A precise method for measuring the density of irregular objects

Abstract

This invention relates to the field of mechanical metrology, specifically a precise method for measuring the density of irregular objects, which can also be used to measure the volume of irregular objects. From an operational and calculation perspective, this method has low requirements for the measured object, and the operation and calculation are simple. From the measurement results, the reading accuracy is high. Based on the cosecant relationship in triangles, a transparent spiral ruler is innovatively used to subdivide a certain unit length during the measurement process; the spiral angle of the transparent spiral ruler is kept as small as possible; the smaller the spiral angle, the higher the reading accuracy. This invention is rationally designed, employing a measurement method using a transparent spiral ruler to subdivide the length of liquid level changes using trigonometric relationships, achieving precise, efficient, multi-field, and multi-functional measurement of the density of irregular objects, and has significant practical application value.

Description

Technical Field

[0001] This invention relates to the field of mechanical metrology, specifically to a precise method for measuring the density of irregular objects, which can also be used to measure the volume of irregular objects. Background Technology

[0002] Density, as a fundamental property of matter, is widely used in scientific experiments, industrial production, and musical instrument manufacturing. For example, in scientific experiments, many physical and chemical studies rely on precise numerical values ​​of material density; in industrial production, factories need to judge the quality of raw materials based on density; and in musical instrument manufacturing, makers can select materials of different densities to adjust the instrument's tone, making material density measurement far more important than volume measurement. Importantly, in these fields, the density measurement of irregular objects still faces challenges such as high cost, operational difficulties, and low accuracy, which urgently need to be addressed.

[0003] When measuring the density of irregular objects, the measurer typically develops different measurement plans, adopts different measurement methods, and selects different measuring tools based on the characteristics of the object being measured. There are two common methods for measuring the density of irregular objects: one using a liquid medium and the other using a solid medium. Specifically, liquid-medium methods are based on Archimedes' principle and can be divided into five types: the displacement method, the counterweight / compression method, the overflow method, and the buoyancy method. The second type uses a solid medium, which is often used to measure the density of solids that are easily soluble in water, and usually involves using small particles such as fine sand. However, both of these methods can only determine approximate data on the density of irregular objects and cannot achieve precise density measurements.

[0004] There are six existing patent applications for measuring the density of general-purpose objects: CN201410146255.9 "Rock Density Measurement Method and Rock Density Measurement Device", CN201480072718.X "Density Measurement Equipment", CN201580061229.9 "Density Measurement System and Method", CN201610591000.2 "A Density Measurement Method Based on the Magnetic Archimedes Principle", CN202010779626.2 "A Physics Teaching Experiment Demonstration System"; and CN202111677185.6 "A Method for Measuring Dual-Weighing Volume and Density". There is one patent application for measuring the density of irregular objects: CN201420624644.3 "Apparatus for Indirectly Determining the Density of Irregular Objects". A comprehensive analysis of the specific content of the above patents reveals that the patents related to the measurement of object density suffer from problems such as high cost, inconvenient operation, or many interfering factors. Furthermore, the measurement of the density of irregular objects focuses primarily on exploring measurement methods, with very little attention paid to improving measurement accuracy.

[0005] In summary, the measurement of the density of irregular objects is of great significance in both basic scientific research and practical applications. However, previous methods were complex to operate and could not guarantee the accuracy of experimental results, thus making them unsuitable for the precise measurement of the density of irregular objects. There is an urgent need to invent a more efficient and accurate method for measuring the density of irregular objects. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing detection technologies and provide a precise method for measuring the density of irregular objects. This method can accurately measure the density of irregular objects while reducing interference factors.

[0007] This invention is achieved using the following technical solution:

[0008] A precise method for measuring the density of irregular objects mainly includes four parts: mass measurement of the irregular object being measured, waterproofing treatment, volume calculation, and density derivation.

[0009] Mass measurement involves placing the irregular object to be measured on a mass measuring instrument, measuring and recording its mass.

[0010] To ensure the accuracy of the measurement results, waterproofing treatment is performed on the non-waterproof irregular object being measured. Specifically, rosin powder and alcohol are mixed in a certain proportion and stirred thoroughly until a viscous consistency is reached. This mixture is then evenly and lightly brushed onto the surface of the irregular object being measured and allowed to air dry.

[0011] Volume calculation consists of two parts: data acquisition and data processing. First, the required data is acquired: First, a vertical ruler and a transparent spiral ruler are attached to the outer wall of the container. To improve accuracy, the spiral angle between the transparent spiral ruler and the bottom of the container should be as small as possible. Then, the vertical height of the container and the length of the transparent spiral ruler are observed and recorded. Second, a fixed amount of liquid is poured into the container, and the length of the transparent spiral ruler at the lowest point of the concave meniscus is observed and recorded at eye level. Third, if the density of the irregular object being measured is less than that of water, a solid with a density greater than that of water is needed to make the object sink. Therefore, a solid with a density greater than that of water is first placed into the container. After the liquid surface settles, the length of the transparent spiral ruler at the lowest point of the concave meniscus after the change is recorded. Finally, the container is emptied and dried, and the same volume of liquid is refilled. The irregular object being measured is fixed together with the solid with a density greater than that of water and placed into the container. After the liquid surface is balanced, the length of the transparent spiral ruler at the lowest point of the concave meniscus after the change is recorded. Second, the collected data is processed: First, the vertical height and volume of a fixed amount of liquid in the container are observed, and then the radius of the container is calculated; second, the ratio constant C of the spiral ruler length to the vertical height is calculated; finally, the volume of an irregular object must be measured before measuring its density.

[0012] Density derivation: Calculate the density of irregular objects using formulas.

[0013] The specific and precise measurement method is as follows:

[0014] Step 1, Measurement

[0015] (1) Place the object to be measured b on the mass measuring instrument, measure and record its mass m. b ;

[0016] (2) The non-extendable transparent scale c is spiraled upwards at an angle of θ and attached to the outer wall of the container a with volume scale; the smaller the angle θ between the transparent spiral scale and the bottom of the container, the higher the reading accuracy.

[0017] (3) Observe and record the vertical height h from the lower to the higher scale of container a. a and the length of the transparent spiral ruler l a ;

[0018] (4) Pour a fixed amount of liquid into container a, observe it from the side and record the lowest point of the concave meniscus as l1 on the transparent spiral ruler.

[0019] (5) When the density of the irregular object b being measured is greater than that of the liquid, the irregular object b being measured is placed in container a. After the liquid settles, the lowest point of the concave liquid surface is recorded as l4 on the spiral ruler scale.

[0020] (6) When the density of the irregular object b being measured is less than that of the liquid, it is necessary to use a solid d with a density greater than that of the liquid so that the irregular object being measured can sink into the liquid. Therefore, the solid d is measured first. The solid d is placed in container a. After the liquid stops, the lowest point of the concave liquid surface is recorded as l2.

[0021] After emptying and drying container a, refill it with the same volume of liquid as before;

[0022] The irregular object b to be measured is fixed together with the solid d and placed in container a. After the liquid settles, the lowest point of the concave meniscus is recorded as l3 on the spiral ruler.

[0023] Step 2, Calculation

[0024] Assume the radius of the experimental container is r. a Given that the vertical height between the lower and higher scale points in container a is h. a The volume is V a ;

[0025] Volume Va = πr a 2 ×h a

[0026] Then the radius of container a

[0027] Due to the length l of the transparent spiral ruler between the low and high scales of container a a and vertical height h a The ratio is a constant, denoted as C;

[0028]

[0029] For an irregular object b with a density greater than that of a liquid, the change in vertical height after the irregular object b sinks into the liquid is Δh, and the corresponding change in the length of the spiral ruler is Δl, where Δl = l4 - l1.

[0030] For an irregular object b with a density less than that of a liquid, after being placed in container a, the vertical height change of the irregular object b and the solid d after sinking into the liquid is Δh, and the corresponding change in the length of the spiral ruler is Δl, where Δl = l3 - l2.

[0031]

[0032] V b =πr 2 ×Δh

[0033]

[0034] More preferably, the lower-order scale is the smallest integer scale, and the higher-order scale is the largest range scale.

[0035] More preferably, the included angle θ is 5° to 15°.

[0036] The principle of this measurement method is as follows:

[0037] First, under the condition that the diameter of the graduated cylinder remains constant, the volume change caused by placing the object being measured inside can be simplified to the change in the height of the volume inside the graduated cylinder, expressed as V = πr. 2 Δh.

[0038] Second, with the base area (radius) of the cylinder constant, the sensitivity relationship between changes in liquid level and volume changes is as follows:

[0039] Third, the sensitivity relationship between changes in the base area (radius) of the cylinder and changes in the liquid level and radius: The smaller the radius of the graduated cylinder, the more sensitive the liquid level is to changes in volume.

[0040] Fourth, by using the unit change in liquid level (D) as the lead around the graduated cylinder spiral, the sensitivity of the reading is improved, increasing the reading sensitivity by a factor of cscθ. 螺旋 =Dcscθ, where the helix angle is θ.

[0041] The technical solution provided by this invention has the following advantages compared with the prior art:

[0042] (1) From the perspective of operation and calculation process, this measurement method has low requirements for the measurement object and is easy to operate and calculate during the measurement process.

[0043] (2) The measurement results show high accuracy. There are two key points: ① Based on the cosecant relationship in the triangle, a transparent spiral ruler is innovatively used to subdivide a certain unit length during the measurement process; ② The spiral angle of the transparent spiral ruler is as small as possible. The smaller the spiral angle, the higher the reading accuracy.

[0044] This invention is rationally designed and uses a transparent spiral ruler winding measurement method to subdivide the liquid level height change into length using trigonometric relationships. This enables accurate, efficient, multi-field, and multi-functional measurement of the density of irregular objects, and has great practical application value. Attached Figure Description

[0045] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This diagram illustrates the experimental process of the method of the present invention.

[0048] Figure 2 This diagram illustrates the angle (helix angle) between the transparent spiral ruler and the bottom surface of the container in the method of this invention. Detailed Implementation

[0049] To better understand the above-mentioned objectives, features, and advantages of the present invention, the solutions of the present invention will be further described below. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.

[0050] Many specific details are set forth in the following description in order to provide a full understanding of the invention, but the invention may also be practiced in other ways different from those described herein; obviously, the embodiments in the specification are only some embodiments of the invention, and not all embodiments.

[0051] The specific embodiments of the invention will now be described in detail with reference to the accompanying drawings.

[0052] A precise method for measuring the density of irregular objects is as follows:

[0053] Step 1, Measurement

[0054] (1) Place the object to be measured b on the mass measuring instrument, measure and record its mass m. b .

[0055] (2) If the object being tested is not waterproof, it needs to be waterproofed with alcohol and rosin.

[0056] (3) The non-stretchable transparent scale c is spirally attached to the outer wall of the container a with volume scale at a winding angle of θ. When attaching the transparent spiral scale, the angle θ (spiral angle) between it and the bottom of the container should be as small as possible. The smaller the spiral angle, the higher the reading accuracy.

[0057] (4) Observe and record the vertical height h from the lower to the higher scale of container a. a and the length of the transparent spiral ruler l a ;

[0058] Here, the lower-order scale is generally the smallest integer scale of container a, and the higher-order scale is generally the largest range scale.

[0059] (5) Pour a measured amount of liquid into container a with a transparent spiral ruler attached, observe at eye level and record the lowest point of the concave liquid surface as l1 on the transparent spiral ruler.

[0060] (6) When the density of the irregular object b being measured is greater than that of the liquid, the irregular object b being measured is placed in container a. After the liquid settles, the lowest point of the concave liquid surface is recorded as l4 on the spiral ruler scale.

[0061] (7) When the density of the irregular object b being measured is less than that of the liquid, it is necessary to use a solid d with a density greater than that of the liquid so that the irregular object being measured can sink into the liquid. Therefore, the solid d is measured first. The solid d is placed in container a. After the liquid stops, the lowest point of the concave liquid surface is recorded as l2.

[0062] After emptying and drying container a, refill it with the same volume of liquid as before;

[0063] The irregular object b to be measured is fixed together with the solid d and placed in container a. After the liquid settles, the lowest point of the concave meniscus is recorded as l3 on the spiral ruler.

[0064] Step 2, Calculation

[0065] Assume the radius of the experimental container is r. a Given that the vertical height between the lower and higher scale points in container a is h. a Volume Va ;

[0066] Container volume Va = πr a 2 ×h a

[0067] Then the radius of container a

[0068] Assume the winding angle of the transparent scale c in this experiment is θ. When the volume of liquid in the container is constant, the ratio of the length of the spiral scale at the lowest point of the concave meniscus to its vertical height is a constant. This constant is also the smallest factor by which the method of this invention can improve the accuracy of density ρ measurement. This method denotes it as C.

[0069] In this method, the vertical height between the lower and higher scales of container a is h. a The transparent spiral ruler has a length of l a ;

[0070]

[0071] For an irregular object b with a density greater than that of a liquid, the change in vertical height after the irregular object b sinks into the liquid is Δh, and the corresponding change in the length of the spiral ruler is Δl, where Δl = l4 - l1.

[0072] For an irregular object b with a density less than that of a liquid, after being placed in container a, the vertical height change of the irregular object b and the solid d after sinking into the liquid is Δh, and the corresponding change in the length of the spiral ruler is Δl, where Δl = l3 - l2.

[0073]

[0074] V b =πr 2 ×Δh

[0075]

[0076] Example 1

[0077] A precise method for measuring the density of an irregular object (piano bridge) is as follows:

[0078] Step 1, Measurement

[0079] (1) In this embodiment, the test object is a 1 / 4-inch wooden violin bridge (also known as a "bridge"). The bridge is 34mm long, 24mm wide, and 4.5mm thick, and has through holes. The function of the violin bridge is to transmit the vibration of the strings to the violin body, causing it to resonate and produce sound. It is known as the "heart" of the violin. The length, width, thickness, and wood density of the bridge all affect the overtone frequency, volume, and timbre of the violin.

[0080] (2) In this embodiment, a graduated cylinder with a volume of 100±0.5ml was selected for measurement. The graduated cylinder used in this measurement was manufactured by Synthware, and its accuracy meets the requirements of international standards such as GB, ISO, ASTM, and DIN.

[0081] (3) Measure the mass of the piano bridge using an electronic scale: Place the piano bridge on the electronic scale, weigh it, and record the scale reading (m). b It is 1.17g.

[0082] (4) Waterproof the bridge to prevent it from getting wet and affecting the experimental results. Mix rosin powder and 98% industrial alcohol in a 3:2 ratio and stir thoroughly until it becomes viscous. Apply the mixture evenly and lightly to the surface of the bridge with a brush and allow it to air dry naturally.

[0083] (5) Attach the non-stretchable transparent ruler spirally upwards to the outer wall of the graduated cylinder. When attaching the transparent ruler, the spiral angle should be as small as possible; the smaller the spiral angle, the higher the reading accuracy. In this embodiment, the transparent ruler is 250cm long and 1cm wide. When attaching, the angle between the transparent ruler and the bottom surface of the graduated cylinder is 10°. Because the bottom wall of the graduated cylinder is curved, to reduce experimental error, the 0cm mark on the spiral ruler is attached starting from the 10ml mark on the graduated cylinder.

[0084] (6) Observe and record the length l of the spiral gauge from the 10ml to the 100ml mark on the graduated cylinder. 90ml It is 166.9cm.

[0085] (7) Observe and record the vertical height h from the 10ml to 100ml mark on the graduated cylinder. 90ml It measures 17.22 cm.

[0086] (8) Pour water into the graduated cylinder to the 20ml mark (with your line of sight level with the lowest point of the concave meniscus). After the liquid surface has settled, record the length l of the spiral ruler at the lowest point of the concave meniscus. 20ml It is 18.5cm.

[0087] (9) Use a waterproof thin thread (to prevent water from splashing out and affecting the experimental results) to slowly put the magnet into 20ml of water, observe and record the changes in the liquid level, and find that the horizontal level becomes 22ml, and the length l2 of the spiral ruler at the lowest point of the concave liquid surface is 22.2cm.

[0088] (10) Pour out the water and magnet from the measuring cylinder and refill with 20ml of water.

[0089] (11) To prevent the bridge from floating on the liquid surface, the bridge was clamped between the magnets and slowly lowered into 20ml of water with a thin thread. After the liquid surface came to rest, the changes in the liquid level were observed and recorded. It was found that the horizontal level rose to the 24ml mark on the graduated cylinder, and the lowest point of the concave liquid surface, the spiral ruler mark l3, was 25.9cm.

[0090] Step 2, Calculation

[0091] (1) In this experiment, since the radius of the graduated cylinder is fixed, πr 2 It is a constant.

[0092] The vertical height h from the 10ml to 100ml mark on the graduated cylinder 90ml It measures 17.22 cm.

[0093] V = πr 2 ×h

[0094]

[0095] The radius of the graduated cylinder is approximately 1.2898 cm.

[0096] πr 2 =3.14159 × 1.2898 2 ≈5.226

[0097] (2) In this embodiment, the winding angle of the transparent spiral ruler is θ = 10°. When the volume of liquid in the measuring cylinder is constant, the ratio of its spiral ruler length to its vertical height is a constant, which is also the factor by which this method can improve the accuracy of density measurement.

[0098] h 90ml =17.22cm

[0099] l 90ml =166.9cm

[0100]

[0101] l3 = 25.9cm

[0102] l2 = 22.2cm

[0103] Δl=l3-l2=25.9-22.2=3.7cm=37mm

[0104]

[0105] Δh≈3.818mm

[0106] V b =πr 2 ×Δh

[0107] =522.6 × 3.818

[0108] ≈1995.29mm 3

[0109] ≈1.995cm 3

[0110]

[0111] Therefore, the density of the wooden bridge for a quarter-inch violin is 0.586 g / cm³. 3 .

[0112] Two points need to be added here: first, this invention measures the average density of irregular objects; second, the accuracy of the electronic scale used to measure mass (m) affects the measurement results.

[0113] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the present invention. Although detailed descriptions have been provided with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments, and all should be covered by the protection scope of the claims.

Claims

1. A method for accurately measuring the density of an irregular object, characterized in that: Includes the following steps: Step 1, Measurement (1) Place the object to be measured b on the mass measuring instrument, measure and record its mass m. b ; (2) The non-extendable transparent scale c is spiraled upwards at an angle of θ and attached to the outer wall of the container a with volume scale; the smaller the angle θ between the transparent spiral scale and the bottom of the container, the higher the reading accuracy. (3) Observe and record the vertical height h from the lower to the higher scale of container a. a and the length of the transparent spiral ruler l a ; (4) Pour a fixed amount of liquid into container a, observe it from the side and record the lowest point of the concave meniscus as l1 on the transparent spiral ruler. (5) When the density of the irregular object b being measured is greater than that of the liquid, the irregular object b being measured is placed in container a. After the liquid settles, the lowest point of the concave liquid surface is recorded as l4 on the spiral ruler scale. (6) When the density of the irregular object b being measured is less than that of the liquid, it is necessary to use a solid d with a density greater than that of the liquid so that the irregular object being measured can sink into the liquid. Therefore, the solid d is measured first. The solid d is placed in container a. After the liquid stops, the lowest point of the concave liquid surface is recorded as l2. After emptying and drying container a, refill it with the same volume of liquid as before; Fix the irregular object b to be measured together with the solid d, put it into the container a, and after the liquid settles, record the lowest point of the concave meniscus as l3; Step 2, Calculation Assume the radius of the experimental container is r. a Given that the vertical height between the lower and higher scale points in container a is h. a The volume is V a ; Volume Va = πr a 2 ×h a Then the radius of container a Due to the length l of the transparent spiral ruler between the low and high scales of container a a and vertical height h a The ratio is a constant, denoted as C. For an irregular object b with a density greater than that of a liquid, the change in vertical height after the irregular object b sinks into the liquid is Δh, and the corresponding change in the length of the spiral ruler is Δl, where Δl = l4 - l1. For an irregular object b with a density less than that of a liquid, after being placed in container a, the vertical height change of the irregular object b and the solid d after sinking into the liquid is Δh, and the corresponding change in the length of the spiral ruler is Δl, where Δl = l3 - l2. V b =πr 2 ×Δh 2. The method for accurately measuring the density of an irregular object according to claim 1, characterized in that: If the irregular object b being tested is not waterproof, then waterproofing treatment should be performed.

3. The method for accurately measuring the density of an irregular object according to claim 2, characterized in that: Mix rosin powder and alcohol in the specified proportions and stir thoroughly until it becomes viscous. Apply the mixture evenly and lightly to the surface of the irregular object b to be tested, and then allow the irregular object b to air dry.

4. The method for accurately measuring the density of an irregular object according to claim 1, characterized in that: In step (3), the lower-order scale is the smallest integer scale, and the higher-order scale is the largest range scale.

5. The method for accurately measuring the density of an irregular object according to claim 1, characterized in that: The included angle θ is 5° to 15°.

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