CN112364522A - Laser single-point curing modeling method applied to 3D printing lens - Google Patents
Laser single-point curing modeling method applied to 3D printing lens Download PDFInfo
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- CN112364522A CN112364522A CN202011312115.6A CN202011312115A CN112364522A CN 112364522 A CN112364522 A CN 112364522A CN 202011312115 A CN202011312115 A CN 202011312115A CN 112364522 A CN112364522 A CN 112364522A
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- 238000000034 method Methods 0.000 title claims abstract description 29
- 238000010146 3D printing Methods 0.000 title claims abstract description 28
- 239000000463 material Substances 0.000 claims abstract description 51
- 238000009826 distribution Methods 0.000 claims abstract description 44
- 229920001187 thermosetting polymer Polymers 0.000 claims abstract description 42
- 238000006243 chemical reaction Methods 0.000 claims abstract description 36
- 238000010606 normalization Methods 0.000 claims abstract description 12
- 238000012546 transfer Methods 0.000 claims abstract description 12
- 230000001052 transient effect Effects 0.000 claims abstract description 12
- 230000000704 physical effect Effects 0.000 claims abstract description 9
- 239000007788 liquid Substances 0.000 claims description 24
- 238000004132 cross linking Methods 0.000 claims description 5
- 238000002310 reflectometry Methods 0.000 claims description 4
- 238000010521 absorption reaction Methods 0.000 claims description 2
- 238000005315 distribution function Methods 0.000 claims description 2
- 238000007711 solidification Methods 0.000 claims 1
- 230000008023 solidification Effects 0.000 claims 1
- 229920000642 polymer Polymers 0.000 abstract description 12
- 230000008569 process Effects 0.000 abstract description 7
- 238000012412 chemical coupling Methods 0.000 abstract description 4
- 238000001723 curing Methods 0.000 description 51
- 230000003287 optical effect Effects 0.000 description 11
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- 230000010354 integration Effects 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000009795 derivation Methods 0.000 description 2
- 239000004205 dimethyl polysiloxane Substances 0.000 description 2
- 229920000435 poly(dimethylsiloxane) Polymers 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 238000001029 thermal curing Methods 0.000 description 2
- 238000004383 yellowing Methods 0.000 description 2
- 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
- -1 Polydimethylsiloxane Polymers 0.000 description 1
- 230000009471 action Effects 0.000 description 1
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- 235000013405 beer Nutrition 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 239000005357 flat glass Substances 0.000 description 1
- 238000005286 illumination Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 239000005304 optical glass Substances 0.000 description 1
- 238000007639 printing Methods 0.000 description 1
- 239000011347 resin Substances 0.000 description 1
- 229920005989 resin Polymers 0.000 description 1
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Abstract
The invention relates to a laser single-point curing modeling method applied to a 3D printing lens, which comprises the following steps: acquiring the physical property of the thermosetting material and the parameter range of the pulse laser; establishing a spatial distribution model of laser heat source power in the thermosetting material; establishing a time domain normalization model of the pulse laser according to parameters of the pulse laser; establishing a thermal energy transfer model of the curing reaction according to the curing reaction kinetic model; combining the spatial distribution model with the time domain normalization model to obtain a time-space distribution model of the laser heat source power in the thermosetting material; establishing a transient heat conduction partial differential equation according to the heat energy transfer model and the time-space distribution model; and solving a transient heat conduction partial differential equation by utilizing multi-physical field integrated simulation software. The method adopts the photo-thermal-chemical coupling multi-physical model to simulate the curing process, can accurately predict the size and the shape of the single-point curing polymer, and provides a theoretical basis for optimizing the size and the shape of the single-point curing polymer.
Description
Technical Field
The invention relates to the technical field of optical manufacturing, in particular to a laser single-point curing modeling method applied to a 3D printing lens.
Background
The optical manufacturing industry covers a range of optical products for different purposes, from window glass, to illumination optics; from spectacle lenses, to camera lenses, nothing is done. In its general concept, optical instrument manufacturing, optical glass manufacturing, optical processing, etc. have been fairly "traditional" mature industries. However, the price of the existing high-quality optical element still reaches to a dozen of thousands yuan or even dozens of thousands yuan, and the processing period is many months, so that the manufacturing cost is high, the period is long, and the wider popularization and application are hindered. 3D printing technology goes into optical applications.
The 3D printing technology currently applied to the field of optical lens manufacturing is mainly based on the principle of ultraviolet light curing or two-photon curing. Although the lens printed by the principle has higher surface resolution, the yellowing phenomenon of the processed lens cannot be overcome, and the application in the field of imaging optics is seriously influenced. The 3D printing technology based on the thermocuring principle can well avoid the problem of lens yellowing, the curing principle is that ultrafast pulse laser is converged on a thermosetting material, laser energy is converted into heat in a very small scale (micron and submicron) and a very short time, and a molecule crosslinking curing reaction in a 'thermo-chemical' sensitive material is accelerated through laser thermal effect, so that the material is cured and molded in a very short time, and 3D printing and manufacturing of the lens are realized.
An important evaluation index for the 3D printing lens is surface roughness, which is closely related to the size of the resolution of the laser single-point curing dimension, so that laser single-point curing modeling is required to analyze the action mechanism of laser curing and predict the shape and the dimension of a cured polymer, and further, a theoretical basis is provided for improving the surface roughness of the 3D printing optical element.
Disclosure of Invention
The invention aims to provide a laser single-point curing modeling method, which simulates a curing process by establishing a light-heat-chemical coupling multi-physical model, can predict the size and the shape of a single-point curing polymer and provides a theoretical basis for improving the surface roughness of a 3D printing optical element.
In order to achieve the above purpose, the invention provides the following technical scheme:
a laser single-point curing modeling method applied to a 3D printing lens comprises the following steps:
the method comprises the following steps: acquiring the physical property of a thermosetting material for finishing 3D printing of the lens and the parameter range of pulse laser;
step two: according to the Gaussian beam model of the pulse laser, establishing a spatial distribution model of the laser heat source power in the thermosetting material;
step three: establishing a time domain normalization model of the pulse laser;
step four: establishing a curing reaction kinetic model according to an Arrhenius equation, and establishing a heat energy transfer model of a curing reaction according to the curing reaction kinetic model;
step five: combining the spatial distribution model with the time domain normalization model to obtain a time-space distribution model of the laser heat source power in the thermosetting material;
step six: establishing a transient heat conduction partial differential equation according to the heat energy transfer model and the time-space distribution model through a heat conduction theory;
step seven: and solving the transient heat conduction partial differential equation by utilizing multi-physical-field integrated simulation software to obtain a time and space distribution numerical solution of a temperature field in the thermosetting material and a space-time distribution numerical solution of a material curing geometric boundary.
The laser single-point curing modeling method applied to the 3D printing lens provided by the invention has the following beneficial effects:
1. the invention adopts a light-heat-chemical coupling multi-physical model to simulate the curing process, and can accurately predict the size and the shape of the single-point cured polymer;
2. the established model constructs the relationship between the size and the shape of the single-point curing polymer and the physical properties of the thermosetting material and the parameters of the pulse laser, and provides a theoretical basis for optimizing the size and the shape of the single-point curing polymer.
Drawings
In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.
FIG. 1 is a schematic flow chart diagram of a laser single-point curing modeling method applied to a 3D printing lens according to an embodiment of the present invention;
fig. 2 is a laser focusing light spot diagram of the rectangular coordinate system with the origin at the liquid surface.
Detailed Description
In order to make the technical solutions of the present invention better understood, those skilled in the art will now describe the present invention in further detail with reference to the accompanying drawings.
Referring to fig. 1, in one embodiment, the present invention provides a laser single-point curing modeling method applied to a 3D printing lens, which includes the following steps:
step one (S100): and acquiring the physical properties of the thermosetting material for completing the 3D printing lens and the parameter range of the pulse laser.
A thermosetting material, such as Polydimethylsiloxane (PDMS), which can be used for 3D lens printing based on the pulsed laser thermal curing principle is selected, and the relevant physical properties of the thermosetting material can be determined.
Optionally, the selected thermoset material requires physical properties including: specific heat capacity, thermal conductivity, density, reaction rate constants, and the like.
Acquiring a parameter range of the pulse laser, wherein the parameters of the pulse laser comprise: central wave band, pulse frequency, pulse period, maximum average power, maximum pulse energy, full width at half maximum, standard deviation, pulse peak power, diffuse spot aperture, reflection coefficient and the like.
Step two (S200): and according to the Gaussian beam model of the pulse laser, establishing a spatial distribution model of the laser heat source power in the thermosetting material.
According to a Gaussian beam model of the pulse laser, a radiation area in the thermosetting material is determined. According to the laser reflectivity and the beer-Lambert law, the total laser radiation energy absorbed by the thin layers of the thermosetting material at different depths can be deduced, the power distribution on the sections at different depths is Gaussian distribution, and finally, a spatial distribution model of the laser heat source power in the thermosetting material is established.
FIG. 2 is a diagram of laser focusing spots at the air-liquid level boundary of the origin of the rectangular coordinate system, where the liquid level is the surface of the thermosetting material in liquid state, the laser focusing beam boundary is the boundary of the focused laser beam, and W in the diagram0Is the laser waist beam radius, beta is the laser divergence angle, WzIs the radius of the light spot at a distance Z from the liquid level, ZDThe radiation distribution of the laser beam on any section perpendicular to the beam axis, that is, the energy radiation distribution of the cross section, is gaussian distribution.
The spatial profile of the laser radiation can be obtained as shown in equation (1):
wherein, WzIs the radius of the spot at a depth z from the liquid surface, W0Is the radius of the lumbar spot, λ is the wavelength of the laser, ZDThe distance between the lumbar plaque and the liquid level.
Laser energy incident on a gas-liquid interface is divided into two parts, wherein a small part of the laser energy is reflected by a liquid surface, the other part of the laser energy is transmitted into liquid and absorbed by the liquid, when the laser is transmitted in the liquid, the energy is absorbed by the liquid according to the beer Lambert law, and the energy absorbed by a material in a cross section below the liquid surface and in z position is as shown in a formula (2):
wherein R isCIn order to obtain a reflectivity of the liquid surface to a laser beam of a certain wavelength band, ACIs the absorptivity, P, of the thermosetting material to laser light of a certain wave bandIIs the instantaneous power of the laser.
The total energy absorbed by the liquid from the surface to the sub-surface z is:
then, by using the differential principle, the energy absorbed by the thin layer dz at the depth z below the liquid level is obtained by differentiating the formula (3) and multiplying the result by dz, as shown in the formula (4):
the average energy absorbed by the thin layer dz per unit volume of material at z below the liquid level is then derived, as shown in equation (5):
where A (z) is the cross-sectional area of the laser irradiated region at the sub-surface depth z.
The power distribution of the laser on any section plane perpendicular to the Z axis is Gaussian distribution, so that the depth Z is0The laser radiation distribution in the cross section is as shown in formula (7):
wherein, P (x, y, z)0) For the distribution of energy in cross-section at the waistband, PzIs the energy at the center of the cross section at the depth zThe peak value of the peak value is,
the gaussian half-width at (c) is also the spot radius at the waist.
Integrating the energy distributed in Gaussian distribution in the section at the position z under the liquid level by utilizing the integration principle to obtain the total energy P in the section at the position z with the depthLAs shown in formula (8); the energy peak value at the center of the section at the liquid level depth z can be deduced according to the fact that the total energy obtained after integration is equal to the total energy in the front derivation section, the formula (9) shows that the energy obtained after integration is equal to the total energy in the front derivation section, and the formula (10) shows that the energy of the peak value at the center of the section at the liquid level depth z is deduced. Equation (11) represents a model of the spatial distribution of the obtained laser heat source power in the thermosetting material.
Wherein, PLFor the total energy in the cross-section at the depth z, r is the integral radius in the cross-section, and can be used
Denotes WzIs the pulsed laser spot radius at depth z.
Wherein, PLIs the total energy in cross-section at depth z, A (z) is the cross-sectional area of the laser radiation region at depth z, PV(z) is the average energy absorbed per unit volume of material at depth z, RCThe reflectivity of the liquid surface of the thermosetting material to laser of a certain wave band, ACThe absorption rate of the thermosetting material to laser in a certain wave band.
Wherein, PzIs the energy peak at the center of the cross-section at depth z.
Step three (S300): and establishing a time domain normalization model of the pulse laser. The instantaneous output power function of the laser pulse is a Gaussian pulse function in a time domain, a normalized model of the pulse laser in the time domain is established according to the parameters of the pulse laser, namely, a time domain normalized model of the pulse laser is established, and the time domain normalized model is shown as a formula (12):
wherein t is a time variable, sigma is a standard deviation of the Gaussian laser pulse signal, and t0Is the position of the pulse peak, T0Is the pulse period.
Step four (S400): and establishing a curing reaction kinetic model according to an Arrhenius equation, and establishing a heat energy transfer model of the curing reaction according to the curing reaction kinetic model.
In the step, a curing reaction kinetic model is established according to an arrhenius equation, and then a heat energy transfer model in the curing process is established.
In the process of curing reaction, the degree of progress of the reaction is expressed by the percentage of the completion of the crosslinking reaction, a curing reaction kinetic model is established according to the Arrhenix equation, and finally, the relation between the polymer curing reaction thermal effect and the curing reaction kinetic model is established by utilizing the polymer curing reaction thermal effect. Equation (13) represents the degree of progress of the curing reaction, equation (14) represents the establishment of a dynamic model of the curing reaction using the arrhenytox equation, and equation (15) represents the established thermal energy transfer model of the curing reaction.
na＝α·nmax (13)
Wherein n isaIs the number of crosslinking reactions occurring during laser curing, nmaxTo complete the total number of crosslinks after curing, α is the percentage of crosslinking reactions that have occurred during curing, the extent to which the curing reactions have reacted, t is a time variable, k0For rate constants, E is the activation energy, R is the molar gas constant, T is the thermodynamic temperature, and m and n are the reaction orders, which are the empirical constants used to calibrate the equations.
Wherein Q iscureT is the time variable, rho is the resin density, H is the exotherm of the curing reactionrIs the total heat of reaction.
Step five (S500): and combining the spatial distribution model with the time domain normalization model to obtain a time-space distribution model of the laser heat source power in the thermosetting material.
And (3) combining the space distribution model of the laser heat source power in the thermosetting material established in the step two with the time domain normalization model of the pulse laser established in the step three to obtain a time-space distribution model of the laser heat source power in the thermosetting material, wherein the time-space distribution model is shown as a formula (16):
wherein, P (x, y, z) is the spatial distribution model established in the second step, and time (t) is the time domain normalization model established in the third step.
Step six (S600): and establishing a transient heat conduction partial differential equation according to the heat energy transfer model and the time-space distribution model through a heat conduction theory.
Establishing a transient heat conduction partial differential equation by the heat energy transfer model of the curing reaction established in the fourth step and the time-space distribution model of the laser heat source power in the thermosetting material established in the fifth step through a heat conduction theory, wherein the transient heat conduction partial differential equation in the laser single-point curing process is shown as a formula (17):
wherein T (x, y, z, T) is a time and space distribution function of a temperature field in the thermosetting material, ρ is the density of the thermosetting material, and CpIs specific heat capacity, is Laplacian, k is the thermal conductivity, PinA unit volume of a thermosetting material absorbs energy of laser light per unit time, QcureThe exotherm for the curing reaction.
Step (S700): and solving the transient heat conduction partial differential equation by utilizing multi-physical-field integrated simulation software to obtain a time and space distribution numerical solution of a temperature field in the thermosetting material and a space-time distribution numerical solution of a material curing geometric boundary.
And finally, solving the transient heat conduction partial differential equation established in the sixth step by utilizing the COMSOL (common analog modeling) software to finally obtain a time and space distribution numerical solution of the temperature field in the thermosetting material and a space-time distribution numerical solution of the material curing geometric boundary.
In the technical scheme, the laser single-point curing modeling method applied to the 3D printing lens provided by the invention has the following beneficial effects:
the method adopts a photo-thermal-chemical coupling multi-physical model to simulate the curing process, can accurately predict the size and the shape of the single-point curing polymer, and provides a theoretical basis for improving the surface roughness of the 3D printing optical element;
the established model constructs the relationship between the size and the shape of the single-point curing polymer and the physical properties of the thermosetting material and the parameters of the pulse laser, and provides a theoretical basis for optimizing the size and the shape of the single-point curing polymer.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (8)
1. A laser single-point solidification modeling method applied to a 3D printing lens is characterized by comprising the following steps:
the method comprises the following steps: acquiring the physical property of a thermosetting material for finishing 3D printing of the lens and the parameter range of pulse laser;
step two: according to the Gaussian beam model of the pulse laser, establishing a spatial distribution model of the laser heat source power in the thermosetting material;
step three: establishing a time domain normalization model of the pulse laser;
step four: establishing a curing reaction kinetic model according to an Arrhenius equation, and establishing a heat energy transfer model of a curing reaction according to the curing reaction kinetic model;
step five: combining the spatial distribution model with the time domain normalization model to obtain a time-space distribution model of the laser heat source power in the thermosetting material;
step six: establishing a transient heat conduction partial differential equation according to the heat energy transfer model and the time-space distribution model through a heat conduction theory;
step seven: and solving the transient heat conduction partial differential equation by utilizing multi-physical-field integrated simulation software to obtain a time and space distribution numerical solution of a temperature field in the thermosetting material and a space-time distribution numerical solution of a material curing geometric boundary.
2. The laser single-point curing modeling method applied to 3D printing lens according to claim 1, wherein the spatial distribution model is as follows:
wherein, WzIs the spot radius of the pulsed laser at a depth z from the liquid surface, ACThe absorption rate of the thermosetting material to laser in a certain wave band, RCThe reflectivity of the liquid surface of the thermosetting material to laser in a certain wave band, PIIs the instantaneous power of the laser.
3. The laser single-point curing modeling method applied to the 3D printing lens according to claim 2, wherein the time domain normalization model is as follows:
wherein t is a time variable, sigma is a standard deviation of the Gaussian laser pulse signal, and t0Is the position of the pulse peak, T0Is the pulse period.
4. The laser single-point curing modeling method applied to 3D printing lens according to claim 3, characterized in that the time-space distribution model is as follows:
wherein, P (x, y, z) is the spatial distribution model, and time (t) is the time domain normalization model.
5. The modeling method for laser single point curing applied to 3D printing lens according to claim 4, wherein the thermal energy transfer model is as follows:
wherein Q iscureT is the time variable, rho is the density of the thermosetting material, HrAlpha is the percentage of crosslinking reaction that has occurred during curing, for the total heat of reaction.
6. The laser single-point curing modeling method applied to the 3D printing lens according to claim 5, wherein the transient thermal conduction partial differential equation is:
wherein T (x, y, z, T) is a time and space distribution function of a temperature field in the thermosetting material, CpThe specific heat capacity is the specific heat capacity,
is Laplace operator, k is the thermal conductivity, PinA unit volume of a thermosetting material absorbs energy of laser light per unit time, QcureThe exotherm for the curing reaction.
7. The laser single-point curing modeling method applied to a 3D printing lens according to any one of claims 1 to 6,
the physical properties of the thermoset material include specific heat capacity, thermal conductivity, density, and reaction rate constants.
8. The laser single-point curing modeling method applied to a 3D printing lens according to any one of claims 1 to 6,
the parameters of the pulse laser comprise a central wave band, a pulse frequency, a pulse period, maximum average power, maximum pulse energy, full width at half maximum, standard deviation, pulse peak power, a diffuse spot caliber and a reflection coefficient.
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Application publication date: 20210212 |