Metal linear expansion coefficient measuring device and method

Abstract

The invention discloses a metal linear expansion coefficient measuring device and method, and relates to the field of metal characteristic measurement, the device comprises a capillary tube, a connecting tube, an injector, a telescopic rod and a heating box; to-be-detected metal is arranged in the heating box; the injector is horizontally arranged; the free end of the to-be-tested metal is connected with the piston end of the injector through the telescopic rod; the capillary tube is vertically arranged; the bottom end of the capillary tube is communicated with the liquid outlet end of the injector through a connecting tube; the capillary tube, the connecting tube and the injector are used for containing liquid. During measurement, the heating box heats to-be-measured metal, so that the to-be-measured metal expands, the telescopic rod connected with the free end of the to-be-measured metal pushes the piston end of the injector to move, liquid in the injector is pushed, and the liquid level height of the liquid in the capillary tube is changed; the liquid level height variation of the liquid in the capillary tube is used for calculating the linear expansion coefficient of the to-be-measured metal. According to the invention, the measurement of the linear expansion coefficient of the metal can be simply, conveniently and accurately realized.

Description

Technical Field

[0001] The present application relates to the field of metal property measurement, and in particular to a device and method for measuring metal linear expansion coefficient. Background Art

[0002] The linear expansion coefficient of metal is a physical quantity that characterizes the change in the length of an object as it changes with temperature. As the ratio of the change in the overall length of a metal when it encounters a significant temperature change, it is a crucial physical indicator.

[0003] The linear expansion coefficient of metal is an important parameter to measure the thermal expansion and contraction characteristics of metal. It plays a very important role in railway tracks, mechanical parts manufacturing, engineering construction, science and technology, etc., and directly affects the efficacy and role of metal in specific applications. Therefore, accurately measuring the linear expansion coefficient of metal can better provide data support for studying the performance of metal materials under temperature changes. For example, in the fields of mechanical engineering, aerospace, etc., accurate thermal expansion measurements of metal materials can be performed to avoid dimensional errors or structural problems caused by expansion, so as to ensure the quality and safety of the product. In addition, the measurement of the linear expansion coefficient of metal can also help promote the development of new material application fields and optimize the design of thermal energy utilization equipment.

[0004] At present, the metal linear expansion coefficient measuring instruments on the market usually involve multiple components and precise mechanical structures, which makes the equipment relatively complex and affects the measurement accuracy. In addition, the accuracy of the operator's readings and the degree of compliance with the experimental steps may cause certain errors in the final results. The difference in skills between different operators may lead to errors in the measurement results.

[0005] When measuring the linear expansion coefficient of metal with existing instruments and equipment in the laboratory, a micrometer is used to measure the tiny displacement of the metal during expansion. When using a micrometer to measure the tiny displacement of the metal, the installation needs to be precisely aligned and it needs to be ensured that the micrometer is fully aligned with the expansion end of the metal. In addition, the external environment has a great influence on the measurement, and it is not easy to observe the phenomenon of metal expansion through experiments. The experiment is relatively abstract.

[0006] In summary, how to simply and accurately measure the linear expansion coefficient of metals has become a problem that needs to be solved urgently. Summary of the invention

[0007] The purpose of the present application is to provide a device and method for measuring the linear expansion coefficient of metal, which can easily and accurately measure the linear expansion coefficient of metal.

[0008] To achieve the above objectives, this application provides the following solutions:

[0009] In a first aspect, the present application provides a device for measuring a metal linear expansion coefficient, comprising: a capillary tube, a connecting tube, a telescopic rod, a syringe, and a heating box;

[0010] The metal to be tested is arranged in the heating box; the syringe is arranged horizontally; the free end of the metal to be tested is connected to one end of the telescopic rod; the other end of the telescopic rod is connected to the piston end of the syringe; the capillary is arranged vertically; the bottom end of the capillary is connected to the liquid outlet end of the syringe through the connecting tube; the capillary, the connecting tube and the syringe are used to place liquid;

[0011] During measurement, the heating box heats the metal to be measured, causing the metal to expand, thereby causing the telescopic rod connected to the free end of the metal to be measured to push the piston end of the syringe to move, thereby pushing the liquid in the syringe, causing the liquid level height of the liquid in the capillary tube to change; the change in the liquid level height of the liquid in the capillary tube is used to calculate the linear expansion coefficient of the metal to be measured.

[0012] In a second aspect, the present application provides a method for measuring a metal linear expansion coefficient, the method for measuring a metal linear expansion coefficient is implemented by using the above-mentioned metal linear expansion coefficient measuring device, and the method for measuring a metal linear expansion coefficient comprises:

[0013] Control the heating box to heat the metal to be tested;

[0014] Record the change in the liquid level in the capillary during the heating process;

[0015] The linear expansion coefficient of the metal to be tested is calculated based on the change in the liquid level in the capillary tube.

[0016] According to the specific embodiments provided by the present application, the present application has the following technical effects: the present application provides a device and method for measuring the linear expansion coefficient of a metal, which can realize the measurement of the linear expansion coefficient of the metal to be measured through a capillary and a syringe, and has a simple structure and is easy to operate; based on the principle of equal volume invariance (that is, the volume change of the liquid in the syringe is equal to the volume change of the liquid in the capillary), the linear expansion coefficient of the metal to be measured is calculated by the change in the liquid level height of the liquid in the capillary, which improves the accuracy of the measurement of the linear expansion coefficient of the metal compared to the micrometer measurement method. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 The relationship between the metal elongation and the temperature when the temperature rises is obtained by linear fitting the measurement results in Table 2;

[0019] Figure 2 A schematic diagram of a metal linear expansion coefficient measuring device provided in one embodiment of the present application;

[0020] Figure 3 This is the measurement data analysis diagram of the measurement module when the magnification is 139;

[0021] Figure 4 This is the measurement data analysis diagram of the measurement module when the magnification is 239;

[0022] Figure 5 It is a schematic diagram of experimental data corresponding to the magnification of the measurement module of 869;

[0023] Figure 6 This is the measurement data analysis diagram of the measurement module when the magnification is 1496;

[0024] Figure 7 This is a relative error trend chart of the same metal under different specifications of measuring devices.

[0025] Reference numerals: capillary tube—1, connecting tube—2, syringe—3, heating box—4, metal linear expansion coefficient tester—5, iron stand—6. DETAILED DESCRIPTION

[0026] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0027] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0028] First, the micrometer measurement method is introduced.

[0029] (1) Experimental principle

[0030] The increase in length of a solid after being heated is called linear expansion. Experience shows that within a certain temperature range, the elongation ΔL of an object with an original length of L after being heated is approximately proportional to the increase in temperature Δt, and is also proportional to the original length L, that is,

[0031] ΔL=αLΔt (1)

[0032] The proportional coefficient α in the formula is called the linear expansion coefficient of the solid (abbreviated as linear expansion coefficient). To measure the linear expansion coefficient, the material is made into a strip or rod. From formula (1), we can see that the rod length L at t1, the elongation ΔL when the temperature reaches t2 after heating, and the temperatures t1 and t2 before and after heating are measured, then the linear expansion coefficient of the material in the (t1, t2) temperature range is:

[0033]

[0034] The main problem in measuring the linear expansion coefficient is how to measure the elongation ΔL. In the existing experimental instruments in the laboratory, a micrometer is used to measure tiny linear expansion.

[0035] (2) Experimental data measurement.

[0036] The experimental data measured using the original experimental instrument are shown in Table 1:

[0037] Table 1 Continuous temperature rise measurement data table

[0038]

[0039] (3) Experimental data processing and analysis.

[0040] From Table 1, we can see that the metal sample changes with time and temperature. The experimental data corresponding to the elongation change ΔL of the metal sample when the temperature is continuously increased by 5°C from 50°C to 95°C are recorded in Table 2.

[0041] Table 2 Elongation variation of metal samples with continuous heating at intervals of 5°C

[0042]

[0043] The measurement results in Table 2 were imported using orgin software, and a linear fit was performed with the temperature change as the horizontal axis and the metal elongation change as the vertical axis. The fitting curve is as follows: Figure 1 As shown in the fitting results, the correlation coefficients of iron, copper and aluminum fitting are 0.99964, 0.99995 and 0.99938 respectively, which have strong correlation. The slopes of the fitting curves are K 铁 =0.00410, K 铜 =0.00587, K 铝 =0.00826.

[0044] According to the linear fitting function formula: y = a + b × x, b = k, and from formula (1) combined with the above formula, we can get:

[0045]

[0046] It is known that the length of the metal rod sample at room temperature is L0 = 370 mm, so the linear expansion coefficient α of the iron, copper and aluminum rods can be calculated by formula (3): and

[0047] According to the calculation formula of absolute error and relative error, we can get:

[0048] (1) The reference value of sample (iron) at 20-100°C is 11.7×10 －6 ℃ －1 , the measured value is 11.08×10 －6 ℃ －1 , thus we can get:

[0049] (2) The reference value of sample (copper) at 20-100°C is 16.6×10 －6 ℃ －1 , the measured value is 15.86×10 －6 ℃ －1 , thus we can get:

[0050] (3) The reference value of the sample (aluminum) at 20-100°C is 23×10 －6 ℃ －1 , the measured value is 22.32×10 －6 ℃ －1 , thus we can get:

[0051] (4) Experimental error analysis.

[0052] When using a micrometer to measure the linear expansion coefficient of metal, the experimenter must read the experimental data of two dials at the same time during the measurement process, and cannot accurately read the experimental data at a certain temperature. During the experiment, the micrometer itself is easily affected by factors such as the external environment and produces errors. In addition, when using a micrometer to measure the linear expansion coefficient of metal, there are also defects such as difficulty in installation and inability to directly observe the phenomenon of metal expansion. This application improves the experimental instrument based on the equal volume method.

[0053] In response to the above problems, the present application adopts an experimental device designed by combining a capillary and a syringe, uses the equal volume method to calculate the change in liquid level to measure the elongation of the metal, optimizes the link that requires precise zeroing in the metal linear expansion coefficient measurement instrument, effectively eliminates the errors caused by improper zeroing operation, and further improves the accuracy and reliability of the experiment.

[0054] The following is an introduction to the experimental principle of measuring the linear expansion coefficient of metals based on the equal volume method.

[0055] When the temperature does not change much, the linear expansion coefficient of the metal is basically fixed and very close to the standard value. When the metal sample expands due to heat, the metal rod will expand and elongate, so that the telescopic rod connected to the free end will push the syringe piston to move, thereby changing the liquid level of the capillary. The height change is Δh. The cross-sectional area of ​​the capillary is S1, and the cross-sectional area of ​​the syringe is S2. Because the capillary and the syringe are a whole, according to the principle of constant equal volume, the volume V1 of the liquid in the syringe is equal to the volume V2 of the liquid in the capillary. Because the piston end of the syringe is connected to the telescopic rod connected to the free end of the metal sample, it can be regarded as a whole. Therefore, the movement distance of the piston of the syringe is equal to the elongation of the metal sample ΔL. It can be known that:

[0056] S1×Δh=S2×ΔL (4)

[0057] Thus:

[0058]

[0059] The physical meaning of the metal linear expansion coefficient α is: when the temperature rises by 1°C, the elongation per unit length of the object is get:

[0060]

[0061] Thus:

[0062]

[0063] It can be seen from the above formula that in actual measurement, what is usually measured is the capillary liquid level change height h1 at temperature T1 and the liquid level height h2 at temperature T2, so as to calculate the liquid level height change Δh between temperatures T1 and T2, and obtain the linear expansion coefficient α.

[0064] The core of this application is the measuring module (i.e. the module composed of the capillary and the syringe), which is of great importance to the entire experimental device. The syringe in the measuring module accurately maps the change in the elongation of the metal sample to the change in the capillary liquid level according to the principle of constant volume. This mapping relationship provides a key basis for obtaining experimental data.

[0065] In order to achieve accurate acquisition of experimental data, the stable connection between the syringe and the telescopic rod connected to the free end of the metal sample is particularly critical. In the present application, an innovative connection method is adopted, that is, the piston part of the syringe is tightly bonded to the telescopic rod connected to the free end of the metal sample, thereby ensuring the stability and reliability of the two during the experiment. This connection method not only avoids the error caused by unstable connection, but also improves the accuracy of the experimental data.

[0066] During the experiment, when the metal sample expands and elongates due to the heat, the measuring module will push the piston of the syringe accordingly, thereby changing the liquid level in the capillary. This design makes the experimental phenomenon more intuitive and provides a convenient means of observation for experimenters. Experimenters can accurately record and analyze the elongation of the metal sample by observing the changes in the liquid level, thereby obtaining accurate experimental results.

[0067] In summary, the measurement module in this application provides reliable data support for the experiment through its unique structure and precise measurement mechanism. This design not only improves the accuracy and reliability of the experiment, but also provides a more intuitive and convenient means of observation for the experimenter, providing a strong guarantee for the smooth progress of the experiment. After accurately planning and designing the measurement module, the theoretical assembly diagram of the new experimental instrument was obtained, as shown in the figure below. Figure 2 shown.

[0068] See also Figure 2 The metal linear expansion coefficient measuring device provided in this embodiment includes: a capillary 1, a connecting tube 2, a syringe 3, a telescopic rod and a heating box 4.

[0069] The metal to be tested is arranged in the heating box 4; the syringe 3 is arranged horizontally; the free end of the metal to be tested is connected to one end of the telescopic rod; the other end of the telescopic rod is connected to the piston end of the syringe 3; the capillary 1 is arranged vertically; the bottom end of the capillary 1 is connected to the liquid outlet end of the syringe 3 through the connecting tube 2; the capillary 1, the connecting tube 2 and the syringe 3 are used to place liquid.

[0070] During measurement, the heating box 4 heats the metal to be measured, causing the metal to expand, and then the telescopic rod connected to the free end of the metal to be measured pushes the piston end of the syringe 3 to move, thereby pushing the liquid in the syringe 3, causing the liquid level height of the liquid in the capillary 1 to change; the change in the liquid level height of the liquid in the capillary 1 is used to calculate the linear expansion coefficient of the metal to be measured.

[0071] In another exemplary embodiment of the present application, please refer to Figure 2The metal linear expansion coefficient measuring device also includes: a metal linear expansion coefficient tester 5; the metal linear expansion coefficient tester 5 is connected to the heating box 4; the metal linear expansion coefficient tester 5 is used to control the heating box 4 to heat the metal to be tested, and display the temperature in the heating box 4 in real time.

[0072] according to Figure 2 , accurately connect the metal linear expansion coefficient tester 5 to the heating box 4. Then, in a predetermined order, connect the syringe 3, the connecting tube 2, and the capillary 1 one by one. After the entire assembly process is completed, a new experimental instrument is obtained to achieve the measurement of the metal linear expansion coefficient.

[0073] In an exemplary embodiment, the heating box 4 is a constant temperature heating box.

[0074] In an exemplary embodiment, the calculation formula of the linear expansion coefficient of the metal to be tested is:

[0075]

[0076] Among them, α represents the linear expansion coefficient of the metal to be tested; S1 represents the cross-sectional area of ​​the capillary 1; S2 represents the cross-sectional area of ​​the syringe 3; Δh represents the change in the liquid level height of the liquid in the capillary 1 from the beginning of heating to the end of heating; ΔT represents the temperature change of the metal to be tested from the beginning of heating to the end of heating; L0 represents the length of the metal to be tested when heating starts.

[0077] In another exemplary embodiment of the present application, the selection of experimental instrument materials is introduced.

[0078] This embodiment mainly selects the syringe 3 as the contact source of the counting module. The syringe 3 is a common tool, which changes the pressure inside the syringe 3 by applying pressure to the piston. The volume of the liquid in the syringe 3 is proportional to the height, so it is only necessary to determine the change in the volume of the liquid in the syringe 3 to obtain the change in the elongation of the measured metal sample. In this embodiment, the reasonable selection of the syringe 3 can minimize the influence of errors in the counting process. First, a comparative analysis is performed based on the magnification of the measured value. Through the analysis of the micrometer, it is found that the magnification of the measured value is 1000, so the magnification of the counting device of the equal volume method should also be about 1000. Therefore, the magnification of the counting device is calculated according to the principle of equal volume invariance, that is, the ratio of the cross-sectional area of ​​the syringe 3 to the capillary 1:

[0079] Therefore, the experiment in this embodiment mainly selected syringes 3 with specifications of 60 ml and 30 ml on the market, and capillaries 1 with inner diameters of 2 mm and 0.8 mm for experimental comparison.

[0080] Syringes 3 with different inner diameters of 60 ml and 30 ml were prepared respectively and combined with capillaries 1 with inner diameters of 2 mm and 0.8 mm. The inner diameters of syringes 3 with different specifications were measured in turn using a vernier caliper, and the average value of multiple measured values ​​was taken as the inner diameter of the syringe 3. The measurement results are shown in Tables 3 and 4.

[0081] Table 3 60ml syringe inner diameter measurement data

[0082] frequency 1 2 3 4 5 average value Syringe inner diameter / mm 15.5 15.5 15.5 15.2 15.6 15.4

[0083] Table 4 30ml syringe inner diameter measurement data

[0084] frequency 1 2 3 4 5 average value Syringe inner diameter / mm 11.8 11.7 11.7 11.7 11.8 11.7

[0085] From Table 3 and Table 4, we can get the magnification of the new experimental measuring device:

[0086] (1) When the inner diameter of syringe 3 is 15.472 mm and the inner diameter of capillary 1 is 2 mm, the measurement magnification is:

[0087] (2) When the specification of syringe 3 is 15.472 mm in inner diameter and capillary 1 is 0.8 mm in inner diameter, the measurement magnification is:

[0088] (3) When the specification of syringe 3 is 11.784 mm in inner diameter and the inner diameter of capillary 1 is 2 mm, the measurement magnification is:

[0089] (4) When the specification of syringe 3 is 11.784 mm in inner diameter and the inner diameter of capillary 1 is 0.8 mm, the measurement magnification is:

[0090] Therefore, in this embodiment, the ratio of the cross-sectional area of ​​the syringe 3 to the cross-sectional area of ​​the capillary 1 satisfies

[0091] In another exemplary embodiment of the present application, the connecting tube 2 is a glass tube or a rubber tube.

[0092] In another exemplary embodiment of the present application, please refer to Figure 2 The metal linear expansion coefficient measuring device also includes: an iron frame 6; the iron frame 6 is used to fix the capillary 1 so that the capillary 1 remains vertical.

[0093] In another exemplary embodiment of the present application, the other end of the telescopic rod is bonded to the piston end of the syringe 3 by using an adhesive.

[0094] In another exemplary embodiment of the present application, the connection between the bottom end of the capillary tube 1 and the connecting tube 2 and the connection between the connecting tube 2 and the liquid outlet end of the syringe 3 are tied and fixed by elastic ropes.

[0095] Compared with the old instrument, the metal linear expansion coefficient measuring device of this embodiment has significant advantages in demonstrating experimental phenomena. The experimental phenomena are obvious and intuitive. Compared with the old experimental instrument, the new instrument does not need to perform cumbersome micrometer zeroing steps before measurement, which greatly simplifies the experimental process. Compared with the old instrument, the new instrument sets different magnifications according to the ratio of the syringe 3 to the capillary 1. During the experiment, students can understand the influence of different magnifications on the measurement of metal linear expansion coefficient, which further increases the interest of the experiment, and can study the accuracy when the magnification of the new instrument is equal to the magnification of the old experimental instrument, adding a new direction for the transformation of the experimental instrument.

[0096] The following is a detailed introduction to the experimental methods and experimental data of the metal linear expansion coefficient measuring device in actual application.

[0097] (I) Experimental procedures.

[0098] 1) Preparation before the experiment.

[0099] (1) Sample installation. Remove the nut on the right side of the linear expansion coefficient measuring device, install the metal rod sample to be measured (copper, iron, or aluminum rod) into the heating tube, and tighten the nut.

[0100] (2) Air tightness test of the measuring module. Check whether the piston end of the syringe 3 is in good contact with the free end of the metal rod sample, adjust the syringe 3 to remove excess gas inside (generally no adjustment is required), and try to avoid the influence of air pressure on the syringe 3. Place the capillary 1 vertically and connect it to the syringe 3 through a rubber tube and tie the connection tightly with an elastic rope. Observe and test whether the air tightness of the connection is good.

[0101] (3) Installation of the measuring module. Fill the syringe 3 with water dyed with ink, place the capillary 1 vertically and connect it to the syringe 3 through a rubber tube, and connect the piston end of the syringe 3 to the free end of the metal rod sample.

[0102] (4) Adjustment of the measuring module. Install the connected capillary 1 on the iron stand 6, use a plumb line to adjust the capillary 1 and the iron stand 6 to remain vertical, and observe that the liquid column in the capillary 1 does not drop, that is, the piston end of the syringe 3 is in good contact with the telescopic rod connected to the free end of the metal rod sample.

[0103] (5) Wire connection. Use No. 2 wire to connect the Pt100 output (the socket on the right side of the metal protective cover) to the Pt100 input socket on the test instrument panel. Connect the heating power line (on the right side of the instrument base) to the heating output on the panel of the metal linear expansion coefficient tester 5. Among them, the constant temperature heating box has a good insulation layer and will not have a significant impact on the external environment.

[0104] 2) Determine the linear expansion coefficient of metal samples.

[0105] (1) Turn on the power switch on the rear panel of the tester, and the PID intelligent temperature regulator display window lights up. The green numbers show the set maximum temperature SV, and the red numbers show the temperature of the metal rod. Set SV = 95.0°C. During the experiment, first check whether the maximum temperature SV displayed by the tester matches the set temperature. If so, record the initial scale value of capillary 1 at room temperature.

[0106] (2) Preheat the metal sample by turning on the heating switch to heat the metal sample. After heating to the highest temperature, turn off the heating switch and wait for the metal sample to cool naturally to room temperature.

[0107] (3) Turn on the heating switch again, the temperature of the metal rod sample begins to rise, and the liquid level in capillary 1 begins to rise slowly after stabilizing. Record the liquid level readings h when the metal rod sample temperature is T = 40°C, 45°C, 50°C, ..., 85°C in Table 5.

[0108] (4) When the temperature of the metal rod sample T>85°C (PV>85°C), turn off the heating switch and stop heating the metal rod sample. Since the piston of the syringe 3 does not have a rebound function, the present application does not consider the measurement of the metal linear expansion coefficient under cooling conditions.

[0109] (5) Replace the syringe 3 and the capillary 1 in sequence, repeat the above steps, and record the experimental data in Tables 6, 7 and 8.

[0110] (6) After the experiment, restore the instrument to its original state.

[0111] (7) It is known that the original length of the metal rod at room temperature is 370 mm. Based on the above data, the linear expansion coefficient α of iron, copper and aluminum under the heating mode is calculated by formula (7). Then find the reference value of the linear expansion coefficient of iron, copper and aluminum at 20-100℃, and calculate the absolute error and relative error.

[0112] (II) Experimental data and analysis

[0113] 1) Experimental data recording.

[0114] Through the above experimental steps, the measuring devices composed of capillaries 1 and syringes 3 of different specifications are tested in turn, and the experimental data are recorded in the following table in turn:

[0115] Table 5: Liquid column height measurement table when heating metal rod (when the magnification of the measuring device is 139)

[0116]

[0117]

[0118] Table 6 Liquid column height measurement table when heating metal rod (when the magnification of the measuring device is 239)

[0119]

[0120] Table 7 Liquid column height measurement table when heating metal rod (when the magnification of the measuring device is 869)

[0121]

[0122] Table 8 Liquid column height measurement table when heating metal rod (when the magnification of the measuring device is 1496)

[0123]

[0124]

[0125] 2) Data processing.

[0126] (1) From the data recorded in Table 5, it can be obtained that when the metal sample is continuously heated under the measuring module with a magnification of 139, the data corresponding to the change Δh of the liquid level height of the capillary tube 1 at every 5°C interval is shown in Table 9.

[0127] Table 9 Experimental data corresponding to the measuring device with a magnification of 139

[0128]

[0129] The measurement results in Table 9 were imported into orgin software, with temperature change as the horizontal coordinate and metal elongation change as the vertical coordinate. Formula (7) was converted into the form of y = a + b × x for linear fitting. According to the fitting results, the correlation coefficients of the linear expansion coefficients of iron, copper and aluminum were 0.99933, 0.99642 and 0.99995 respectively, and the slopes of the fitting curves were K 铁 =0.834, K 铜 =1.113, K 铝 =1.315, the fitting curve is as follows Figure 3 shown.

[0130] According to the linear fitting function formula: y = a + b × x, b = k, and combined with formula (7), we can get:

[0131]

[0132] It is known that the length of the metal rod sample at room temperature is L0 = 370 mm, so Figure 3 The linear expansion coefficients α of iron, copper and aluminum bars can be calculated as follows:

[0133] According to the calculation formula of absolute error and relative error, we can get:

[0134] ① The reference value of sample (iron) at 20~100℃ is 11.7×10 －6 ℃ －1 , the measured value is 16.23×10 －6 ℃ －1 , thus we can get:

[0135] ② The reference value of sample (copper) at 20~100℃ is 16.6×10 －6 ℃ －1 , the measured value is 21.66×10 －6 ℃ －1 , thus we can get:

[0136] ③ The reference value of sample (aluminum) at 20~100℃ is 23×10 －6 ℃ －1 , the measured value is 25.59×10 －6 ℃ －1 , thus we can get:

[0137] After calculating the measurement results and recognized value of aluminum in the three metals, 23×10 －6 ℃ －1 Compared with the smaller errors, the relative errors of iron and copper are both above 25%, which is a large relative error. This shows that the accuracy of the experimental measurement device is too low and is not suitable for classroom experiments.

[0138] (2) From the data recorded in Table 6, it can be obtained that when the measuring module with a magnification of 239 continuously heats the metal sample, the data corresponding to the change Δh of the liquid level height of the capillary tube 1 at every 5°C interval is shown in Table 10.

[0139] Table 10 Experimental data corresponding to the measuring device with a magnification of 239

[0140]

[0141] The measurement results in Table 10 were imported into orgin software, with temperature change as the horizontal coordinate and metal elongation change as the vertical coordinate. Formula (7) was converted into the form of y = a + b × x for linear fitting. According to the fitting results, the correlation coefficients of the linear expansion coefficients of iron, copper and aluminum were 0.9957, 0.99809 and 0.99568 respectively, and the slopes of the fitting curves were K 铁 =1.259, K 铜 =1.768, K 铝 =2.243, the fitting curve is as follows Figure 4 shown.

[0142] According to the linear fitting function formula: y = a + b × x, b = k,

[0143] Combining formula (7) with the above formula, we can get:

[0144]

[0145] It is known that the length of the metal rod sample at room temperature is L0 = 370 mm, so Figure 4 The linear expansion coefficients α of iron, copper and aluminum bars can be calculated as follows:

[0146] Through the above fitting data, we can get:

[0147] ① The reference value of sample (iron) at 20~100℃ is 11.7×10 －6 ℃ －1 , the measured value is 14.42×10 －6 ℃ －1 , thus we can get:

[0148] ② The reference value of sample (copper) at 20~100℃ is 16.6×10 －6 ℃ －1 , the measured value is 19.96×10 －6 ℃ －1 , thus we can get:

[0149] ③ The reference value of sample (aluminum) at 20~100℃ is 23×10 －6 ℃ －1 , the measured value is 25.36×10 －6 ℃ －1 , thus we can get:

[0150] (3) From the data recorded in Table 7, it can be obtained that when the measuring device is magnified to 869 and the temperature of the metal sample is continuously increased, the data corresponding to the change Δh of the liquid level in the capillary tube 1 at every 5°C interval is shown in Table 11.

[0151] Table 11 Corresponding data when the magnification of the measuring device is 869

[0152]

[0153] The measurement results in Table 11 were imported into orgin software, with temperature change as the horizontal coordinate and metal elongation change as the vertical coordinate. Formula (7) was converted into the form of y = a + b × x for linear fitting. According to the fitting results, the correlation coefficients of the linear expansion coefficients of iron, copper and aluminum were 0.99845, 0.9981 and 0.9947 respectively, and the slopes of the fitting curves were K 铁 =3.407, K 铜 =5.578, K 铝 =7.956, the fitting curve is as follows Figure 5 shown.

[0154] According to the linear fitting function formula: y = a + b × x, b = k, and combined with formula (7), we can get:

[0155]

[0156] It is known that the length of the metal rod sample at room temperature is L0 = 370 mm, so the linear expansion coefficients α of iron, copper and aluminum rods can be calculated from 5:

[0157] Through the above fitting data, we can get:

[0158] ① The reference value of sample (iron) at 20~100℃ is 11.7×10 －6 ℃ －1 , the measured value is 10.26×10 －6 ℃ －1 , thus we can get:

[0159] ② The reference value of sample (copper) at 20~100℃ is 16.6×10 －6 ℃ -1[20～21] , the measured value is 17.37×10 －6 ℃ －1 , thus we can get:

[0160] ③ The reference value of sample (aluminum) at 20~100℃ is 23×10 －6 ℃－1[20～21] , the measured value is 24.74×10 －6 ℃ －1 , thus we can get:

[0161] After calculating the measurement results of copper in the three metals and the recognized value of 16.6×10 －6 ℃ －1 The relative error is 4.64%, which is larger than that of iron and copper. The relative errors are both around 9%, which is smaller. This shows that the experimental measurement device has higher accuracy and is more suitable for classroom experiments.

[0162] (4) From the data recorded in Table 8, it can be obtained that when the test module with a magnification of 1496 continuously heats the metal sample, the data corresponding to the change Δh of the liquid level height of the capillary tube 1 at every 5°C interval is shown in Table 12.

[0163] Table 12 Corresponding change data of the measuring device with a magnification of 1496

[0164]

[0165]

[0166] The measurement results in Table 12 were imported into orgin software, with temperature change as the horizontal coordinate and metal elongation change as the vertical coordinate. Formula (7) was converted into the form of y = a + b × x for linear fitting. According to the fitting results, the correlation coefficients of the linear expansion coefficients of iron, copper and aluminum were 0.99836, 0.99996 and 0.99795 respectively, and the slopes of the fitting curves were K 铁 =6.531, K 铜 =8.854, K 铝 =12.896, the fitting curve is as follows Figure 6 shown.

[0167] According to the linear fitting function formula: y = a + b × x, b = k, and combined with formula (7), we can get:

[0168]

[0169] It is known that the length of the metal rod sample at room temperature is L0 = 370 mm, so Figure 6 The linear expansion coefficients α of iron, copper and aluminum bars can be calculated as follows:

[0170] Through the above fitting data, we can get:

[0171] ① The reference value of sample (iron) at 20~100℃ is 11.7×10 －6 ℃ －1 , the measured value is 12.07×10 －6 ℃ －1 , thus we can get:

[0172] ② The reference value of sample (copper) at 20~100℃ is 16.6×10 －6 ℃ －1 , the measured value is 15.99×10 －6 ℃ －1 , thus we can get:

[0173] ③ The reference value of sample (aluminum) at 20~100℃ is 23×10 －6 ℃ －1 , the measured value is 23.29×10 －6 ℃ －1 , thus we can get:

[0174] After calculation, the measurement results of the three metals have smaller errors than the recognized values, and the relative error ratio is about 3%, indicating that the experimental measurement device has high accuracy, stable measurement results and meets the design requirements.

[0175] Combining the above data with Excel, we can get the relative error analysis diagram of the linear expansion coefficients of three metals, iron, copper and aluminum, measured under different magnifications of measuring devices, such as Figure 7 As shown. Figure 7 The analysis shows that the experimental data error of the metal measured by the measuring device with a magnification of 1496 is the smallest, and the experimental results are the most accurate. Through comparative analysis, it is found that when the ratio of the cross-sectional area of ​​the capillary 1 to the syringe 3, that is, the larger the magnification, the higher the measurement accuracy and the more stable the measured data, that is, the new experimental method has the lowest relative error in the measurement value of the linear expansion coefficient of metal copper, and the measurement results are relatively stable.

[0176] In this embodiment, the ratio of the cross-sectional area of ​​the syringe 3 to the cross-sectional area of ​​the capillary 1 is 1496.

[0177] The following is a comparative analysis of the experiments based on the equal volume method and the micrometer method for measuring the linear expansion coefficient of metals.

[0178] By using the newly designed experimental instrument to measure the linear expansion coefficient of metals, and comparing the experimental results with those obtained with the old instrument, it was shown that the new instrument exhibited more stable performance in terms of the relative error of the measurement results and had significant advantages.

[0179] (1) Comparative analysis based on experimental measurement results. Through the measured experimental data, it was found that when the micrometer method was used to measure the linear expansion coefficient of metallic copper, its measurement results showed large fluctuations and a significant relative error. Relatively speaking, the relative error of the measured value using the equal volume method was more stable, and the error ratio was roughly maintained at around 3%, which to a certain extent enhanced the credibility of the experimental data. From the perspective of measurement accuracy, the equal volume method showed a slight advantage over the micrometer method and was more conducive to improving the accuracy of experimental measurements.

[0180] (2) Comparison from the operation of the measuring instruments. By comparing the data collection process of the two methods, it is found that the new instrument is more simple and practical than the old instrument. The data measurement of the old experiment depends on the rotation of the micrometer. However, under the condition of temperature fluctuation, the rotation speed of the micrometer dial is too fast, which makes it difficult to accurately record the data, thus causing certain experimental errors. In contrast, the new experiment is measured by observing the change of the liquid level in the capillary 1. This method not only makes the experimental phenomenon more intuitive, but also adds interest to the experimental process. After in-depth analysis of the operation process, when the old instrument measures data, the zeroing and fixing process of the micrometer must strictly comply with the operating specifications, and the skill differences of different operators may lead to errors in the measurement results. The new instrument effectively avoids this problem, and its measurement principle is based on the transfer of liquid. As long as the capillary 1 is placed vertically and the syringe 3 is tightly attached to the free end and kept horizontal, the change in the elongation of the metal sample after thermal expansion can be intuitively observed.

[0181] In summary, the improvement of the present application not only improves the accuracy of the experiment, but also effectively stimulates students' interest and enthusiasm in the experiment. The new instrument of the present application meets the expected design requirements in practical applications and shows good use effects.

[0182] The following is an analysis of the experimental error in measuring the linear expansion coefficient of metals based on the equal volume method.

[0183] After an in-depth analysis of the experimental operation and measurement results of the new instrument, it was found that the measured values ​​of the metal wire expansion coefficient had relatively large errors. The following possible sources of error were summarized:

[0184] (1) Instrument placement problem. During the experiment, if the syringe 3 is not kept absolutely horizontal, the piston may be affected by unnecessary friction when it is pushed. This friction will interfere with the actual measurement value of the metal wire expansion system, thereby increasing the error.

[0185] (2) Reading error. If the reading of experimental data is not accurate, it will directly lead to calculation errors in the subsequent data processing. This error will further affect the accuracy of the measured value of the metal wire expansion coefficient.

[0186] (3) Problem with connecting tube 2. If the connecting tube 2 used in the experiment is slightly longer, it may affect the transfer of liquid between the syringe 3 and the capillary 1. In addition, the connecting tube 2 will be deformed by the liquid force during the experiment. This influence will interfere with the stability of the experimental process and increase the error of the measured value of the metal wire expansion system.

[0187] (4) The gravity of the liquid itself. As the liquid continues to rise, its gravity continues to increase, which has a certain hindering effect on the liquid's rise.

[0188] In order to ensure the accuracy of the experimental results, it is recommended to carefully check and optimize the above aspects when measuring the metal wire expansion system.

[0189] The measurement of the linear expansion coefficient of metals occupies a pivotal position. As an important part of thermodynamic experiments, its experimental results are of great significance for understanding the thermal properties of metal materials. The linear expansion coefficient not only plays a key role in academic research, but also occupies an important position in practical applications. In the fields of metal heat measurement, automobile engine water temperature control, and industrial production automation control, the linear expansion coefficient of metals plays a key role. Therefore, the precise measurement and research of the linear expansion coefficient of metals has a far-reaching impact on promoting the development of related industries and improving the quality of production and life.

[0190] This application first conducts a comprehensive and in-depth theoretical exploration and experimental research on the experimental instruments for measuring the linear expansion coefficient of metals in the laboratory. Through a detailed analysis of the measurement principle, the scientific basis for experimental measurement of the linear expansion coefficient of metals is also explored in depth. At the same time, the overall hardware layout of the experimental device and the functions of key components are systematically introduced, providing experimental personnel with a clear and stable understanding of the hardware structure. On the basis of the original experimental instruments in the laboratory, a new set of experimental instruments was designed using components such as capillary 1, connecting tube 2, and syringe 3, and the measuring device was improved. The measurement module was designed using the equal volume method as the main working principle. The change in the liquid level of capillary 1 is used as a medium to deduce the change in the elongation of the metal. The designed measurement modules were assembled and integrated to obtain a new set of experimental instruments. The new experimental instruments were used for experiments, and the results showed that the accuracy of the experimental measurement increased with the increase in the magnification of the measurement device. When the magnification was 1496, the measurement results of the linear expansion coefficients of iron, copper, and aluminum were 12.07×10 -6 ℃ -1 , 16.05×10 -6 ℃ -1, 23.29×10 -6 ℃ -1 The relative errors are 3.16%, 3.31%, and 1.26%. The linear expansion coefficients of iron, copper, and aluminum were 11.08×10 -6 ℃ -1 , 15.86×10 -6 ℃ -1 , 22.32×10 -6 ℃ -1 , the relative errors are 3.73%, 4.46%, and 2.96%. Then the results of the two experimental methods are compared. The relative error of the linear expansion coefficient of metals measured by the new instrument is smaller, and the relative errors of the linear expansion coefficient measurement values ​​of the three metal samples are more stable, indicating that the new instrument has higher accuracy and more accurate measurement results.

[0191] After careful experimental observation, the new instrument has significant advantages in displaying experimental phenomena, and its performance is obvious and intuitive. At the same time, the new instrument is relatively tolerant of the operator's skill requirements, and no longer has strict requirements on the operator's fine movements like the old instrument. It is particularly worth mentioning that the new instrument does not need to perform cumbersome micrometer zeroing steps before measurement, which greatly simplifies the experimental process. The combined design of the capillary 1 and the syringe 3 in the new instrument optimizes the link that requires precise zeroing in the old experiment, effectively eliminates the errors caused by improper zeroing operation, and further improves the accuracy and reliability of the experiment.

[0192] The metal linear expansion coefficient measuring device of this application also has room for optimization. Through the use of experimental instruments and analysis of the data measurement process, subsequent researchers can expand and improve it in the following aspects:

[0193] (1) After each measurement of experimental data, the piston of the syringe 3 needs to be readjusted to be in close contact with the telescopic rod connected to the free end of the metal sample. Subsequent researchers can add a device that can make the two fit tightly together.

[0194] (2) If the capillary 1 needs to be vertically processed after the experimental position is changed, the entire adjustment process also has room for optimization. It is hoped that subsequent researchers can design a device to vertically fix the capillary 1 so that the capillary 1 can remain vertical, thereby minimizing the experimental error.

[0195] (3) The improved design of the measuring device used many instruments, including capillary 1, connecting tube 2, and syringe 3. It would be better if all the instruments could be combined into one instrument using relevant tools. It is hoped that subsequent researchers can conduct improved design research on these issues during their research.

[0196] Based on the same inventive concept, the embodiment of the present application also provides a method for measuring the linear expansion coefficient of a metal using the above-mentioned device for measuring the linear expansion coefficient of a metal. The implementation scheme for solving the problem provided by the method is similar to the implementation scheme recorded in the above-mentioned device, so the specific limitations in one or more embodiments of the method for measuring the linear expansion coefficient of a metal provided below can refer to the limitations of the device for measuring the linear expansion coefficient of a metal above, and will not be repeated here.

[0197] In an exemplary embodiment, a method for measuring the linear expansion coefficient of a metal is provided, comprising: controlling a heating box 4 to heat the metal to be measured; recording a change in the liquid level of the liquid in the capillary 1 during the heating process; and calculating the linear expansion coefficient of the metal to be measured based on the change in the liquid level of the liquid in the capillary 1.

[0198] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0199] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A device for measuring a metal linear expansion coefficient, characterized in that: The metal linear expansion coefficient measuring device comprises: a capillary tube, a connecting tube, a syringe, a telescopic rod and a heating box; The metal to be tested is arranged in the heating box; the syringe is arranged horizontally; the free end of the metal to be tested is connected to one end of the telescopic rod; the other end of the telescopic rod is connected to the piston end of the syringe; the capillary is arranged vertically; the bottom end of the capillary is connected to the liquid outlet end of the syringe through the connecting tube; the capillary, the connecting tube and the syringe are used to place liquid; During measurement, the heating box heats the metal to be measured, causing the metal to expand, thereby causing the telescopic rod connected to the free end of the metal to be measured to push the piston end of the syringe to move, thereby pushing the liquid in the syringe, causing the liquid level height of the liquid in the capillary tube to change; the change in the liquid level height of the liquid in the capillary tube is used to calculate the linear expansion coefficient of the metal to be measured.

2. The metal linear expansion coefficient measuring device according to claim 1, characterized in that: The calculation formula of the linear expansion coefficient of the metal to be tested is: Among them, α represents the linear expansion coefficient of the metal to be tested; S1 represents the cross-sectional area of ​​the capillary; S2 represents the cross-sectional area of ​​the syringe; Δh represents the change in the liquid level in the capillary from the beginning to the end of heating; ΔT represents the change in temperature of the metal to be tested from the beginning to the end of heating; L0 represents the length of the metal to be tested when heating starts.

3. The metal linear expansion coefficient measuring device according to claim 2, characterized in that: The ratio of the cross-sectional area of ​​the syringe to the cross-sectional area of ​​the capillary satisfies 4. The metal linear expansion coefficient measuring device according to claim 3, characterized in that: The ratio of the cross-sectional area of ​​the syringe to the cross-sectional area of ​​the capillary is 1496.

5. The metal linear expansion coefficient measuring device according to claim 1, characterized in that: The metal linear expansion coefficient measuring device also includes: a metal linear expansion coefficient tester; the metal linear expansion coefficient tester is connected to the heating box; the metal linear expansion coefficient tester is used to control the heating box to heat the metal to be tested, and display the temperature in the heating box in real time.

6. The metal linear expansion coefficient measuring device according to claim 1, characterized in that: The connecting tube is a glass tube or a rubber tube.

7. The metal linear expansion coefficient measuring device according to claim 1, characterized in that: The metal linear expansion coefficient measuring device also includes: an iron frame; The iron frame is used to fix the capillary so that the capillary remains vertical.

8. The metal linear expansion coefficient measuring device according to claim 1, characterized in that: The other end of the telescopic rod is bonded to the piston end of the syringe by using an adhesive.

9. The metal linear expansion coefficient measuring device according to claim 1, characterized in that: The connection between the bottom end of the capillary tube and the connecting tube and the connection between the connecting tube and the liquid outlet end of the syringe are tied and fixed by elastic ropes.

10. A method for measuring a metal linear expansion coefficient, characterized in that: The metal linear expansion coefficient measuring method is implemented by using the metal linear expansion coefficient measuring device according to any one of claims 1 to 9, and the metal linear expansion coefficient measuring method comprises: Control the heating box to heat the metal to be tested; Record the change in the liquid level in the capillary during the heating process; The linear expansion coefficient of the metal to be tested is calculated based on the change in the liquid level in the capillary tube.

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