Thermal Compensation and Fuzzy Control for Develop

Journal of Mechanics Engineering and Automation 8 (2018) 189-197

doi: 10.17265/2159-5275/2018.05.001

D

DAVID PUBLISHING

Thermal Compensation and Fuzzy Control for

Developing a High-Precision Optical Lens Mold

Chung-Ching Huang, Fu Zhang and Yi-Jen Yang

Department of Mold and Die Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan, ROC

Abstract: Precision plastic lenses often exhibit dimensional deviations due to the thermal expansion of the mold during injection

molding. Although this deviation is smaller in micron-sized (1–5 μm) lenses, it exceeds the tolerance requirement of such lenses. It is

difficult to resolve this dimensional issue by using injection molding parameters (e.g., melt temperature, injection speed, and hold

pressure). In this study, the thermal analysis of a mold was conducted, and it was confirmed that the deviation of lens dimension was

caused by the thermal instability and thermal expansion of the mold. Due to the inconsistent heat distribution of the fixed and the

movable side of the mold, the position of the location system was displaced approximately 1 to 5 μm. In this study, thermal

compensation technology for this the mold was investigated. The temperature on both sides of the mold was measured, and mold

temperature could be adjusted automatically using a control strategy based on fuzzy theory. During the mold preheating or mass

production stage, the temperature on both sides of the mold could be easily adjusted to quickly obtain the required temperature range.

The dilatation on both sides of the mold was revised to improve the alignment accuracy of the cavity, and the decenter error of these

injection lenses was reduced to 1 μm. This technology can markedly improve the production yield and efficiency of plastic products

requiring an extremely high dimensional accuracy.

Key words: Fuzzy control, temperature compensation, decenter error.

All Rights Reserved.

displacement of the mold was generated using

thermal–structural coupling analysis. The thermal

Recently, with the considerable increase in

expansion of a mold is the crucial factor in

demand for injection molding, related products are

minimizing the decenter error.

generally short, small, light, and thin, and injection

Herein, the decenter error of a precision plastic lens

molded with high precision. This enables the accurate

was taken as the main quality index and molding

production of optical lenses. Precision injection

conditions were discussed to evaluate the influence of

molding is essential in manufacturing small and

eccentricity. Two temperature controllers were

precise plastic lenses for phone cameras. Numerous

employed for the mold. Mold expansion effects were

critical factors must be satisfied to meet the requested

observed after temperature modification. According to

specifications of high-quality plastic lenses. Severe

the effects of mold temperature modification on mold

tolerance limits are required to ensure such optical

expansion, when mold temperature is controlled using

lenses are of a high quality. Moreover, product

fuzzy theory [4], the decenter error is reduced to

quality is affected by the displacement and

achieve lens eccentricity.

deformation of the mold used [1]. The most

The fuzzy theory, first proposed by Zadeh [4] from

common causes of mold deformation are derived from

the University of California, Berkeley in the United

pressure, temperature [2]. ANSYS (ANSYS, Inc.) was

Sates, combines the experience and intellectual

used to analyze mold deformation when it was

reasoning process of human beings. It directly applies

subjected to a high pressure [3], and large

to controllers, and can indirectly reduce reliance on

mathematical

models.

This

method

is

markedly

Corresponding author: Yi-Jen Yang, Ph.D. student,

research field: plastic processing.

beneficial for the control of uncertain processes in

1. Introduction

190

Thermal Compensation and Fuzzy Control for Developing a High-Precision Optical Lens Mold

Fig. 1 Basic structure of the fuzzy control process.

displacement of the lens (Fig. 5). The eccentricity of

the lens was affected by product design, mold design,

process parameters, and mold deformation. The

2. Research Method

pressure and thermal expansion of the mold were the

Polyester (OKP optical plastic) (OSAKA GAS

main influencing factors for mold deflection. The

experiment was conducted in three stages without

CHEMICALS-OKP1) was used for analysis, which is

All Rights ering product or mold designs. First,

an amorphous material with a flow index of 250 g/10

computer-aided engineering (CAE; Moldflow) was

min at 250 °C for a load of 2.16 kg. The mold material

used to analyze the effects of molding parameters on

used was M333, which exhibits excellent polishing

lens eccentricity. In the second stage, the influence of

ability machinability, and high-temperature corrosion

molding parameters on volume shrinkage was

resistance, in addition to favorable wear resistance.

determined through a single factor experiment. The

The insulation plate used was composed of glass fiber,

injection molding parameters are presented in Table 1.

which was employed to avoid transferring heat from

Third, CAE (ANSYS) was used to analyze the

the mold to the injection molding machine.

The study materials consisted mainly of a cold

effect of mold deformation on lens eccentricity.

Optimal control factors of mold deformation for

runner mold and a 16-cavity aspheric plastic lens (Fig.

eccentricity and control specifications were

2). The models for mold flow (MoldFlow, Autodesk

investigated. The decenter error can be controlled

Inc.) and structural (ANSYS, ANSYS Inc.) analyses

are presented in Figs. 3 and 4, respectively. The

within the range of ±1 μm using fuzzy control to

compensate for changes in mold temperature. The

ejection system of the mold was not considered in the

boundary conditions for the CAE analysis are shown

structural analysis model, but the insulation plate and

in Table 2.

the fixed and moved plates of the injection molding

The volume shrinkage of each node can be

machine were.

The decenter error of a lens is calculated by

calculated using mold flow analysis. Ten nodes were

employed to calculate the average and differences

measuring the center axis displacement and tilt angle

of the lens. In this study, a decenter error was

(standard deviation) between the volume shrinkage

generated and considered as the center axis

value obtained from each node

studies [5-7]. The basic structure of a complete fuzzy

logic control system is shown in Fig. 1.

Thermal Compensation and Fuzzy Control for Developing a High-Precision Optical Lens Mold

191

Fig. 2 A 16-cavity injection mold.

Fig. 3 Moldflow analysis model.

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Fig. 4 Model of ANSYS structure analysis.

Fig. 5 Decenter error of an aspheric lens.

192

Thermal Compensation and Fuzzy Control for Developing a High-Precision Optical Lens Mold

Table 1 Injection molding parameters.

Mold temperature (°C)

Melt temperature (°C)

Packing pressure (MPa)

Packing time (s)

Cooling time (s)

90/110/130

270

10/55/100

0/2.5/5

15

Table 2 Boundary conditions for ANSYS analysis.

Ambient temperature

Initial temperature

Air heat conduction coefficient

Coolant temperature of the moved

plate

25 °C

25 °C

0.026 W/m-K

90/95/100/105/110/115/

118.3/125/130 °C

100/105/110/115/118.3/

Coolant temperature of fixed plate

125/130 °C

Maximum cavity pressure 55 MPa

Initial mold temperature sprue 271 °C

Initial mold temperature runner 273 °C

Initial mold temperature cavity 275 °C

Injection time 0.2 s

Mold opening time

5 s

The method for determining the displacement of the

central axis of the lens is shown in Fig. 6. Nodes a, b,

All Rights c and d, e, and f were obtained at the circular

feature positions of lenses S1 and S2, respectively.

The angle between each node was 120°, and the

coordinates of nodes a, b, and c and d, e, and f

were respectively used to calculate the center

coordinates of S1 and S2, and the decenter error of the

lenses was calculated using the obtained center

coordinates.

The method for determining mold eccentricity is

presented in Fig. 7. The nodes in the center of the S1

and S2 lenses on the mold were set to calculate the

mold eccentricity by measuring the deformation

position of these lenses. The decenter error is positive

when the moved plate expands more than the fixed

plate and negative when the opposite occurs.

Four temperature sensors were installed in the mold,

and the positions of these sensors are displayed in Fig.

8. Mold temperatures were monitored to investigate

the relationship between coolant temperature, average

temperature of the fixed plate and moved plate, mold

temperature difference and the decenter error. The

average temperature of the fixed plate, moved plate,

mold temperature difference ∆T, and average bulk

temperature are calculated as below:

Fig. 6 Decenter error calculation with Moldflow analysis.

Fig. 7 Decenter error calculation with ANSYS analysis.

Thermal Compensation and Fuzzy Control for Developing a High-Precision Optical Lens Mold

193

Fig. 8 Positions of temperature sensors.