of table

xw

m

Positional change of driving mechanism axis

Tm

Nm

0.32

Output torque of motor

Table 1: Definitions of all parameters proposed simultaneous three-axis and four-axis motions for identifying the geometric deviations. The author (7, 8, 9) proposed a number of identification methods for geometric deviations. Some of them used simultaneous five-axis motion. Influence of backlash and rotational fluctuation on motion was accounted in a paper wrote by the author (9). Apart from geometric deviations, many other features of rotary tables were also accounted by researchers. W. Chang Zongyu et. al. (10) studied the dynamics of the roller gear cam system with the clearance taken into account. Ryuta et. al. (11, 12) carried out some motion control techniques on the rotary table driven by worm gear. In their works, the main sources of inaccuracies such as servo response, rotational fluctuation, backlash, and signal delay of rotary encoder were investigated. However, there are no any references on comparison of the characteristics which affect the motion performance of the rotary tables such as rotational fluctuation, rigidity etc.

To fill the gap, as the first stage the performance of mechanically driven rotary tables were considered. In the second stage the performance of mechanically and electrical motor driven rotary tables will be considered. In this paper, the characteristics of the two rotary tables which are driven by worm gear mechanism and roller gear cam mechanism are measured and compared. The positioning accuracy and repeatability was measured according to the evaluation method described in ISO 230-2(13). Apart from this rotational fluctuation, backlash effect, frequency response, and influence of unbalance mass on rotational motion were also measured. For the measurements, two encoders attached to the motor and the output axis were used. To reduce the influence of other parameters to the motion, the motor, controller and rotary encoders were kept the same for both rotary tables. Furthermore, the simulations were carried out by mathematical models which were proposed by two of the

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authors and the results were compared with measured results. From the simulation results, the torsional stiffness and friction torque were identified and also compared. The comparison shows that the measured and simulated results have a good agreement and also it shows that the performance of the rotary table driven by roller gear cam is better than that of rotary table driven by worm gear. 2. MODELING OF ROTARY TABLE 2.1. Driving Mechanism A variety of drive systems have been devised for precision NC rotary tables such as worm gear, roller gear cam, etc. The mechanisms that drived the rotary tables which were accounted in this research are shown in Figs.1 and 2. They are worm gear and roller gear cam mechanisms. As shown in Fig.2(a) worm gear mechanism consists of worm engaging with and driving a worm wheel which is attached to the output table. This is the most applied mechanism in NC tables. Though this mechanism is good for transferring power, due to the unavoidable toothing tolerances, backlash and rotational fluctuation that affect to the precision motion control also exist. Apart from that sliding friction is acting in between the worm wheel teeth and worm. This action results in significant frictional losses but it can also be used as the natural brake for the table.

The roller gear cam mechanism (14) consists of a globoidal cam and roller gear as illustrated in Fig.2(b). The roller gear is made by assembling cam followers which capable of rotating about their own axis around a turret at equal spacing. These special cam followers lead to smooth contact with cam and thus eliminate the rotational fluctuations. The most important feature of this mechanism is that backlash is avoided within the mechanism by applying preload at the assembly level as illustrated in Fig.2(b). Further more rolling friction is acting in between the cam and the follower. 2.2. Modeling of rotary table A mathematical model is necessary to carry out simulations for identifying some characteristics of the system. In this paper a model which was proposed by two of the authors (15) is used. In their work the rotary table and driven mechanism was represented by four degrees of freedom model as shown in Fig.3. According to the figure the system consists of motor, gear box, main driving mechanism, and table. By considering the model, the mathematical equations were drawn for motor, driving mechanism and table respectively as given in Eqs.(1), (2) and (3). Definitions of all the parameters are given in Table 1. Some of these parameters were calculated by using designed data and others were identified by matching the experimental and simulation data. All the values of parameters for worm and roller gear cam mechanisms are given in Table 1. J mθ&&m + Cmθ&m + RgTg + Rg Cig ( Rgθ&m − θ&w ) + f m = Tm

(

(1)

)

(

)

J wθ&&w + Cwθ&w + RwTw + RwCiw Rwθ&w + rx& w − θ&t + f w = Tg + Cig Rgθ&m − θ&w ⎫ ⎪ ⎬ (2) T C M w &x&w + Cb x& w + K b xw + w + iw θ&t − Rwθ&w − rx& w = 0 ⎪ r r ⎭

(

(a) Worm gear

(b) Roller gear cam (Sankyo Seisakusho Co.)

Fig.1 Models of driving mechanisms Output table Backlash Worm wheel Worm

Drive shaft (a) Worm gear mechanism

J tθ&&t + Ctθ&t + f t = Tw + Ciw ( Rwθ&w + rx& w − θ&t )

(3)

In these equations, Coulomb’s friction torque f for motor (fm), driving mechanism (fw) and table (ft) are defined respectively as below. f m = f cm sgn(θ&m ) , f w = f cw sgn(θ&w ) , f t = f ct sgn(θ&t ) And also according to the conditions below, the output torque of gear box (Tg) and the output torque of driving mechanism (Tw) are changed. The backlash of gear box and driving mechanism constrain these conditions.

| R gθ m − θ w |≥ θ bg else

Output table

)

}

Tg = K g ( R gθ m − θ bg − θ w ) Tg = 0

Preload

Turret Cam follower

Zero backlash

| R wθ w + rx w − θ t |≥ θ bw else

Globoidal Cam Drive shaft (b) Roller gear cam mechanism

Fig.2 Configurations of driving mechanisms

}

Tw = K w ( R wθ w + rx w − θ bw − θ t ) Tg = 0

Furthermore for simulations the following equation which represents the gear fluctuation was used.

3


Gear Fluctuation = W sin θ w

output from the model is rotating angle of table. In the rotary axis, particularly, the signal delay of rotary encoder attached to motor influences to the synchronous accuracy. Though the synchronous accuracy is not accounted in this work, signal delay and backlash of the driving mechanism are modeled as dead time in the block diagram.

Where W is the amplitude of fluctuation and θ is the input angle of driving mechanism. The block diagram of the rotary table and driving mechanism which was extracted from mathematical model is illustrated in Fig.4. The input to the model is motor torque and Table

θt

4-DOF model θm

θw

gear

Kw

θbw Motor Spur gear

Tm

r

Kg

θm θbg Jm

Rwθw+rxw

θw

Mw，Jw

Rg

Cm，fm

Ct，ft

Ciw

Table

Cw，fw

Cig

Kb

Motor

θt Jt

Gear xw Cb

Fig.3 Dynamic model of rotary table driven by worm or roller gear cam 1 θt

1

+ -

J t s + Ct

s

( )

f tc sgn θ&t Ciw + + K w

1 s

+

Dead Zone

1 r

+ -

C ig +

+ -

1 Jm s + Cm

f mc sgn (θ&m )

Rg

r

+

+

Kb

Rg

Tm

1 M w s + Cb

+ -

1 s

s

Rw Kg

+ +

+

Dead Zone

+ -

1 J w s + Cw

f wc sgn (θ&w )

Fig.4 Block diagram rotary table and driving mechanism

Servo motor with rotary encoder PC with DSP board

Rw

3. EXPERIMENTAL SETUP The experimental setup is illustrated in Fig.5. This setup consists of a personal computer with DSP board, servo amplifier, servo motor with rotary encoder, and rotary table with an encoder attached to the output axis. The resolution of the encoder which was attached to the output axis of rotary table is 0.0001°. Such high resolution encoder was used to reduce the measurement errors, which directly affects the characteristics of rotary table. The rotating angle of motor and table can be measured by using the encoders attached to them. In this system, since no specific controller is used it is possible to apply any controllers and compensators via computer. The rotary table was controlled by a controller under torque commands input. This controller was prepared by means of Simulink blocks provided in MATLAB software in the personal computer. The block diagram of controller is shown in Fig.6. As illustrated in this figure, Kpp is the position loop gain and Kvp and Kvi are the proportional gain and integral gain of velocity loop respectively. The controller is a discrete-time system which has a control frequency of Tc [s]. The input to the controller is the position of table with respect to time. Therefore any type of motion can be performed by simply inputting the motion trajectory data to the controller. The analog torque command is passed to the servo amplifier of motor through Digital-Analog board. The encoder reading is input to the personal computer through counter board, as illustrated, and this signal is used as a feed back parameter. The servo amplifier was configured suitably. By using this controller, semi-closed loop and fullclosed loop control can be carried out. In the semi-closed loop control the feedback parameter for both position loop and velocity loop is the rotating angle of motor. In the full-closed loop control the feed back parameters for velocity loop and Position control Loop gain (proportional)

Table with rotary encoder

r+

−

K pp +

+

K vp

−

Tc z z −1

+ DA

Servo amp. Jm

R Switch for changing feed back signal

θt

θb θm

K vi 1 − z −1 Tc

Servo amp.

Torque command input

Velocity control Loop gain (Proportional+Intregral)

Counter board

Counter board

Kθ

Jt

θ m : Rotating angle of motor

θt

: Rotating angle of table

PC with DSP board

Fig.5 Experimental setup

Fig.6 Block diagram of controller

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position loop are the rotating angle of motor and the rotating angle of table respectively. The controller was designed such that to switch between the two modes simply by using the switch which is provided.

influence of unbalanced mass and geometric deviations as to simplify the measurement process. However in this paper geometric deviations are not considered because these deviations are always measured with respect to the reference plane and in this work no any reference plane was considered. For five groups except geometric deviations, five different tests were conducted. Among them the evaluation method of positioning accuracy and repeatability is extracted from ISO230-2(13). The tests which used and the test results are explained in this section.

4. EVALUATION METHODS In order to evaluate the systems, the characteristics of each system which affect the motion performance were measured. These characteristics were categorized into six groups as frequency response, friction torque, positioning accuracy and repeatability, rotational fluctuation and backlash,

Angle deg

13 12 11

10Hz Time s

0.25 0.24 0.23 0.22 0.21 0.2

0.6 Angle deg

10 0.5

200Hz Time s

0.045

350Hz

0.04 0.5

Time s

0.6

(a) Worm gear mechanism

Rotation angle of table

7 6 5

4 0.5 0.04

10Hz 0.6

Time s

0.03 0.02 0.5

0.6 Angle deg

0.5 0.05

200Hz 0.6

Time s

0.004 0.003 0.5

500Hz 0.55

Time s

(b) Roller gear cam mechanism

Fig.7 Measured angles at different frequencies Experiment

Simulation

40

Gain (db)

20

0

-20 100

Frequency (Hz) (a) Worm gear

500

40

Gain (db)

Angle deg

Angle deg

Angle deg

Rotation angle of motor × gear ratio

20

0

-20 100

Frequency (Hz) (b) Roller gear cam

500

Fig. 8 Frequency response of tables

4.1. Frequency responce of tables The frequency response of rotary tables is a very important feature which draws a clear picture of stiffness and damping of the rotary tables. This is well expressed by D. J. Ewins (16). Low stiffness and low damping of rotary table causes various effects on machining, such as chattering etc. In order to measure the frequency response, the systems were driven at open loop condition by inputting sinusoidal torque wave, in which the band width was 10Nm (±5Nm). This process was repeated by changing the frequency of sinusoidal wave within the range of 10~600Hz at 10Hz steps. At each step the rotation angle of both the motor and the table were measured against time. Near the resonance points this test was carried out at 1Hz steps for better accuracy. The measured data at 10Hz, 200Hz and 350Hz are given in Fig.7, so as to get an idea about the test data. It can be seen from the measured data that the rotating angle of the motor and the table have a good agreement at the frequencies apart from the resonance frequencies. Near the resonance frequencies, rotating angle of table shows higher value than rotating angle of motor as according to measured data. To calculate the frequency response from the measured data, 10 base logarithmic value of the ratio of oscillating amplitudes of table and motor were calculated and plotted against frequency. Fig.8 illustrates the calculated data from experiment and simulation. According to Fig.8 it can be found that there are two natural frequencies for each table. The natural frequencies of the table driven by worm gear mechanism are 230Hz and 280Hz and that of the table driven by roller gear cam are 270Hz and 430Hz. From the results it can be seen that the natural frequencies of the table driven by roller gear cam mechanism are higher than that of the table driven by worm gear mechanism. These natural frequencies are connected with the stiffness and damping matrices of the systems. Therefore to identify torsional stiffness and internal damping, simulations were carried out. This was done such that the simulation results and the frequency response results were matched. Fig.8 shows the calculated frequency responses and simulated results. It can be seen from the figure that the simulated results for roller gear cam shows good agreement with calculated results, while simulated results for worm gear are not identically matched with calculated results. However the resonance peaks of simulated results for worm gear matched those of the calculated

5


results. Therefore these results can be used to identify the stiffness and damping values. Torsional stiffness was identified by matching the natural frequencies, and internal damping was identified by matching the amplitude of resonance peak. The identified values are given in Table 1. According to these results, it can be seen that the torsional stiffness of roller gear cam driven table is significantly higher than that of the worm gear driven table. 4.2 Friction torque of tables The Coulomb’s friction torques, viscous damping coefficients and motor output torque are interrelated as expressed in the mathematical model. Also each coefficient significantly affects on motor output torque. Therefore these relationships can be used to identify these coefficients. To identify the Coulomb’s friction torques and viscous damping coefficients, the tables were driven at full closed loop condition by inputting a simple harmonic motion in which amplitude was 30° and cycle time was 3s. This was done by changing the cycle time of harmonic motion to achieve better accuracy and measured the output torque of motor. Then simulations were carried out such that to fit the output torque curve. Measured and simulated data are shown in Fig.9. From the parameters which used for the simulation Coulomb’s friction torque and viscose damping coefficient were identified. Identified values are given in Table 1.

According to the results, Coulomb’s friction torque of the table driven by roller gear cam mechanism is nearly same with that of the table driven by worm gear mechanism. Though the friction torque leads to friction losses, it applies damping effect on the system and works as a natural brake system. 4.3 Positioning accuracy and repeatability The positioning accuracy and repeatability of rotary tables are very important indicators which express the accuracy level of them. Accuracy is the difference between the actual position and the position measured by a reference measurement device such as rotary encoder, linear encoder, etc. Repeatability is defined as the range of positions attained when the system is repeatedly commanded to one location under identical conditions. These points are expressed very well by J. A. Baughman (17). Unidirectional repeatability is measured by approaching the point from one direction, and ignores the effects of backlash or hysteresis within the system. Bidirectional repeatability measures the ability to return to the same point from both directions. The evaluation method of these indicators is described in ISO230-2 (13). All the measurements in this section were carried out according to ISO standards. This test was carried out at semi-closed loop condition. In this test the table was positioned to every 30° up to 360°. x↑

Experiment

Deviation arc-sec

Torque Nm

3

0

0

4

Time (s) (a) Worm gear

8

Deviation arc-sec

Torque Nm

x

90 180 270 Angular displacement deg (a) Worm gear

360

0

90 180 270 Angular displacement deg (b) Roller gear cam

360

30

0

0

-30

-3 4

x ↓ ±2 s ↓

0

12

3

0

x ↑ ±2 s ↑

0

-50

-3

x↓

10

Simulation

8

Time (s) (b) Roller gear cam

12

Fig.10 Calculated values of

x ↑, x ↓, ( x ↑ ±2s ↑), ( x ↓ ±2s ↓), x

Fig.9 Output torque of motor

6


Worm gear mechanism

Roller gear cam mechanism

Axis deviation (arc-sec)

Unidirectional↑

Unidirectional ↓

Bidirectional

Unidirectional↑

Unidirectional ↓

Bidirectional

Mean reversal value B

Not applicable

Not applicable

32.8

Not applicable

Not applicable

2.7

Repeatability of positioning R

1.9

2.4

34.5

2.3

3.0

3.6

Accuracy A

7.7

6.0

38.6

8.5

9.1

10.6

Table 2. Calculated values of B , R and A

At each position the table stopped for 1S and measured the table position by using the encoder fixed to the table. The resolution of this encoder is 0.0001°. The test was repeated 5 times in CCW and CW directions. By using the measured data, mean unidirectional positional deviation at a

Deviation (deg)

0.01

position ( x ↑, x ↓ ), estimator of the unidirectional standard uncertainty of positioning at a position ( s ↑, s ↓ ), and mean by-directional positional deviation at a position ( x ) were calculated. The arrow indicates the direction of rotation. Thus

←CW 0

-0.01

CCW→ -0.02

x ↑, x ↓, ( x ↑ ±2s ↑), ( x ↓ ±2s ↓)

x are and plotted against angular displacement of rotary table. The plotted graphs are shown in Fig.10. From the calculated values

90

360

180 270 Rotation angle (deg) (a) Worm gear

0.01

Deviation (deg)

mean reversal value ( B ), repeatability of positioning (R) and accuracy (A) were calculated. The mean reversal value gives an indication of backlash. The calculated values are given in Table 2. According to the table the rotary table driven by roller gear cam shows relatively higher performance than the rotary table driven by worm gear.

←CW

0

CCW→

-0.01

-0.02

360 180 270 Rotation angle (deg) (b) Roller gear cam Fig.11. Rotational fluctuation of rotary tables

Power spectral density (deg2)

4.4 Rotational fluctuation The rotational fluctuation is the deviation of rotation angle of the table from that of the motor. This can be categorized as a systematic deviation. This occurs due to the pitch error of the driving mechanism. To measure the rotational fluctuation the table was rotated at a speed of 180 deg/min. The test was carried out at semi-closed loop condition. While rotating, the rotation angle of table and motor were measured continuously and the difference was calculated. The calculated values are given in Fig.11. Fig.12 illustrated the power spectrum of calculated values which related to worm gear mechanism. According to Fig.11 it can be seen that the rotational fluctuation that appears in the worm gear, cannot be seen significantly in the roller gear cam. According to Fig.12 it can be found that the number of fluctuations is the same as the number of tooth in worm wheel. Therefore the conclusion can be drawn that the rotational fluctuation is directly related to tooth shape of worm wheel. And also the deviation between CW and CCW paths in Fig.11(a) represents the backlash of the

0

0

90

0.0025

CCW CW

0.002 0.0015

72 cycle/rev

0.001 0.0005 0 10 -1

10 0

10 1 10 2 Frequency (cycle/rev)

10 3

10 4

Fig.12. Power spectrum of rotational fluctuation (worm gear)

drive. Backlash appears only in worm gear drive according to the figure. This is also a main drawback of this driver.

7


was rotated at a speed of 360 deg/min in semi-closed loop condition. The measured data are shown in Fig.14. According to Fig.14, the table with worm gear drive shows a step like deviation, while the table with roller gear cam is not influenced. This step appears at the point where the

Deviation deg

0.015

←CW

0

CCW→

-0.015 0

90 180 270 Angular displacement deg

Fig.13 Experimental setup

(a) Worm gear

0.015

4.5 Influence of unbalance mass As a rotary table, it should be capable of using in any position on a machine bed such as vertical, horizontal or anglular. To check the capability a test was designed, in which the principle that considered is the gravitational force acting on the table when it is inclined. This gravitational force can be used to represent the cutting force on the work in real machining. Though this does not fully cover the effect of cutting force on table performance it is sufficient to fulfill the objective of this test. The experimental setup is shown in Fig. 13. As illustrated, the table was fixed in the vertical plane and a mass was attached in a position offset to the center of the table. To measure the influence of the unbalance mass the table

Deviation deg

←CW

0

CCW→

-0.015 0

90 180 270 Angular displacement deg (b) Roller gear cam

Roller gear cam

Frequency response (Hz)

230Hz, 280Hz

270Hz, 430Hz

Torsional stiffness (Nm/rad)

3.1*105

1.11*106

Friction torque (Nm)

0.26

0.32

32.8

2.7

Repeatability of positioning R

34.5

3.6

Accuracy A

38.6

10.6

Rotational fluctuation

exist

Cannot significantly identified

Influence of unbalance mass

Influenced

No any influence

Backlash

exist

Cannot significantly identified

Mean reversal value

360

Fig.14 Influence of unbalance mass

Worm gear

Positioning accuracy and repeatability (arc/second)

360

B

Table 3. Comparison between driving mechanisms

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moment of unbalanced mass goes higher than the friction torque of the driving mechanism. At this point, the drive recovers the loose contact. Therefore it can be said that the source of the step is the backlash of the worm gear. 5. COMPARISON BETWEEN THE DRIVING MECHANI SMS A comparison of the results is instructive. Table 3 shows the features that measured in this work. According to the table, the natural frequencies of the rotary table driven by roller gear cam are 270Hz and 430Hz. These values are higher than that of worm gear mechanism. The torsional stiffness of the rotary table driven by the roller gear cam also shows a significantly higher value than that of worm gear driven rotary table, while friction torque of both tables is nearly the same. Regarding the positioning accuracy and repeatability, mean reversal value of rotary table with roller gear cam shows very minute value. This is significantly larger in rotary table with worm gear. This indicates the backlash of driving mechanisms of rotary tables. The features of repeatability of positioning and accuracy of rotary table driven by roller gear cam are in a higher level compared to rotary table driven by worm gear. No any rotational fluctuations can be identified in the motion trajectory of roller gear cam driven rotary table. However this can be easily recognized in the motion trajectory of rotary table driven by worm gear. Furthermore the unbalance mass does not affect to the motion of the table with roller gear cam. Therefore it can be said that the performance of roller gear cam driven rotary table is significantly better than that of worm gear driven rotary table. 6. CONCLUSIONS In this paper the characteristics which affect to motion performance of rotary tables driven by worm gear mechanism and roller gear cam mechanism were measured and compared. Mainly five tests were carried out and measured a number of features. Some of the features such as torsional stiffness, friction torque, etc were identified through simulations which were conducted by using a mathematical model. The tables were controlled through a personal computer with a DSP board. All the measurements were carried out by using rotary encoders which were attached to the motor and rotary table respectively. To reduce the influence of other parameters to the motion, the motor, controller and rotary encoders were kept the same for both rotary tables. Among the tests, assessment of accuracy and repeatability of rotary tables was conducted according to ISO230-2. The following conclusions were derived, (1) The frequency response of a rotary table driven by roller gear cam is higher than that of a rotary table driven by worm gear. (2) The torsional stiffness of a table with roller gear cam is significantly higher than that of a table with worm gear while the friction torque is nearly the same. (3) A rotary table driven by roller gear cam shows a very high

positioning accuracy and repeatability. (4) A rotary table driven by worm gear shows rotational fluctuations on the motion and that cannot be clearly identified on the motion of a table driven by roller gear cam. (5) The unbalance mass influences only on the motion of the table driven by worm gear. (6) Backlash exists in the worm gear mechanism, whereas in the roller gear cam mechanism this cannot be identified. REFERENCE (1) E. L. J. Bohez, Five-axis milling machine tool kinematic chain design and analysis, International Journal of Machine Tools and Manufacture 42(2002) 505-520. (2) F.C. Chen, On the structural configuration synthesis and geometry of machining centers, Proceedings of Institute of Mechanical Engineers, Vol. 215 part C, (2001) 641-652. (3) Psang Dain Lin, Ming Far Lee, Applications of D-H Notation in machining and on-line measurement of roller gear cams on 5-axis machine tools, Vol. 119 (1997) 393401. (4) S. -H. Suh, E. -S. Lee and S. -Y. Jung, Error Modeling and Measurement for the Rotary Table of Five-axis Machine Tools, International Journal of Advance Manufacturing Technology, vol.14 (1998), 656-663. (5) M.Tsutsumi and A.Saito, Identification and compensation of systematic deviations particular to 5-axis machining centers, International Journal of Machine Tools and Manufacture 43(2003) 771-780. (6) 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 Tools and Manufacture 44(2004) 1333-1342. (7) K.M. Muditha Dassanayake, Masaomi Tsutsumi, Akinori Saito, A strategy for identifying static deviations in universal spindle head type multi-axis machining centers, International Journal of Machine Tools and Manufacturing , 46(2006)1097-1106 (8) K.M. Muditha Dassanayake, Ken Yamamoto, Masaomi TSUTSUMI, A methodology for identifying inherent deviations in universal spindle head type multi-axis machines by simultaneous five-axis control motions , Proceedings of IMECE2006, ASME International Mechanical Engineering Congress and Exposition, (Chicago, USA), (2006). (9) K.M. Muditha Dassanayake, Masaomi TSUTSUMI, Kenji HIGASHIYAMA and Ken YAMAMOTO, An approach to estimate the inherent deviations by means of simultaneous five-axis motion, Proceedings of The third International Conference on Leading Edge Manufacturing in 21st Century, (Fukuoka, Japan), (2007). (10) Chang Zongyu, Zhang Ce, Yang Yuhu, Wang Yuxin, A study on dynamics of roller gear cam system considering clearance, 36 (2001) 143-152.

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(11) Ryuta SATO, Daisuke ENDO and Masaomi TSUTSUMI, Motion control techniques of Rotary table for 5-axis machining centers, Proceedings of International Conference on Leading Edge Manufacturing in 21st Century, (2007) (12) Ryuta SATO, Yuya YOKOBORI, and Masaomi TSUTSUMI, Synchronous accuracy of translational and rotary axes in 5-axis machining centers, Proceedings of International Conference on Leading Edge Manufacturing in 21st Century, (2005) (13) ISO 230-2: Test code for machine tools - Part 2: Determination of accuracy and repeatability of positioning numerically controlled axes (1997-E). (14) http://www.sankyo-seisakusho.co.jp/english/2index.htm (15) Yuhki TANIYAMA, Ryuta SATO, and Masaomi TSUTSUMI, Mathematical model of CNC rotary table with worm gear mechanism, Proceedings of the Annual Conference of the Japan Society for Precision Engineering in Autumn, 2007, pp.167-168 (in Japanese). (16) D. J. Ewins, Modal Testing – theory, practice and application, Research Studies Press Ltd., England, 2000 (second edition). (17) J.A. Baughman, Multi-axis machining with APT, in: W.H.P. Leslie(Ed.), Numerical control user’s Handbook, McGrowHill, New York, (1970)

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