Device for determining jointed rock sample crushing energy consumption in SHPB test and use method thereof

Abstract

The invention discloses a device for determining jointed rock sample crushing energy consumption in an SHPB test and a using method thereof.The device comprises a protection box, the protection box is cylindrical, a cavity is formed in the center of the protection box, holes connected with an incident bar and a transmission bar are formed in the front end and the rear end of the protection box correspondingly, the holes communicate with the cavity, and a plurality of mounting holes are formed in the peripheral face of the protection box in the circumferential direction; a rigid rod is slidably connected into the mounting hole, one end of the rigid rod is located in the cavity and arranged relative to the jointed rock sample, the other end of the rigid rod is located on the outer side of the protection box and connected with a shape memory alloy, one end of the shape memory alloy is connected with the peripheral face of the protection box, the heating device is connected with the protection box, and the 3D scanner and the infrared thermal imager are arranged relative to the protection box. In the process that the jointed rock sample is impacted, fragments impact the rigid rod to enable the shape memory alloy to deform, and meanwhile, the infrared thermal imager is adopted to obtain temperature change in the protection box, so that kinetic energy and dissipated heat energy of ejection of the fragments of the jointed rock sample can be accurately obtained.

Description

Technical Field

[0001] The invention relates to the technical field of rock dynamics performance testing, and in particular to a device for determining the energy consumption of fracture of a jointed rock sample in a SHPB test and a method for using the device. Background Art

[0002] There are a large number of joints inside natural rock mass. The dynamic characteristics of jointed rock largely determine the strength and stability of the entire rock mass. The study of the dynamic characteristics of jointed rock is of great engineering significance for efficient rock breaking, improving rock breaking effect, and increasing tunnel excavation speed. It also has important theoretical guiding significance for the prevention and control of rock geological disasters. The study of the dynamic characteristics of jointed rock is often carried out with the help of Split Hopkinson Pressure Bar (SHPB) test. The SHPB system includes bullets, incident rods, transmission rods, absorption rods, dynamic strain collectors, etc. During the test, the bullet impacts the incident rod, and then the incident rod impacts the jointed rock sample placed between the incident rod and the transmission rod, realizing the dynamic impact on the jointed rock sample and studying the dynamic characteristics of the jointed rock sample. The dynamic characteristics include dynamic strength characteristics, stress wave propagation characteristics, energy dissipation characteristics, etc. Among them, the energy dissipation characteristics are one of the key areas of attention and research. Energy dissipation is the fundamental reason for rock deformation and failure. Analyzing the energy dissipation characteristics helps to recognize and understand the nature of deformation and failure of brittle materials such as jointed rocks under dynamic loads. It is of great significance for reducing the consumption of explosives in blasting rock, efficiently breaking rocks under impact loads, and improving energy utilization efficiency.

[0003] The SHPB test is accompanied by the input, conversion and dissipation of energy. The total energy dissipated by the jointed rock sample during the test is the sum of the incident energy minus the reflected energy and the transmitted energy. The total energy dissipated by the jointed rock sample is actually composed of three parts, namely, the crushing energy, the kinetic energy of the fragments ejected, and the dissipated heat energy. The crushing energy is the energy used to generate cracks and crack extension in the jointed rock sample, which is the energy absorbed by the destruction of the jointed rock sample in a strict sense.

[0004] The ratio of crushing energy consumption to input energy is the rock breaking energy utilization rate. Since crushing energy consumption is difficult to measure, researchers often use the ratio of total dissipated energy to input energy for research and analysis, or multiply the total dissipated energy by a reduction factor to approximate the crushing energy consumption. However, the kinetic energy of the ejected fragments is not fixed, but changes with the impact velocity. Therefore, there is a certain error in the calculation using the above simplified method, which leads to inaccurate calculated rock breaking energy utilization rate. Summary of the invention

[0005] The purpose of the present invention is to overcome the defects and problems of low accuracy in calculating rock breaking energy utilization in the prior art, and to provide a device with high accuracy for determining the energy consumption of fracture of jointed rock samples in SHPB tests and a method for using the same.

[0006] To achieve the above purpose, the technical solution of the present invention is: a device for determining the crushing energy consumption of jointed rock samples in SHPB tests, the device comprising a protective box, a heating device, a 3D scanner, and an infrared thermal imager, the protective box is cylindrical, a cavity for accommodating jointed rock samples is provided at the center of the protective box, holes connected to the incident rod and the transmission rod in the SHPB system are respectively provided on the front and rear end surfaces of the protective box, the holes are connected to the cavity, a plurality of mounting holes are provided on the outer peripheral surface of the protective box along the circumferential direction, a rigid rod is slidably connected in the mounting hole, one end of the rigid rod is located in the cavity and arranged relative to the jointed rock sample, the other end of the rigid rod is located outside the protective box and connected to a shape memory alloy, one end of the shape memory alloy is connected to the outer peripheral surface of the protective box, the heating device is connected to the protective box, and the 3D scanner and the infrared thermal imager are respectively arranged relative to the protective box;

[0007] The heating device is used to heat the deformed shape memory alloy to restore it to its original state;

[0008] The 3D scanner is used to scan the peripheral volume of the protection box before and after the SHPB test;

[0009] The infrared thermal imager is used to record the temperature change in the protection box during the SHPB test.

[0010] The heating device comprises a plurality of heating tubes, and the plurality of heating tubes are plugged into the inner wall of the protection box along the circumferential direction.

[0011] A fixing frame is arranged outside the protection box, two ends of the protection box are connected to the fixing frame through connecting rods, and the 3D scanner is movably connected to the fixing frame along the circumferential direction of the protection box.

[0012] The fixing frame includes a base and two circular rings, the two circular rings are respectively connected to the upper side of the base and are coaxially arranged on the outside of the protective box, both circular rings are slidably connected with a ring, a rotating rod is connected between the two rings, and the 3D scanner is installed in the middle of the rotating rod.

[0013] The protection box comprises an upper half box and a lower half box, one side of the upper half box and the lower half box are connected to each other through a hinge, and the other side of the upper half box and the lower half box are buckled and connected.

[0014] A method for using a device for determining the energy consumption of fracture of a jointed rock sample in a SHPB test, the method comprising the following steps:

[0015] Step 1: Place the jointed rock sample to be tested in the middle of the incident rod and the transmission rod of the SHPB system, place the protective box outside the jointed rock sample, start the test to impact the jointed rock sample, and calculate the total energy consumption of the jointed rock sample during the test. ;

[0016] Step 2: Use a 3D scanner to scan the outer volume of the protective box before and after the test, and calculate the kinetic energy of the fragments of the jointed rock sample ;

[0017] Step 3: The kinetic energy of the fragments ejected calculated in step 2 After correction, the kinetic energy of the fragment ejection is ;

[0018] Step 4: Use an infrared thermal imager to record the temperature changes in the protective box during the test and calculate the dissipated heat energy during the impact of the jointed rock sample. ;

[0019] Step 5: Calculate crushing energy consumption based on the principle of energy conservation , the calculation formula is as follows:

[0020] ;

[0021] Step 6: Use a heating device to heat the protective box, restore the deformed shape memory alloy to its original state through temperature increase and heat conduction, and conduct the SHPB test of the next jointed rock sample.

[0022] In step 1, the total energy consumption of the jointed rock sample during the test The calculation formula is:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] Where: is the cross-sectional area of ​​the incident bar of the SHPB system; is the elastic modulus of the incident rod of the SHPB system; is the velocity of longitudinal waves propagating in the incident bar of the SHPB system; The time for the test; , , are the incident strain, reflected strain and transmitted strain recorded by the dynamic strain collector of the SHPB system, is the incident energy, is the reflected energy, is the transmission energy.

[0028] In the step 2, the kinetic energy of the ejection of the fragments of the jointed rock sample is The calculation formula is:

[0029] ;

[0030] in, is the number of all rigid rods, is the deformation stiffness of a single shape memory alloy, is the sum of the cross-sectional areas of all rigid rods, is the volume change of the protective box.

[0031] In the step 4, the heat dissipated during the impact of the jointed rock sample The calculation formula is:

[0032] ;

[0033] in, is the mass of the jointed rock sample, is the specific heat capacity of the jointed rock sample, is the temperature change value inside the protective box.

[0034] Kinetic energy of the fragment ejection after correction The calculation formula is:

[0035] ;

[0036] ;

[0037] in, , are the diameter and height of the cylindrical cavity enclosed by all rigid rods close to the jointed rock sample, is the friction coefficient of the inner wall of the mounting hole, is the total deadweight of the rigid rod, is the sum of the cross-sectional areas of all rigid rods, is the volume change of the protective box, is the correction factor.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. In the device and method for using the device for determining the energy consumption of the fracture of the jointed rock sample in the SHPB test of the present invention, by setting the shape memory alloy and the rigid rod, the protective box can prevent the fragments of the jointed rock sample from splashing to the outside, and play a certain protective role. The jointed rock sample will be broken during the impact process, and the fragments will hit the rigid rod and push the rigid rod to move outward. Since the rigid rod is connected to the shape memory alloy, the shape memory alloy will be deformed, that is, the kinetic energy of the ejection of the fragments of the jointed rock sample during the impact process is cleverly converted into deformation energy, and then the deformation energy is visualized by scanning with a 3D scanner, so as to realize the quantitative calculation of the kinetic energy of the ejection of the fragments of the jointed rock sample. At the same time, an infrared thermal imager is used to obtain the temperature change in the protective box, so that the kinetic energy of the ejection of the fragments and the dissipated heat energy when the jointed rock sample is damaged by impact in the SHPB test can be accurately obtained, which can effectively improve the accuracy of the calculation of the rock breaking energy utilization rate. Therefore, the present invention has high safety and high calculation accuracy.

[0040] 2. In the device for determining the energy consumption of the fracture of jointed rock samples in the SHPB test and the method for using the device, a heating tube is provided, and the heating tube restores the deformed shape memory alloy to its original state by heating, so that the device can be reused to improve the utilization rate; by providing a fixed frame, the 3D scanner can make a circular motion along the center of the fixed frame on the fixed frame, so as to achieve the effect of comprehensively and evenly scanning the periphery of the protective box; the protective box adopts a hinge connection method, and after the test, the inside of the protective box can be cleaned and the components can be replaced by opening the protective box. Therefore, the present invention is simple to operate, easy to use, and has low test cost.

[0041] 3. In the device for determining the energy consumption of the fracture of the jointed rock sample in the SHPB test and the method for using the device, a 3D scanner is used to scan the peripheral volume of the protective box before and after the test and calculate the volume change, and the energy consumption caused by the friction between the rigid rod and the side wall of the mounting hole during the movement of the rigid rod is considered. The kinetic energy of the ejection of the fragments is corrected by calculating the friction energy consumption, thereby achieving quantitative calculation of the kinetic energy of the ejection of the jointed rock sample fragments and improving the accuracy of the calculation results. Therefore, the present invention is easy to operate and has high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a side view schematic diagram of the present invention.

[0043] Figure 2 It is a front view schematic diagram of the present invention.

[0044] Figure 3 It is a structural schematic diagram of the protection box in the present invention.

[0045] Figure 4 It is a partial structural schematic diagram of the protection box, rigid rod and shape memory alloy in the present invention.

[0046] In the figure: jointed rock sample 1, incident rod 2, transmission rod 3, protective box 4, upper half box 41, lower half box 42, cavity 43, hole 44, mounting hole 45, hinge 46, heating device 5, heating tube 51, rigid rod 6, shape memory alloy 7, fixing frame 8, base 81, ring 82, sleeve ring 83, rotating rod 84, connecting rod 9, 3D scanner 10, infrared thermal imager 11. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0048] Embodiment 1:

[0049] See also Figures 1 to 4 , a device for determining the energy consumption of fracture of jointed rock samples in SHPB test, the device comprising a protective box 4, a heating device 5, a 3D scanner 10, and an infrared thermal imager 11, the protective box 4 is cylindrical, a cavity 43 for accommodating the jointed rock sample 1 is provided at the center of the protective box 4, holes 44 connected to the incident rod 2 and the transmission rod 3 in the SHPB system are provided on the front and rear end surfaces of the protective box 4, respectively, the holes 44 are connected to the cavity 43, a plurality of mounting holes 45 are provided on the outer peripheral surface of the protective box 4 along the circumferential direction, a rigid rod 6 is slidably connected in the mounting hole 45, one end of the rigid rod 6 is located in the cavity 43 and arranged relative to the jointed rock sample 1, the other end of the rigid rod 6 is located outside the protective box 4 and connected to a shape memory alloy 7, one end of the shape memory alloy 7 is connected to the outer peripheral surface of the protective box 4, the heating device 5 is connected to the protective box 4, the 3D scanner 10 and the infrared thermal imager 11 are arranged relative to the protective box 4 respectively;

[0050] The heating device 5 is used to heat the deformed shape memory alloy 7 to restore it to its original state;

[0051] The 3D scanner 10 is used to scan the peripheral volume of the protection box 4 before and after the SHPB test;

[0052] The infrared thermal imager 11 is used to record the temperature change in the protection box 4 during the SHPB test.

[0053] In this embodiment, the protective box 4 is a hollow structure with a plurality of mounting holes 45 evenly distributed on the surface. The diameter of the mounting holes 45 is 0.5 cm. The rigid rod 6 is vertically placed in the mounting hole 45 on the surface of the protective box 4. The shape memory alloy 7 is spirally shaped. One end of the shape memory alloy 7 is welded to the outer surface of the protective box 4, and the other end is welded to the end of the rigid rod 6. The rigid rod 6 is a steel cylindrical rod that is not easily deformed.

[0054] Embodiment 2:

[0055] The basic content is the same as that of Example 1, except that:

[0056] See also Figure 3 The heating device 5 includes a plurality of heating tubes 51 , and the plurality of heating tubes 51 are plugged into the inner wall of the protection box 4 along the circumferential direction.

[0057] In this embodiment, the heating tube 51 can be an electric heating tube. The heating tubes 51 are arranged at equal intervals in the protective box 4. The heating tubes 51 are connected to the circuit. When power is turned on, the heating tubes 51 are heated, thereby driving the shape memory alloy 7 to return to its original state.

[0058] Embodiment 3:

[0059] The basic content is the same as that of Example 1, except that:

[0060] See also Figures 1 to 3 A fixing frame 8 is provided on the outside of the protection box 4, and both ends of the protection box 4 are connected to the fixing frame 8 through connecting rods 9. The 3D scanner 10 is movably connected to the fixing frame 8 along the circumferential direction of the protection box 4. The fixing frame 8 includes a base 81 and two circular rings 82. The two circular rings 82 are respectively connected to the upper side of the base 81 and are coaxially arranged on the outside of the protection box 4. The two circular rings 82 are slidably connected with a collar 83. A rotating rod 84 is connected between the two collars 83. The 3D scanner 10 is installed in the middle of the rotating rod 84.

[0061] The protection box 4 includes an upper half box 41 and a lower half box 42 . One side of the upper half box 41 and the lower half box 42 are connected to each other through a hinge 46 , and the other side of the upper half box 41 and the lower half box 42 are buckled and connected.

[0062] In this embodiment, the end of the rotating rod 84 can be connected to the gear ring, and the gear ring can be driven to rotate by a motor, thereby driving the 3D scanner 10 to move circumferentially along the ring 82. After the test, the upper half box 41 and the lower half box 42 can be opened, the jointed rock sample 1 can be cleaned and replaced, and subsequent tests can be carried out.

[0063] Embodiment 4:

[0064] A method for using the device for determining the energy consumption of fracture of a jointed rock sample in a SHPB test as described in Example 1, the method comprising the following steps:

[0065] Step 1: Place the jointed rock sample 1 to be tested in the middle of the incident rod 2 and the transmission rod 3 of the SHPB system, place the protective box 4 outside the jointed rock sample 1, start the test to impact the jointed rock sample 1, and calculate the total energy consumption of the jointed rock sample 1 during the test according to the formula :

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] Where: is the cross-sectional area of ​​the incident rod 2 of the SHPB system; is the elastic modulus of the incident rod 2 of the SHPB system; is the velocity of the longitudinal wave propagating in the incident rod 2 of the SHPB system; The time for the test; , , are the incident strain, reflected strain and transmitted strain recorded by the dynamic strain collector of the SHPB system, is the incident energy, is the reflected energy, is the transmission energy.

[0071] Step 2: Use a 3D scanner 10 to scan the outer volume of the protective box 4 before and after the test, and calculate the kinetic energy of the fragments of the jointed rock sample 1 ejected. :

[0072] ;

[0073] in, is the number of all rigid rods 6, is the deformation stiffness of shape memory alloy 7, is the sum of the cross-sectional areas of all rigid rods 6, is the volume change of the protection box 4;

[0074] Step 3: The kinetic energy of the fragments ejected calculated in step 2 Correction is made, and the kinetic energy of the fragments ejected after correction for:

[0075] ;

[0076] ;

[0077] in, , are the diameter and height of the cylindrical cavity surrounded by the end of all rigid rods 6 close to the jointed rock sample 1, is the friction coefficient of the inner wall of the mounting hole 45, is the total deadweight of the rigid rod 6, is the sum of the cross-sectional areas of all rigid rods 6, is the volume change of the protection box 4, is the correction factor;

[0078] Considering that the radial ejection of the sample fragments is restricted by the presence of the incident rod 2 and the transmission rod 3 during the ejection process, the ejection kinetic energy of the fragments in this part cannot be recorded by the device described in the present invention. Since the rigid rod 6 and the shape memory alloy 7 are only arranged on the side surface of the protection box 4 in this embodiment, only the circumferential ejection kinetic energy of the fragments in the sample crushing process is recorded, while the front and rear end surfaces of the protection box 4 are not included. In order to consider this influence, the correction coefficient In addition, the energy consumption caused by the friction between the rigid rod 6 and the side wall of the mounting hole 45 during the movement is: (According to the friction energy dissipation formula in physics, since not all rigid rods 6 have friction effect, the friction effect is more obvious for the rigid rods 6 arranged horizontally, so it is multiplied by a coefficient of 2 / 3 for reduction);

[0079] Step 4: Use an infrared thermal imager 11 to record the temperature change in the protective box 4 during the test, and calculate the dissipated heat energy of the jointed rock sample 1 during the impact process. :

[0080] ;

[0081] in, is the mass of jointed rock sample 1, is the specific heat capacity of jointed rock sample 1, is the temperature change value in the protection box 4;

[0082] Step 5: Calculate crushing energy consumption based on the principle of energy conservation , the calculation formula is as follows:

[0083] ;

[0084] Step 6: Use the heating device 5 to heat the protection box 4, so that the deformed shape memory alloy 7 is restored to its original state through temperature increase and heat conduction, and then the next SHPB test of the jointed rock sample 1 is carried out.

Claims

1. A device for determining the energy consumption of fracture of a jointed rock sample in a SHPB test, characterized in that: The device comprises a protective box (4), a heating device (5), a 3D scanner (10), and an infrared thermal imager (11); the protective box (4) is cylindrical; a cavity (43) for accommodating a jointed rock sample (1) is provided at the center of the protective box (4); holes (44) connected to an incident rod (2) and a transmission rod (3) in a SHPB system are provided on the front and rear end surfaces of the protective box (4); the holes (44) are connected to the cavity (43); and a plurality of mounting holes (45) are provided on the outer peripheral surface of the protective box (4) along the circumferential direction. A rigid rod (6) is slidably connected in the mounting hole (45), one end of the rigid rod (6) is located in the cavity (43) and arranged relative to the jointed rock sample (1), the other end of the rigid rod (6) is located outside the protection box (4) and is connected to a shape memory alloy (7), one end of the shape memory alloy (7) is connected to the outer peripheral surface of the protection box (4), the heating device (5) is connected to the protection box (4), and the 3D scanner (10) and the infrared thermal imager (11) are respectively arranged relative to the protection box (4); The heating device (5) is used to heat the deformed shape memory alloy (7) to restore it to its original state; The 3D scanner (10) is used to scan the peripheral volume of the protection box (4) before and after the SHPB test; The infrared thermal imager (11) is used to record the temperature change in the protection box (4) during the SHPB test.

2. A device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 1, characterized in that: The heating device (5) comprises a plurality of heating tubes (51), and the plurality of heating tubes (51) are plugged into the inner wall of the protection box (4) along the circumferential direction.

3. A device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 1, characterized in that: A fixing frame (8) is arranged on the outside of the protection box (4), two ends of the protection box (4) are connected to the fixing frame (8) via connecting rods (9), and the 3D scanner (10) is movably connected to the fixing frame (8) along the circumferential direction of the protection box (4).

4. A device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 3, characterized in that: The fixing frame (8) comprises a base (81) and two circular rings (82), the two circular rings (82) are respectively connected to the upper side of the base (81) and are coaxially arranged on the outside of the protective box (4), the two circular rings (82) are slidably connected with a ring (83), a rotating rod (84) is connected between the two rings (83), and the 3D scanner (10) is installed in the middle of the rotating rod (84).

5. The device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 1, characterized in that: The protective box (4) comprises an upper half box (41) and a lower half box (42); one side of the upper half box (41) and the lower half box (42) are connected to each other via a hinge (46); the other side of the upper half box (41) and the lower half box (42) are buckled and connected.

6. A method for using the device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 1, characterized in that: The method of use comprises the following steps: Step 1: Place the jointed rock sample (1) to be tested in the middle of the incident rod (2) and the transmission rod (3) of the SHPB system, place the protection box (4) outside the jointed rock sample (1), start the test to impact the jointed rock sample (1), and calculate the total energy consumption of the jointed rock sample (1) during the test. ; Step 2: Use a 3D scanner (10) to scan the outer volume of the protective box (4) before and after the test, and calculate the kinetic energy of the fragments of the jointed rock sample (1) ejected. ; Step 3: The kinetic energy of the fragments ejected calculated in step 2 After correction, the kinetic energy of the fragment ejection is ; Step 4: Use an infrared thermal imager (11) to record the temperature change in the protective box (4) during the test, and calculate the dissipated heat energy of the jointed rock sample (1) during the impact process. ; Step 5: Calculate crushing energy consumption based on the principle of energy conservation , the calculation formula is as follows: ； Step 6: Use the heating device (5) to heat the protective box (4), so that the deformed shape memory alloy (7) is restored to its original state through temperature increase and heat conduction, and then the SHPB test of the next jointed rock sample (1) is carried out.

7. The method for using the device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 6, characterized in that: In the step 1, the total energy consumption of the jointed rock sample (1) during the test is The calculation formula is: ； ； ； ； Where: is the cross-sectional area of ​​the incident rod (2) of the SHPB system; is the elastic modulus of the incident rod (2) of the SHPB system; is the velocity of the longitudinal wave propagating in the incident bar (2) of the SHPB system; The time for the test; , , are the incident strain, reflected strain and transmitted strain recorded by the dynamic strain collector of the SHPB system, is the incident energy, is the reflected energy, is the transmission energy.

8. The method for using the device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 6, characterized in that: In the step 2, the kinetic energy of the ejection of the fragments of the jointed rock sample (1) is The calculation formula is: ； in, is the number of all rigid rods (6), is the deformation stiffness of a single shape memory alloy (7), is the sum of the cross-sectional areas of all rigid rods (6), is the volume change of the protection box (4).

9. The method for using the device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 6, characterized in that: In step 4, the heat energy dissipated during the impact of the jointed rock sample (1) The calculation formula is: ； in, is the mass of the jointed rock sample (1), is the specific heat capacity of the jointed rock sample (1), is the temperature change value inside the protection box (4).

10. The method for using the device for determining the crushing energy consumption of a jointed rock sample in a SHPB test according to claim 6, characterized in that: Kinetic energy of the fragment ejection after correction The calculation formula is: ； ； in, , are the diameter and height of the cylindrical cavity enclosed by all rigid rods (6) at one end close to the jointed rock sample (1), is the friction coefficient of the inner wall of the mounting hole (45), is the total deadweight of the rigid rod (6), is the sum of the cross-sectional areas of all rigid rods (6), is the volume change of the protection box (4), is the correction factor.

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