JP2006187941A - Optical element manufacturing apparatus, optical element manufacturing method and optical capacity analyzing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an optical element manufacturing apparatus capable of manufacturing an optical element of a high capacity by directly and quantitatively calculating the residual stress or optical characteristics in the production of the optical element such as a scanning lens (fθ optical system) or the like of an optical scanner used in an image forming apparatus such as a laser beam printer or a digital copier and preliminarily estimating a change in the double refraction in a molded product with the elapse of time, an optical element manufacturing method using it and an optical capacity analyzing method. <P>SOLUTION: The same condition as a heat cycle environment test or annealing treatment is set, and the analysis of non-steady heat conductivity and the analysis of viscoelastic stress are performed on the basis of the residual stress in the molded product calculated theretofore according to the condition (S17, S18). Then, when a predetermined time of conversion with the elapse of time is elapsed (S19), a double refraction distribution being the optical capacity is calculated on the basis of the final residual stress in the molded product after the analysis of a change with the elapse of time (S20, S21). <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to an optical element manufacturing apparatus, an optical element manufacturing method, and an optical performance analysis method, and in particular, manufactures an optical element such as a scanning lens (fθ optical system) of an optical scanning device used in a laser beam printer, a digital copying machine, or the like. The present invention relates to a technique for analyzing the optical performance of the manufactured optical element.

  2. Description of the Related Art Conventionally, in an optical scanning device used in an image forming apparatus such as a laser beam printer or a digital copying machine, a long aspheric toric is used as a scanning lens (fθ optical system) for the purpose of improving the performance and cost of the lens. A lens is used. Such a scanning lens has a long lens shape in the main scanning direction in order to form an image of a light beam deflected by an optical deflector such as a polygon mirror on the surface to be scanned.

  Usually, such a long scanning lens is formed by injection molding using plastic as a material. The plastic lens formed in this way has birefringence and refractive index distribution in the sub-scanning direction depending on the lens shape and molding conditions.

  In general, birefringence is roughly divided into two types depending on the generation factor. One is birefringence caused by molecular orientation distortion due to flow residual stress in the lens molding, and the other is birefringence caused by thermal stress in the cooling process after filling the mold. is there. Birefringence due to molecular orientation strain in the former is due to the polymer chain deformed by shear stress when filling the mold in injection molding, trying to return to the original state after filling the mold, but before returning to its original state, it cools below the glass transition point. It occurs because it is solidified. On the other hand, the birefringence due to the latter thermal stress is caused by local strain caused by non-uniform cooling due to, for example, non-uniform shrinkage due to a difference in temperature distribution, even if the state of the polymer chain deformed returns to the equilibrium state. Generated due to stress. When comparing the birefringence due to the flow residual stress and the birefringence due to the thermal stress, the birefringence due to the thermal stress is more dominant by two orders of magnitude than the birefringence due to the flow residual stress.

  Further, the refractive index distribution is generated in the process in which the lens immediately after molding is cooled from the periphery of the lens outer shape toward the thick portion at the center of the lens. At the outer periphery where cooling begins, the temperature gradient is large and the cooling proceeds rapidly, resulting in a refractive index distribution. On the other hand, the thick portion at the center of the lens is cooled with a relatively uniform temperature gradient, so that a refractive index distribution is unlikely to occur.

  Furthermore, it is preferable that the plastic lens also take into account changes accompanying relaxation of internal residual stress in the use environment after molding. Even if the required accuracy is satisfied immediately after molding, the residual stress inside the lens may change depending on the subsequent use environment, and the optical characteristics and shape accuracy may change. Usually, in order to know the change in the optical characteristics and shape accuracy, a heat cycle environmental test is performed on the molded product after molding under the assumed use environment, but this test takes a lot of time. . In addition, annealing treatment is performed in advance to relieve the residual stress inside the lens as necessary, but determination of the annealing conditions for relieving the residual stress requires trial and error. In order to know the change in the optical characteristics and the shape accuracy, it is preferable to carry out the heat cycle environmental test as described above. However, it takes a lot of time.

As a conventional example of analysis of optical performance such as birefringence and refractive index of a conventional optical performance analysis molded article, Patent Document 1 focuses on the shear stress obtained from three-dimensional flow analysis, and determines the residual as a cumulative result. It describes that distortion, refractive index characteristics, birefringence characteristics, polarization characteristics, transmitted wavefront characteristics, and field curvature characteristics can be estimated. However, there is no description of specific means for quantitatively predicting deformation and residual stress accompanying molding shrinkage after the flow process, and indirectly such as birefringence distribution from shear stress obtained from three-dimensional flow analysis. The optical performance is only estimated qualitatively, which is insufficient in that the residual stress and the optical performance cannot be predicted directly and quantitatively.

  Patent Document 2 discloses an optical system design including a heat and structure analysis unit that calculates the amount of thermal deformation of a member on which an optical component is placed, and an optical analysis unit that analyzes a trajectory of light passing between the optical components. In the system, based on the analysis result output from the heat and structure analysis unit and the initial value of the optical system data, the light and structure of the light and structure provided with the conversion unit for calculating the position of the optical component after the member is thermally deformed A complex analysis system is described. However, in this example as well, it is not suggested to perform the flow analysis and the structural analysis to calculate the residual stress of the molded product and directly predict the optical characteristics such as the refractive index and birefringence.

  On the other hand, Non-Patent Document 1 uses the Leonov model as a viscoelastic constitutive equation for resin flow to calculate the stress at the time of flow, and applies the stress optical law (Breester's law) to the birefringence of the molded product. The method of predicting is shown. However, the applied viscoelastic constitutive equation (Leonov model) is related to resin flow, and it has a dominant influence on the subsequent birefringence. The phenomenon is not taken into account, and it cannot be said that birefringence can be accurately predicted.

  Here, in order to predict the more accurate optical performance of plastic molded products by analysis, filling pressure holding cooling analysis using mold cavity surface temperature obtained from conventional steady-state temperature analysis, between shrinkage start point and room temperature The method of performing linear elastic analysis (thermal stress analysis) based on the shrinkage strain is not sufficient.

  For example, it is known that the optical performance of plastic molded products varies greatly depending on the time from the start of molding to the time of taking out the molded product, and the cooling gradient during that time, as well as the shape accuracy. In normal cases, the cooling time is short. It is known that the refractive index and birefringence are reduced when the length is longer than the case.

  As is well known, this is due to the fact that the resin is a material having viscoelastic properties typified by creep and stress relaxation, and it is kept longer at a higher temperature in the mold. This is because the internal stress in the molded article is relaxed.

  Further, when the resin is cooled and solidified in the mold, the molded product is restrained by the mold and free shrinkage is prevented, and there are many portions where internal stress is accumulated. This is because the stress level and the degree of time change are different in the constrained part in the mold compared to other unconstrained parts, and it is accompanied by the release of stress such as spring back when the molded product is taken out. This is because deformation occurs.

  In contrast to the above-described conventional example, the applicant of the present invention disclosed in Patent Document 3 in the entire process from flow holding pressure cooling analysis to structural analysis for a molded product that requires high precision shape accuracy such as a plastic optical element. Analytical models that take into account molds and molded products at the same time, especially the effects of temperature and pressure factors during molding, viscoelastic properties such as resin stress relaxation and creep, and molded products It was shown that the shape accuracy at the time when the molded product reached room temperature after mold release can be obtained with high accuracy by taking into account the effects of unsteady heat transfer and mold restraint.

JP 2001-277323 A JP-A-6-288864 JP 2001-293748 A “Prediction of residual stress in injection molded products”; Molding, Vol. 2, no. 4, 317 (1990)

  The present application further develops the technique described in Patent Document 3, and pays attention to the fact that Patent Document 3 calculates the residual stress accompanying thermal shrinkage deformation inside the molded product at the same time as the shape accuracy of the molded product. It shows that the birefringence distribution inside the molded product can be accurately calculated by applying the optical law (Breester's law). In addition, the birefringence inside the lens when the molded product reaches room temperature after the mold release, annealing treatment to further relax, and the birefringence inside the molded product in a heat cycle environment test simulating the actual use environment It shows that a change with time can be predicted in advance.

  That is, an object of the present invention is directed to an optical element such as a scanning lens (fθ optical system) of an optical scanning device used in an image forming apparatus such as a laser beam printer or a digital copying machine, and residual stress in the production of this optical element. Optical element manufacturing apparatus and optical element manufacturing capable of manufacturing high-performance optical elements by directly and quantitatively determining optical performance and optical performance, and predicting birefringence change with time in the molded product in advance It is to provide a method and an optical performance analysis method.

  Therefore, in the present invention, an optical element manufacturing apparatus for manufacturing an optical element by molding an optical element using a mold, the heat transfer analysis of the mold and the molded product of the optical element, and the molded product Flow analysis means for performing thermal fluid analysis to calculate the temperature of the mold and the pressure and temperature of the molded product, and using the calculated pressure and temperature as initial values, the mold of the mold and the molded product The residual stress distribution is calculated by conducting a structural analysis taking into account the restraint and the viscoelastic properties of the resin, and the calculated residual stress distribution is used as an initial value for the heat cycle condition or annealing condition according to the use environment of the molded product. A structural analysis means for calculating the residual stress distribution of the molded product by setting at least one of the two, a birefringence distribution is calculated from the residual stress distribution finally calculated by the structural analysis means, and the birefringence distribution is calculated As standards, it is characterized in that comprises a optical performance analysis means for determining the molding conditions of the optical element so as to satisfy a predetermined optical performance.

  An optical element manufacturing method for manufacturing an optical element by molding an optical element using a mold, wherein the heat transfer analysis of the mold and the molded product of the optical element and the thermal fluid of the molded product Analyzing the flow and calculating the temperature of the mold and the pressure and temperature of the molded product, and using the calculated pressure and temperature as initial values, the mold constraint between the mold and the molded product, and Residual stress distribution is calculated by conducting a structural analysis taking into account the viscoelastic properties of the resin, and the calculated residual stress distribution is used as an initial value, and at least one of heat cycle conditions and annealing conditions according to the use environment of the molded product The birefringence distribution is calculated from the structural analysis step of calculating the residual stress distribution of the molded product by setting the residual stress distribution finally calculated by the structural analysis means, and based on the birefringence distribution Characterized in that had, optical performance analysis step of determining the molding conditions of the optical element so as to satisfy a predetermined optical performance.

  Furthermore, it is an optical performance analysis method of an optical element when an optical element is manufactured by molding an optical element using a mold, the heat transfer analysis of the mold and the molded product of the optical element, and the molded product The flow analysis step of calculating the temperature of the mold and the pressure and temperature of the molded product, and the calculated pressure and temperature as initial values, the mold and the molded product Residual stress distribution is calculated by performing structural analysis in consideration of mold constraint and resin viscoelastic properties, and the calculated residual stress distribution is used as an initial value, and heat cycle conditions or annealing conditions according to the use environment of the molded product A structural analysis step of calculating the residual stress distribution of the molded product by setting at least one of the above, a birefringence distribution is calculated from the residual stress distribution finally calculated by the structural analysis means, and the birefringence distribution is calculated. As standards, it is characterized in that anda optical performance analysis step of evaluating a predetermined optical performance.

  According to the above configuration, with the residual stress distribution calculated for the molded article as an initial value, the residual stress of the molded article is set by setting at least one of a heat cycle condition or an annealing condition according to the use environment of the molded article. The distribution is calculated, the birefringence distribution is calculated from the finally calculated residual stress distribution, and the molding conditions of the optical element are determined so as to satisfy the predetermined optical performance based on this birefringence distribution. An optical element can be manufactured by predicting in advance the time-dependent change in birefringence inside a molded article in an annealing process for relaxing the heat treatment or a heat cycle environment test simulating an actual use environment.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 is a diagram showing a configuration of analysis processing and its procedure of an optical element manufacturing apparatus according to an embodiment of the present invention.

  As shown in FIG. 1, this apparatus includes a shape defining unit 1 that defines a shape and divides an element for finite element analysis to create an analysis model, a heat transfer analysis between a mold and a resin, Flow analysis part 2 for analyzing pressure-holding cooling process, structure for structural analysis considering viscoelastic properties such as resin creep and stress relaxation, and mold constraint between mold and molded product during resin cooling The analysis unit 3 and the optical performance analysis unit 4 that performs birefringence analysis using the residual stress result of the molded product obtained by the structure analysis unit 3 are configured. Specifically, each of these units is configured by a computer executing the following processing according to a program.

In the shape definition shape definition unit 1, shape definition and mesh division are performed (S1). In the process of step S1, the CAD system defines the shape of the mold to be analyzed and the molded product, and then performs element division such as a finite element method by an element division preprocessor to create an analysis model.

Flow Analysis Next, the flow analysis unit 2 analyzes the process in which resin is filled in the mold by the flow analysis and is kept pressure-cooled (S3). As the analysis program, commercially available general-purpose fluid analysis software is used, and this is a relational expression in which the viscosity, which is the property of a resin as a non-Newtonian fluid, depends on temperature and shear rate, that is, a viscosity equation and a holding pressure analysis. A PVT equation of state, which is a relational expression of required pressure, temperature and specific volume, is defined using a user subroutine attached to the software. In addition, in order to perform the above flow analysis, physical property data (viscosity, specific volume, thermal conductivity, specific heat, etc.) of resin and mold, molding conditions (injection speed, resin temperature, pressure holding value, pressure holding time, etc.) and analysis Conditions are defined and input data for flow analysis is created (S2). Based on this input data, a flow analysis (S3) including the process of filling the mold into the mold and the mold in the subsequent holding pressure cooling process is performed to obtain the analysis results such as pressure and temperature (S4). ).

Structural analysis Next, in the structural analysis unit 3, the viscoelastic properties (stress of the resin) are determined based on the shape input data including various boundary conditions such as initial data of temperature, pressure, load, and restraint obtained in the flow analysis unit 2. A structural analysis is performed in consideration of mold restraint (contact state) between the resin and the mold during cooling in the mold (S5), and a residual stress analysis result is obtained based on this structural analysis (S6). ).

Optical performance analysis Finally, the optical performance analysis unit 4 performs an optical performance analysis using the residual stress of the final molded product obtained from the structural analysis (S7), and calculates the birefringence distribution inside the molded product. (S8).

  The analysis result obtained by the above processing is evaluated, and if the optical performance of the molded product is within the required tolerance, the processing is terminated. On the other hand, if the optical performance of the molded product is not within the required tolerance, the process returns to step S1, and the molding is performed by changing the shape of the molded product, the mold design, and the molding condition parameters and repeatedly performing the analysis. Optimize product optical performance.

Detailed Structural Analysis FIG. 2 is a diagram showing details of the structural analysis processing in step S5 shown in FIG. 1, in which stress due to mold restraint (contact state between resin and mold during cooling in the mold) is shown. In consideration of relaxation (viscoelastic properties of the resin), the residual stress of the molded product is finally obtained.

  The flow analysis (S3) has already created element analysis data, input data for structural analysis such as boundary conditions (temperature, load, constraint), and flow analysis results of temperature and pressure. Use these data ( S10) and structural analysis is performed.

  First, in step S11, unsteady heat conduction analysis is sequentially performed at predetermined time intervals, and a state in which the subsequent mold and the entire molded product are cooled is obtained also in the structural analysis. By this process, every time the predetermined time elapses, a change in temperature and stress at an arbitrary position of the molded product is obtained. Thus, a heat shrinkage strain is obtained from the PVT equation of state, and this value is sequentially used for structural analysis. . FIG. 6 is a diagram showing the relationship between specific volume, temperature, and pressure calculated from the PVT equation of state.

(Viscoelastic stress analysis in structural analysis)
In the next step S12, viscoelastic stress analysis is performed. That is, the mold part is considered as a deformable body (elastic body), and the resin molded part is considered as a thermorheologically simple material (that is, a model to which the time-temperature conversion law can be applied), and shifted. A viscoelastic stress analysis is performed by introducing a linear viscoelastic model capable of approximating a relaxation elastic modulus by a function and a Prony series. As the stress relaxation function (Prony series) and the shift function, the following mathematical formulas (1) and (2) are used, respectively. Note that the time-temperature conversion rule is that when a certain temperature T ₀ is taken, behavior at a higher temperature is a short-time behavior at the reference temperature, and behavior at a lower temperature than the above criteria is the standard. Above is the law that corresponds to long-time behavior. That is, time and temperature can be equivalently converted.

  The structural analysis program uses a commercially available general-purpose non-linear structural analysis program, and the molded product part, which is a resin, is considered to be a thermorheologically simple material to which the time-temperature conversion rule can be applied. The linear viscoelastic model capable of defining the relaxation elastic modulus according to 1)) is used, and the shift function (Equation (2)) is analyzed using a user subroutine.

Here, G _{∞ is the} equilibrium elastic modulus, t ′ is the relaxation time, and λ _{n is the} relaxation time coefficient.
log _{10 AT} (T) = C ₀ + C ₁ · T + C ₂ · T ² +... + C _n · T ⁿ (2)
Here, log _{10 AT} (T): temperature shift factor, C _n : coefficient, and T: temperature.

(Viscoelastic properties in structural analysis)
When the structural analysis by viscoelasticity in this step S12 is performed, the temperature behavior of the resin that is the molded product is in the solidified state near the mold wall surface during flow, but the interior of the molded product is in a molten state. It gradually cools and solidifies in a mixed state. Therefore, the relaxation elastic modulus of the resin requires both a solid state and a molten state. By measuring the viscoelastic properties of the resin in the solidified state (forced torsion method) and the molten state (shearing method) using the dynamic viscoelasticity test method and superimposing the two, the relaxation elastic modulus of the entire solidification-melting region (Prony series), time-temperature conversion rule (shift function) is calculated. FIG. 4 is a diagram showing the relationship of the relaxation elastic modulus G (t) with respect to temperature by approximating the Prony series shown in Equation (1). FIG. 5 is a diagram of a shift function (time-temperature transfer factor) obtained by approximation using the polynomial shown in Equation (2).

  In step S13, the unsteady heat conduction analysis (S11) between the molded product and the mold described above, and the viscoelastic stress analysis (S12) taking into account the stress relaxation due to the mold restraint, the time interval as the molding condition is counted. The process is repeated until a predetermined release time (mold take-out time) is obtained.

  Next, in steps S14 and S15, after releasing the mold (the molded product is released from the restraint by the mold), only the molded product excluding the mold is cooled until it is naturally cooled to the room temperature. The target unsteady heat conduction analysis (S14) and viscoelastic stress analysis (S15) are performed (S16). Note that this room temperature is also determined in advance, and in the present embodiment, the time to reach this room temperature is determined in advance, and the time interval is counted as described above to determine that this room temperature has been reached.

  When it is determined that a sufficient predetermined time for the molded product to reach room temperature has passed (S16), the molded product is subjected to unsteady heat conduction analysis (S17) and viscoelastic stress analysis (S18) due to changes over time.

  As described above, in order to improve the accuracy of the molded product of the plastic lens, it is necessary to take into account the change accompanying relaxation of the internal residual stress in the use environment after molding. Even if the required accuracy is satisfied immediately after molding, the residual stress inside the lens changes depending on the subsequent use environment, and the optical characteristics and shape accuracy may change. Usually, in order to know the change in the optical characteristics and the shape accuracy, a heat cycle environment test under an assumed use environment is performed on the molded product after molding, but this test takes a lot of time. In addition, annealing treatment is performed in advance to relieve the residual stress inside the lens as necessary, but determination of the annealing conditions for relieving the residual stress requires trial and error. In order to know the change in the optical characteristics and the shape accuracy, it is necessary to conduct a heat cycle environmental test, which requires a lot of time.

  Therefore, in one embodiment of the present invention, in steps S17 and S18, the above processing is performed in order to obtain a change in the residual stress inside the molded product when the heat cycle environment test or annealing treatment of the molded product after molding is performed. 15 (a), (b) and FIGS. 16 (a), (b), as will be described later, based on the residual stress inside the molded product obtained in (5), the same conditions as in the heat cycle environment test and annealing treatment are used. Set and conduct unsteady heat conduction analysis and viscoelastic stress analysis. This analysis may use either a heat cycle environment test or an annealing treatment.

  Then, when a predetermined time for conversion with time, which is counted in the same manner as described above, has elapsed (S19), a birefringence distribution that is optical performance is calculated based on the residual stress inside the final molded product that has undergone analysis of changes over time. (S20, S21). This makes it possible to evaluate the final optical performance inside the lens in the subsequent optical performance analysis (S7).

Details of Optical Performance Analysis Next, the optical performance analysis for calculating the birefringence distribution, which is the optical performance of the molded product, from the residual stress of the molded product shown in step S7 of FIG. 1 will be described. FIG. 3 is a flowchart showing details of this process, and shows a procedure for calculating the birefringence distribution.

First, the main stress is calculated from the residual stress result (S30) finally obtained by performing the structural analysis in consideration of the stress relaxation, and the main stress difference is obtained (S31, S32). In the case of a three-dimensional analysis, it can be calculated as three values σ ₁ , σ ₂ , and σ ₃ . The birefringence of the resin is closely related to the residual stress distribution inside the molded product, and this relationship can be expressed by the following equation based on the stress optical law (Breester's law).
Δn = C · Δσ (3)
Here, Δn: birefringence, C: stress optical coefficient (photoelastic coefficient), Δσ: main stress difference The birefringence can be calculated from the above formula (3) (S33, S34). The lens optical path of the molded product is evaluated based on the calculated birefringence (S35, S36).

[Example]
Shape to be analyzed and molding conditions An example of a toric lens shape having an optical surface shape of radius R1 = 259.2 mm and radius R2 = 156.12 mm in a rectangular shape having an outer length of 102 mm and a width of 11.6 mm The birefringence inside the molded product is obtained by analysis.

  The flow of the whole analysis follows the analysis procedure shown in FIG. 1, FIG. 2, and FIG. FIG. 7 shows an analysis model obtained by dividing the shape of the lens molded product to be analyzed into meshes. FIG. 8 is a diagram showing an analysis model of the overall mold model including a lens-shaped mold. Since the lens width is symmetric in the longitudinal direction at the center of the lens width, the model is ½. This overall mold model is a model composed of a mold and a molded product on each of the fixed side and the movable side. The total number of elements is divided into about 7000 elements.

The molding conditions of this lens molded product are as shown below.
-Resin used Polyolefin resin-Resin temperature 270 ° C
・ Filling time 3.0sec
・ Mold temperature 120 ℃ (constant)
・ Pressure holding pressure Actual measured value in the mold 85MPa
・ Pressure holding time 30 sec
・ Cooling time 120sec

Flow analysis First, the process of filling the mold into the mold and holding and cooling is performed by flow analysis. From the filling to the holding and cooling process in order to consider the heat transfer between the molded product and the mold. On the other hand, unsteady heat conduction analysis is also performed. The analysis program uses commercially available general-purpose fluid analysis software, and the viscosity equation based on the Cross-WLF equation in which the viscosity, which is the property of the resin as a non-Newtonian fluid, depends on the temperature and shear rate, and pressure retention analysis A Tait PVT equation of state, which is a relational expression of pressure, temperature, and specific volume that is sometimes required, is defined using a user subroutine attached to the software.

  FIG. 9 is a diagram showing the temperature distribution of the entire molded product / mold at the time when the resin flow stops during the holding pressure cooling process (in this analysis example, 15 seconds after the start of holding pressure).

Structural analysis Next, the structural analysis uses the element division model used in the flow analysis as it is, and performs the structural analysis using the final results of temperature and pressure at the time when the flow of the resin in the flow analysis stops as initial data. Then, the unsteady temperature analysis between the molded product and the mold and the structural analysis considering the mold constraint are performed while being coupled with the thermal analysis until the mold release. In this analysis, the mold and the molded part are both analyzed as a deformed body, and the molded product is subjected to thermal stress analysis considering viscoelasticity.

  In addition, the interface between the mold and the molded product is considered as a contact analysis problem, and the influence of mold constraints such as contact and dissociation between the molded product surface and the mold surface due to cooling and solidification is considered. At the time of contact determination, the heat transfer rate between the molded product and the mold is set, and at the time of dissociation determination, the heat transfer coefficient is set so as to insulate between the surface of the molded product and the cavity space, and the analysis proceeds. The analysis program uses a commercially available general-purpose nonlinear structural analysis program, and considers the molded part part, which is a resin, as a thermorheologically simple material to which the time-temperature conversion law can be applied, and stress due to the aforementioned Prony series. A linear viscoelastic constitutive expression (formula (1)) and a shift function (formula (2)) capable of approximating the relaxation function are defined using analysis input data and a user subroutine for analysis.

  In this process, the temperature and pressure (hydrostatic pressure) at any place of the molded product at every time increment are obtained, the specific volume is calculated from the above-mentioned PVT equation of state, and the heat shrinkage strain is calculated. Perform analysis considering the effect of (hydrostatic pressure). In addition, the viscoelastic property value used in this analysis is the polyolefin resin shown in the above-mentioned embodiment.

  The above calculation is performed until a mold release time (in this analysis, a cooling time of 120 sec), which is a molded product take-out time, and when this time is reached, a mold release process (the molded product is released from restraint by the mold) is performed. After that, the heat conduction condition between the molded product and the mold is changed to the boundary condition of heat conduction from the molded product to the atmosphere, and then the free shrinkage behavior due to natural cooling in the atmosphere continues to the room temperature. Unsteady heat conduction analysis and viscoelastic stress analysis are repeatedly calculated until final deformation, residual stress, residual strain, and other calculation results are output. FIG. 10 shows the temperature distribution of the entire lens molded product / mold immediately after mold release.

  Next, unsteady heat conduction analysis and viscoelastic stress analysis are performed in consideration of changes over time. Here, the birefringence value calculated by the birefringence calculation performed based on the structural analysis result that does not consider such a change with time is on the order of 1.0E-4, and the birefringence value is 1 It is desirable to reduce to the order of 0.0E-5.

  For this reason, an analysis assuming an annealing treatment is performed on the obtained molded product to examine whether birefringence can be reduced. Since the resin in this example is a polyolefin resin and has a Tg point of 138 ° C., as shown in FIG. 15 (a), an analysis was performed with the annealing temperature set at 150 ° C. and the annealing time set at 5 hours. It was.

  A specific analysis method is the above-described annealing treatment conditions based on the residual stress inside the molded product after a sufficient time for the molded product to reach room temperature in steps S17 and S18 shown in FIG. Unsteady heat conduction analysis and viscoelastic stress analysis (S17 and S18 in FIG. 2) are performed. And finally, birefringence distribution which is optical performance is calculated based on the residual stress inside the molded product (S20, S21 in FIG. 2). This makes it possible to evaluate the birefringence inside the lens.

  FIG. 15B is a diagram showing the result of birefringence of the cross section (between R1-2 in FIG. 14) of the lens molded product after the annealing treatment. It can be seen that birefringence can be reduced to the order of 1.0E-5 under the annealing conditions.

  Next, it is verified by analysis how much the birefringence of the lens molded product reduced by the annealing treatment changes by the heat cycle environmental test.

  Since the product in which the target lens is incorporated is assumed to be used in the range of −20 ° C. to 60 ° C., the heat cycle environment test conditions start from room temperature as shown in FIG. The birefringence inside the lens is evaluated when the cycle of holding at 20 ° C. for 5 hours, then holding at 60 ° C. for 5 hours and again holding at −20 ° C. for 5 hours is repeated five times.

  The specific analysis method is the same as the analysis method during annealing.

  FIG. 16B is a diagram showing the birefringence result of the cross section (between R1-2) of the lens molded product after the heat cycle environment test. Since the birefringence is first reduced to the order of 1.0E-5 by the annealing treatment (FIG. 15B), it is understood that the change in birefringence is small in the subsequent heat cycle environment test.

Optical Performance Analysis Next, a method for calculating the birefringence distribution which is the optical performance of the molded product from the residual stress of the molded product will be described. The procedure for calculating the birefringence distribution follows FIG.

First, the main stress is calculated from the residual stress result (S30) finally obtained by performing the structural analysis in consideration of the stress relaxation, and the main stress difference is obtained (S31, S32). In the case of a three-dimensional analysis, the maximum principal stress σ ₁ , the intermediate principal stress σ ₂ , and the minimum principal stress σ ₃ can be calculated. FIG. 11 is a diagram showing the distribution of the maximum principal stress in the cross section of the central part of the lens molded product. Similarly, FIG. 12 is a diagram showing the distribution of the minimum principal stress. The principal stress difference can be obtained from these principal stress values. FIG. 13 is a diagram showing the directions of the maximum principal stress, the intermediate principal stress, and the minimum principal stress in the cross section of the central part of the lens molded product. The maximum principal stress direction generally represents the longitudinal direction of the lens, the intermediate principal stress direction generally represents the width direction of the lens, and the minimum principal stress direction generally represents the optical axis direction of the lens.

As described above, the birefringence is related to the main stress difference obtained from the residual stress distribution inside the molded product, and this relationship can be expressed by the following equation based on the stress optical law (Breester's law).
Δn = C · Δσ (3)
Δn: birefringence, C: stress optical coefficient (photoelastic coefficient), Δσ: main stress difference Birefringence can be calculated from the above formula (3) (S33, S34). The lens optical path of the molded product is evaluated based on the calculated birefringence (S35, S36).

FIG. 14B shows a birefringence distribution Δn based on three main stress differences of Δσ ₁₂ , Δσ ₂₃ , and Δσ ₃₁ in the optical axis direction R1-2 in the cross section of the central part of the lens molded product (FIG. 14A). ₁₂ is a diagram showing Δn ₂₃ , Δn ₃₁ . In this embodiment, the optical axis of the lens moldings central cross section because it is R1-2 direction shown in FIG. 14 (a), can be evaluated in the optical performance by noting the value of [Delta] n _23.

  As described above, the birefringence distribution inside the lens molded product can be quantitatively predicted by this analysis method. Further, it is possible to obtain and evaluate the change in the internal residual stress of the molded product in advance by analysis when the molded product is subjected to a heat cycle environmental test or annealing treatment.

It is a figure which shows the structure of the optical element manufacturing apparatus which concerns on one Embodiment of this invention, and the analysis processing procedure by it. It is a flowchart which shows the detail of the structure analysis process shown in FIG. It is a flowchart which shows the detail of the optical performance analysis process shown in FIG. It is a figure which shows an example of the relationship of the relaxation elastic modulus G (t) with respect to temperature. It is a figure which shows the result of having approximated the time-temperature transfer factor with the polynomial by the shift function. It is a figure which shows the relationship of the specific volume calculated from a PVT equation of state, temperature, and a pressure. It is a figure which shows the shape of the specific molded article in one Example of this invention. It is a figure which shows the analysis model which divided | segmented the shape of the whole metal mold | die of the said molded article into about 5000 elements. It is a figure which shows the temperature distribution of the metal mold | die and the molded article at the time of the flow of resin stopping. It is a figure which shows the temperature distribution of the metal mold | die and the whole molded article immediately after mold release. It is the figure which showed distribution of the largest principal stress of a lens molded product center part cross section. It is the figure which showed distribution of the minimum principal stress of a lens molded product center part cross section. It is the figure which showed the direction of the maximum principal stress of a lens molded product center part cross section, intermediate | middle principal stress, and minimum principal stress. (A) is the figure which showed the lens molded product center part cross section, (b) is the figure which showed birefringence (DELTA) n between R1-2 of the lens molded product center part cross section. (A) is the figure which showed annealing treatment conditions, (b) is the figure which showed birefringence (DELTA) n of the lens molded article center part cross section (between R1-2) after annealing treatment. (A) is the figure which showed the heat cycle environment test conditions, (b) is a lens molded product cross section (R1-) after implementing a heat cycle environmental test with respect to the lens molded product after annealing. It is the figure which showed birefringence (DELTA) n of (between 2).

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Shape definition part 2 Flow analysis part 3 Structure analysis part 4 Optical performance analysis part

Claims (3)

An optical element manufacturing apparatus for manufacturing an optical element by molding an optical element using a mold,
Flow analysis means for performing heat transfer analysis of the mold and the molded article of the optical element and thermal fluid analysis of the molded article to calculate the temperature of the mold and the pressure and temperature of the molded article;
Using the calculated pressure and temperature as initial values, the residual stress distribution is calculated by performing a structural analysis in consideration of the mold constraint between the mold and the molded product and the viscoelastic properties of the resin, and the calculated residual stress. Structural analysis means for calculating a residual stress distribution of the molded product by setting at least one of a heat cycle condition or an annealing condition according to a use environment of the molded product as an initial value of the distribution,
An optical performance analyzing means for calculating a birefringence distribution from the residual stress distribution finally calculated by the structure analyzing means, and for determining molding conditions of the optical element so as to satisfy a predetermined optical performance based on the birefringence distribution; ,
An optical element manufacturing apparatus comprising: An optical element manufacturing method for manufacturing an optical element by molding an optical element using a mold,
A flow analysis step of performing heat transfer analysis of the molded product of the mold and the optical element and thermal fluid analysis of the molded product, and calculating a temperature of the mold and a pressure and a temperature of the molded product;
Using the calculated pressure and temperature as initial values, the residual stress distribution is calculated by performing a structural analysis in consideration of the mold constraint between the mold and the molded product and the viscoelastic properties of the resin, and the calculated residual stress. A structural analysis step of calculating a residual stress distribution of the molded product by setting at least one of a heat cycle condition or an annealing condition according to a use environment of the molded product as an initial value of the distribution;
An optical performance analysis step of calculating a birefringence distribution from the residual stress distribution finally calculated by the structural analysis means, and determining molding conditions of the optical element so as to satisfy a predetermined optical performance based on the birefringence distribution; ,
An optical element manufacturing method characterized by comprising: An optical element performance analysis method for producing an optical element by molding an optical element using a mold,
A flow analysis step of performing heat transfer analysis of the molded product of the mold and the optical element and thermal fluid analysis of the molded product, and calculating a temperature of the mold and a pressure and a temperature of the molded product;
Using the calculated pressure and temperature as initial values, the residual stress distribution is calculated by performing a structural analysis in consideration of the mold constraint between the mold and the molded product and the viscoelastic properties of the resin, and the calculated residual stress. A structural analysis step of calculating a residual stress distribution of the molded product by setting at least one of a heat cycle condition or an annealing condition according to a use environment of the molded product as an initial value of the distribution;
An optical performance analysis step of calculating a birefringence distribution from the residual stress distribution finally calculated by the structural analysis means, and evaluating a predetermined optical performance based on the birefringence distribution;
An optical performance analysis method characterized by comprising:

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