Method for calibrating thermal expansion coefficient of material through laser steady-state method

Abstract

The invention discloses a laser steady-state method material thermal expansion coefficient calibration method, which comprises the following steps: placing a to-be-measured sample in a constant-temperature environment and at the center of two groups of measurement light paths, and enabling the to-be-measured length direction of the to-be-measured sample to be parallel to two parallel measurement light paths of a laser interference length measurement system; measuring the to-be-measured sample at a plurality of preset temperature points by adopting a steady-state method, and collecting sample length data measured by the laser interference length measurement system after each temperature point is kept at a constant temperature until the uniformity of the internal temperature and the external temperature of the sample reaches a preset threshold value; and based on the sample length data collected at the plurality of temperature points, a matrix algorithm is adopted to calculate a primary term expansion coefficient and a quadratic term expansion coefficient of the sample, and the thermal expansion coefficient at any temperature point t in the measurement temperature area is calculated. The laser refractive index real-time correction is introduced into the material expansion coefficient measurement, the laser wavelength is subjected to data correction in a real-time environment, and the laser wavelength error caused by the refractive index is reduced to the maximum extent.

Description

Technical Field

[0001] This invention relates to the field of thermal expansion coefficient calibration, specifically a laser steady-state method for calibrating the thermal expansion coefficient of materials. Background Technology

[0002] The coefficient of thermal expansion is one of the fundamental physical parameters of a material. It refers to the relative change in length (linear thermal expansion coefficient) or relative change in volume (volume thermal expansion coefficient) of a solid material when its temperature changes by 1°C. Accurate measurement of the coefficient of thermal expansion is of great significance for basic scientific research, precision measurement, and engineering applications. In fields such as spacecraft thermal control, precision instrument manufacturing, and electronic chip packaging, the thermal expansion characteristics of materials directly affect the performance stability and service life of products.

[0003] Currently, techniques for measuring the coefficient of thermal expansion of materials are mainly divided into two categories: dynamic methods and static methods. Each method has certain technical limitations. Dynamic methods typically involve continuous heating. During measurement, an initial temperature T1 and an ending temperature T2 are set. The temperature is raised from T1 to T2 at a constant rate while dynamically changing. A displacement sensor collects the change in sample length, and the coefficient of thermal expansion is calculated using a formula. However, in dynamic methods, the sample is constantly in a state of temperature change, making thermal equilibrium impossible. Thermocouples used for temperature measurement are usually placed next to the sample, measuring the center temperature of the furnace chamber, not the exact internal temperature of the sample, resulting in a temperature difference. Furthermore, temperature data is sampled at a time frequency, and the collected temperature data are mostly non-integer temperature points (e.g., 20.15℃, 21.32℃), leading to discrepancies in the formula calculation. It does not correspond precisely to L0. and There is a temperature error, so it is impossible to obtain the coefficient of thermal expansion of the sample at standard integer temperature points.

[0004] The push-rod displacement sensor method is a classic method for measuring thermal expansion. It uses a quartz rod in contact with the sample to transmit the length change of the sample during heating to the displacement sensor. Traditional displacement sensors (such as inductive sensors or optical scales) can only achieve an absolute measurement accuracy on the order of 0.5 μm, which is only sufficient for 1×10⁻⁶ measurements. -7 Measurement requirements for the coefficient of thermal expansion of materials at / ℃. For narrow temperature ranges and coefficients of thermal expansion less than 1×10⁻⁶. -7For materials with a temperature range of / ℃, sensors often struggle to detect minute length changes in the sample. Using a long probe (typically exceeding 300mm) as the displacement transfer medium is problematic. During measurement, the probe itself deforms, and unevenness at its end face can cause lateral sliding of the sample, resulting in the sensor's axis being out of sync with the sample's deformation direction, leading to Abbe error. Single-beam laser interferometry, employing the Michelson interferometry principle, uses a laser beam reflected from the sample or intermediate interface to interfere with the incident light. The coefficient of thermal expansion is calculated by counting the movement of interference fringes. However, in non-vacuum environments, the air refractive index hinders laser wavelength propagation. Traditional methods lack real-time, accurate correction for air refractive index, resulting in measurement errors. Furthermore, the high coefficient of thermal expansion of materials in laser chambers and other components also affects measurement results with temperature variations.

[0005] In summary, existing thermal expansion coefficient measurement technologies generally suffer from the following common technical problems: dynamic methods cannot guarantee the uniformity of temperature and thermal balance inside and outside the sample, leading to inaccurate temperature measurements; steady-state methods have long measurement cycles and low efficiency; traditional contact measurement methods are limited by sensor accuracy and mechanical transmission errors, making it difficult to meet the measurement requirements of materials with ultra-low thermal expansion coefficients; systematic error sources such as Abbe error and changes in laser wavelength caused by environmental factors (temperature, air pressure, humidity) lack effective real-time compensation methods; and the traditional two-point method calculation model has limited accuracy and cannot accurately describe the nonlinear characteristics of the material's thermal expansion coefficient as a function of temperature. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a laser steady-state method for calibrating the thermal expansion coefficient of materials.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a laser steady-state method for calibrating the thermal expansion coefficient of materials, comprising: A. The sample to be tested is placed in a constant temperature environment and at the center of the two sets of measurement optical paths, so that the length direction to be measured of the sample is parallel to the two parallel measurement optical paths of the laser interferometric length measurement system. B uses a steady-state method to measure the sample at multiple preset temperature points. At each temperature point, the sample is kept at a constant temperature until the temperature uniformity between the inside and outside of the sample reaches a predetermined threshold. Then, the sample length data measured by the laser interferometric length measurement system is collected. Based on the sample length data collected at the multiple temperature points, C uses a matrix algorithm to calculate the first-order expansion coefficient of the sample. and quadratic expansion coefficient Calculate the coefficient of thermal expansion at any temperature point t within the measured temperature range. The formula is as follows: .

[0008] Furthermore, in step B, the structure of the two parallel measurement optical paths ensures that the measurement reference line and the deformation direction of the sample are on the same straight line to eliminate Abbe error.

[0009] Further, in step B, the temperature, air pressure, humidity, and CO2 concentration inside the constant temperature chamber are monitored in real time; based on the environmental parameters, the current air refractive index n is calculated, and the laser wavelength λ used by the laser interferometric length measurement system is corrected using the following formula: , in The wavelength of the laser in a vacuum.

[0010] Furthermore, the sample mounting step specifically includes: using a plane mirror made of zero-expansion material with a flatness of less than 0.05 μm as a reference lens and a reflector; and using an optical contact method to tightly attach the reference lens and the reflector to the ultra-precision machined end faces at both ends of the sample to be tested to form an optical path closure.

[0011] On the other hand, a laser steady-state method material thermal expansion coefficient calibration device includes: A precision temperature-controlled chamber is used to contain samples for testing and provide a controlled temperature environment. A laser interferometric length measurement system includes a laser, a beam splitter group, a reference lens, and a reflector. The optical path output end of the laser is connected to the optical path input end of the beam splitter group, and the reference lens and the reflector are sequentially arranged at the output end of the beam splitter group. The temperature monitoring system includes multiple temperature probes that are embedded inside the sample and attached to the outer surface of the sample to monitor the temperature uniformity of the sample space. An environmental parameter monitoring system, including sensors for monitoring temperature, air pressure, humidity and CO2 concentration inside a constant temperature chamber; The sample to be tested is placed between the reference lens and the reflector. The laser interferometric length measurement system generates two measurement optical paths parallel to the length direction of the sample to be measured. Based on the data of the environmental parameter monitoring system, the refractive index of the laser wavelength is corrected in real time. At multiple set constant temperature points, the thermal expansion coefficient of the sample is calculated by matrix algorithm based on the corrected laser length measurement data and temperature data.

[0012] Furthermore, the temperature control of the constant temperature chamber is configured to perform a steady-state measurement method, specifically including: setting multiple constant temperature points within a set measurement temperature zone, and controlling the heating rate between the constant temperature points to be below 0.5℃ / hour.

[0013] This invention provides a laser steady-state method for calibrating the coefficient of thermal expansion of materials, which has the following advantages: This invention introduces real-time laser refractive index correction into the measurement of material expansion coefficient, and corrects the laser wavelength under the actual environment to minimize the laser wavelength error caused by refractive index. Attached Figure Description

[0014] Figure 1 This is a schematic diagram illustrating the steps of a laser steady-state method for calibrating the coefficient of thermal expansion of materials according to the present invention. Figure 2 This is a schematic diagram of the optical path measurement principle of a laser steady-state method for calibrating the thermal expansion coefficient of materials according to the present invention. Figure 3 This is an optical path diagram of a laser steady-state method for calibrating the thermal expansion coefficient of materials according to the present invention. Detailed Implementation

[0015] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0016] like Figure 1 As shown, the present invention includes the following steps: A. The sample to be tested is placed in a constant temperature environment and at the center of the two sets of measurement optical paths, so that the length direction to be measured of the sample is parallel to the two parallel measurement optical paths of the laser interferometric length measurement system. B uses a steady-state method to measure the sample at multiple preset temperature points. At each temperature point, the sample is kept at a constant temperature until the temperature uniformity between the inside and outside of the sample reaches a predetermined threshold. Then, the sample length data measured by the laser interferometric length measurement system is collected. Based on the sample length data collected at the multiple temperature points, C uses a matrix algorithm to calculate the first-order expansion coefficient of the sample. and quadratic expansion coefficient Calculate the coefficient of thermal expansion at any temperature point t within the measured temperature range. The formula is as follows: .

[0017] This embodiment provides a complete laser steady-state method for calibrating the coefficient of thermal expansion of materials, which mainly includes the following parts: The precision constant temperature chamber adopts a double-layer heat insulation design and is filled with a heat-conducting gas medium (such as dry air or nitrogen). The chamber is equipped with a high-precision upper heater (2) and lower heater (3), which can independently control the temperature. The temperature control stability of the constant temperature chamber is less than ±0.01℃ / hour.

[0018] The laser interferometric length measurement system uses a frequency-stabilized helium-neon laser as the light source, with a vacuum wavelength of λ0. After passing through a beam splitter group, the laser beam forms two completely parallel and symmetrically distributed measurement optical paths. Each optical path includes a reference mirror and a reflecting mirror made of a zero-expansion material such as ULE glass, with a mirror flatness of less than 0.05 μm. These two optical paths convert the sample's length variation into the movement of interference fringes, which is received and counted by a photodetector.

[0019] To accurately measure the coefficient of thermal expansion of the material and ensure sample temperature uniformity, the sample was machined into a cuboid with dimensions of (9×35×100) mm. The two end faces to be measured underwent ultra-precision machining, achieving a flatness of less than 0.05 μm, a parallelism of less than 1 μm, and a roughness Ra of less than 0.01 μm. The sample was precisely clamped between a reference mirror and a reflecting mirror via optical contact, ensuring that the measurement optical path was strictly parallel to the direction of the sample's length change, thus completely eliminating Abbe error from a physical structural perspective. 1) Eliminate the temperature difference between the sample core and the furnace center, improving sample temperature uniformity. The dynamic method measurement was changed to a steady-state method measurement. Taking 20℃ as an example, in order to obtain the coefficient of thermal expansion (CTE) of the material at 20℃... (20) The measurement temperature range was set to (15~35)℃, with an initial temperature of 15℃ and an ending temperature of 35℃. Five constant temperature points were set at 15℃, 20℃, 25℃, 30℃, and 35℃. Three deep holes were evenly distributed on the sample, and temperature probes were embedded in the holes. Three temperature probes were also placed on the outer surface of the sample. After maintaining the constant temperature for 6 hours, the temperature uniformity measured by the six probes was less than 0.005℃ (i.e., the range was less than 0.005℃). Temperature data and sample length data measured by laser were collected. When heating from the current temperature point to the next temperature point, the heating rate was set to be less than 0.5℃ / hour.

[0020] The temperature probes are embedded inside the sample under test. Circular probes are evenly distributed at half-height (35mm) along the sample's direction. Surface-mount probes are attached to the outer surface of the sample, with staggered heights to capture the spatial temperature gradient at different locations, ensuring uniform sample temperature. When the uniformity of the six temperature probes is less than 0.005℃, the internal and external temperatures of the sample are considered known, indicating that thermal equilibrium has been reached. The temperature difference between the probes and the sample core is sufficiently small to affect the measurement results.

[0021] 2) Calculation method for coefficient of thermal expansion Before starting the test, obtain the sample length at 20°C. L 0. Combining the steady-state method, multiple temperature points of 15℃, 20℃, 25℃, 30℃, and 35℃ are set within the measurement temperature range. The measurement data are then calculated using formula (3) to obtain the coefficient of thermal expansion of the sample. α With the quadratic expansion coefficientβ The coefficient of thermal expansion at 20℃ is calculated according to formula (4). Formulas (3) and (4) are shown below: L t = L 0×{1+ α ×(t-20)+ β ×(t-20) 2}(3) In the formula: L t — Sample length at t℃, in meters (m); L Sample length at 0–20℃, in meters (m); α —The coefficient of thermal expansion of the sample in the first term, in K. -1 ; β —The quadratic expansion coefficient of the sample, in Kelvin. -1 ; t——Temperature at t℃, in degrees Celsius (℃); CTE (20) = α +2× β ×(t-20)(4) In the formula: α —The coefficient of thermal expansion of the sample in the first term, in K. -1 ; β —The quadratic expansion coefficient of the sample, in Kelvin. -1 ; t——Temperature at t℃, in degrees Celsius (℃); CTE (20) — Coefficient of thermal expansion at t℃, in K -1 ; The result is obtained by solving formula (3) at multiple temperature points. α and β， The calculation accuracy is less than the calculation accuracy of the first and last points in formula (1), and the final result is... α and β， Formula (4) can be used to obtain the coefficient of thermal expansion at any temperature point within the measurement temperature range.

[0022] 3) Laser refractive index correction under varying temperature conditions Traditional displacement sensors, using inductive sensors or grating rulers, have insufficient measurement accuracy for narrow temperature ranges and samples with low coefficients of thermal expansion; the measurement accuracy of displacement sensors is only 1×10⁻⁶. -7The coefficient of thermal expansion of the material was measured at / ℃, and the coefficient of thermal expansion was less than 1×10. -7 Materials at / ℃ are difficult to measure. This invention uses a laser interferometer and designs a novel measurement optical path combined with a specially made planar interferometer array for zero-expansion materials as a sensor for measuring material expansion and deformation.

[0023] Traditional laser interferometry relies on counting interference fringes, with the light source wavelength measured in a vacuum. This invention, however, requires measurement under varying temperature conditions to preserve the gaseous medium for thermal conductivity. Therefore, the laser wavelength needs correction to ensure accurate length measurement. This necessitates the use of high-precision temperature sensors, high-precision humidity sensors, and high-precision CO2 sensors.

[0024] A modified formula is introduced to calculate the refractive index under different conditions. The relationship between refractive index and wavelength is as follows: λ 0= λ ×n(5) In the formula λ 0 represents the laser wavelength in a vacuum. λ The corrected laser wavelength, where n is the corrected refractive index.

[0025] First, the standard experimental environment is set at 20℃, pressure 100000Pa, and CO2 concentration 0.04%. Let (n-1) s The refractive index of air under standard test conditions:

[0026] Let (n-1) x Air refractive index at a CO2 concentration deviation of 0.04% from the standard:

[0027] In the formula, x is the current CO2 concentration.

[0028] Let (n-1) tp The refractive index of air under different temperature and pressure conditions:

[0029] In the formula p Current pressure, in Pa. t The current temperature is expressed in °C.

[0030] Refractive index under different humidity conditions n tpf for:

[0031] In the formula PSV for: Corrected wavelength λ for

[0032] This allows us to obtain the corrected laser wavelength under different air pressure and humidity conditions within a temperature range of (10~35)℃, reducing the measurement error caused by substituting the refractive index and thus improving the accuracy of laser length measurement.

[0033] 4) Measurement optical path design The sample dimensions are designed to be (9×35×100) mm. The flatness of the (9×35) mm end face is less than 0.05 μm, the parallelism of the two end faces is less than 1 μm, and the roughness Ra of the two end faces is less than 0.01 μm. Lenses are installed at both ends of the (9×35) mm cross-section; one end is a 60 mm diameter lens, and the other end is a 60 mm diameter reflector. Figure 3 The diagram shows the principle of optical path measurement. The sample is located at the center of the two sets of measurement optical paths. The direction of the change in the length to be measured is parallel to the two sets of measurement optical paths to minimize Abbe error. The average value of the optical path change of the two sets of parallel optical paths is the sample change.

[0034] The flatness of the sample end face is less than 0.05μm, the lens adheres well to the sample surface, and the lens is made of a material with zero coefficient of expansion. The flatness of the lens surface is less than 0.05μm. Therefore, even if temperature changes occur during the measurement process, the lens will not deform and will not be displaced in non-measurement directions, ensuring that the measurement axis remains parallel to the direction of sample length change, which conforms to the Abbe measurement principle.

[0035] In another implementation example, the sample to be tested is prepared as (9×35×400) mm, the flatness of the two ends of the (9×35) mm sample is less than 0.05 μm, the roughness Ra of the two ends is less than 0.01 μm, and the parallelism of the two ends is less than 1 μm.

[0036] Prepare a 60mm diameter, 20mm thick zero-expansion material plane mirror block, coated on one side of the plane. Mount the sample to be tested between the two coated plane mirrors. The installation diagram is shown below. Figure 2 As shown.

[0037] Prepare to measure the coefficient of thermal expansion of the sample at 20℃. Set the measurement temperature range to (15~35)℃, the starting temperature to 15℃, and the ending temperature to 33℃. Set 5 constant temperature points, namely 15℃, 20℃, 25℃, 30℃, and 33℃. Record the data according to formula (3). The data is shown in the table below.

[0038] L t = L 0×{1+ α ×(t-20)+ β ×(t-20) 2}(3) In the formula Lt Let be the length of the sample at temperature t℃. The data recorded by the laser at five points (15℃, 20℃, 25℃, 30℃, and 33℃) represent the increments between adjacent temperature points. The right side of the equation... L Move 0 and the number 1 to the left side of the equation. The left side of the equation needs to be transformed:

[0039] The right side of formula (3) remains unchanged: Formula (6) The measurement data are shown in the table below. ; The formula can be viewed as a system of equations A = BX + CY, where A, B, and C are constant terms, and X and Y are α and β to be solved. Substituting the data into the above formula (6), we obtain the following system of equations: -5.18343E-08=-4.5194×α+20.42497636×β 0 = 0 × α + 0 × β 5.22823E-08=4.5255×α+20.48015025×β 1.05717E-07=9.1107×α+83.00485449×β 1.59666E-07=13.6984×α+187.6461626×β Solving the above system of equations yields α = 0.000011508 and β = 0.0000000107. Substituting these values ​​into Formula 4 allows us to calculate the coefficients of thermal expansion at various temperatures. See the table below. CTE= α +2× β ×(t-20) ; When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0040] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0041] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A laser steady-state method for calibrating the coefficient of thermal expansion of materials, characterized in that, include: A. The sample to be tested is placed in a constant temperature environment and at the center of the two sets of measurement optical paths, so that the length direction to be measured of the sample is parallel to the two parallel measurement optical paths of the laser interferometric length measurement system. B uses a steady-state method to measure the sample at multiple preset temperature points. At each temperature point, the sample is kept at a constant temperature until the temperature uniformity between the inside and outside of the sample reaches a predetermined threshold. Then, the sample length data measured by the laser interferometric length measurement system is collected. Based on the sample length data collected at the multiple temperature points, C uses a matrix algorithm to calculate the first-order expansion coefficient of the sample. and quadratic expansion coefficient Calculate the coefficient of thermal expansion at any temperature point t within the measured temperature range. The formula is as follows: 。 2. The laser steady-state method for calibrating the coefficient of thermal expansion of materials according to claim 1, characterized in that, In step A, the structure of the two parallel measurement optical paths ensures that the measurement reference line and the deformation direction of the sample are on the same straight line to eliminate Abbe error.

3. The laser steady-state method for calibrating the coefficient of thermal expansion of materials according to claim 1, characterized in that, In step B, the temperature, air pressure, humidity, and CO2 concentration inside the constant temperature chamber are monitored in real time. Based on the environmental parameters, the current air refractive index n is calculated, and the laser wavelength λ used by the laser interferometric length measurement system is corrected using the following formula: ， in The wavelength of the laser in a vacuum.

4. The laser steady-state method for calibrating the coefficient of thermal expansion of materials according to claim 1, characterized in that, The sample mounting steps specifically include: using a plane mirror made of zero-expansion material with a flatness of less than 0.05 μm as a reference lens and a reflector; and using optical contact to tightly attach the reference lens and the reflector to the ultra-precision machined end faces of both ends of the sample to be tested to form an optical path closure.

5. A laser steady-state method for calibrating the coefficient of thermal expansion of materials, used to perform the method as described in any one of claims 1-4, characterized in that, include: A precision temperature-controlled chamber is used to contain samples for testing and provide a controlled temperature environment. A laser interferometric length measurement system includes a laser, a beam splitter group, a reference lens, and a reflector. The optical path output end of the laser is connected to the optical path input end of the beam splitter group, and the reference lens and the reflector are sequentially arranged at the output end of the beam splitter group. The temperature monitoring system includes multiple temperature probes that are embedded inside the sample and attached to the outer surface of the sample to monitor the temperature uniformity of the sample space. An environmental parameter monitoring system, including sensors for monitoring temperature, air pressure, humidity and CO2 concentration inside a constant temperature chamber; The sample to be tested is placed between the reference lens and the reflector. The laser interferometric length measurement system generates two measurement optical paths parallel to the length direction of the sample to be measured. Based on the data of the environmental parameter monitoring system, the refractive index of the laser wavelength is corrected in real time. At multiple set constant temperature points, the thermal expansion coefficient of the sample is calculated by matrix algorithm based on the corrected laser length measurement data and temperature data.

6. The laser steady-state method material thermal expansion coefficient calibration device according to claim 5, characterized in that, The temperature control of the constant temperature chamber is configured to perform a steady-state measurement method, specifically including: setting multiple constant temperature points within a set measurement temperature zone, and controlling the heating rate between the constant temperature points to be below 0.5℃ / hour.

Images