Sensor-Less Force Control for Injection Molding

8/7/2019 Sensor-Less Force Control for Injection Molding

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Sensor-less Force Control for Injection MoldingMachine Using Reaction Torque Observer

Yuzuru OhbaSendai National College of Technology

4-16-1 Ayashichuo Aobaku Sendai

Miyagi 989-3128

Japan

[email protected]

Kiyoshi Ohishi and Seiichiro KatsuraNagaoka University of Technology

1603-1 Kamitomiokamachi Nagaoka

Niigata 940-2188

Japan

[email protected]

[email protected]

Yukio Yoshizawa, Koichi Kageyamaand Katsuyuki Majima

Niigata Machine Techno Co., LTD.

1300 Okayama, Higashi-ku

Niigata 950-0821

Japan

[email protected]

[email protected]

[email protected]

Abstract —In recent years, the industrial researchers have paid attention

to thenot only position control but also force control. The onetarget of force

control researches is the injection molding machine. The conventional force

control system uses the force sensor to detect the inserted force. However,

the force control system using force sensor has some problems such as the

noise, the frequency band and so on.This paper newly proposes that the reaction torque observer is applied

to the injection molding machine using ball screw. The reaction torque ob-

server solves this problem of force sensor. However, it is well-known that

the ball screw system has the resonant frequency caused by the torsion

phenomenon. Hence, this torsion vibration affects both performances of

force control and reaction torque estimation. This paper proposes a new

reaction torque observer considering the torsion phenomenon and the fric-

tion torque. The proposed reaction torque observer estimates the reaction

torque accurately. Moreover, as the outside of proposed reaction torque

observer has its friction model, this friction model can be tuned without

considering the stability condition of force control feedback system. The

validity of proposed force control system is confirmed by the experimental

results. This paper realizes the low cost and space-saving injection molding

machine by using the proposed force sensor-less control method.

I. INTRODUCTION

In these years, many plastic products have been produced and

used. These plastic products are mostly manufactured by injec-

tion molding machine. The first screw injection molding ma-

chine was developed in 1946. The plastic injection molding ma-

chine has been growing up until now. The injection molding

machine has been driven by the hydraulic actuator before 1980.

After 1980, as the motor control technology has been devel-

oped, its power source has turned from hydraulic actuator into

”electric actuator”. The electric-powered injection molding ma-

chine has the performances of high-speed response and energy

saving specification, in comparison with that of hydraulically-

operated injection molding machine. Therefore, the motor con-

trol technology makes it possible to produce the many plastic

products at low cost. Many researches of electric-powered in-

jection molding machine have been carried out[1], such as the

electric-powered injection molding machine using DD(Direct-

Drive) motor and/or parallel AC motor drive mechanism. DD

motor has the ability of high injection speed and quick response

[2]. These methods enable the high power injection molding

machine without oil pressure [3].

The precise assembly and short task period are attained by

high performance position control. As a result, the high perfor-

mance position control makes possible by large-scale produc-

tion. However, as the quality of plastic products depends on the

injection force, it is important to develop not only the high per-

formance position control system but also the fine force control

system. The conventional force control methods have used the

force sensor to obtain the force information. Most of force sen-

sors transform from the inserted force into the distortion. Thesesensors measure the distortion as the resistance of strain gage

or capacitance change. These force sensors have some problem

such as the non-collocation problem, the cost, the strength of

sensor and so on.

In an ordinary force control system, the actuator is mounted

in the different position of force sensor. As a result, it is difficult

to realize the instantaneous force sensing process. Next prob-

lem is the strength of force sensor structure. The ordinary force

sensor transforms from the force information into the electrical

signal. Therefore, the strength of ordinary force sensor is weak.

Furthermore, the high performance force sensor is not econom-

ical. In order to overcome these problems, the force sensor-less

control method using the reaction torque observer has been ap-

plied [4][5][6]. The reaction torque observer is based on the

disturbance observer. This force sensor-less method uses only

the motor current information and the motor position informa-

tion. In other words, this torque estimation algorithm requires

no additional sensor.

In this paper, the reaction torque observer is applied to the

injection molding machine using ball screw. However, it is

well-known that the servo system using the ball screw has theresonant frequency and the friction phenomenon [7][8][9][10].

Hence, this torsional vibration affects on both performances of

force control and reaction torque estimation. This paper pro-

poses a new reaction torque observer considering the torsion

phenomenon and the friction phenomenon. The proposed reac-

tion torque observer has little influence on the resonant vibration

and the friction torque. Moreover, since the proposed reaction

torque observer has its friction model at the outer area of reac-

tion torque observer, this friction model can have the self-tuning

process independent of the stability problem of feedback con-

trol system. This paper confirms the effectiveness of the pro-

posed force sensor-less control for injection molding machine

by experimental results.

978-1-4244-1706-3/08/$25.00 ©2008 IEEE.



II . OVERVIEW OF INJECTION MOLDING MACHINE

This paper realizes the force sensor-less control for injection

molding machine. Fig.1 is the photo of experimental system.

This experimental system is composed of ball screw, AC servo

motor, timing belt, pulley, force sensor and so on. The ball screw

changes from the revolving movement to the horizontal move-

ment. The ball screw is often used in industrial area. The force

of ball screw is described in equation (1). The position of ball

screw is described in equation (2).

f = Rg2π

pt τ m (1)

x =1

Rg

pt

2π θ m (2)

where,τ m : motor torque;

f : thrust force of ball screw;

θ m : motor position;

x : ball screw position;

Rg : pulley ratio;

pt : pitch of ball screw.

Fig.2 illustrates the conventional experimental injection

molding machine using ball screw. The conventional injection

Fig. 1. Photo of experimental injection molding machine system

AC ServoMotor

ForceSensor

InjectionForce

Primarypuly

Secondarypuly

Ball screw

Ball screw

Timing belt

Slide guide

Slide guide

Fig. 2. Schematic diagram of ordinary injection molding machine using force

sensor

Pressure [MPa]

Time [s]

21 3 4

Pc

Fig. 3. Pattern of force reference

molding machine controls the pressure as shown in Fig.3. Theforce patterns divide into 4 parts as follows,

1 Stop;

2 Filling ;

3 Holding;

4 Charging.

The initial condition of injection molding machine is stop mo-

tion whose speed is zero. In this condition, plastic pellets are

melted by heating and screw-rotation, and it is poured into the

reservoir. The rotation of screw accelerates melt state in this

condition. In the next condition, the screw injects the melted

plastic into the mold. This state keeps the constant pressure.The injection molding machine keeps the constant pressure un-

til the plastic product has hardened. Finally, the injection mold-

ing machine move the screw backward and the plastic pellets

are poured into the barrel again. The cycle is completed when

the mold opens and the product is ejected with the assistance of

ejector pins.

In this system, the force information from the environment

is detected by force sensor. The ordinary force sensor utilizes

the strain from external force to get the force information. The

conventional force control system enables the high resolution

force sensor. However, the high sensitive force sensor is not

economical, and the force sensor has some problems such as the

noise, the frequency band and so on. One of these problems

is the stiffness of force sensor. The force sensor is required to

strain from small force to get the high resolution.

In ideal force control system, the force sensor should require

to attach the same location of actuator in order to realize the in-

stantaneous force sensing process. However, in the conventional

actual servo system, the force sensor is mounted in the different

position of actuator. As a result, the accurate and instantaneous

force sensing becomes difficult. The cost price of force sensor

is not small. In other words, the force sensor generates initial

cost and running cost. In order to overcome these problems, this

paper proposes a new force sensor-less control system using re-

action torque observer.



III. REACTION TORQUE OBSERVER USING ONE -INERTIA

MECHANICAL MODEL

A. Overview of reaction torque observer

The disturbance observer estimates the disturbance torque of

AC servo motor by using the motor current and the motor posi-

tion. The disturbance torque is described as follows,

τ dis = τ ext + Dω m + τ fric× sgn(ω m).

(3)

The disturbance observer estimates the sum of external force

τ ext , viscosity friction Dω m and coulomb friction τ fric. If the

friction model is known, the proposed disturbance observer esti-

mates only the external force. Furthermore, the frequency band-

width of force estimation can be wider than force sensor. In

this paper, the proposed reaction torque observer has a reaction

model outside the observer. Then the proposed reaction torque

observer makes the friction model easy to design.

Fig.4 shows the block diagram of ordinary reaction torque

observer, whose plant system is one-inertia mechanical model.In Fig.4, J denotes the total inertia in motor shaft equivalent. D

denotes the total viscosity in motor shaft equivalent. K t denotes

the torque constant. J n denotes the nominal total inertia. gd

denotes the filter gain of disturbance observer. τ dis denotes the

disturbance torque. τ fric denotes the coulomb friction.

B. Experimental results

In order to confirm the validity of the force sensor-less

force control using ordinary reaction torque observer, this pa-

per shows the experimental results of the injection molding ma-

chine. The proposed control system is implemented by 32bit

fixed point calculation DSP.

The pole of tested reaction torque observer is 100[rad/sec].

This bandwidth of observer is lower than that of its resonant

frequency. Then, the control performance has little influence

on this resonant frequency. Fig.5 is the experimental results

of force control of tested injection molding machine using the

reaction torque observer whose plant system is one-inertia me-

chanical model. In Fig.5, the tested force control system uses

the force information from force sensor. The reaction torque

observer is used as only observation. In Fig.5, the experimental

Disturbance Observer

g d

s

g d J n

disext

I q 1

JsK t

K tn

m

dis ext fric

fric

+ +

+

+

-

--

-

Dm

Dm

Fig. 4. Reaction torque observer based on ordinary disturbance observer

results point out that reaction torque observer well estimates the

external torque in steady state.

Fig.6 shows the experimental results of force sensor-less force

control system. In Fig.6, as the pressure response has a just large

vibration (in the dashed line circle), the quality of manufactured

product is low. Hence, it is necessary for the reaction torque ob-

server to narrow its bandwidth to improve the pressure response.

Fig.7 is the experimental result of force sensor-less force con-

trol using the narrow bandwidth reaction torque observer whose

pole of observer is 50 [rad/sec]. Fig.8 is the expansion figure

of Fig.7. Fig.8 indicates that the force sensor-less control sys-

tem using the narrow bandwidth reaction torque observer has

the good pressure response in comparison with that of Fig.6.

In Fig.8, the expansion waveform of reaction torque observer

has the overshoot in transient state (in the dashed line circle).

Because, as this reaction torque observer is designed by one-

inertia plant model, this observer is affected by torsion vibra-

tion of shaft. These experimental results have the periodic spike

noise whose frequency is about 1[Hz]. The control performance

has little influence on this periodic noise, because this noise is

500ms/div

120

100

80

60

40

20

0

Pressure [MPa]

Time [s]

Load cell

Reaction torque observer

Fig. 5. Reaction force estimation response of reaction torque observer using

one-inertia model

500ms/div

120

100

80

60

40

20

0

Pressure [MPa]

Time [s]

Load cell


Fig. 6. Experimental result of force sensor-less force control using one-ineria

model(observer pole is 100[rad/s])



500ms/div

120

100

80

60

40

20

0

Pressure [M

Pa]

Time [s]

Load cell


Fig. 7. Experimental result of force sensor-less force control using one-ineria

model(observer pole is 50[rad/s])

100ms/div

120

100

80

60

40

20

0

Pressure [MPa]

Time [s]

Load cell


Fig. 8. Expansion figure of Fig. 7

the observation data of the oscilloscope which is separated from

the control DSP.

IV. TWO -INERTIA MECHANICAL MODEL OF INJECTION

MOLDING MACHINE

In previous chapter, this paper proposes the force sensor-less

force control system using ordinary reaction torque observer.

However, it is well-known that the actual ball screw system has

the resonance frequency caused by torsion vibration of shaft.

Fig.9 is the open-loop frequency characteristic of transfer

function from the torque command to the motor speed in the

tested injection molding machine. Fig.9 points out that the

tested injection molding machine has the resonant frequency

180[Hz] and the anti-resonant frequency 130[Hz]. Hence, the

tested injection molding machine is treated as the two-inertia

resonant system. Fig.10 shows the block diagram of two-inertia

resonant system.

In Fig.10, I q is the motor torque current, K t is the torque con-

stant of motor, J m is the motor inertia, Dm is the viscosity of

20

0

-20

-40

-60

-80

200

-90

-180

-270

-360

Magnitude[dB]

Phase[deg]

0.1 1 10 100 1000

Frequency[Hz]

Fig. 9. Open-loop frequency characteristic of transfer function from torque

command to motor speed of tested injection molding machine

+

1

J Ls + DL

1

J ms + Dm

K t

ω L

ωm

1

Rg

1

Rg

τ ext

θsK s

1

s

+

+

-

-

-

I q

Fig. 10. Block diagram of two-inertia resonant system for injection molding

machine

motor, K s is the sprint constant, J L is the load inertia, DL is the

viscosity of load, τ ext is reaction torque from environment, θ s is

the torsion angle of shaft, ω m is the motor speed and ω L is the

load side speed.

The state equation of two-inertia resonant system is con-

structed from Fig.10. Equation (4) and equation (5) express the

state equations of two-inertia resonant system.

d

dt xxx = Axxx + Buuu (4)

yyy = Cxxx + Duuu (5)

AAA =

⎡⎢⎣

0 −1 1Rg

K sJ L

−DLJ L

0

− K sJ mRg

0 −DmJ m

⎤⎥⎦ ,BBB =

⎡⎣ 0

0K t J m

⎤⎦

C T =

⎡⎣ 0

0

1

⎤⎦

, xxx =

⎡⎣ θ s

ω L

ω m

⎤⎦

, u = K t I q

The transfer function from the torque current I q to the angular

speed ω m is led to equation (6).



Pn(s) =ω m(s)

I q(s)

=b1s2 + a3b1s + a4b1

s3 + (a1 + a3)s2 + (a1a3 + a2a5 + a4)s(6)

+ a1a4 + a2a3a5

a1 =Dm

J m, a2 =

K s

J mRg, a3 =

DL

J L, a4 =

K s

J L,

a5 =1

Rg

, b1 =K t

J m

ω r =

K s

J mR2g

+K s

J L(7)

ω ar = K s

J L

(8)

The transfer function of the plant system using the resonant fre-

quency and the anti-resonant frequency is led to equation (9)

from equations (6)-(8), on condition that the viscosity friction is

equal to zero.

Pn(s) =ω m(s)

I q(s)=

b1(s +ω ar )2

s(s +ω r )2(9)

The two-inertia system has the resonant frequency ω r and the

anti-resonant frequency ω ar in equation (7) and equation (8).

The resonant frequency affects the estimation of the reactiontorque. Then, this paper proposes a new reaction torque observer

considering mechanical torsion phenomenon, whose plant sys-

tem is treated as two-inertia mechanical model.

V. REACTION TORQUE OBSERVER CONSIDERING

RESONANT FREQUENCY

A. Reaction torque observer using two-inertia mechanical

model

It is well-known that the injection molding machine using the

ball screw and the timing belt is treated as two-inertia mechan-

ical model. In order to consider the mechanical torsion phe-

nomenon, this paper proposes a new reaction torque observerconsidering its resonant frequency. When the disturbance torque

is treated as a step-like function, the disturbance torque is ex-

pressed by equation (10).

d

dt τ ext = 0 (10)

The disturbance torque is added to one of state variables. The

proposed observer is designed from this state equation using

gopinath’s observer design method [11], [12]. The state equa-

tion of observer is derived from (4), (5) and (10). The state

equation of reaction observer is described as follows,

d

dt xxxo = Axxxo + Buuuo (11)

yyyo = Cxxxo + Duuuo (12)

τ ext = τ dis−DLω L−τ fric (13)

AAA =

⎡⎢⎣

0 K sJ mRg

l1 0

0 K sJ mRg

l2 −1

− 1J L

K sJ L

+ K sJ mRg

l3 0

⎤⎥⎦ ,uuuo =

ω L

I q

BBB =

⎡⎢⎣

K sJ mRg

l1l2 − K t J m

l1

−l3 + K sJ mRg

l22 + 1

Rg− K t

J ml2

K sJ L

l2−1

J Ll1 + K s

J mRgl2l3 − K t

J ml3

⎤⎥⎦

C C C =

⎡⎣

0 0 1

0 1 0

1 0 0

⎤⎦ , DDD =

⎡⎣

l1 0

l2 0

l3 0

⎤⎦ ,yyyooo =

⎡⎣

ω M

θ s

τ dis

⎤⎦ .

where, l1, l2 and l3 are the parameters which determine the

pole location of reaction torque observer. The proposed reaction

torque observer estimates the actual reaction torque without tor-

sion torque of shaft. As a result, the force control system using

the proposed observer estimates the accurate and instantaneous

reaction torque.

B. Experimental results of reaction torque observer using two-

inertia mechanical model

In order to confirm the validity of the proposed reaction

torque observer using two-inertia mechanical model, this paper

shows the experimental results of force sensor-less force controlsystem of injection molding machine using the proposed reac-

tion torque observer using two-inertia mechanical model. The

poles of this reaction torque observers are 100[rad/sec].

Fig.11 shows the experimental results of the reaction torque

observer considering torsion of the shaft. In Fig.11, the force

control system uses force information from only force sensor.

The reaction torque observer considering torsion of the shaft

is also used as only observation. Fig.11 points out that the

proposed reaction torque observer using two-inertia mechanical

model well estimates the external torque.

Fig.12 is the experimental results of the force sensor-less

force control system using the proposed reaction torque observerconsidering torsion of the shaft. Fig.13 is also the expansion fig-

ure of Fig.12. Fig.13 indicates that the proposed reaction torque

observer well estimates the external torque without torsion vi-

bration.

From Fig.12, the proposed reaction torque observer well es-

timates the external torque in steady state and transient state

(in the dashed line circle). As a result, the bandwidth of pro-

posed reaction torque observer considering resonant frequency

becomes wider than that of reaction torque observer using one-

inertia mechanical model. These experimental results also have

the periodic spike noise whose frequency is about 1[Hz]. This

control performance also has little influence on this periodic

noise.



500ms/div

120

100

80

60

40

20

0

Pressure [MPa]

Time [s]

Load cell


Fig. 11. Reaction force estimation response of reaction torque observer using

two-inertia model

500ms/div

120

100

80

60

40

20

0

Pressure [MPa]

Time [s]

Load cell


Fig. 12. Experimental result of force sensor-less force control using two-ineria

model

100ms/div

120

100

80

60

40

20

0

Pressure [MPa

]

Time [s]

Load cell


Fig. 13. Expansion figure of Fig. 12

V I. CONCLUSIONS

The conventional force control system uses the force informa-

tion from the force sensor. However, the force sensor has some

problems such as non-colocation, its cost, its noise, its strength

and so on. In order to overcome the problems of force sensor,

this paper proposes a new force sensor-less control system us-

ing reaction torque observer for injection molding machine. The

injection molding machine often uses the ball screw and timingbelt, which has the resonant frequency. The resonant frequency

affects both the control performance and reaction torque estima-

tion performance. Therefore, this paper proposes a new reaction

torque observer considering the resonant frequency, whose plant

system is two-inertia mechanical model.

This paper shows the experimental result of force sensor-less

force control system of injection molding machine using the

proposed reaction torque observer. As a result, the proposed re-

action torque observer well estimates the reaction torque quickly

and accurately. From these experimental results, the proposed

force sensor-less force control system has the validity on the

force control system of injection molding machine.

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Sensor-Less Force Control for Injection Molding

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