Measuring dowel

Abstract

The invention relates to a measuring dowel for determining a deformation of a body having a bore, which bore has a first bore end having an at least partially conical blind hole; wherein: the measuring dowel can be arranged in the bore; the measuring dowel is formed along a longitudinal axis and has a first end and a second end along the longitudinal axis; the first end faces the blind hole in the installed state; the measuring dowel has a central region which is located between the first end and the second end of the ends; the central region has a substantially rectangular cross-section perpendicular to the longitudinal axis; the central region has four surfaces; at least one measuring element is attached to at least two of the four surfaces of the central region; each measuring element is configured to detect a deformation of the respective surface; and the first end is designed such that, upon contact with a conical blind hole, it is in annular contact with the conical region of the blind hole.

Description

Measuring dowel Technical area

[0001] Die Erfindung betrifft einen Messdübel zur Ermitt- Deformation of a body. State of the art

[0002] Messdübel erfassen eine Verformung eines Körpers. The deformation of a body is generally caused by external forces that deform the body. For example, the body can be subjected to pressure, which, in conjunction with a surface on which the pressure acts, exerts a force on the body. Forces can also act directly on the body.

[0003] Der Messdübel wird zur Erfassung der kraftinduzier-The material is introduced into a cavity in the body after deformation of the body. The cavity is usually a bore. A bore usually extends in a straight line from a surface of the body into the body. Bores are created, for example, by machining the body, such as drilling, sawing, grinding, turning, or milling. For the purposes of this description, bores also include other cavities that extend from a surface of the body into the body. Thus, cavities in the body can also be provided in casting molds for manufacturing the body.

[0004] Bekannt sind piezoelektrische Messdübel, welche in The piezoelectric measuring plug is fixed in the hole in such a way that a deformation of the surrounding material, usually a stretching or a W 64 4 K Compression of the body along the bore axis can be recorded. When the general term "deformation" is used below, this refers to either stretching or compression along the bore axis.

[0005] Ein piezoelektrischer Messdübel ist aus EP0283524A1known. The measuring dowel is inserted into a hole in a body and can determine the deformation of the body along the hole axis. The hole usually has a diameter of 50 mm to 120 mm. The hole has a blind hole, which represents the end of the hole facing away from the body surface. However, to determine the deformation of the body, it is essential that the blind hole, which usually initially has a conical end, is precisely remachined to provide a flat support surface for a first end of the measuring dowel. This is disadvantageous because, particularly in the area of ​​large machines and harsh working environments, such remachined holes are considered delicate. In harsh working environments, remachining of the hole is unusual. Furthermore, such remachining is associated with additional effort and expense.

[0006] Im piezoelektrischen Messdübel der EP0283524A1 istThe measuring dowel is disclosed based on the piezoelectric measuring principle. A piezoelectric crystal is used as the measuring element. When a force is applied, piezoelectric charges are generated, which are measured via lines connected to a charge amplifier. This places high demands on the electrical insulation of the lines and electrical connections, which are difficult to achieve, especially in harsh working environments. W 64 4 K However, with the piezoelectric measuring principle, only relatively rapid changes in forces can be determined, since even with very good insulation, charges can flow away unintentionally over time.

[0007] Unter rauen Arbeitsumgebungen wird beispielsweise This refers to environments with dust, strong vibrations, humidity, or oily or solvent-based substances. Large machines in this area include large engines, tunnel boring machines, mining equipment, etc.

[0008] Es sind auch Sensoren bekannt, welche piezoresisti-ve or strain gauge measurement technology. Here, a deformation-sensitive element is applied to a structure, and its deformation is determined. With piezoresistive or strain gauge measurement technology, the electrical resistance of the measuring element changes depending on the deformation of the structure. In order to achieve the greatest possible deformation and to keep force shunts through the structure to which the measuring element is applied negligible, the measuring element is usually applied to a particularly delicate structure, as known from EP4202391 or WO06060452A2. Although normally desirable, this has the disadvantage that the hole with the inserted measuring dowel has a different stiffness than the rest of the material surrounding the hole. The body therefore has different deformation characteristics than a body without a hole. The hole represents a weakening of the body.This is particularly undesirable in harsh working environments and / or on large machines.

[0009] Aufgabe der Erfindung ist es einen Messdübel für harsh working environments that meet the above-mentioned O W 64 4 K Another object of the invention is to provide an economical measuring dowel suitable for determining the deformation of a body with a bore. Description of the invention

[0010] Die Aufgabe wird durch die Merkmale des unabhängi- claim resolved.

[0011] Die Erfindung betrifft einen Messdübel geeignet zum Determining the deformation of a body with a bore. The bore has a first bore end with an at least partially conical blind hole. A conical blind hole is also known as a conical or tapered blind hole. Typical bores are drilled with a metal drill and, depending on the drill, have a cone angle, also called a taper angle, between 115° and 140°.

[0012] Der Messdübel ist in der Bohrung anordbar. DerThe measuring dowel is designed along a longitudinal axis and has a first end and a second end along the longitudinal axis. The first end faces the bottom hole when installed.

[0013] Der Messdübel weist einen mittleren Bereich auf, which is arranged between the first end and the second end. The central region has a largely rectangular cross-section perpendicular to the longitudinal axis. This results in a largely cuboid-shaped central region. This is advantageous because the cuboid-shaped central region is thus stably constructed from solid material and has no delicate structures. W 64 4 K

[0014] Der mittlere Bereich weist so vier Flächen auf. DieThe surfaces are arranged parallel to the respective sides of the rectangular cross-section and parallel to the longitudinal axis. The four surfaces form the outer surfaces of the cuboid-shaped central area. At least one measuring element is applied to at least two of the four surfaces. Each of the measuring elements is designed to detect a deformation of the respective surface. Due to the stable central area, the measuring anchor behaves in the borehole largely like the surrounding material of the body, so that the body exhibits only a slight change in its deformability due to the borehole.

[0015] Das erste Ende des Messdübels ist derart ausge- This means that when it comes into contact with a conical blind hole, it forms an annular contact with the conical area of ​​the blind hole. This has the advantage that the hole does not require remachining. Any deformation of the surrounding body is transferred to the measuring plug and thus to the central area through the annular contact.

[0016] Der Messdübel zeichnet sich durch eine Langzeit-measurement capability. Deformations can be measured over a long period of time, up to several hours or longer. This is not possible with piezoelectric measurement technology. Therefore, the measuring anchor uses exclusively piezoresistive measuring elements or strain gauges (DMS for short).

[0017] Weitere Vorteile und Aspekte der Erfindung sind in the embodiments disclosed. O W 64 4 K Short description of the drawings

[0018] Im Folgenden wird die Erfindung beispielhaft unter Explained in more detail with reference to the figures. They show: Fig. 1 shows a schematic view of an embodiment of a measuring anchor, Fig. 2 shows a schematic view of an embodiment of a measuring anchor arranged in a bore, Fig. 3 shows a schematic sectional view of an embodiment of a measuring anchor, Fig. 4 shows a further schematic sectional view of an embodiment of a measuring anchor, Fig. 5 shows a further schematic sectional view of an embodiment of a measuring anchor.

[0019] Gleiche Bezugszeichen bezeichnen in den Figurensame objects or features. Ways of carrying out the invention

[0020] In den Fig. 1 bis Fig. 3 ist eine erste Ausfüh- tion form of an exemplary measuring anchor 1 is shown. The same reference numerals in the figures denote the same features of the respective embodiment shown.

[0021] Fig. 1 zeigt ein Ausführungsbeispiel eines Measuring dowel 1. The measuring dowel 1 is designed along a longitudinal axis Z and has the first end 4 and the second end 6 along the longitudinal axis Z. The middle area 5 is between-O W 64 4 K between the first end 4 and the second end 6. The central region 5 has four surfaces 8, 8', 8'', 8''', of which one surface 8 is shown in plan view in Fig. 2 and two surfaces 8' and 8''' are shown perpendicular to the viewing plane. The fourth surface 8'' is arranged opposite the first surface 8 and is not visible in Fig. 1. Each surface normal that is perpendicular to the respective surface 8, 8', 8'', 8''' is also largely perpendicular to the longitudinal axis Z.

[0022] In der figürlich dargestellten Ausführungsform istA measuring element 9, 9', 9'', 9''' is applied to each of the four surfaces 8, 8', 8'', 8''' of the central region 5. Each measuring element 9, 9', 9'', 9''' is configured to determine a deformation of the respective surface 8, 8', 8'', 8'''.

[0023] Das Messelement 9,9’,9’’,9’’’ ist auf der Fläche The measuring element can be glued, welded, soldered, or directly sputtered onto the surface.

[0024] Fig. 2 zeigt den Messdübel 1 aus Fig. 1 angeordnet in a bore 3. The bore 3 has a first bore end 13 with an at least partially conical blind hole 13. The measuring anchor 1 is arranged in the bore 3. The bore is designed to be largely rotationally symmetrical along a bore axis W. The longitudinal axis Z of the measuring anchor and the bore axis W are parallel to each other when installed. The bore is shown sectioned along the bore diameter to illustrate the measuring anchor in the bore. The measuring anchor 1 itself is not shown in a sectional view. O W 64 4 K

[0025] Fig. 3 zeigt eine Schnittansicht des Messdübels 1 and the body 2 with the bore 3 along the cutting mark AA shown in Fig. 2. The cut is perpendicular to the longitudinal axis Z. The central region 5 has a largely rectangular cross-section Q. The corners of the rectangular cross-section Q are rounded in this embodiment. Largely rectangular cross-sections are understood to mean cross-sections that have four edges, two of which are parallel to each other and the angle between non-parallel edges is approximately 90°. However, the edges can be connected by curves or chamfers.

[0026] In den figürlich dargestellten Ausführungsbeispie-The central region 5 is largely cuboid-shaped. The first end 4 is largely designed as a cap 15 of a rotational body around the longitudinal axis Z as the axis of rotation. The surface normals of the four surfaces 8, 8', 8'', 8''' of the largely cuboid-shaped central region 5 are parallel to the first transverse direction X and the second transverse direction Y of the measuring anchor 1, respectively. The first transverse direction X, the second transverse direction Y, and the longitudinal axis Z form an orthogonal coordinate system.

[0027] Unter einem Rotationskörper wird hier und allgemein In geometry, a body is understood as a body whose surface is created by rotating a curve around an axis of rotation. The axis of the figure, or figure axis for short, is also called the axis of rotation or axis of rotation and lies in the same plane as the curve. A well-known solid of revolution is the torus, which is created by rotating a circle. An ellipsoid of revolution is created by rotating an ellipse. W 64 4 K

[0028] In den figürlich dargestellten Ausführungsbeispie-The first end 4 is designed as a rotational ellipsoid cap 15. The rotational ellipsoid cap 15 is a cap created by cutting a rotational ellipsoid perpendicular to the axis of rotation. The rotational ellipsoid cap 15 can be designed as a prolate rotational ellipsoid cap 15 or as an oblate rotational ellipsoid cap 15. A rotational ellipsoid cap 15 allows the anchor to be easily arranged in a bore 3 with a conical bottom hole 13. The rotational ellipsoid cap 15 is centered by its shape upon contact with the bottom hole 13 such that an annular contact 7 is created between the bottom hole 13 and the first end. The annular contact 7 is intrinsically determined by the interaction of the cone of the blind hole 13 and the rotational ellipsoid cap 15 during insertion and fixing of the measuring plug 1 and the bore 3. Inserted, this directly results in a substantial centering of the annular contact 7 around the bore axis B.This is advantageous because the measuring dowel 1 does not tilt in the bore 3 and a deformation of the body 2 surrounding the bore 3 affects all sides of the central region 5 equally.

[0029] Besonders vorteilhaft ist das erste Ende 4 als Ku- The spherical cap 15' is designed as shown in Fig. 4. The sectional view AA of this embodiment is similar to Fig. 3 and is not shown again. Spherical caps are easier to manufacture than other rotationally ellipsoidal caps.

[0030] Üblicherweise weist eine Bohrung 3 ein Grundloch 13 with a predetermined cone angle α. The cone angle is twice the angle between the bore axis B and the flank of the blind hole 13. The measuring anchor 1 is set up in a W 64 4K to be able to be installed in a blind hole 13 with a predetermined cone angle α. For the particularly advantageous embodiment of a measuring anchor 1, in which the first end 4 is designed as a spherical cap 15', the spherical cap 15' has a radius. The radius R of the spherical cap 15' is between R=a∙D / cos(α), with a bore diameter D and a constant a, with a∈[0.5,0.9], preferably a∈[0.6,0.8], particularly preferably a∈[0.65,0.75]. This has the advantage that the annular contact 7, which transfers the deformation of the body to the measuring anchor, is transferred as uniformly as possible to the central region. The force flow, which occurs due to the deformation on the central region 5, is thus largely parallel to the bore axis B and thus also largely parallel to the longitudinal axis Z of the measuring anchor. With a large radius, the force flow would have a larger component along the transverse axes X and Y.And with a smaller radius, the diameter of the annular contact 7 would be small. This would adversely affect the centering of the measuring dowel 1.

[0031] In einem alternativen, in Fig. 5 dargestellten Aus- In this exemplary embodiment, the first end 4 is designed as a paraboloid cap 15''. The sectional view AA of this embodiment is the same as in Fig. 3 and is not shown again. The advantages are analogous to the embodiment shown in Figs. 1 to 3 of a rotational ellipsoid cap 15 shown in Fig. 1 or an embodiment of a spherical cap 15' shown in Fig. 4: centering of the annular contact 7 between the paraboloid cap 15'' and the blind hole 13.

[0032] Besonders vorteilhaft weisen alle Ausführungsformen of the measuring plug 1 an annular contact 7 with a ring-O W 64 4 K diameter (D) of 50% to 90% of the bore diameter (B), particularly advantageously between 65% and 75% of the bore diameter (B). This has the advantage that the annular contact 7, which transfers the deformation of the body 2 to the measuring dowel 1, is transferred as evenly as possible to the central region. The force flow, which occurs due to the deformation on the central region 5, is thus largely parallel to the bore axis B and thus also largely parallel to the longitudinal axis Z of the measuring dowel. With a larger radius, the force flow would have a larger component along the transverse axes X and Y. And with a smaller radius, the diameter of the annular contact 7 would be small. This would have a detrimental effect on the centering of the measuring dowel 1.

[0033] Vorteilhafterweise beträgt für alle Ausführungsfor-of the measuring anchor 1, the largely rectangular cross-section Q of the central region 5 in a diagonal between two corners of the rectangular cross-section Q is at least 60% of the bore diameter B. This has the advantage that the bore 3 is largely filled and the bore 3 largely does not adversely weaken the body 2. Despite the bore 3, the body 2 has largely similar deformation characteristics to a body without a bore, since the largely cuboid-shaped central region 5 is solid. The term solid is understood here relative to the bore diameter.

[0034] Besonders vorteilhaft für alle Ausführungsformen The measuring anchor 1 is at least partially made of a metallic material. This has the advantage that the measuring anchor 1 is particularly robust and therefore particularly suitable for the W 64 4 K It is suitable for use in harsh working environments where the body 2 is also made of a metallic material. Despite the bore 3, the body 2 exhibits largely similar deformation characteristics to a body 2 without a bore, since the largely cuboid-shaped central region 5 is solid.

[0035] Alternativ und besonders im Fall, dass der Körper 2 is made of a non-metallic material, the measuring anchor 1 can be made at least partially of the same material class as the body 2 in order to achieve largely similar deformation characteristics of the body 2 with measuring anchor 1 as a body without a bore.

[0036] Bevorzugt ist zumindest der mittlere Bereich 5 undThe first end 4 is constructed in one piece. "Integral" means that the middle section 5 and the first end 4 are made from a single piece of solid material. Accordingly, "integral" means that the first end 4 and the middle section 5 are not joined together in any way from two parts. This has the advantage that the measuring dowel is made from fewer individual parts. This reduces the manufacturing effort, since otherwise parts would have to be joined together and adjusted to each other.

[0037] Besonders bevorzugt weist der mittlere Bereich 5 a square cross-section Q perpendicular to the longitudinal axis Z. This means that the four surfaces 8, 8', 8'', 8''' allow identical mounting of the measuring elements. This simplifies the mounting of the measuring elements 9, 9', 9'', 9'''. In addition, the deformation properties of the middle O W 64 4 K Area 5 along the first transverse axis X and the second transverse axis Y are identical.

[0038] Bevorzugt ist auf jeder der vier Flächen 8, 8’ ,8’’,8''' of the middle area 5 at least one measuring element 9, 9', 9'', 9''' is applied. Each measuring element 9, 9', 9'', 9''' is designed to determine a deformation of the respective surface 8, 8', 8'', 8'''. The four measuring elements 9, 9', 9'', 9''' are designed either as strain gauges 9, 9', 9'', 9''' or piezoresistive measuring elements 9, 9', 9'', 9'''. A strain gauge is a strain gauge. The four measuring elements 9, 9', 9'', 9''' form a full-bridge circuit. This has the advantage that the full-bridge circuit has a high measuring signal and excellent common-mode rejection. In addition, temperature influences are compensated particularly well in the full-bridge circuit.

[0039] Bevorzugt sind alle vier Messelemente 9,9’,9’’,9’’’ each aligned parallel to the longitudinal axis Z. This advantageously also compensates for any deformations occurring transversely to the longitudinal axis Z when determining the deformation.

[0040] Das zweite Ende 6 des Messdübels 1 weist eine Fi-Fixing device 10. The fixing device 10 is designed to be fixed with a counterpart 11 of the bore 3. The task of the fixing device is to fix the measuring anchor 1 in the bore 3 in such a way that the measuring anchor 1 is under prestress. This has the advantage that the annular contact 7 to the blind hole 13 is well defined and has no gaps, even if the surrounding material of the body is deformed. Thus, a determination of W 64 4 K Both tensile and compressive forces can be determined as stretching or compression of the body along the bore axis.

[0041] Die Fixiervorrichtung 10 ist beispielsweise als zu-at least partially circumferential web or at least partially circumferential shoulder. The measuring anchor 1 can be fixed into an internal thread 14 of the bore 3 by means of a mounting nipple 12. The internal thread of the bore represents the counterpart 11. A mounting nipple 12 has a surface that engages the fixing device 10 and an external thread that interacts with the internal thread 14 of the bore 3. This prevents torsion of the measuring anchor 1, in particular of the central region 5, during installation in the bore 3 under prestress.

[0042] Alternativ kann Gegenstück 11 auch als Aussengewin-de, i.e., as a spiral-shaped circumferential shoulder (not shown). The mounting nipple 12 has both an external thread and an internal thread, which have opposite handedness. The counterpart 11 and the internal thread 14 of the bore 3 also have different handedness. The pitch of the external thread of the counterpart 11 and the internal thread 14 of the bore 3 are selected to be different such that the measuring anchor 1 moves along the bore axis B to the first end 13 of the bore 3 when the mounting nipple 12 is rotated. Thus, the measuring anchor 1 can be fixed in the bore 3 under preload by rotating the mounting nipple 12. Torsion of the measuring anchor 1, particularly of the central region 5 during installation in the bore 3 under preload, is thus avoided. In this context, an external thread is considered a spiral-shaped circumferential shoulder. O W 64 4 K

[0043] Der Messdübel 1 ist mittels Fixiervorrichtung 10with mounting nipple 12 and counterpart 11, to fix at least the middle area 5 under pre-tension in the bore 3.

[0044] In der Anwendung wird der Messdübel 1 immer als Use a system consisting of a measuring dowel 1 fixed in a bore 3 of a body 2. Advantageously, the material of the measuring dowel 1 has a thermal expansion coefficient that deviates by less than 20% from the thermal expansion coefficient of the body 2. This avoids temperature-induced mechanical stresses between the body 2 and the measuring dowel 1.

[0045] Es sind explizit in dieser Schrift auch Ausfüh- forms of embodiments that have a combination of the features of the embodiments described herein. O W 64 4 K List of reference symbols 1 Messdübel 2 Körper 3 Bohrung4 First end 5 Middle area 6 Second end 7 Annular contact 8 ,8',8'',8''' surface, first surface, second surface, third surface, fourth surface 9,9',9'',9''' Measuring element 10 Fixing device 11 Counter part 12 Mounting nipple 13 First bore end / blind hole 14 Internal thread 15 Cap, rotational ellipsoid cap 15' Spherical cap 15'' Paraboloid cap ^^ Cone angle ^^ Bore diameter D Ring diameter rectangular cross-section / square Q cross-section R Radius O W 64 4 K W Bohrungsachse X First transverse axisY Second transverse axisZ Longitudinal axisA-A Section axisO W 64 4 K

Claims

1. A measuring dowel (1) for determining a deformation of a body (2) with a bore (3), which bore (3) has a first bore end (13) with an at least partially conical bottom hole (13); wherein the measuring dowel (1) can be arranged in the bore (3); wherein the measuring dowel (1) is designed along a longitudinal axis (Z) and has a first end (4) and a second end (6) along the longitudinal axis (Z); wherein the first end (4) faces the bottom hole (13) in the installed state; wherein the measuring dowel (1) has a central region (5) which is arranged between the first end (4) and the second end (6); wherein the central region (5) has a largely rectangular cross-section (Q) perpendicular to the longitudinal axis (Z); wherein the central region (5) has four surfaces (8, 8', 8'', 8'''); wherein at least one measuring element (9, 9', 9'', 9''') is applied to at least two of the four surfaces (8, 8', 8'', 8''') of the central region (5);wherein each measuring element (9, 9', 9'', 9''') is configured to determine a deformation of the respective surface (8, 8', 8'', 8'''); wherein the first end (4) is designed such that, upon contact with a conical bottom hole (13), it has an annular contact (7) with the conical region of the bottom hole (13).

2. Measuring dowel (1) according to claim 1, wherein the central region (5) is designed largely cuboid-shaped; and that the first end (4) is designed largely as a cap (15) of a rotational body about the longitudinal axis (Z) as the rotational axis. O; W 64 4K3. Measuring dowel (1) according to one of the preceding claims, wherein the first end (4) is designed as a prolate rotational ellipsoid cap (15) or an oblate rotational ellipsoid cap (15).

4. Measuring dowel (1) according to one of the preceding claims, wherein the first end (4) is designed as a spherical cap (15).

5. Measuring dowel (1) according to the preceding claim, wherein the measuring dowel is designed to be installable in a blind hole (13) with a predetermined cone angle (^); wherein the radius (R) of the spherical cap (15) is between ^ = ^ ∙^ ^^^ ^, with ^ ∈ [0.5,0.9], preferably ^ ∈ [0.6,0.8], particularly preferably ^ ∈ [0.65,0.75].

6. Measuring dowel (1) according to one of claims 1 or 2; wherein the first end (4) is designed as a paraboloid cap (15).

7. Measuring dowel (1) according to one of the preceding claims, wherein the annular contact (7) has a ring diameter (D) of 50% to 90% of the bore diameter (B), particularly advantageously between 65% and 75% of the bore diameter (B). 8.Measuring dowel (1) according to one of the preceding claims, wherein the largely rectangular cross-section (Q) of the central region (5) in a diagonal between two corners of the rectangular cross-section (Q) is at least 60% of the bore diameter B.O. W 64 4K9. Measuring dowel (1) according to one of the preceding claims, wherein the measuring dowel (1) is at least partially made of a metallic material.

10. Measuring dowel (1) according to one of the preceding claims, wherein at least the central region (5) and the first end (4) are made in one piece; wherein "in one piece" means that the central region (5) and the first end (4) are made of a solid material.

11. Measuring dowel (1) according to one of the preceding claims, wherein the central region (5) has a square cross-section (Q) perpendicular to the longitudinal axis (Z).12.Measuring dowel (1) according to the preceding claim, wherein at least one measuring element (9, 9', 9'', 9''') is applied to each of the four surfaces (8, 8', 8'', 8''') of the central region (5); wherein each measuring element (9, 9', 9'', 9''') is configured to determine a deformation of the respective surface (8, 8', 8'', 8'''); and wherein the four measuring elements (9, 9', 9'', 9''') are designed as strain gauges (9, 9', 9'', 9''') or piezoresistive measuring elements (9, 9', 9'', 9''') and form a full-bridge circuit.

13. Measuring dowel (1) according to one of the preceding claims, wherein the second end (6) has a fixing device (10); which fixing device (10) is designed to be fixed to a counterpart (11) of the bore (3); and wherein the measuring dowel (1) is set up by means of the fixing device (10) and counterpart (11). W 64 4K is to fix at least the central region (5) under prestress in the bore (3).

14. Measuring dowel (1) according to one of the preceding claims; wherein the fixing device (10) is designed as an at least partially circumferential web or at least partially circumferential shoulder; and wherein the measuring dowel (1) can be fixed by means of a mounting nipple (12) in an internal thread (14) of the bore (3).

15. System consisting of a measuring dowel fixed in a bore (3) of a body according to one of the preceding claims, wherein the material of the measuring dowel has a thermal expansion coefficient that deviates by less than 20% from the thermal expansion coefficient of the body (2). W 64 4 K

Images