JP2001277323A - Method for manufacturing optical element using flow analysis - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for optimizing a set value and molding conditions by obtaining optical characteristic change after molding occurring by a shearing stress to be applied when molded by numerically inferring or calculating particularly in the case of manufacturing a thick optical component by resin molding. SOLUTION: A method for manufacturing an optical element comprises the steps of injection filling a molten raw material in a mold, dwelling in the mold, cooling in the mold, and then taking out the molding. The method further comprises the steps of dividing the element in the mold into a plurality of three-dimensional finite elements, obtaining a shearing stress when molded at each element by a three-dimensional finite element method with the molding conditions such as a mold temperature, a temperature gradient in the mold or the like as parameters, obtaining characteristics such as an image surface curve, a double refraction, polarizing characteristics, a transmission wavefront and the like due to a residual strain, a refractive index distribution, a refractive index change after molding according to a qualitative relation of a relaxation of the shearing stress, and correcting a designing value and the molding conditions based on the characteristics.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention performs a flow analysis at the time of molding an optical component by using a three-dimensional finite element method to obtain optical characteristics of an optical element after molding.
The present invention relates to a method for determining design values and molding conditions for obtaining necessary optical characteristics.

[0002]

2. Description of the Related Art An fθ lens 1 as shown in FIG. 3 is incorporated in a scanning optical system such as a laser printer, a copying machine, a facsimile printing unit or the like. Axial direction of drum)
Is converged in the main scanning direction and the sub-scanning direction while performing fθ correction, and irradiates the photosensitive drum with spot light. The fθ lens 1 is generally formed into an aspherical shape, and has a large thickness in order to increase the length in the main scanning direction.

As shown in FIG. 4, resin molding of the fθ lens 1 is performed by filling a mold 2 with a molten resin, performing pressure holding and cooling in the mold, and then molding the fθ lens 1 as a molded product. Is performed by releasing the mold. The above-mentioned holding pressure equalizes the pressure gradient remaining from the tip of the gate toward the end of the cavity immediately after filling, and applies a secondary pressure from the gate to compensate for the shrinkage due to cooling of the resin. Further, the above cooling is to cool the molded product until the molded product can be released after the gate is sealed (end of pressure holding) due to the resin curing of the gate portion. The contraction is performed in a balanced state. Further, at the time of mold release, the molded product is taken out of the mold, and if there is residual strain constrained by the mold, it is released with deformation.

[0004]

When the above-mentioned fθ lens is manufactured by resin molding, the diameter of the spot irradiated on the photosensitive drum becomes larger than a design value, and there is a problem that it is difficult to increase the resolution. .

[0005] This is because birefringence occurs in the fθ lens due to residual strain after resin molding, and extraordinary refraction occurs in which the refractive index varies depending on the direction of the light vibrating surface. Research literature describing the behavior of the resin during resin molding has been published, so molding conditions such as mold temperature, packing pressure, cooling time, etc. Can be considered, but these relationships cannot be clarified numerically.

An optical element manufactured by resin molding is:
There are many types other than the fθ lens. Each optical element differs in a main point of interest for improving performance according to its use. For example, an optical element whose birefringence should be reduced in order to increase the resolution, an optical element that emphasizes polarization characteristics, an optical element that emphasizes field curvature due to a change in refractive index, and an optical element that emphasizes a transmitted wavefront, such as the above-mentioned fθ lens There is. These properties or properties are closely related to residual strain, as they are determined as a result of the accumulation of shear stress. Therefore, by numerically examining the process of generation or fluctuation of shear stress, these properties or characteristics can be estimated, and design values and molding conditions optimized for necessary optical characteristics can be determined. become. However, heretofore, the process of generation or fluctuation of shear stress cannot be numerically clarified, so that this method cannot be adopted.

Therefore, the design values and the molding conditions for obtaining the necessary optical characteristics are determined by trial and error of optically inspecting a prototype manufactured according to an experienced person or the like. This required a great deal of time and effort.

Accordingly, the present invention provides, by inputting molding conditions as parameters, residual distortion after molding, refractive index distribution, field curvature due to refractive index fluctuation, birefringence, polarization characteristics, and the like.
It is an object of the present invention to provide a method capable of calculating or estimating characteristics such as a transmitted wavefront numerically by computer simulation to obtain optical characteristics after molding and optimizing set values and molding conditions.

[0009]

According to a first aspect of the present invention, there is provided a method for manufacturing an optical element using flow analysis, wherein a molten material is injected and injected into a mold, and pressure holding and cooling are performed in the mold. In a method of manufacturing an optical element to be taken out later, an optical element in a mold is divided into a plurality of three-dimensional finite elements, and a flow analysis using a three-dimensional finite element method is performed using molding conditions including mold temperature as parameters. By determining the shear stress at the time of forming each element, a forming condition for reducing the residual strain determined as the cumulative result of the shear stress is determined.

According to a second aspect of the present invention, there is provided a method for manufacturing an optical element using flow analysis, wherein a molten material is injected into a mold, and after holding and cooling in the mold, the optical element is taken out. In the manufacturing method of (1), the optical element in the mold is divided into a plurality of three-dimensional finite elements, and the molding conditions including the mold temperature are used as parameters, and the flow analysis using the three-dimensional finite element method is performed. By calculating the shear stress of
It is characterized in that the density distribution determined as the cumulative result of the shear stress is predicted and the characteristics of the refractive index distribution are obtained.

According to a third aspect of the present invention, in the method for manufacturing an optical element using the flow analysis according to the second aspect, the characteristic of the field curvature due to the change in the refractive index is determined based on the obtained refractive index distribution. Is obtained.

According to a fourth aspect of the present invention, there is provided a method of manufacturing an optical element using flow analysis, wherein a molten material is injected and injected into a mold, and after holding and cooling in the mold, the optical element is taken out. In the manufacturing method of (1), the optical element in the mold is divided into a plurality of three-dimensional finite elements, and the molding conditions including the mold temperature are used as parameters, and the flow analysis using the three-dimensional finite element method is performed. By calculating the shear stress of
It is characterized in that a characteristic of birefringence determined as an accumulation result of shear stress is obtained.

According to a fifth aspect of the present invention, there is provided a method of manufacturing an optical element using flow analysis, wherein a molten material is injected into a mold, and after holding and cooling in the mold, the optical element is taken out. In the manufacturing method of (1), the optical element in the mold is divided into a plurality of three-dimensional finite elements, and the molding conditions including the mold temperature are used as parameters, and the flow analysis using the three-dimensional finite element method is performed. By calculating the shear stress of
It is characterized in that a polarization characteristic determined as a cumulative result of shear stress is obtained.

According to a sixth aspect of the present invention, there is provided a method of manufacturing an optical element using flow analysis, wherein a molten material is injected and injected into a mold, and after holding and cooling in the mold, the optical element is taken out. In the manufacturing method of (1), the optical element in the mold is divided into a plurality of three-dimensional finite elements, and the molding conditions including the mold temperature are used as parameters, and the flow analysis using the three-dimensional finite element method is performed. By calculating the shear stress of
A characteristic of a transmitted wavefront determined as a cumulative result of shear stress is obtained.

According to a seventh aspect of the present invention, there is provided a method of manufacturing an optical element using flow analysis, wherein necessary optical characteristics are obtained based on characteristics obtained by at least one of the methods described in the second to sixth aspects. In order to obtain, at the design stage, both or one of the design value and the molding condition is corrected.

According to an eighth aspect of the present invention, there is provided a method for manufacturing an optical element using flow analysis according to any one of the first to seventh aspects, wherein the molding conditions for relaxing the obtained shear stress are determined. It is characterized in that the cumulative result of shear stress is estimated from a qualitative relationship.

According to a ninth aspect of the present invention, in the method for manufacturing an optical element using flow analysis according to any one of the first to seventh aspects, in addition to the calculation of the shear stress during molding, It is characterized in that the relaxation is also calculated by a flow analysis using a three-dimensional finite element method.

According to a tenth aspect of the present invention, in the method for manufacturing an optical element using the flow analysis according to any one of the first to ninth aspects, a temperature gradient is given to the mold, and the temperature gradient is reduced. It is characterized in that a flow analysis using a three-dimensional finite element method is performed in addition to the calculation elements.

According to an eleventh aspect of the present invention, in the method for manufacturing an optical element using flow analysis according to any one of the first to tenth aspects, the molten material is a synthetic resin, and the optical element is It is an fθ lens.

[0020]

[Embodiment] The "residual strain" after resin molding, which is a problem in the present invention, is obtained by multiplying "shear stress", which is a stress generated at each moment of the molding process, by a weight in consideration of the effect of relaxation. , Integrated over time (convolution integral value [a kind of history]). This "shear stress" is an instantaneous value determined by the unevenness of the pressure direction applied to the resin during resin molding, and follows the flow path shape, compression / expansion and viscosity change due to temperature change, and the like. When "shear stress" is continuously applied, the residual stress of the resin increases, but the residual stress decreases due to the relaxation due to the flow and deformation of the resin, and the final residual stress decreases due to birefringence etc. It causes "residual distortion".

Since the resin immediately after being injected into the mold has high fluidity, the residual stress hardly accumulates, and the resin is quickly relaxed. During the pressure-holding step, the heat is deprived by the mold and the viscosity of the resin increases, and the curing proceeds.As a result, the residual stress due to the shear stress increases, while the relaxation action gradually decreases, and the curing is usually performed. The residual stress is maximized at the final stage of the dwelling process in which is started. In the cooling step, the supply of the secondary pressure from the gate is cut off, so that the residual stress hardly increases, and the residual stress is relaxed as the expansion of the resin due to the pressure decrease and the contraction of the resin due to the cooling are offset. Will be At the time of mold release, the molded product is released from the mold, so that the residual stress restrained by the mold is released at once.

Focusing on the above phenomena, if the accumulation of shear stress during resin molding and the final result of its relaxation are obtained,
The magnitude of residual strain after resin molding that causes birefringence or the like can be determined. In this case, the shear stress history and
Although it is possible to calculate the relaxation following all the steps of molding, as a result of the flow analysis using the three-dimensional element method of the present inventor, FIGS. 1A and 1B and FIG. 2 (a)
As shown in (b), it was confirmed that the generation pattern of the shear stress at the time when the curing of the resin was started (at the completion of the pressure holding, etc.) substantially coincided with the generation pattern of the birefringence (described later in detail). Described). That is, the residual strain after resin molding that causes birefringence is dominated by the magnitude of the shear stress at the time when the curing of the resin is started, and the flow analysis using the three-dimensional element method reveals that Find the magnitude of the shear stress,
By correcting with the magnitude of the relaxation after this, the magnitude of the residual strain after resin molding can be estimated.

In the flow analysis using the three-dimensional finite element method for obtaining the shear stress at the time of resin molding, as shown in FIGS. 5 and 6, an optical component to be molded is divided into a plurality of three-time elements, and Is to determine the physical behavior of the resin in each step of resin molding by solving a differential equation with respect to flow velocity, temperature, and change in viscosity with temperature.

The magnitude of the relaxation used for the above correction is
The following qualitative relationship exists between the shear stress and the molding conditions: mold temperature, cooling time, and dwell time.

The lower the mold temperature, the greater the shear stress, the more difficult it is to alleviate the residual stress, and the greater the residual strain.

The shorter the cooling time, the smaller the residual strain, but if the cooling time is too short, the "warp" and "deformation" will occur.
The amount of becomes large.

Since the increase and decrease of the holding pressure, "shear stress" and "relaxation" act in the opposite direction to "residual strain",
The change in the holding pressure has little effect on the residual strain.

From the above, the study of "birefringence" is mainly based on the correlation with "temperature", the correlation with "holding pressure" is treated as secondary, and the "cooling time" is considered as "warpage". And "deformation".

An analysis example supporting the above-described method of the present invention will be described.

The following analysis example is an analysis example in which four pieces of the fθ lens 1 having the shape shown in FIG. 3 are resin-molded simultaneously with the mold 2 shown in FIG. The mold 2 includes a fixed mold 2a.
And the movable mold 2b, and a gate, a runner, and a cavity are formed. The flow analysis by the three-dimensional finite element method described below uses the flow analysis of Timon. In this flow analysis, the fθ lens is divided into finite elements as shown in FIGS.

In this analysis, the resin used was Zeon
ex E48R1 is used, and the molding conditions are as follows:
The following values (basic conditions) are used.

Cycle time 440 sec Room temperature 23 ° C. Injection resin temperature 290 ° C. Mold temperature 142.5 ° C. Filling time 12 sec Filling rate 100% Injection speed 10 mm / sec Injection pressure 200 MPa Holding time (primary) 10 sec Holding time (secondary) 5 seconds Holding pressure (primary) 100 MPa Holding pressure (secondary) 80 MPa Cooling time after holding 400 seconds In addition, as shown in FIG. 7, the temperature of the mold is adjusted by connecting a pipe 3 for passing a cooling medium such as water into the mold. This is performed by controlling the temperature of the cooling medium to a temperature higher by 5 ° C. than the set value of the mold temperature.

Under the above-mentioned basic conditions, a flow analysis was performed on the longitudinal section of the fθ lens at the end of the pressure holding, and a shear stress was obtained. As a result, an analysis result as shown in FIG.
In this figure, the magnitude of the shear stress is color-coded according to a rod-shaped legend shown on the right side (the numbers also indicate the unit is PMa; the same applies hereinafter). This figure shows that the central portion of the lens has the smallest shear stress, and the outer surface portions at both ends of the lens show portions having the largest shear stress.

FIG. 1B shows the result of examining the birefringence distribution of the fθ lens actually molded under the molding conditions. The birefringence was obtained by irradiating natural light through a polarizing plate and photographing light emitted from the fθ lens through a polarizing plate having a polarization direction different from that of the polarizing plate by 90 °.

From the comparison of FIGS. 1 (a) and 1 (b), the pattern of the shear stress and the birefringence are closely related, and by examining the magnitude of the shear stress, the state of the occurrence of the birefringence can be numerically evaluated. It is understood that it can be caught.

FIGS. 2 (a) and 2 (b) show the same tendency as the cross section of the fθ lens shown in FIG. 1 under the same conditions. .

The shear stress calculated as shown in FIG. 1 and FIG. 2 can be obtained by setting the calculation time point to the time point at which the residual stress has the greatest effect (for example, at the end of the holding pressure at which hardening starts). This can be considered to be substantially equivalent to the residual stress at the time. The magnitude at which this shear stress (residual stress) is relaxed in the subsequent steps depends on the molding conditions such as mold temperature,
An analysis example in which the relationship between the cooling time and the dwell time is examined will be described.

Analysis Example of Mold Temperature and Consideration Under the above basic conditions, the temperature of the cooling medium was set to 132.5 ° to 162.5 ° C.
Set in 5 steps in the range of 2.5 ° (the mold temperature is 5
C is kept low. 8) to 11 show the results of the analysis performed. With respect to the change in the mold temperature (cooling medium temperature), the maximum value and the minimum value of the ballistic stress after the holding pressure and after the cooling change as shown in FIG. These figures show that the magnitude of the shear stress increases as the mold temperature decreases. This is consistent with the known fact that the lower the mold temperature, the greater the occurrence of birefringence.

FIG. 9 (after filling), FIG. 10 (after holding pressure), FIG.
1 (after cooling) is the mold temperature (cooling medium temperature) under the above conditions
The shear stress as a result of the flow analysis performed while changing the color is displayed in different colors in a perspective view and an XY cross-sectional view, and FIG. 8 is obtained from these analysis results. Looking at FIG. 9 (after filling), a pressure gradient from the gate toward the end of the cavity remains in the injected resin.
Looking at (after holding pressure), this has been resolved. From the start of filling to the final stage of packing pressure, the fluidity is kept high and relaxation is sufficiently performed, so the ratio of shear stress remaining as residual stress during this period is small, and it is based on the shear stress at the end of packing pressure. Therefore, it can be inferred that the residual stress should be estimated.

In general, the lower the mold temperature, the lower the resin temperature, and the longer the time required for relaxation tends to be. That is, the strain generated due to the shear stress is hard to be alleviated, and the degree of remaining as a residual strain is large.

According to the results of the above flow analysis, the lower the mold temperature, the greater the occurrence of shear stress, the longer the time required to relax the shear stress, and the more likely it is for residual stress to remain. It is considered that the magnitude of the “birefringence” changes significantly as a result of the combination.

That is, as the mold temperature is lower, the shear stress is larger, the residual stress is less likely to be relaxed, and the residual strain is more likely to be increased. This relationship is qualitative, and it is possible to obtain a numerical ratio of the relationship by performing some trial production experiments on a fixed molded product and molding conditions.

Examples of Analysis and Considerations on Cooling Time FIGS. 12 and 13 show analysis results obtained by changing only the cooling time in three stages within the range of 400 to 500 seconds under the above basic conditions. FIG. 12 shows a state in which the maximum value and the minimum value of the ballistic stress after cooling change with respect to the cooling time, and FIG. 13 shows the result of the analysis used to create the graph of FIG. A certain elasticity is displayed in a different color as a perspective view, an XY sectional view, and an XZ sectional view.

According to the analysis results, the "shear stress" tends to increase as the cooling time is shorter. on the other hand,
Examining the birefringence of a molded product actually prototyped under these molding conditions, it is better to remove it during a short cooling time,
The magnitude of “birefringence” tends to be smaller, and has the opposite relationship. The relationship between this cooling time and residual strain is
This will be explained by considering the relationship with "extraction" from the mold after cooling.

During the cooling period, while the resin is being cured,
Relaxation of the residual stress at the completion of the pressure holding progresses. However, since it is restricted by the mold, the relaxation of the residual stress is moderate. On the other hand, when taking out after cooling, since the mold is released from the mold, the deformation is free, and the distortion accumulated inside the molded article is rapidly (though not completely) released. Therefore, if the cooling time is long, the final shear stress will be small, but the residual stress will not be released sufficiently due to the constraint of the mold and the curing will proceed, and even if it is taken out, this residual stress will not be released, The ratio that remains as residual strain increases. On the other hand, if the cooling time is short, the final shear stress is large, but the cumulative time of the shear stress during this period is short, and the residual stress is released in a state where the mold is released from the constraint by the subsequent removal, so the residual stress is released. The distortion is smaller.

As described above, the shorter the cooling time, the smaller the residual strain can be. However, if the cooling time is too short, the amount of “warpage” and “deformation” will be increased due to the rapid release of residual stress upon removal. Becomes large, and deterioration of optical characteristics on this surface becomes a problem. This has been confirmed by experimental examples.

An example of analysis of the holding pressure and its consideration Under the above basic conditions, the holding pressure was increased to 60 MPa, 100 MPa,
The results of analysis performed at three levels of 0 MPa are shown in FIGS.
As shown in FIG. With respect to the holding pressure, the maximum value and the minimum value of the ballistic stress after the pressure holding and after the cooling change as shown in FIG. FIGS. 14 (after filling), FIG. 16 (after holding pressure),
FIG. 17 (after cooling) summarizes the results of the flow analysis of the shear stress. FIG. 15 (after filling) shows the state before the dwelling, and the shear stress has the same distribution.

FIG. 14 shows that as the holding pressure increases, the shear stress decreases. On the other hand, according to the experimental results, it was found that the higher the holding pressure, the more easily birefringence appears.

This is probably because, as generally known, the higher the dwell pressure, the longer the time required for "relaxation". In other words, the higher the dwell pressure, the smaller the value of the “shear stress”, but the longer the “relaxation” of the generated “shear stress”, the longer the “residual stress”.
It is easy to remain as. In the above experimental results, the higher the packing pressure, the larger the birefringence.The reason for the change in the packing pressure under this condition is that the factor of "relaxation" is larger than that of "shear stress". It is considered to be.

The following summarizes the analysis results of the above-described mold temperature, cooling time, and holding pressure, and their considerations.

In relation to the above-mentioned "mold temperature", the tendency of "shear stress" and "relaxation" are the same, so that the tendency of "relaxation" is smaller than the tendency of "shear stress" obtained. Is the same, the “birefringence” tendency can be determined based on the result of the “shear stress”.

From the above results, consideration can be made on the relationship with the cooling time based on the “shear stress”. The considerations for cooling time may be unique.

From the above results, the tendency of "shear stress" and "relaxation" are opposite in relation to the dwelling pressure, so that it cannot be determined simply by only "shear stress". However, the fact that the tendency is reversed means that the sensitivity is low (the same tendency is obtained in the measurement of birefringence), and it is sufficient to consider it secondarily.

From the above, the study of “birefringence” is based on the “temperature”
The correlation with "holding pressure" is treated as a secondary one, and the "cooling time" may be considered with respect to "sledding" and "deformation".

Although the above study is conducted on birefringence, it is considered that the refractive index distribution caused by "change in density" is also deeply related to the behavior of the resin in the process of holding pressure and cooling, as described above. In other words, the effect of "residual stress" due to flow is "birefringence", and "density change" is "refractive index distribution".
Can be presumed to be deeply involved. Therefore, it can be easily inferred that if the residual strain that causes birefringence is reduced, the “density distribution” will be reduced accordingly.

According to the results of the above examination, the influence on the residual stress is largely due to the mold temperature. Looking at each analysis result, the bias of the shear stress is particularly large in the central portion where the thickness of the fθ lens is large and in the peripheral portion where the thickness is small. Therefore, if a temperature gradient is given to the mold,
It is presumed that the residual strain can be further reduced. Therefore, the following conclusions were obtained as a result of an experiment for examining the influence of the temperature distribution of the mold on the shear stress.

1: If a temperature gradient (temperature distribution) is provided in the mold, "birefringence" can be further reduced.

2: As for the temperature gradient, it is effective to increase the temperature in a thin portion and lower the temperature in a thick portion.

3: When providing the above-mentioned temperature gradient in an actual mold, it is necessary to take care not to lower the temperature of the whole mold.

An experiment in which the above conclusion was obtained will be described. In this experiment, as shown in FIG. 18, a mold 2 in which a cooling medium pipe 4 was provided in a direction orthogonal to the longitudinal direction of the fθ lens was used, and as shown in FIG.
Was arranged by vertically arranging three pipes 4 so as to sandwich them in the thickness direction, and changing the temperature of the cooling medium to check the change in shear stress.

The first experiment of this analysis was carried out by changing only the temperature of the pipe 4 at the center under the above-mentioned basic conditions as follows. In the following Table 1, solid and the like indicate pipes (see FIG. 19), and a to e indicate units of each experiment.

Table 1 Solidified Solidified Available Available Available a 147.5 ° C 250 ° C 147.5 ° C 147.5 ° C 250 ° 147.5 ° C b 147.5 ° C 200 ° 147.5 ° C 147.5 ° C 200 ° C 147.5 ° C c 147.5 ° C 147.5 ° C 147.5 ° C 147.5 ° C 147.5 ° C 147.5 ° C d 147.5 ℃ 100 ℃ 147.5 ℃ 147.5 ℃ 100 ℃ 147.5 ℃ e 147.5 ℃ 50 ℃ 147.5 ℃ 147.5 ℃ 50 ℃ 147.5 ℃ This result is shown in FIG. 20 to FIG. Shows a slight improvement in the distribution, but the distribution after cooling has not improved.
Rather worse. This is because the temperature of the whole mold has fluctuated because the temperature of the central part has been raised and lowered greatly.
It is considered that the improvement effect due to the temperature gradient is hidden by the effect due to the difference in the mold temperature and is invisible.

However, the "shear stress" after the completion of the dwelling still shows a slight improvement tendency. From this, it can be inferred that the distribution of "shear stress" from the dwelling stage to the initial stage of cooling is mainly dominant in the occurrence of "birefringence".

Therefore, in order to keep the temperature of the entire mold unchanged, a second experiment was conducted by changing the temperatures at the center and both ends as shown in Table 2 below.

Table 2 Solidification Solidification Possible Possible Possible a 117.5 ° C 220 ° C 117.5 ° C 117.5 ° C 220 ° C 117.5 ° C b 132.5 ° C 185 ° C 132.5 ° C 132.5 ° C 185 ° C 132.5 ° C c 147.5 ° C 147.5 ° C 147.5 ° C 147.5 ° C 147.5 ° C 147.5 ° C d 162.5 ℃ 115 ℃ 162.5 ℃ 162.5 ℃ 115 ℃ 162.5 ℃ e 177.5 ℃ 80 ℃ 177.5 ℃ 177.5 ℃ 80 ℃ 177.5 ℃ This result is as shown in FIG. Has a clear improvement tendency. As described in the above discussion, since "shear stress" is considered to be dominant in the initial stage of cooling after completion of pressure holding, an effect of improving "birefringence" in actual molded products can be expected. .

After cooling is completed, no clear improvement effect is observed, but the tendency of the shape of the generation of “shear stress” is changing, and the behavior of the resin is changed in some way. Inferred.

The experiment 2 can be considered as follows. By providing a temperature distribution in the mold while keeping the temperature of the entire mold unchanged, the distribution of “shear stress” especially after the completion of the pressure holding can be improved. It is considered that this is because the behavior of the resin during the dwelling and cooling processes changes due to the temperature gradient. The distribution of “shear stress” after the completion of cooling does not show a clear improvement tendency, but the shape of the distribution is changing, and the peak position of “shear stress” is approaching the center.

From the above, when the holding pressure is completed, a clear improvement tendency is observed in the “shear stress”, but there is no change in the generated shape, and after the completion of cooling, the “shear stress” is improved. Although there is no change, it can be compared in that the shape of occurrence is changing.

Considering that “birefringence” is obtained by considering the effect of “relaxation” on “shear stress”, the above result clearly indicates a tendency to improve “birefringence”. It can be determined that there is.

From these, it can be concluded as in the above 1, 2 and 3, and by using this to provide a temperature gradient in the mold, the birefringence can be further reduced.

In order to determine the molding conditions 1, 2, and 3, the temperature distribution of the mold is determined in order to determine the optimum temperature condition while grasping the overall mold temperature and the state of the temperature distribution. Need to be able to measure.

The reason why the three-dimensional element method is employed in the flow analysis of the present invention is to determine the molding conditions of a thick optical part such as an fθ lens. When the flow analysis for the fθ lens is performed, FIG.
(A) As shown in (b), the distribution of the "shear stress" as described above cannot be obtained. In two-dimensional analysis, cooling from the side cannot be used as a calculation element.
Since it is treated as being cooled only in the thickness direction, the analysis result deviates from the actual phenomenon.

The above analysis describes the case where the flow analysis is performed by the three-dimensional finite element method of TIMON excluding the calculation for relaxation, but is represented by a dashpot using a viscoelastic constitutive equation. It is also possible to perform flow analysis on the relaxation of residual stress by introducing such a viscous effect.In this case, it is necessary to directly calculate the residual strain without correcting by estimating the magnitude of the relaxation. it can.

In the above-described embodiment, the residual strain is considered, but this consideration can be made for the optical characteristics which are important according to the type of the optical element to be manufactured. Types of this optical element include, for example, an optical element that emphasizes a decrease in resolution due to birefringence, an optical element that emphasizes polarization characteristics, an optical element that emphasizes field curvature due to a change in refractive index, and a laser that emphasizes a transmitted wavefront. Optical elements. These optical characteristics are determined as a result of the accumulation of the shear stress, similarly to the residual strain, and the optical characteristics can be directly obtained by considering the process of generating the shear stress and the like as factors.

In the above embodiment, only the molding conditions are considered. In addition to correcting the molding conditions in accordance with the determined optical characteristics after molding, the design values of the optical element (the mold shape)
Can be modified. In this case, the optical characteristics can be obtained by simultaneously obtaining a plurality of types.

[0076]

The invention according to claim 1 of the present invention is characterized in that the shear stress and the residual strain at the time of resin molding are closely related to each other. Focusing on the fact that the distribution of shear stress is required even if the optical component to be formed is thick, the molding conditions are numerically evaluated and determined to reduce the residual strain that greatly affects the optical characteristics. In addition, optimization of molding conditions can be performed accurately.

The invention according to claims 2 to 6 of the present invention provides a method for determining the optical characteristics after molding for each type. These are obtained as the cumulative result of the shear stress, but by adding the generation process of the shear stress to the consideration conditions according to the optical characteristics to be obtained, the distribution characteristics of the refractive index due to the density distribution, the refractive index fluctuation , The birefringence characteristic, the polarization characteristic, and the transmitted wavefront characteristic can be obtained.

According to a seventh aspect of the present invention, a design value and a molding condition are obtained in a design stage based on the characteristics obtained by the methods described in the second to sixth aspects, in order to obtain necessary optical characteristics. Modify both or one. As a result, the work of determining the design values and design conditions for obtaining the necessary optical characteristics can be facilitated.

According to an eighth aspect of the present invention, in the method described in the first to seventh aspects, the residual strain is estimated from the qualitative relationship of relaxation with respect to the determined shear stress.
In this method, the flow analysis may be performed without considering the relaxation, and the analysis operation can be simplified.

According to a ninth aspect of the present invention, in the method according to any one of the first to seventh aspects, in addition to the calculation of the shear stress at the time of molding, the relaxation is also calculated by a three-dimensional finite element method. The strain can be determined and the residual strain can be determined directly.

According to a tenth aspect of the present invention, a mold is provided with a temperature gradient, and this temperature gradient is added to an operation element,
Since the flow analysis is performed by the three-dimensional finite element method, the residual strain can be further reduced.

According to the eleventh aspect of the present invention,
It is possible to actually provide an fθ lens having performance as designed.

[Brief description of the drawings]

FIG. 1 is a distribution diagram of shear stress of a resin-molded fθ lens analyzed by a three-dimensional finite element method of the present invention (a).
FIG. 6 is a longitudinal sectional view showing a state in which birefringence of an actual prototype is generated (b).

FIG. 2 is a cross-sectional view showing the analysis results shown in FIG. 1 as a cross-sectional view of a shear stress distribution diagram of an fθ lens, and a comparison diagram of a birefringence occurrence state of an actual prototype (b).

FIG. 3 is a perspective view of an fθ lens which is an example of an optical component to be analyzed according to the present invention.

FIG. 4 is a perspective view of a mold for producing the fθ lens of FIG. 3;

FIG. 5 is a three-period element division diagram of an fθ lens formed in the mold of FIG. 3;

FIG. 6 is a perspective view showing a three-period element division diagram of FIG. 5 for one fθ lens.

FIG. 7 is a perspective view showing an arrangement of a cooling medium pipe in the mold of FIG. 4;

FIG. 8 is a diagram showing changes in the maximum value and the minimum value of the shear stress with respect to the mold temperature after the pressure holding (a) and after the cooling (b).

FIG. 9 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the distribution of shear stress after filling when the mold temperature (cooling medium temperature) is changed at each temperature.

FIG. 10 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing distribution of shear stress after holding pressure when the mold temperature (cooling medium temperature) is changed at each temperature.

FIG. 11 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the distribution of shear stress after cooling when the mold temperature (cooling medium temperature) is changed at each temperature.

FIG. 12 is a diagram showing the maximum value and the minimum value of the analysis value of the shear stress after cooling with respect to the fluctuation of the cooling time by the three-time element method.

13 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the distribution of shear stress after cooling calculated for obtaining the data of FIG. 12 for each cooling time.

FIG. 14 is a diagram showing the maximum value and the minimum value of the shear stress with respect to the change in the holding pressure obtained by the three time element method, after the holding pressure (a) and after the cooling (b).

FIG. 15 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing distribution of shear stress after filling when the holding pressure is changed, for each holding pressure.

FIG. 16 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing distribution of shear stress after the holding pressure when the holding pressure is changed, for each holding pressure;

FIG. 17 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing distribution of shear stress after cooling when the holding pressure is changed, for each holding pressure.

FIG. 18 is a perspective view showing an example of the arrangement of piping for a cooling medium in a mold when a temperature gradient is provided in the mold.

19 is a front view showing the positional relationship between the pipe shown in FIG. 18 and the fθ lens.

FIG. 20 is a partial cross-sectional perspective view showing the distribution of shear stress at the center of the lens at the time of completion of pressure holding when only the mold temperature corresponding to the center of the fθ lens is changed, for each changed temperature.

21 shows fθ after filling under the analysis conditions of FIG. 20.
FIG. 3 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the shear stress distribution of the entire lens at each changed temperature.

22 shows fθ after holding pressure under the analysis conditions of FIG. 20.
FIG. 3 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the shear stress distribution of the entire lens at each changed temperature.

23 shows fθ after cooling under the analysis conditions of FIG. 20.
FIG. 3 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the shear stress distribution of the entire lens at each changed temperature.

FIG. 24 is a diagram showing the distribution of the shear stress in the center of the lens at the time of completion of the pressure holding when the mold temperatures corresponding to the center and the periphery of the fθ lens are changed, respectively. Sectional perspective view.

25 shows fθ after filling under the analysis conditions of FIG. 24.
FIG. 3 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the shear stress distribution of the entire lens at each changed temperature.

26 shows fθ after holding pressure under the analysis conditions of FIG. 24.
FIG. 3 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the shear stress distribution of the entire lens at each changed temperature.

27 shows fθ after cooling under the analysis conditions of FIG. 24.
FIG. 3 is a perspective view, a longitudinal sectional view, and a transverse sectional view showing the shear stress distribution of the entire lens at each changed temperature.

FIG. 28 is a distribution diagram of shear stress when a two-dimensional finite element analysis is performed on the fθ lens of FIG. 3;

[Explanation of symbols]

 1 fθ lens 2 Mold with uniform temperature distribution 3 Mold with temperature gradient 4 Coolant piping

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁷ Identification symbol FI Theme coat ゛ (Reference) G06F 17/50 680 G06F 17/50 680A // B29L 11:00 B29L 11:00 F term (reference) 4F202 AE10 AH73 AM23 AR14 AR15 CA11 CB01 CD03 CK06 CS10 4F206 AE10 AH73 AM23 AR014 AR064 AR14 AR15 JA07 JL09 JN25 JP13 JP17 JP30 5B046 AA05 DA08 GA01 JA07

Claims (11)

[Claims] 1. A method for manufacturing an optical element in which a molten material is injected and injected into a mold, and after taking out pressure after holding and cooling in the mold, the optical element in the mold is converted into a plurality of three-dimensional finite elements. Divide and use molding conditions including mold temperature as parameters,
A flow analysis characterized by determining the shear stress at the time of forming each element by flow analysis using a three-dimensional finite element method to determine the forming conditions under which residual strain determined by the cumulative result of shear stress is reduced. A method for manufacturing an optical element using the method. 2. A method of manufacturing an optical element in which a molten material is injected and injected into a mold, and after taking out pressure after holding and cooling in the mold, the optical element in the mold is converted into a plurality of three-dimensional finite elements. Divide and use molding conditions including mold temperature as parameters,
The flow analysis using the three-dimensional finite element method determines the shear stress at the time of forming each element, predicts the density distribution determined as the cumulative result of the shear stress, and obtains the refractive index distribution characteristics. Of manufacturing optical elements using flow analysis. 3. The method for manufacturing an optical element using flow analysis according to claim 2, wherein a characteristic of a curvature of field due to a change in refractive index is obtained based on the obtained refractive index distribution. 4. A method for manufacturing an optical element in which a molten material is injected and injected into a mold, and after taking out pressure after holding and cooling in the mold, the optical element in the mold is converted into a plurality of three-dimensional finite elements. Divide and use molding conditions including mold temperature as parameters,
The flow analysis using the three-dimensional finite element method determines the shear stress at the time of forming each element, thereby obtaining the birefringence characteristics determined as the cumulative result of the shear stress. Device manufacturing method. 5. A method for manufacturing an optical element in which a molten material is injected and injected into a mold, and after taking out pressure after holding and cooling in the mold, the optical element in the mold is converted into a plurality of three-dimensional finite elements. Divide and use molding conditions including mold temperature as parameters,
The flow analysis using the three-dimensional finite element method determines the shear stress at the time of forming each element, and determines the polarization characteristics determined as the cumulative result of the shear stress. Production method. 6. A method of manufacturing an optical element in which a molten material is injected and injected into a mold, and after taking out pressure after holding and cooling in the mold, the optical element in the mold is converted into a plurality of three-dimensional finite elements. Divide and use molding conditions including mold temperature as parameters,
Optical analysis using flow analysis characterized by finding the shear stress at the time of forming each element by flow analysis using the three-dimensional finite element method, and obtaining the characteristics of the transmitted wavefront determined as the cumulative result of shear stress. Device manufacturing method. 7. A design value and / or a molding condition are modified in a design stage based on characteristics obtained by at least one of the methods according to claim 2 to obtain necessary optical characteristics. A method for manufacturing an optical element using flow analysis. 8. The method according to claim 1, wherein a cumulative result of the shear stress is estimated from a qualitative relationship with respect to a molding condition for relaxation of the determined shear stress.
A method for manufacturing an optical element using the flow analysis described in the paragraph. 9. The method according to claim 1, wherein, in addition to the calculation of the shear stress at the time of forming, the relaxation is also calculated by a flow analysis using a three-dimensional finite element method. Of manufacturing optical element using flow analysis. 10. The method according to claim 1, wherein a temperature gradient is given to the mold, and the temperature gradient is added to a calculation element to perform flow analysis using a three-dimensional finite element method. A method for manufacturing an optical element using the flow analysis described in the paragraph. 11. The method for manufacturing an optical element using flow analysis according to claim 1, wherein the molten material is a synthetic resin, and the optical element is an fθ lens.