CN114611221B - Mold core and mold limit deviation design method in precision glass molding process - Google Patents
Mold core and mold limit deviation design method in precision glass molding process Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 44
- 238000000465 moulding Methods 0.000 title claims abstract description 19
- 239000011521 glass Substances 0.000 title claims abstract description 18
- 239000000463 material Substances 0.000 claims abstract description 31
- 230000005484 gravity Effects 0.000 claims abstract description 13
- 230000005855 radiation Effects 0.000 claims abstract description 11
- 238000013178 mathematical model Methods 0.000 claims abstract description 8
- 230000000704 physical effect Effects 0.000 claims abstract description 4
- UONOETXJSWQNOL-UHFFFAOYSA-N tungsten carbide Chemical compound [W+]#[C-] UONOETXJSWQNOL-UHFFFAOYSA-N 0.000 claims description 7
- 230000001133 acceleration Effects 0.000 claims description 2
- 238000004519 manufacturing process Methods 0.000 abstract description 9
- 230000003287 optical effect Effects 0.000 abstract description 8
- 230000000694 effects Effects 0.000 abstract description 2
- 230000009286 beneficial effect Effects 0.000 abstract 1
- 239000011162 core material Substances 0.000 description 78
- 238000004364 calculation method Methods 0.000 description 3
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 description 1
- XAGFODPZIPBFFR-UHFFFAOYSA-N aluminium Chemical compound [Al] XAGFODPZIPBFFR-UHFFFAOYSA-N 0.000 description 1
- 229910052782 aluminium Inorganic materials 0.000 description 1
- 239000005387 chalcogenide glass Substances 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000006073 displacement reaction Methods 0.000 description 1
- 238000001125 extrusion Methods 0.000 description 1
- 238000010438 heat treatment Methods 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 230000010076 replication Effects 0.000 description 1
- 230000001052 transient effect Effects 0.000 description 1
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- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P40/00—Technologies relating to the processing of minerals
- Y02P40/50—Glass production, e.g. reusing waste heat during processing or shaping
- Y02P40/57—Improving the yield, e-g- reduction of reject rates
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Abstract
A method for designing limit deviation of a mold core and a mold in a precision glass molding process belongs to the technical field of optical manufacturing. The process causes inconsistent selection of mold core and mold materials due to cost and forming effect, and temperature parameters change within hundreds of ℃, so that no design standard for limiting deviation of the mold core and the mold is suitable for the process at present. The invention comprises the following steps: 1. according to the physical properties of the material, the instantaneous thermal expansion coefficient of the material is obtained; 2. obtaining a steady-state size mathematical model of the mould according to the influence of temperature and gravity on the sizes of the mould and the mould core; 3. and obtaining a limit deviation design method suitable for the process according to the limit and the matching standard of the mold core and the mold at normal temperature and a steady-state size mathematical model and combining the property of heat radiation. The invention is beneficial to improving the assembly precision of the mold core and the mold, controlling the dimensional precision of the molded lens, guiding the selection of the mold core and the mold material, and reducing the difficulty of mold core compensation.
Description
Technical Field
The invention relates to a method for designing limit deviation of a mold core and a mold in a precision glass molding process, and belongs to the technical field of optical manufacturing.
Background
An optical system is miniaturized by reducing the use of optical elements by realizing the performance of a multi-piece spherical lens group using one piece of optical lens of a complex shape. The use of precision glass molding techniques, which are replication techniques, to manufacture large volume high precision complex shape optical elements will help reduce manufacturing costs. This technique is an efficient method of manufacturing to replicate optical features from a mold core onto a glass preform at high temperatures. The most expensive and time-consuming process is the manufacture of optical molds.
At present, the design of the limit deviation of the mold core and the mold in the precision glass molding process is closely related to the limit manufacturing capacity of tungsten carbide. To control costs, the mold material is typically chosen to be inferior to the mold core material, i.e., the coefficients of thermal expansion of the mold core and the mold are typically different. Also, because the precision glass molding process is typically performed in a temperature range of several hundred degrees celsius, high machining precision manufacturing of the mold does not mean that the mold has high assembly precision, and the limit deviation design method in the current industrial manufacturing will not be fully applicable.
Disclosure of Invention
The invention aims to improve the assembly precision of a mold core and a mold in the whole forming process, and provides a mold core and mold limit deviation design method in a precision glass molding process.
The method of the invention comprises the following steps:
1. according to the physical properties of the material, the instantaneous thermal expansion coefficient of the material is obtained;
2. obtaining a steady-state size mathematical model of the mould according to the influence of temperature and gravity on the sizes of the mould and the mould core;
3. And obtaining a limit deviation design method suitable for the process according to the limit and the matching standard of the mold core and the mold at normal temperature and a steady-state size mathematical model and combining the property of heat radiation.
The limit deviation design method of the mold core and the mold in the precision glass molding process is used for discussing the limit deviation design of the mold core and the mold under the three conditions that the thermal expansion coefficient of the mold core is equal to, smaller than and larger than that of the mold.
When the core thermal expansion coefficient is equal to the die thermal expansion coefficient, it is assumed that both the core and the die material are J05 grade tungsten carbide and the forming temperature is 700 ℃. When the inner diameter of the die is 60.002mm at the lower limit of the dimension and the diameter of the die core is 59.998mm at the upper limit of the dimension, C FT is 0.004mm, namely the clearance requirement is met. When the inner diameter of the die is 60.004mm at the upper limit of the dimension, and the diameter of the die core is 59.996 mm at the lower limit of the dimension, C FT is 0.008mm, namely the clearance requirement is met at the moment. The mould core in this case is therefore of the sizeThe die size is/>
When the core thermal expansion coefficient is smaller than the die thermal expansion coefficient, it is assumed that the core and the die material are J05 and M45 grade tungsten carbide, respectively, and the forming temperature is 700 ℃. When the inner diameter of the die is 60.002mm at the lower limit of the dimension and the diameter of the die core is 59.998mm at the upper limit of the dimension, C FT is 0.053mm, namely the clearance requirement is met. Since C FT is larger than 0.049mm at this time, the die thermal expansion coefficient is larger than the die core thermal expansion coefficient, and the lower limit of the die core diameter size is set to 59.996mm. The die core diameter was then calculated as its lower dimension limit such that C FT was equal to the die inner diameter at 0.076mm and was taken as the upper dimension limit of the die inner diameter. The calculation was 60.023mm, at which point C 20 was equal to 0.027mm, i.e. the clearance requirement was met at this time. The ES value is then reduced appropriately. If the upper limit of the size of the inner diameter of the die is 60.004mm, C FT is 0.057mm, namely the clearance requirement is met at the moment. In this case, therefore, the mould core is dimensioned asThe die size is/>
When the core thermal expansion coefficient is greater than the die thermal expansion coefficient, the core and die materials are assumed to be microcrystalline aluminum RSA905 and M45 grade tungsten carbide, respectively, and the forming temperature is 220 ℃. The combination is applied to mold a chalcogenide glass lens having a diffractive surface. When the inner diameter of the die is its lower size limit 60.002mm, the core diameter at which C FT is equal to 0 is calculated and taken as the upper size limit of the core diameter. The calculation was 59.844mm, at which point C 20 was equal to 0.158mm, i.e., the clearance requirement was not met at this time. When the inner diameter of the die was 60.004mm as the upper limit of the dimension, the diameter of the die core was calculated so that C 20 was 0.092mm, and the lower limit of the dimension was 59.912mm. In this case, C FT is equal to-0.066 mm, which means that when the core and the mold are not assembled together and the temperature is 220 ℃, the core diameter is 0.066mm larger than the mold inner diameter. Such a fit will result in extrusion between the core and the die during the forming process, which will increase the number of iterations of the core processing. The solution to this is to use a material with a smaller coefficient of thermal expansion as the core material or a material with a larger coefficient of thermal expansion as the mold material. For example, S136 is substituted as the mold material. When the inner diameter of the die is its lower size limit 60.002mm, the core diameter at which C FT is equal to 0 is calculated and taken as the upper size limit of the core diameter. The calculation was 59.918mm, at which point C 20 was equal to 0.084mm, i.e. the clearance requirement was met. When the inner diameter of the die was 60.004mm as its upper limit, the core diameter at which C 20 was equal to 0.092mm was calculated and taken as the lower limit, and 59.912mm was calculated, while C FT was equal to 0.008mm, at which time the gap requirement was satisfied. In this case, therefore, the mould core is dimensioned asThe die size is/>
Drawings
FIG. 1 is a sectional view showing the assembly of the upper and lower mold cores and the upper and lower molds.
Fig. 2 is a simplified schematic illustration of the initial dimensions of the mold core and mold.
FIG. 3 is a flow chart of the design of the extreme deviations of the core diameter and the inside and outside diameters of the mold.
Detailed Description
The process of the present invention is further described below.
In the first step, the instantaneous thermal expansion coefficient of the material is obtained according to the physical properties of the material. As the workpiece temperature changes from T 1 to T 2, its volume also changes from V 1 to V 2 accordingly. To describe this variation, the average bulk thermal expansion coefficient of the material is defined
The corresponding average linear thermal expansion coefficient is
For isotropic materials, the volumetric thermal expansion coefficient is equal to 3 times the linear thermal expansion coefficient, i.e.:
β＝3α (3)
Wherein: alpha is the true linear thermal expansion coefficient and beta is the true volumetric thermal expansion coefficient. When the temperature is changed from T 1 to T 2, the length of the workpiece is changed from L 1 to L 2. The relationship between the average volume thermal expansion coefficient β m and the average linear thermal expansion coefficient α m is:
if equation (3) is used to derive the dimensional model of the mold and the core at high temperature, the model becomes very complex. Therefore, equation (4) is used as a tie for the subsequent derivation of the size model. Under certain conditions, the transient coefficient of linear thermal expansion can better reflect the real coefficient. The instantaneous linear thermal expansion coefficient alpha I of the material at a temperature of T m
Wherein L 293 is the length of the workpiece at a temperature of 293 Kelvin (about 20deg.C). In this case, α I is considered to be the true linear coefficient of thermal expansion at temperature T m. Expansion over a limited temperature range can be approximated by a polynomial expression
Where L is the length of the workpiece at temperature T and a 0、a1、a2、a3 is the coefficient of the polynomial.
And secondly, obtaining a steady-state size mathematical model according to the influence of temperature and gravity on the sizes of the die and the die core. The mold cores and dies in the single station die press are shown in fig. 1, which is simplified for ease of discussion to the form of an assembly of a cylindrical mold core and a hollow cylindrical die.
Assume that the initial height and radius of the cylindrical mold core are H 0 and R 0, respectively, as shown in FIG. 2 (a). When the working temperature is changed from T 1 to T 2, the steady-state height and the steady-state radius of the mold core are H and R respectively. The change in temperature is defined as Δt. As the temperature of the material changes, so will the young's modulus. The temperature dependence of Young's modulus E (T) can be well fitted with equation (8).
E(T)＝[1-bTexp(-T0/T)]E(0) (8)
E (0) is Young's modulus at 0 Kelvin. T 0 is a parameter that depends on the material properties. T is absolute temperature. b is a parameter that depends on the nature of the material. When T > T 0, equation (8) can be simplified to equation (9).
E＝E0(1+aEΔt) (9)
Wherein E 0 is the initial Young's modulus, a E is the Young's modulus temperature coefficient, and E is the Young's modulus of the material after temperature change delta t. The deformation of the mold core in the height direction is the sum of the deformation Δh 1 caused by the thermal expansion of the material and the deformation Δh 2 caused by the change in young's modulus. The above relationship is represented by formula (10).
ΔH＝ΔH1+ΔH2 (10)
ΔH1＝H0αmΔt (11)
As shown in fig. 2 (a), there is a micro-segment dx from the core support surface x. The vertical load on a micro-segment is the weight of the material above the micro-segment. I.e.
Where g is the gravitational acceleration, F x is the vertical load, ρ is the density of the mold core. The line stress divided by the line strain equals Young's modulus. The amount of change in height divided by the initial height is the line strain. The force of the vertical cross section divided by its cross sectional area is the line stress. Thus, the deformation Δdx/dx caused by F x is
Under the influence of gravity, the variation of mold core height is:
Because a EΔt＜＜1,1-(aEΔt)2 =1. Equation (14) can be converted to equation (15).
When the temperature is changed, the deformation in the height direction of the mold core is a temperature-dependent part in the formula (15), that is, the formula (16). Therefore, when the temperature changes, the steady-state height H of the core is formula (17).
When the action of gravity is not considered, the steady-state height H of the mold core is
H＝H0+H0αmΔt (18)
According to the formulas (4) and (17), the steady-state radius of the mold core after temperature change in consideration of the action of gravity is obtained, namely the formula (19).
The steady state radius of the mold core after the temperature change, equation (20), is calculated according to equations (4) and (18) without taking gravity into account.
Since the linear expansion coefficient is on the order of 10 -6, the powers 2 and 3 are almost equal to 0. Equation (20) can be converted to equation (22) according to construction equation (21).
Assuming that the initial inner and outer diameters of the mold shown in fig. 2 (b) are D 0 and D 0, respectively, the steady-state inner and outer diameters after temperature change are D and D, respectively. Since the die outer diameter is free to expand, D is expressed by equation (23).
D＝D0+D0αmΔt (23)
The definition of F x、Δdx、Δ、ΔH1 and Δh 2 is similar to that when calculating the core. Thus (2)
ΔH1＝H0αmΔt (27)
Therefore, when the temperature is changed, the steady-state height of the hollow cylindrical mold is shown in formula (29) when the influence of gravity is considered, and is shown in formula (30) when the influence of gravity is not considered.
H＝H0+H0αmΔt (30)
The steady-state inner diameter of the hollow cylindrical mold after the temperature change is obtained according to the formulas (4) and (29) is shown in the formula (31) when the influence of gravity is considered, and the steady-state inner diameter of the hollow cylindrical mold after the temperature change is obtained according to the formulas (4) and (30) is shown in the formula (32) when the influence of gravity is not considered. The dimensional model of the cylindrical mold core and the hollow cylindrical mold after the temperature change is shown in table 1.
TABLE 1 steady-state dimensional model of cylindrical mold core and hollow cylindrical mold after temperature change
Thirdly, obtaining a limit deviation design method suitable for the process according to the limit and the matching standard of the mold core and the mold at normal temperature and a steady-state size mathematical model and combining the property of heat radiation.
In order to adapt the mold core and the mold to the extremely severe environment in which the precision glass molding process is located, the best preferred matches for the mold core mold are H7/H6, H8/H7, H8/H9 and H8/H8. Table 2 lists the upper/lower size limits and the maximum/small gap amounts for the preferred fit described above when the nominal size is 60 mm. The nominal dimensions of the core diameter and the die inner diameter were assumed to be 60mm, and the nominal dimensions of the die outer diameter were assumed to be 110mm. In designing the extreme deviations of the core diameter and the mold inner diameter, the maximum gap should be smaller than in table 2, both at room temperature and at the forming temperature. When a hard brittle tungsten carbide material is used for the mold core or the mold, the minimum gap between the mold core and the mold should be greater than the minimum gap in table 2, i.e., greater than 0.
TABLE 2 upper/lower limit values and maximum/minimum gap for the preferred dimensions when the nominal dimension is 60mm
The mold core, the mold and the glass preform are heated by the Toshiba precision glass molding press GMP-415V in an infrared heating mode. The heat is applied to the mold by heat radiation during precision glass molding and then transferred from the mold to the mold core by heat radiation (when the mold is not in contact with the mold core) or heat conduction (when the mold is in contact with the mold core).
The wien's law of displacement, which expresses equation (33), shows that the peak radiation wavelength is shorter at higher blackbody temperatures.
λmaxT＝2898μm·K (33)
Lambda max is the peak radiation wavelength. Tungsten carbide, although not a blackbody, has a characteristic wavelength of about 10 to 3 μm when used as a heat source at temperatures of 20 to 700 ℃ (about 293 to 973 kelvin). When the side gap between the mold core and the mold is equal to the characteristic wavelength of heat radiation, the near-field radiation heat exchange becomes remarkable. Therefore, the maximum clearance between the mold core and the mold in the molding process is controlled within 3-10 μm as much as possible. FIG. 3 is a basic flow chart of the core diameter and die inside diameter limit deviation design for three cases. ES and EI are the upper and lower limit deviations of the mold inner diameter, respectively, and ES and EI are the upper and lower limit deviations of the mold core diameter, respectively. C 20 is the clearance between the mould and the mould core at 20 ℃, and C FT is the clearance between the mould and the mould core at the forming temperature. The meaning of "meeting the clearance requirement" in the flow chart is that the designed fit clearance should be less than the maximum clearance of the selected fit, while should be greater than 0. The sentence "properly lowering the ES value and increasing the ei value to obtain the final ES/ei" verifies whether the clearance between the mold and the core can be such that the molded lens satisfies the out-of-plane requirements on the drawing sheet and the clearance is reduced as much as possible to promote heat transfer. Because a E in equations (17) and (29) is difficult to obtain, the flow chart does not relate to the effect of gravity on size.
Claims (4)
1. A design method of limit deviation of mold core and mold in precision glass molding process is characterized in that (1) according to physical property of material, calculating instantaneous thermal expansion coefficient; (2) Obtaining a steady-state size mathematical model of the mould according to the influence of temperature and gravity on the sizes of the mould and the mould core; (3) And obtaining a limit deviation design method suitable for the process according to the size limit and the matching standard of the mold core and the mold at normal temperature and a steady-state size mathematical model and combining the property of heat radiation.
2. The method for designing limit deviation of mold core and mold in precision glass molding process according to claim 1, wherein when the temperature is changed from T 1 to T 2, the length of the work piece is changed from L 1 to L 2, and the instantaneous thermal expansion coefficient of the work piece material can be obtained by formulas (1) to (3);
Wherein: l 1 is the length of the workpiece before undergoing a temperature change, L 2 is the length of the workpiece after undergoing a temperature change, L 293 is the length of the workpiece at 293 kelvin, T 1 is the temperature of the workpiece before undergoing a temperature change, T 2 is the temperature of the workpiece after undergoing a temperature change, α I is the instantaneous coefficient of thermal expansion of the material at temperature T m, L is the length of the workpiece at temperature T, and a 0、a1、a2、a3 is the coefficient of the polynomial.
3. The method for designing limit deviation of mold core and mold in precision glass molding process according to claim 1, wherein steady-state dimensional models of the cylindrical mold core and hollow cylindrical mold after temperature change are obtained from table 1 and formulas (4) to (13);
H＝H0+H0αmΔt (6)
D＝D0+D0αmΔt (9)
H＝H0+H0αmΔt (11)
wherein: when the temperature is changed from T 1 to T 2, the initial height and the radius of the cylindrical mold core are H 0 and R 0 respectively, and the steady-state height and the steady-state radius of the cylindrical mold core are H and R respectively after the temperature is changed; the initial inner diameter and the outer diameter of the die are D 0 and D 0 respectively, and the steady-state inner diameter and the steady-state outer diameter of the die are D and D respectively after the temperature is changed; l 1 is the length of the workpiece before undergoing a temperature change, L 2 is the length of the workpiece after undergoing a temperature change, E 0 is the Young's modulus of the workpiece material at 0 Kelvin, Δt is the amount of temperature change, a E is the Young's modulus temperature coefficient, g is the gravitational acceleration, ρ is the density, and α m is the average linear thermal expansion coefficient.
TABLE 1 steady-state dimensional model of cylindrical mold core and hollow cylindrical mold after temperature change
4. The method for designing limit deviations of a mold core and a mold in a precision glass molding process according to claim 1, wherein the upper/lower limit values of the preferred dimensions and the maximum/minimum gap amounts are shown in table 2 when the nominal size is 60 mm; when the limit deviation of the mold core diameter and the mold inner diameter is designed, the maximum gap of the mold core diameter and the mold inner diameter is smaller than the maximum gap in table 2 at room temperature or at the molding temperature; when the mold core or the mold is made of hard brittle tungsten carbide material, the minimum clearance between the mold core and the mold is larger than the minimum clearance in table 2, namely larger than 0; and the maximum clearance between the mold core and the mold in the molding process is controlled within 3-10 mu m as much as possible by combining the property of heat radiation.
TABLE 2 upper/lower limit values for the preferred dimensions and maximum/minimum clearance for a nominal dimension of 60mm
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0850886A1 (en) * | 1996-12-26 | 1998-07-01 | Hoya Corporation | Manufacturing method for glass molded products |
| TW200634353A (en) * | 2004-06-25 | 2006-10-01 | Fuji Photo Film Co Ltd | Optical compensatory film, process for producing the same, and polarizing plate and liquid crystal display employing the same |
| JP2008074646A (en) * | 2006-09-19 | 2008-04-03 | Olympus Corp | Method for producing optical element |
| CN106353842A (en) * | 2016-11-29 | 2017-01-25 | 中国科学技术大学 | Manufacturing method of microlens |
| CN109641771A (en) * | 2016-08-26 | 2019-04-16 | 康宁股份有限公司 | It is used to form the device and method of glassware |
| CN208800676U (en) * | 2018-06-21 | 2019-04-30 | 吴冬梅 | A kind of concentricity mold |
-
2020
- 2020-12-07 CN CN202011404098.9A patent/CN114611221B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0850886A1 (en) * | 1996-12-26 | 1998-07-01 | Hoya Corporation | Manufacturing method for glass molded products |
| TW200634353A (en) * | 2004-06-25 | 2006-10-01 | Fuji Photo Film Co Ltd | Optical compensatory film, process for producing the same, and polarizing plate and liquid crystal display employing the same |
| JP2008074646A (en) * | 2006-09-19 | 2008-04-03 | Olympus Corp | Method for producing optical element |
| CN109641771A (en) * | 2016-08-26 | 2019-04-16 | 康宁股份有限公司 | It is used to form the device and method of glassware |
| CN106353842A (en) * | 2016-11-29 | 2017-01-25 | 中国科学技术大学 | Manufacturing method of microlens |
| CN208800676U (en) * | 2018-06-21 | 2019-04-30 | 吴冬梅 | A kind of concentricity mold |
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