Design of Acceleration Command for Feed Drive System in Corner

Motion

Yuki Nomura

, Kazuma Tanaka

and Takanori Yamazaki

Graduate school of Science and Engineering, Graduate school of Tokyo Denki University, Ishizaka, Hatoyama, Hiki,

Saitama, 350-0394 Japan

School of Science and Engineering, Tokyo Denki University, Ishizaka, Hatoyama, Hiki, Saitama, 350-0394 Japan

Keywords: Machine Tools, Numerical Control, Acceleration Command, Corner Motion.

Abstract: CNC (Computer Numerical Control) machine tools are required to have high accuracy and production

efficiency. CNC machine tools generally generate trajectories such as position and speed within the NC

system for commands (usually G code), and then drive each axis. However, in actual contouring motion, the

machine often does not move perfectly as commanded, due to tracking errors such as response delays in the

control system. NC device manufacturers seem to apply deceleration process to reduce these errors, but their

methods have not been disclosed. In this research, we focused on contouring motion with steep

acceleration/deceleration, discussed the contouring accuracy when driving the feed drive mechanism with the

acceleration/deceleration command generated by the motion controller and our proposed method. Typical NC

control controller for machine tools generate trapezoidal or S shaped acceleration/deceleration commands.

We propose a command design method based on the Preshaping method which is also known as a vibration

suppression method and report the contouring accuracy when applying this method.

1 INTRODUCTION

In recent years, numerical control machine tools have

been in high demand for the production of

semiconductors and measurement components,

requiring both high accuracy and production

efficiency. CNC control system with high contouring

accuracy is very important in order to achieve

products with high accuracy and complex shapes.

Previous studies have revealed that driving the

machine tools with high-speed using servo motors

leads to excitation of machine vibrations during

acceleration/deceleration due to the inertial forces. It

makes lower the quality about product surface of the

machining (Sato, 2020). In the manufacturing sites,

CAM systems are used to generate trajectories for each

axis from CAD drawings and convert them into NC

data. The machine tool is controlled based on the NC

data, and feedforward control is used to reduce the

tracking error (Otsuki, 2019). However, high-speed

motion in contouring steeply changing trajectory, such

as a corner motion, leads to overshooting and tracking

errors. NC device manufacturers seem to apply

deceleration process to reduce these errors, but their

methods have not been disclosed.

In this paper, we first compare trapezoidal and S

curve acceleration/deceleration, which are generally

used in motion controllers. Additionally, we propose

a new acceleration/deceleration command based on

the Preshaping method. Generating a velocity

command for corner motion using this method, input

it to the motion controller, and discuss the contouring

accuracy of driving the feed drive mechanism.

2 EXPERIMENTAL DEVICES

2.1 Feed Drive Mechanism

The feed drive used in the experiment is shown in

Figure 1. This device consists of a table, a servo motor

(made by Panasonic), a ball screw, two sets of

guideways (made by IKO) and a base. The servo

motor is connected to the ball screw by a coupling.

Servo motor has a rated output of 200 W, rated

current of 1.5 A, rated torque of 0.64 N·m, and rated

rotational speed of 3000 rpm, which are the same for

both the X and Y axes.

Nomura, Y., Tanaka, K. and Yamazaki, T.

Design of Acceleration Command for Feed Drive System in Corner Motion.

DOI: 10.5220/0012239700003543

In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2023) - Volume 2, pages 311-315

ISBN: 978-989-758-670-5; ISSN: 2184-2809

311

Figure 1: Feed drive system.

The angular position is controlled by such a semi-

closed loop and converted to linear motion through a

ball screw. The rotary encoder is 17 bits, and the lead

of the ball screw is 5 mm, resulting in a minimum

position resolution of 38 nm.

2.2 Control System

The control device included a servo amplifier and a

motion controller (PMAC made by OMRON) as a

host device. The servo amplifier was supplied with

100V AC and 24V DC converted by a switching

power supply, simultaneously.

The control method is a semi-closed loop. A

velocity command is output from the PMAC

(Programmable Multi-Axis Controller) to the servo

amplifier, the servo amplifier drives the motor, and

the rotary encoder attached to the motor detects the

rotational angle and feed it back to the servo amplifier

and PMAC. EtherCAT is used for communication

between the PC and PMAC, and various control data

for the X and Y axes can be gathered at 4 kHz,

synchronously. Since this experiment was performed

in velocity control, the PMAC handle the position

loop and the amplifier handle by the velocity and

current loops.

Table 1: Control system setting.

Symbol Value

Current Loop

Cp 3500

Ci 350

Velocity Loop

Vp 300

Vi 0

Position Loop

Kp 0.012

Kvfb 0.3

Ki 0.000001

Ball screw lead l 5 mm

Figure 2 shows a block diagram of the control

system. The control system consists of a PMAC and

a servo amplifier (one for each axis), with command

generation and data gather performed by a PC. The

PMAC can select either torque or velocity control

mode.

3 FEED EXPERIMENTS

3.1 Control System Setting

We fixed the gains of the control system to compare

the contouring accuracy of the corners for various

commands. The contouring accuracy evaluated by the

distance from the corner vertex to the actual trajectory,

with a reference line 45 degrees direction from the

corner vertex. This distance is referred to as the inner

tracking error. These values were set to give a

tracking error of about 200 µm for trapezoidal

commands shown in Figure 3. The gains set are

summarized in Table 1, and these are the same for the

X and Y axes. Figure 4 shows the experimental

results when only the proportional gain Kp is changed

in the range of 0.010 to 0.012, and Kp=0.012 was

selected as satisfy the tracking error condition.

Figure 2: Block diagram of feed drive system.

Linear guideways

Moto

Cou

lin

Table

Ball screw

Base

ICINCO 2023 - 20th International Conference on Informatics in Control, Automation and Robotics

312

Figure 3: Trapezoidal commands.

3.2 Velocity Commands

In this paper, we performed 100 mm corner motion

with three acceleration/deceleration patterns. The

feed speed was set to 60 mm/s (3600 mm/min), and

the acceleration was set within 0.3 G (3000 mm/s

) of

the acceleration driven by a ball screw, generally.

The first acceleration pattern is trapezoidal

command, and if the feed speed reaches 60 mm/s at

0.3 G, the acceleration time is 20 ms. The second

acceleration pattern is S curve acceleration, which is

shown in Figure 5(a). Where, if the acceleration time

is 20 ms as in the trapezoid acceleration, t

in the

figure is 10 ms. For these, commands installed in

PMAC are used. The third acceleration pattern is the

acceleration designed by the Preshaping method.

It is a suppression method of vibration that cancels

out the original vibration by giving an impulse half a

period after the natural period of the vibration

(Singer, 1988).

Using this method, the acceleration pattern has the

shape shown in Figure 5(b). Note that the acceleration

time t

on the Preshaping method is determined by the

natural period of the feed drive system, so it is

Figure 4: Trapezoidal responses for proportional gain Kp.

different from the acceleration time used for

trapezoidal acceleration. In the experiment, this

command is generated in the form of a velocity time

series using MATLAB, send to the PMAC and

converted to a position command on the PMAC.

4 EXPERIMENT RESULTS

At first, we measured the vibration period of the feed

drive system. For this purpose, we intentionally

excited the vibration by increasing the proportional

gain Kp at 100 µm step feeds. Figure 6 shows the

enlarged view of step feed experiment. From this

result, the natural frequency of the feed drive system

was approximately 62.5 Hz and the acceleration time

on the Preshaping method, t

=16 ms.

(a) S curve (b) Preshaping

Figure 5: Acceleration time setting.

X Axis

𝑡



Y Axis

99.5 99.6 99.7 99.8 99.9 100

X Displacement mm

-0.1

0.1

0.2

0.3

0.4

Reference

Kp=0.012

Kp=0.011

Kp=0.010

Vmax

𝑡



𝑡



𝑡



𝑡



Vmax

Design of Acceleration Command for Feed Drive System in Corner Motion

313

Figure 6: Responses for 100 µm step feed.

Feed experiment results using four different

acceleration/deceleration commands were shown in

Figure 7, which is trapezoidal, S curve, Preshaping

without consideration of vibration period, and

Preshaping with consideration of vibration period. In

Figure 7, (a) is contouring error and (b) is velocity in

corner motion. about trapezoidal and Preshaping

commands with consideration of vibration period.

Figure 7(a) shows that the Preshaping without

consideration of vibration period does not contribute

particularly to contouring accuracy compared to

trapezoidal command. S Curve command seems to be

a little better than that. The contouring accuracy of the

Preshaping with consideration of vibration period

was improved about 30 % (60 µm) for trapezoidal

commands.

(a) Contouring error in corner motion (b) Velocity in corner motion

Figure 7: Responses for differential commands.

(a) Contouring error in corner motion (b) Velocity in corner motion

Figure 8: Responses for differential commands.

Y Displacemen

99.5 99.6 99.7 99.8 99.9 100

X Displacement mm

-0.1

0.1

0.2

0.3

0.4

Reference

Pre. (tp=16 ms)

Trap. (ta=32 ms)

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314

According to Figure 7(b), for the trapezoidal

commands, the actual velocity of the X-axis is about

12.8 mm/s when Y-axis velocity rises. On the other

hand, it is 8.6 mm/s using the Preshaping method. The

trapezoidal command has a large inner tracking error

because the Y-axis moves before the X-axis

decelerates. However, the acceleration time for the

trapezoid command is 20 ms, whereas the Preshaping

is 32 ms, the total travel time is longer.

For this purpose, we conducted an experiment by

setting the acceleration time with trapezoidal

command in the same as the Preshaping command.

That is t

=32 ms. The results shown in Figure 8,

where (a) is contouring error and (b) is velocity in

corner motion. The contouring accuracy was

improved about 12 % (20 µm) compared to

trapezoidal commands when using the Preshaping

command.

5 CONCLUSIONS

In this paper, we performed experiments of corner

motion with several types of acceleration/

deceleration commands using two axis feed drive

system. As a result, it was found that using a

Preshaping command with consideration of

vibration period improves the accuracy of the

contouring motion compared to the trapezoidal

command.

In general, increasing the proportional gain with

the trapezoidal command causes oscillations in the

actual velocity. The Preshaping method has the effect

of suppressing oscillations, the proportional gain will

be made higher than usual. It means that improved

response of the feed drive system and contributes to

reducing machining time.

REFERENCES

Sato R. Hayashi H. Shirase K. (2020). Active vibration

suppression of NC machine tools for high-speed

contouring motions. Journal of Advanced Mechanical

Design, Systems, and Manufacturing.

Otsuki T. Sahara H. Sato R. (2019). Method to evaluate

speed and accuracy performance of CNC machine tools

by speed-error 2-D representation. Journal of Advanced

Mechanical Design, Systems, and Manufacturing.

Singer, C, N. Seering, P, W. (1988). Preshaping command

Inputs to Reduce System Vibration. Journal of

Dynamic Systems, measurement, and Control.

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