Device and method for measuring rigidity of pressurizing corrugated pipe with large length-diameter ratio

Abstract

The invention relates to a device and a method for measuring the rigidity of a pressurizing corrugated pipe with a large length-diameter ratio. The device comprises a testing machine, a left tension-compression joint, a right tension-compression joint, a support, a fixed sleeve, a left fixed inner cylinder, a right fixed inner cylinder, a left sleeve type iron wire protective net and a right sleeve type iron wire protective net, two longitudinal stainless steel rods are arranged at two ends of the testing machine, one sides of the left tension-compression joint and the right tension-compression joint are respectively sleeved on the two longitudinal stainless steel rods, and the other sides of the left tension-compression joint and the right tension-compression joint are respectively welded with one sides of the left fixed inner cylinder and the right fixed inner cylinder; a to-be-tested corrugated pipe test piece is clamped between the other sides of the left fixed inner cylinder and the right fixed inner cylinder; the lower end of the support is welded on the tester, and the upper end is fixedly connected with the fixed sleeve; the fixed sleeve is sleeved outside a to-be-tested corrugated pipe test piece; and the left sleeve type iron wire protective net and the right sleeve type iron wire protective net are symmetrically sleeved on two sides of the corrugated pipe test piece.

Description

Technical Field

[0001] This invention relates to a device and method for measuring the stiffness of a high aspect ratio pressurized bellows, belonging to the field of hydraulic measurement. Background Technology

[0002] Booster bellows are used to pressurize hydraulic systems and automotive turbocharger systems, storing and releasing fluid as temperature changes occur. The working principle of a booster bellows generally involves installing it into the mechanism. A certain volume and pressure of working fluid is added to the system; the system oil pressure compresses the bellows, providing back pressure. When the working fluid temperature drops, its volume decreases, and the booster bellows rebounds, releasing the fluid. When the working fluid temperature rises, its volume expands, increasing the fluid pressure, allowing the booster bellows to continue compressing, storing the fluid. Therefore, the compression and rebound capabilities of the booster bellows affect its performance; its stiffness is a crucial technical indicator for performance evaluation and needs to be verified during the performance testing phase.

[0003] Existing equipment and methods for testing the stiffness of pressurized bellows are mostly designed for bellows with a small number of corrugated plates (small length-to-diameter ratio). The patent "A Bellows Tensile-Compression Testing Device and Method" designs a bellows tensile-compression testing device. An upper and lower tension-compression joint are connected to both ends of a longitudinally placed pressurized bellows. The upper and lower tension-compression joints are connected to the upper and lower platforms of the testing device, respectively, thus fixing the bellows on the device. The fixing device includes a fixed inner cylinder connected to the upper tension-compression joint and a fixed sleeve connected to the lower tension-compression joint, preventing the bellows specimen from bending and ensuring axial tensile and compressive deformation. Then, the tensile rate, tensile force, and tensile displacement of the testing machine are set according to the experimental requirements to complete the tensile and compression tests and collect the measurement data. This method has high testing efficiency, high testing accuracy, and is easy to promote. However, due to the large number of corrugated plates in high-aspect-ratio pressurized bellows, the gravitational force exerted on the upper corrugated plates varies at different positions during longitudinal stiffness testing. Furthermore, the weight of the central support structure in some multi-corrugated bellows further amplifies this effect, leading to uneven stress and different deformation states among the corrugated plates. Simultaneously, due to gravity, high-aspect-ratio pressurized bellows are already in a compressed state when freely placed longitudinally, requiring consideration of gravity in compression and springback analysis, and making them more prone to bending deformation during testing. Considering these factors, this method is not suitable for heavy, high-aspect-ratio multi-corrugated bellows. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and propose a measuring device and method for the stiffness of a high aspect ratio pressurized bellows, which solves several problems that the existing pressurized bellows stiffness testing methods are not applicable to high aspect ratio pressurized bellows.

[0005] The technical solution of this invention is: a measuring device for the stiffness of a high length-to-diameter ratio pressurized bellows, comprising: a testing machine, a left tension-compression joint, a right tension-compression joint, a support, a fixed sleeve, a left fixed inner cylinder, a right fixed inner cylinder, a left sleeve-type wire mesh, and a right sleeve-type wire mesh; two longitudinal stainless steel rods are provided at both ends of the testing machine, one side of the left tension-compression joint and the right tension-compression joint are respectively fitted onto the two longitudinal stainless steel rods, and the other side is respectively welded to one side of the left fixed inner cylinder and the right fixed inner cylinder; the other side of the left fixed inner cylinder and the right fixed inner cylinder clamps the bellows test piece to be tested in the middle; the lower end of the support is welded to the testing machine, and the upper end is fixedly connected to the fixed sleeve; the fixed sleeve is fitted onto the outside of the bellows test piece to be tested; the left sleeve-type wire mesh and the right sleeve-type wire mesh are symmetrically fitted onto both sides of the bellows test piece.

[0006] The corrugated pipe test piece is a two-section pressurized corrugated pipe, which includes a corrugated plate, a spring and a central support; the left sleeve type wire mesh and the right sleeve type wire mesh are symmetrically distributed on both sides of the central support and are sleeved on the outside of the corrugated plate.

[0007] The testing machine is a stainless steel frame structure. Two longitudinally opposite stainless steel surfaces are welded perpendicularly to the platform. Each stainless steel surface is 1m high, 20-30cm wide, and 3-5cm thick, with a 1m distance between them. A transverse stainless steel rod is installed on the platform between the two longitudinally opposite stainless steel surfaces. Another transverse stainless steel rod is installed between the top ends of the two longitudinally opposite stainless steel surfaces. The two transverse stainless steel rods are located on a vertical plane passing through the center point of the stainless steel surfaces and are spaced 0.8m apart. The two ends of the two longitudinal stainless steel rods are slidably connected to the two transverse stainless steel rods via sliding fixing devices. The two longitudinal stainless steel rods, through the sliding fixing devices, drive the left and right tension joints to move laterally and remain fixed.

[0008] The left and right tension joints are equipped with sliding fixing devices at the joints with the longitudinal stainless steel rod, so that the tension joints can move and be fixed longitudinally on the longitudinal stainless steel rod.

[0009] The lower end of the support is welded to the horizontal stainless steel rod at the bottom, and the upper end is fixed to the fixed sleeve by a clamp. The two sides of the clamp of the fixed sleeve are of equal length.

[0010] There are gaps between the left sleeve type wire mesh and the right sleeve type wire mesh and the fixed sleeve and corrugated plate. The outer envelope of the left sleeve type wire mesh and the right sleeve type wire mesh is cylindrical, smooth and without protrusions, and the mesh size is sufficient to avoid interference with the structure of the corrugated pipe test piece.

[0011] When the corrugated pipe test specimen is a multi-section pressurized corrugated pipe, i.e., there are two or more intermediate support structures, a segmented sleeve-type wire mesh protective net should be installed, i.e.:

[0012] The first and last sections of the corrugated pipe test piece are equipped with sleeve-type wire mesh protective nets. The length of the sleeve-type wire mesh protective nets is equal to the length of the first and last sections of the corrugated pipe test piece, respectively, and the inner diameter is equal to the outer diameter of the corrugated plate.

[0013] The remaining sections of the corrugated pipe test piece are also equipped with sleeve-type wire mesh protective netting. The installation length of the sleeve-type wire mesh protective netting is equal to the length of the remaining corrugated pipe sections, and the inner diameter is equal to the outer diameter of the central support.

[0014] A method for measuring the stiffness of a high aspect ratio pressurized bellows using a measuring device, comprising:

[0015] S1. Install the corrugated pipe test piece to be tested in the fixed sleeve, so that the corrugated pipe test piece is in a free state;

[0016] S2. Adjust the position of the stainless steel rod of the testing machine and the positions of the left tension and compression joint and the right tension and compression joint, so that the left fixed inner cylinder and the right fixed inner cylinder abut against both sides of the bellows test piece and the contact surface is not under force.

[0017] S3. Conduct a stiffness test, the process is as follows:

[0018] Select either the left or right fixed inner cylinder and adjust its position so that it applies stress to the contact surface of the bellows test specimen. Keep the other fixed inner cylinder in its original position. Stop the test when the required compression displacement is reached and record the compression force of the bellows test specimen at that compression displacement.

[0019] S4. Combining Hooke's Law, the compressive force of the bellows test piece under different displacements is recorded. The test is repeated multiple times and the average value is taken to finally obtain the stiffness of the bellows test piece.

[0020] The advantages of this invention compared to the prior art are:

[0021] (1) The present invention has designed a special stiffness testing equipment for the stiffness testing of high length-to-diameter ratio pressurized bellows, and formed a systematic stiffness testing process design.

[0022] (2) The present invention fully considers the characteristics of large length-to-diameter ratio pressurized bellows with many corrugated plates and heavy weight, and sets up a horizontally fixed sleeve. By placing the bellows test piece horizontally, the influence of the bellows' own weight on the stiffness test accuracy is eliminated.

[0023] (2) In this invention, a segmented sleeve wire mesh is added to the corrugated pipe test piece in conjunction with the central support structure, and then the whole piece is placed in the fixed sleeve. During the stiffness test, the fixed sleeve and the protective mesh together fix the radial position of the corrugated pipe test piece, which ensures the test accuracy of the stiffness of the corrugated pipe test piece, effectively prevents the corrugated pipe test piece from bending or fragments from splashing during the stiffness test, and improves the safety of the test process; the segmented protective mesh is adapted to the large length-to-diameter ratio pressurized corrugated pipe with segmented corrugated pipe structure.

[0024] (3) The present invention provides fixed inner cylinders horizontally along the axial direction on both sides of the fixed sleeve, so that the corrugated pipe test piece can be subjected to force more evenly from left to right during stiffness testing, thereby improving the accuracy of stiffness testing.

[0025] (4) The present invention allows for the selection of fixed sleeves with different inner diameters, and the height of the fixed tension and compression joint can be adjusted to calibrate the coaxiality of the fixed inner cylinder and the bellows test piece, thereby expanding the size range of the bellows test piece for stiffness testing. Attached Figure Description

[0026] Figure 1 This is a diagram of the bellows stiffness testing mechanism (including the bellows test specimen).

[0027] Figure 2 This is a diagram of the bellows stiffness testing mechanism (excluding the bellows test specimen).

[0028] Figure 3 This is a diagram showing the composition of the corrugated pipe test piece. Detailed Implementation

[0029] like Figure 1 , 2 As shown, this invention is a measuring device for the stiffness of a high length-to-diameter ratio pressurized bellows, comprising: a testing machine 2, a left tension-compression joint 3, a right tension-compression joint 4, a support 5, a fixed sleeve 6, a left fixed inner cylinder 7, a right fixed inner cylinder 8, a left sleeve-type wire mesh 9, and a right sleeve-type wire mesh 10; the testing machine 2 has two longitudinal stainless steel rods at both ends, one side of the left tension-compression joint 3 and the right tension-compression joint 4 are respectively fitted onto the two longitudinal stainless steel rods, and the other side is respectively welded to one side of the left fixed inner cylinder 7 and the right fixed inner cylinder 8; the other side of the left fixed inner cylinder 7 and the right fixed inner cylinder 8 holds the bellows test piece 1 to be tested in the middle; the lower end of the support 5 is welded to the testing machine 2, and the upper end is fixedly connected to the fixed sleeve 6; the fixed sleeve 6 is fitted onto the outside of the bellows test piece 1 to be tested; the left sleeve-type wire mesh 9 and the right sleeve-type wire mesh 10 are symmetrically fitted onto both sides of the bellows test piece 1.

[0030] like Figure 3As shown, the corrugated pipe test piece 1 is a two-section pressurized corrugated pipe, including a corrugated plate, a spring and a central support; the left sleeve-type wire mesh 9 and the right sleeve-type wire mesh 10 are symmetrically distributed on both sides of the central support and are sleeved on the outside of the corrugated plate.

[0031] The testing machine 2 is a stainless steel frame structure. Two longitudinally opposite stainless steel surfaces are welded perpendicularly to the platform. Each stainless steel surface is 1m high, 20-30cm wide, and 3-5cm thick, with a 1m distance between them. A transverse stainless steel rod is installed on the platform between the two longitudinally opposite stainless steel surfaces. Another transverse stainless steel rod is installed between the top ends of the two longitudinally opposite stainless steel surfaces. The two transverse stainless steel rods are located on a vertical plane passing through the center point of the stainless steel surfaces and are spaced 0.8m apart. The two ends of the two longitudinal stainless steel rods are slidably connected to the two transverse stainless steel rods via sliding fixing devices. The two longitudinal stainless steel rods, through the sliding fixing devices, drive the left tension joint 3 and the right tension joint 4 to move laterally and be fixed.

[0032] The left and right tension joints 3 and 4 are fitted with sliding fixing devices at the joints with the longitudinal stainless steel rod, so that the tension joints can move and be fixed longitudinally on the longitudinal stainless steel rod.

[0033] The lower end of the support 5 is welded to the horizontal stainless steel rod at the bottom, and the upper end is fixed to the fixed sleeve 6 by a clamp. The two sides of the clamp of the fixed sleeve 6 are of equal length.

[0034] There are gaps between the left sleeve type wire mesh 9 and the right sleeve type wire mesh 10 and the fixed sleeve 6 and the corrugated plate. The outer envelope of the left sleeve type wire mesh 9 and the right sleeve type wire mesh 10 is cylindrical, smooth and without protrusions, and the mesh size is sufficient to avoid interference with the structure of the corrugated pipe test piece 1.

[0035] When the corrugated pipe test specimen 1 is a multi-section pressurized corrugated pipe, that is, there are two or more intermediate support structures, then a segmented sleeve-type wire mesh protective net is installed, i.e.:

[0036] The first and last sections of the corrugated pipe test piece 1 are equipped with sleeve-type wire mesh. The length of the sleeve-type wire mesh is equal to the length of the first and last sections of the corrugated pipe test piece 1, respectively, and the inner diameter is equal to the outer diameter of the corrugated plate.

[0037] The remaining sections of the corrugated pipe test piece 1 are also equipped with sleeve-type wire mesh protective netting. The installation length of the sleeve-type wire mesh protective netting is equal to the length of the remaining corrugated pipe sections, and the inner diameter is equal to the outer diameter of the central support.

[0038] This invention also relates to a method for measuring the stiffness of a high aspect ratio pressurized bellows using a measuring device, comprising:

[0039] S1. Install the corrugated pipe test piece 1 to be tested in the fixed sleeve 6, so that the corrugated pipe test piece 1 is in a free state;

[0040] S2. Adjust the position of the stainless steel rod of the testing machine 2 and the positions of the left tension-compression joint 3 and the right tension-compression joint 4, and use the left fixed inner cylinder 7 and the right fixed inner cylinder 8 to hold the bellows test piece 1 against both sides without the contact surface being stressed.

[0041] S3. Conduct a stiffness test, the process is as follows:

[0042] Select either the left fixed inner cylinder 7 or the right fixed inner cylinder 8, adjust its position so that it applies stress to the contact surface of the bellows test piece 1, and keep the other fixed inner cylinder in its original position. Stop the test when the required compression displacement is reached, and record the compression force of the bellows test piece at that compression displacement.

[0043] S4. Combining Hooke's Law, the compressive force of the bellows test piece under different displacements is recorded. The test is repeated multiple times and the average value is taken to finally obtain the stiffness of the bellows test piece.

[0044] An embodiment of the test method for measuring the stiffness of a pressurized bellows involved in this invention is as follows:

[0045] S1. On the testing machine table, there are two longitudinally opposite stainless steel surfaces welded perpendicularly to the table. The stainless steel surfaces are about 1m high, 20-30cm wide, and 3-5cm thick, with a distance of about 1m between them. Two stainless steel rods are welded perpendicularly to the two stainless steel surfaces, ensuring that they are on a vertical plane passing through the center point of the stainless steel surfaces and have a distance of about 0.8m between them. Then, two stainless steel rods with sliding fixing devices welded to both ends are set up, with a length of about 0.8m, so that they fit onto the two stainless steel rods on the aforementioned transversely welded stainless steel surfaces. The sliding fixing devices allow the stainless steel rods to satisfy both left-right sliding and fixed states.

[0046] S2. Place the corrugated pipe test specimen with the sleeve-type wire mesh protective netting installed inside the fixed sleeve. The protective netting is divided into left-sleeve and right-sleeve type wire mesh protective netting. The protective netting is made of 1-3mm diameter steel wire woven mesh, ensuring that the outer envelope of the structure is cylindrical, smooth, and without protrusions. The mesh size is sufficient to prevent the protective netting from interfering with the surrounding structure. Figure 3 The diagram shows interference in the corrugated pipe structure. Each section of the protective mesh has the same free length as the corresponding corrugated pipe section, and a gap of ≤1mm is allowed between them radially and between the protective mesh and the fixed sleeve. Each section of the protective mesh is aligned with the edges of each corrugated pipe section (the edges at both ends of the middle support) and the edge of the fixed sleeve to ensure its fixation and smooth contact between its inner and outer surfaces and the corrugated pipe test piece and the fixed sleeve, preventing wear or abrasion with the corrugated pipe test piece. The relative position of the protective mesh to the fixed sleeve, corrugated pipe test piece, etc., can be determined without the use of a limiting structure.

[0047] S3. Fix the fixing sleeve on the support of the stiffness testing device, ensuring that the length of the fixing sleeve on both sides of the clamp is consistent. The selected fixing sleeve size should enclose the corrugated pipe test piece, and the length should be consistent with the free state of the corrugated pipe test piece, ensuring that the corrugated pipe test piece will not bend or deform during the stiffness test, thus affecting the test accuracy.

[0048] S4. Install the corrugated pipe test piece in the fixed sleeve, so that it is in a free state.

[0049] S5. Both the tension / compression joint and the fixed joint are equipped with sliding fixing devices, allowing them to move and be fixed longitudinally on the stainless steel rod as needed. Weld the tension / compression joint to the fixed inner cylinder, and adjust the lateral position of the stainless steel rod and the longitudinal position of the tension / compression joint to make the tension / compression joint, the fixed inner cylinder, and the corrugated plates on both sides of the bellows test piece coaxial.

[0050] S6. Stiffness test procedure:

[0051] Arbitrarily select one fixed inner cylinder and adjust its position so that it applies stress to the contact surface of the bellows test specimen 1. The other fixed inner cylinder remains in its original position. Stop the test when the required compressive displacement is reached, and record the compressive force F of the bellows test specimen at that displacement.

[0052] The testing machine is adjusted so that the left fixed inner cylinder contacts the left side of the bellows test piece, and the right fixed inner cylinder begins to contact the right side of the bellows test piece. The left fixed inner cylinder applies stress to the contact surface of the bellows test piece, while the other platform remains fixed. The test stops when the required compression displacement is reached, and the compressive force of the bellows test piece at that displacement is recorded. The measurement frequency of the compression displacement of the fixed inner cylinder of the testing device can be set according to the testing requirements, such as recording data in 5cm increments. The available compressive force, moving loading rate, and displacement range of the fixed inner cylinder of the testing device can be selected according to the requirements of the bellows test piece, such as selecting an available compressive force of 0–10 kN, a moving loading rate of 0.1–1 cm / s, and a displacement range of 0–100 cm.

[0053] S7. Data Processing: Combining Hooke's Law

[0054] F=kΔx

[0055] Where F is the compressive force exerted by the fixed inner cylinder on the bellows test specimen, Δx is the compressive displacement of the bellows test specimen, and k is the stiffness of the bellows test specimen.

[0056] The compressive force of the bellows test specimen at different displacements was recorded. The test was repeated 3 times and the average value was taken to obtain the stiffness of the bellows test specimen.

[0057] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention based on the above-disclosed technical content without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A measuring device for the stiffness of a high aspect ratio pressurized bellows, characterized in that, include: The test machine comprises a left tension / compression joint, a right tension / compression joint, a support, a fixing sleeve, a left fixed inner cylinder, a right fixed inner cylinder, a left sleeve-type wire mesh, and a right sleeve-type wire mesh. Two longitudinal stainless steel rods are installed at both ends of the test machine. One side of the left and right tension / compression joints is respectively fitted onto the two longitudinal stainless steel rods, and the other side is welded to one side of the left and right fixed inner cylinders, respectively. The other side of the left and right fixed inner cylinders holds the corrugated pipe test piece in the middle. The lower end of the support is welded to the test machine, and the upper end is fixedly connected to the fixing sleeve. The fixing sleeve is fitted onto the outside of the corrugated pipe test piece. The left and right sleeve-type wire meshes are symmetrically fitted onto both sides of the corrugated pipe test piece.

2. The measuring device for the stiffness of a high aspect ratio pressurized bellows according to claim 1, characterized in that, The corrugated pipe test piece is a two-section pressurized corrugated pipe, which includes a corrugated plate, a spring and a central support; the left sleeve type wire mesh and the right sleeve type wire mesh are symmetrically distributed on both sides of the central support and are sleeved on the outside of the corrugated plate.

3. The measuring device for the stiffness of a high aspect ratio pressurized bellows according to claim 2, characterized in that, The testing machine is a stainless steel frame structure. Two longitudinally opposite stainless steel surfaces are welded perpendicularly to the platform. Each stainless steel surface is 1m high, 20-30cm wide, and 3-5cm thick, with a 1m distance between them. A transverse stainless steel rod is installed on the platform between the two longitudinally opposite stainless steel surfaces. Another transverse stainless steel rod is installed between the top ends of the two longitudinally opposite stainless steel surfaces. The two transverse stainless steel rods are located on a vertical plane passing through the center point of the stainless steel surfaces and are spaced 0.8m apart. The two ends of the two longitudinal stainless steel rods are slidably connected to the two transverse stainless steel rods via sliding fixing devices. The two longitudinal stainless steel rods, through the sliding fixing devices, drive the left and right tension joints to move laterally and remain fixed.

4. The measuring device for the stiffness of a high aspect ratio pressurized bellows according to claim 3, characterized in that, The left and right tension joints are equipped with sliding fixing devices at the joints with the longitudinal stainless steel rod, so that the tension joints can move and be fixed longitudinally on the longitudinal stainless steel rod.

5. The measuring device for the stiffness of a high aspect ratio pressurized bellows according to claim 1, characterized in that, The lower end of the support is welded to the horizontal stainless steel rod at the bottom, and the upper end is fixed to the fixed sleeve by a clamp. The two sides of the clamp of the fixed sleeve are of equal length.

6. The measuring device for the stiffness of a high aspect ratio pressurized bellows according to claim 1, characterized in that, There are gaps between the left sleeve type wire mesh and the right sleeve type wire mesh and the fixed sleeve and corrugated plate. The outer envelope of the left sleeve type wire mesh and the right sleeve type wire mesh is cylindrical, smooth and without protrusions, and the mesh size is sufficient to avoid interference with the structure of the corrugated pipe test piece.

7. The measuring device for the stiffness of a high aspect ratio pressurized bellows according to claim 1, characterized in that, When the corrugated pipe test specimen is a multi-section pressurized corrugated pipe, i.e., there are two or more intermediate support structures, a segmented sleeve-type wire mesh protective net should be installed, i.e.: The first and last sections of the corrugated pipe test piece are equipped with sleeve-type wire mesh protective nets. The length of the sleeve-type wire mesh protective nets is equal to the length of the first and last sections of the corrugated pipe test piece, respectively, and the inner diameter is equal to the outer diameter of the corrugated plate. The remaining sections of the corrugated pipe test piece are also equipped with sleeve-type wire mesh protective netting. The installation length of the sleeve-type wire mesh protective netting is equal to the length of the remaining corrugated pipe sections, and the inner diameter is equal to the outer diameter of the central support.

8. A method for measuring the stiffness of a high aspect ratio pressurized bellows as described in claim 4, characterized in that, include: Install the corrugated pipe test specimen to be tested in the fixed sleeve, so that the corrugated pipe test specimen is in a free state; Adjust the position of the stainless steel rod of the testing machine and the positions of the left tension and compression joint and the right tension and compression joint, so that the left fixed inner cylinder and the right fixed inner cylinder can hold the bellows test piece against both sides without any force on the contact surface; The stiffness test was conducted as follows: Select either the left or right fixed inner cylinder and adjust its position so that it applies stress to the contact surface of the bellows test specimen. Keep the other fixed inner cylinder in its original position. Stop the test when the required compression displacement is reached and record the compression force of the bellows test specimen at that compression displacement. By combining Hooke's law, the compressive force of the bellows test specimen under different displacements was recorded. The test was repeated many times and the average value was taken to finally obtain the stiffness of the bellows test specimen.

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