Engine piston skirt rigidity measuring device and method

Abstract

The application provides an engine piston skirt rigidity measuring device and method, and relates to the technical field of engine pistons. The engine piston skirt rigidity measuring device and method are suitable for measuring the rigidity of the engine piston skirt, adopt a full-displacement constraint mode to completely fix the piston, adopt a symmetrical pressurizing mode to pressurize the piston skirt measuring points, ensure that the piston skirt measuring points are balanced in stress, adopt a high-precision laser displacement sensor to non-contact accurately measure the piston stress points and surrounding measuring points, can accurately measure the displacement of the piston measuring points and surrounding stress deformation points, and can further solve the rigidity value of the piston. Not only can the application provide important data support for high-strength and lightweight piston design, but also can provide reliable boundary input parameters for piston dynamics calculation, and has extremely important significance for the service life of the piston and the research on the economy, reliability and safety of the engine.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of engine piston, in particular to a device and method for measuring the rigidity of the skirt of an engine piston. BACKGROUND

[0002] In the field of internal combustion engines, the piston is the core component of the engine. During the operation of the engine, under the action of high-temperature and high-pressure gas generated by fuel combustion, the piston makes high-speed reciprocating motion in the cylinder liner, and the working environment is very harsh. During the high-speed reciprocating motion, the piston skirt plays a supporting and guiding role for the piston, and the rigidity of the piston skirt directly determines the motion state of the piston, and thus has an important influence on the reliability and durability of the engine. Therefore, the rigidity of the piston skirt is an important factor that must be considered in the design of the piston. If the rigidity of the skirt is too high, it will not only cause the cylinder to be pulled due to excessive contact pressure of the skirt, but also increase the weight of the piston, resulting in an increase in engine noise; and if the rigidity is too small, it will cause the skirt to wear out and be insufficient in strength, resulting in an increase in friction loss, and even causing the skirt to collapse. Therefore, accurate measurement of the rigidity of the piston skirt is of great significance to the service life of the piston and the research on the economy, reliability and safety of the engine. At present, the rigidity of the piston skirt is mostly measured by software simulation calculation, and the software simulation calculation result is only a theoretical simulation and cannot replace the actual experimental measurement data. SUMMARY

[0003] The present application aims to provide a device and method for measuring the rigidity of the skirt of an engine piston, so as to accurately measure the rigidity of the skirt of an engine piston.

[0004] In order to achieve the above-mentioned purpose, the technical solution adopted by the present application is as follows:

[0005] A device for measuring the rigidity of the skirt of an engine piston, comprising a base, a support frame, a top seat, a piston clamping table, an upper pressure head, a left pressure head, a first probe, a right pressure head, a second probe, a first laser displacement sensor, a second laser displacement sensor and a collection control system.

[0006] The base is connected to the top seat through the support frame, and the top seat is located above the base.

[0007] The upper end of the base is provided with the piston clamping table, and the piston clamping table is used to clamp one end of the piston.

[0008] The lower end of the top seat is provided with the upper pressure head, which can be extended in the vertical direction to apply a set pressure, and the lower end of the upper pressure head is provided with a chuck, which is used to clamp the other end of the piston.

[0009] The left side of the base is provided with the left pressing head, which can extend along the horizontal direction to apply a set pressure, and the left pressing head is provided with the first probe, which extends along the horizontal direction, and the first probe is provided with a positioning plate;

[0010] The right side of the base is provided with the right pressing head, which can extend along the horizontal direction to apply a set pressure, and the right pressing head is provided with the second probe, which extends along the horizontal direction;

[0011] The first probe and the second probe are located on the same straight line, and the ends of the first probe and the second probe are used to abut against the skirt of the piston;

[0012] The sensing end of the first laser displacement sensor faces the positioning plate, and the second laser displacement sensor is provided in a plurality of numbers, and the sensing end of the second laser displacement sensor is used to face the skirt of the piston;

[0013] The acquisition control system is respectively connected to the control ends of the upper pressing head, the left pressing head, the right pressing head, the first laser displacement sensor and the second laser displacement sensor through signal cables.

[0014] Preferably, the opposite sides of the upper end of the piston clamping table are provided with clamping blocks, the clamping blocks on the opposite sides jointly clamp one end of the piston, and the distance between the clamping blocks on the opposite sides is adjustable.

[0015] Preferably, the other end of the piston is connected with a piston pin, and the collet clamps the piston pin.

[0016] Preferably, the lower end of the upper pressing head is provided with a rotary table, and the rotor of the rotary table is provided with the collet.

[0017] Preferably, the left side of the base is provided with a left lifting table, the left lifting table can be lifted along the vertical direction, and the left pressing head is arranged on the left lifting table; the right side of the base is provided with a right lifting table, the right lifting table can be lifted along the vertical direction, and the right pressing head is arranged on the right lifting table.

[0018] Preferably, the acquisition control system is further connected to the control ends of the left lifting table and the right lifting table through signal cables.

[0019] Preferably, the acquisition control system comprises an upper pressure control unit, a symmetric pressure control unit, a displacement sensing data transmission unit and a computer; the computer is connected with the upper pressure control unit, the symmetric pressure control unit and the displacement sensing data transmission unit through signal cables respectively, the upper pressure control unit is connected with the control end of the upper pressure head through a signal cable, the symmetric pressure control unit is connected with the control end of the left pressure head and the right pressure head through signal cables respectively, and the displacement sensing data transmission unit is connected with the control end of the first laser displacement sensor and the second laser displacement sensor through signal cables respectively.

[0020] An engine piston skirt rigidity measurement method using the engine piston skirt rigidity measurement device described above;

[0021] From one side of the piston skirt, a longitudinal section is selected every interval of a set angle along the circumference of the piston, a set number of points are selected on each longitudinal section along the axial direction of the piston and numbered from bottom to top, the ith point is taken as the first measuring point, and the jth point around the ith point is taken as the second measuring point;

[0022] The method is as follows:

[0023] Step 1: The head of the piston is clamped by the piston clamping table, the piston pin on the piston is clamped by the clamp, and the upper pressure head is controlled by the acquisition control system to extend downward to apply a set pressure to fix the piston;

[0024] The end of the first probe abuts against the first measuring point, the end of the second probe abuts against the point opposite to the first measuring point, the sensing end of the first laser displacement sensor faces the positioning plate, and the sensing ends of the plurality of second laser displacement sensors face the second measuring points;

[0025] Step 2: The left pressure head is controlled by the acquisition control system to extend rightward, and the right pressure head is controlled by the acquisition control system to extend leftward synchronously, when the acquisition control system senses the pressure value through the left pressure head and / or the right pressure head, the displacement values sensed by the first laser displacement sensor and the second laser displacement sensor at this time are taken as zero points, the left pressure head continues to extend rightward, and the right pressure head continues to extend leftward to apply an equal set pressure Fi;

[0026] Step 3: The acquisition control system acquires the displacement values sensed by the first laser displacement sensor 51 and the second laser displacement sensor 52 under the set pressure Fi;

[0027] Step 4: Steps 1 to 3 are repeated to obtain the rigidity matrix K, and the formula is as follows:

[0028]

[0029] Wherein,

[0030] F1 is the radial force on the first point, F2 is the radial force on the second point, F nRadial force at the nth point, F1, F2…F n Measured by the left and / or right pressure head;

[0031] S 11 Radial deformation of the first point, S 12 , S 13 …S 1n Radial deformation of each j point around the first point when the first point is stressed, S 11 Measured by the first laser displacement sensor, S 12 , S 13 …S 1n Measured by the second laser displacement sensor;

[0032] S 22 Radial deformation of the second point, S 21 , S 23 …S 2n Radial deformation of each j point around the second point when the second point is stressed, S 22 Measured by the first laser displacement sensor, S 21 , S 23 …S 2n Measured by the second laser displacement sensor;

[0033] S nn Radial deformation of the nth point, S n1 , S n2 , S n3 …Radial deformation of each j point around the nth point when the nth point is stressed, S nn Measured by the first laser displacement sensor, S n1 , S n2 , S n3 …Measured by the second laser displacement sensor.

[0034] The beneficial technical effects of the present application are:

[0035] The engine piston skirt rigidity measuring device and method of the present application is suitable for measuring the rigidity of the engine piston skirt. The piston is completely fixed by adopting full displacement constraint. The measuring points of the piston skirt are stressed by adopting symmetric stressing, which ensures that the measuring points of the piston skirt are stressed evenly. The high-precision laser displacement sensor is used to accurately measure the displacement of the measuring points of the piston and the surrounding points after stress deformation, so as to solve the rigidity value of the piston. Not only can it provide important data support for high-strength and lightweight piston design, but also can provide reliable boundary input parameters for piston dynamics calculation, which has extremely important significance for the service life of the piston and the economy, reliability and safety of the engine. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 Structure diagram of engine piston skirt rigidity measuring device in an embodiment of the present application is shown in the figure.

[0037] Figure 2 Distribution diagram of laser displacement sensor in an embodiment of the present application is shown in the figure.

[0038] Figure 3 Distribution diagram of piston skirt measuring point in an embodiment of the present application is shown in the figure. Figure 3 12 circles on the piston skirt are measuring points. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical scheme and beneficial effects of the present application clearer and more apparent, the present application will be further described in detail below in combination with specific embodiments and with reference to the drawings. Some but not all embodiments of the present application will be shown in the drawings. In fact, various embodiments of the present application can be implemented in many different forms, and should not be interpreted as being limited to the embodiments described herein; on the contrary, these embodiments are provided to meet the applicable legal requirements.

[0040] In the description of the present application, it should be noted that the terms "inner", "outer", "upper", "lower", "front", "back" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. In addition, the terms "first" and "second" are only for descriptive purposes and should not be understood as indicating or implying relative importance.

[0041] In an embodiment of the present application, an engine piston skirt rigidity measuring device and an engine piston skirt rigidity measuring method are provided, please refer to Figures 1 to 3 shown.

[0042] An engine piston skirt rigidity measuring device, comprising a base 11, a support frame 12, a top seat 13, a piston clamping table 2, an upper pressure head 31, a left pressure head 321, a first probe 41, a right pressure head 322, a second probe 42, a first laser displacement sensor 51, a second laser displacement sensor 52 and a collection control system.

[0043] The base 11 is connected to the top seat 13 through the support frame 12, and the top seat 13 is located directly above the base 11.

[0044] The upper end of the base 11 is provided with a piston clamping table 2 for clamping one end of the piston 6. The opposite sides of the upper end of the piston clamping table 2 are provided with clamping blocks 21, and the clamping blocks 21 on the opposite sides jointly clamp one end of the piston 6. The distance between the clamping blocks 21 on the opposite sides is adjustable. Specifically, the clamping blocks 21 are slidingly connected to the piston clamping table 2. The inner end of the clamping block 21 is provided with an arc-shaped groove, and the outer end of the clamping block 21 is connected to the piston clamping table 2 through a bolt 22. The arc-shaped grooves of the clamping blocks 21 on the opposite sides are clamped with the piston 6, and the position of the clamping block 21 is adjusted by rotating the bolt 22, so as to adapt to pistons 6 of different diameters and realize the fixing and limiting of one end of the piston 6 of different diameters.

[0045] The lower end of the top seat 13 is provided with an upper pressing head 31, which can extend in the vertical direction to apply a set pressure. The lower end of the upper pressing head 31 is provided with a chuck 311 for clamping the other end of the piston 6. The other end of the piston 6 is connected with a piston pin 61, and the chuck 311 clamps the piston pin 61. Through the cooperation of the chuck 311 and the piston pin 61, the other end of the piston 6 is fixed and limited.

[0046] The lower end of the upper pressing head 31 is connected with the stator of a rotating table 312, and the rotor of the rotating table 312 is provided with the chuck 311. When measuring different angle measuring points of the skirt of the piston 6, the rotor of the rotating table 312 rotates relative to the stator to drive the chuck 311 to rotate circumferentially.

[0047] Under the pressing action of the upper pressing head 31 and through the fixing and limiting of the two ends of the piston 6 as described above, the piston 6 is completely fixed.

[0048] The left side of the base 11 is provided with a left pressing head 321, which can extend in the horizontal direction to apply a set pressure. The left pressing head 321 is provided with a first probe 41, which extends in the horizontal direction. The first probe 41 is provided with a positioning plate 411.

[0049] The right side of the base 11 is provided with a right pressing head 322, which can extend in the horizontal direction to apply a set pressure. The right pressing head 322 is provided with a second probe 42, which extends in the horizontal direction.

[0050] The first probe 41 and the second probe 42 are located on the same straight line, and the distal end of the first probe 41 and the distal end of the second probe 42 are used to abut against the skirt of the piston 6. In this way, the distal end of the first probe 41 abuts against the first measuring point, and the distal end of the second probe 42 abuts against the point opposite to the first measuring point, so that the piston 6 is balanced in force, and the overall piston 6 is prevented from being skewed, so as to improve the measurement accuracy. It should be noted that compared with arranging a support component (such as an arc-shaped seat) in a surface shape structure opposite to the first measuring point of the piston 6, the arrangement of the second probe 42 can make the displacement value measured by the second laser displacement sensor 52 more accurate.

[0051] The left side of the base 11 is provided with a left lifting platform 331, which can be lifted along the vertical direction, and the left pressure head 321 is arranged on the left lifting platform 331. The right side of the base 11 is provided with a right lifting platform 332, which can be lifted along the vertical direction, and the right pressure head 322 is arranged on the right lifting platform 332. According to different height positions of the measuring points, the left pressure head 321 and the right pressure head 322 are adjusted in height by adjusting the left lifting platform 331 and the right lifting platform 332 to lift along the vertical direction, so that the first probe 41 and the second probe 42 are aligned with the measuring points arranged on the skirt of the piston 6.

[0052] The sensing end of the first laser displacement sensor 51 faces the positioning plate 411, and the second laser displacement sensor 52 is arranged in a plurality of groups. The second laser displacement sensor 52 is supported by the support rod 53, and the sensing end of the second laser displacement sensor 52 is used to face the skirt of the piston 6.

[0053] The acquisition control system is connected to the control ends of the upper pressure head 31, the turntable 312, the left pressure head 321, the right pressure head 322, the left lifting platform 331, the right lifting platform 332, the first laser displacement sensor 51 and the second laser displacement sensor 52 through signal cables.

[0054] Specifically, the acquisition control system includes an upper pressure control unit 71, a symmetric pressure control unit 72, a displacement sensing data transmission unit 73 and a computer 8. The computer 8 is connected to the upper pressure control unit 71, the symmetric pressure control unit 72 and the displacement sensing data transmission unit 73 through signal cables. The upper pressure control unit 71 is connected to the control ends of the upper pressure head 31 and the turntable 312 through signal cables. The symmetric pressure control unit 72 is connected to the control ends of the left pressure head 321, the right pressure head 322, the left lifting platform 331 and the right lifting platform 332 through signal cables. The displacement sensing data transmission unit 73 is connected to the control ends of the first laser displacement sensor 51 and the second laser displacement sensor 52 through signal cables.

[0055] The computer 8 controls the upper pressure head 31 to apply a set pressure and the rotation angle of the rotor of the turntable 312 through the upper pressure control unit 71. The computer 8 controls the left pressure head 321 and the right pressure head 322 to apply a set pressure and the lifting height of the left lifting platform 331 and the right lifting platform 332 through the symmetric pressure control unit 72. Moreover, the computer 8 collects the pressure values applied by the left pressure head 321 and the right pressure head 322 in real time through the symmetric pressure control unit 72. The computer 8 collects the displacement values sensed by the first laser displacement sensor 51 and the second laser displacement sensor 52 through the displacement sensing data transmission unit 73.

[0056] In the embodiment of the application, an engine piston skirt stiffness measurement method is also provided, which applies the engine piston skirt stiffness measurement device described above.

[0057] From one side of the piston 6 skirt, a longitudinal section is selected every interval angle along the piston 6 circumferential, a certain number of points are selected along the piston 6 axial on each longitudinal section and numbered from bottom to top, the i point is taken as the first measuring point, and the j point around the i point is taken as the second measuring point;

[0058] The method is as follows:

[0059] Step 1, clamp the head of the piston 6 by the clamp block 21 on the piston clamping table 2, clamp the piston pin 61 on the piston 6 by the clamp head 311, control the upper pressing head 31 to extend downward to apply a certain pressure by the acquisition control system, and fix the piston 6;

[0060] The end of the first probe 41 abuts against the first measuring point, the end of the second probe 42 abuts against the point opposite to the first measuring point, the sensing end of the first laser displacement sensor 51 faces the positioning plate 411, and the sensing ends of a plurality of second laser displacement sensors 52 face the second measuring point;

[0061] Step 2, control the left pressing head 321 to extend rightward and the right pressing head 322 to extend leftward synchronously by the acquisition control system, when the acquisition control system senses the pressure value by the left pressing head 321 and / or the right pressing head 322, take the displacement values sensed by the first laser displacement sensor 51 and the second laser displacement sensor 52 at this time as zero point, continue to extend the left pressing head 321 rightward and the right pressing head 322 leftward to apply equal certain pressure Fi;

[0062] Step 3, the acquisition control system acquires the displacement values sensed by the first laser displacement sensor 51 and the second laser displacement sensor 52 under the certain pressure Fi;

[0063] Step 4, repeat steps 1 to 3, and obtain the stiffness matrix K formula as follows:

[0064]

[0065] Wherein,

[0066] F1 is the radial force on the first point, F2 is the radial force on the second point, F n is the radial force on the n point, F1, F2…F n measured by the left pressing head 321 and / or the right pressing head 322;

[0067] S 11 is the radial deformation of the first point when the first point is stressed, S 12 , S 13 …S 1n is the radial deformation of each j point around the first point when the first point is stressed, S 11 measured by the first laser displacement sensor 51, S 12, S 13 …S 1n measured by the second laser displacement sensor 52;

[0068] S 22 is the radial deformation of the second point when force is applied to the second point, S 21 , S 23 …S 2n is the radial deformation of each j point around the second point when force is applied to the second point, S 22 measured by the first laser displacement sensor 51, S 21 , S 23 …S 2n measured by the second laser displacement sensor 52;

[0069] S nn is the radial deformation of the n-th point when force is applied to the n-th point, S n1 , S n2 , S n3 …is the radial deformation of each j point around the n-th point when force is applied to the n-th point, S nn measured by the first laser displacement sensor 51, S n1 , S n2 , S n3 …measured by the second laser displacement sensor 52.

[0070] Thus far, the present embodiment has been described in detail in conjunction with the accompanying drawings. Based on the above description, those skilled in the art should have a clear understanding of the engine piston skirt rigidity measuring device of the present application. The engine piston skirt rigidity measuring device and method of the present application are suitable for measuring the rigidity of the skirt of an engine piston. The piston 6 is completely fixed by using a full-displacement constraint method. The measuring points on the skirt of the piston 6 are pressurized by using a symmetrical pressurizing method, so as to ensure that the measuring points on the skirt of the piston 6 are balanced in force. The force points and surrounding measuring points of the piston 6 are accurately measured by using high-precision laser displacement sensors (the first laser displacement sensor 51 and the second laser displacement sensor 52) in a non-contact manner. The displacement amounts of the measuring points and surrounding force-deformed points of the piston 6 can be accurately measured, and the rigidity value (rigidity matrix) of the piston 6 can be solved. Not only can important data support be provided for high-strength and lightweight piston design, but also reliable boundary input parameters can be provided for piston dynamics calculation. This has extremely important significance for the service life of the piston and the economy, reliability and safety of the engine.

[0071] The above-described specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above-described specific embodiments are merely examples of the present application and are not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A device for measuring the stiffness of an engine piston skirt, characterized in that: It includes a base, support frame, top seat, piston clamping stage, upper pressure head, left pressure head, first probe, right pressure head, second probe, first laser displacement sensor, second laser displacement sensor, and acquisition and control system; The base is connected to the top seat via a support frame, and the top seat is located above the base; The piston clamping platform is provided at the upper end of the base, and the piston clamping platform is used to clamp one end of the piston; The upper pressure head is provided at the lower end of the top seat. The upper pressure head can extend vertically to apply a set pressure. A clamp is provided at the lower end of the upper pressure head. The clamp is used to hold the other end of the piston. The left pressure head is provided on the left side of the base. The left pressure head can extend horizontally to apply a set pressure. The left pressure head is provided with the first probe, which extends horizontally and is provided with a positioning plate. The right pressure head is provided on the right side of the base. The right pressure head can extend horizontally to apply a set pressure. The right pressure head is provided with a second probe, which extends horizontally. The first probe and the second probe are located in a straight line, and the ends of the first probe and the second probe are used to abut against the skirt of the piston. The sensing end of the first laser displacement sensor faces the positioning plate, and several second laser displacement sensors are provided, with the sensing end of the second laser displacement sensor facing the skirt of the piston. The acquisition and control system is connected to the control terminals of the upper pressure head, left pressure head, right pressure head, first laser displacement sensor and second laser displacement sensor via signal cables; The piston clamping platform has locking blocks on opposite sides at the upper end. The locking blocks on opposite sides together clamp one end of the piston, and the distance between the locking blocks on opposite sides is adjustable. The piston is connected to a piston pin at the other end, and the chuck holds the piston pin. The lower end of the upper pressure head is provided with a turntable, and the rotor of the turntable is provided with the chuck; A left lifting platform is provided on the left side of the base, which can be raised and lowered vertically, and a left pressure head is provided on the left lifting platform; a right lifting platform is provided on the right side of the base, which can be raised and lowered vertically, and a right pressure head is provided on the right lifting platform.

2. The engine piston skirt stiffness measuring device according to claim 1, characterized in that: The data acquisition and control system is also connected to the control terminals of the left and right lifting platforms via signal cables.

3. The engine piston skirt stiffness measuring device according to claim 1, characterized in that: The acquisition and control system includes an upper pressure control unit, a symmetrical pressure control unit, a displacement sensing data transmission unit, and a computer. The computer is connected to the upper pressure control unit, the symmetrical pressure control unit, and the displacement sensing data transmission unit via signal cables. The upper pressure control unit is connected to the control terminal of the upper pressure head via a signal cable. The symmetrical pressure control unit is connected to the control terminals of the left and right pressure heads via signal cables. The displacement sensing data transmission unit is connected to the control terminals of the first laser displacement sensor and the second laser displacement sensor via signal cables.

4. A method for measuring the stiffness of an engine piston skirt, characterized in that, The engine piston skirt stiffness measuring device according to any one of claims 1 to 3 is used; Starting from one side of the piston skirt, select a longitudinal section at predetermined angles along the piston circumference. On each longitudinal section, select a predetermined number of points along the piston axis and number them from bottom to top. i Point 1 is used as the first measurement point, and the second point is used as the third measurement point. i Around the point j Point 1 was used as the second measuring point. The method is as follows: Step 1: Clamp the piston head with the piston clamping table, clamp the piston pin on the piston with the chuck, and control the upper pressure head to extend downward to apply a set pressure to fix the piston. The end of the first probe is brought into contact with the first measuring point, the end of the second probe is brought into contact with the point opposite the first measuring point, the sensing end of the first laser displacement sensor is directed toward the positioning plate, and the sensing ends of several second laser displacement sensors are directed toward the second measuring point. Step 2: Control the left pressure head to extend to the right and the right pressure head to extend to the left simultaneously via the data acquisition and control system. When the data acquisition and control system senses the pressure value through the left pressure head and / or the right pressure head, take the displacement values ​​sensed by the first laser displacement sensor and the second laser displacement sensor at this time as the zero point, and continue to extend the left pressure head to the right and the right pressure head to the left to apply equal set pressure. Fi ; Step 3: The data acquisition and control system acquires the set pressure. Fi The displacement values ​​sensed by the first laser displacement sensor and the second laser displacement sensor; Step 4: Repeat steps 1 to 3 to obtain the stiffness matrix. K The formula is as follows: F 1 F 2… F n ； in, F 1 represents the radial force at point 1. F 2 represents the radial force at point 2. F n The radial force at point n. F 1. F 2… F n Measured by the left indenter and / or the right indenter; S 11 The radial deformation at point 1 when force is applied. S 12 , S 13 … S 1n When applying force to point 1, the area around point 1... j Radial deformation of a point S 11 Measured by the first laser displacement sensor, S 12 , S 13 … S 1n Measured by the second laser displacement sensor; S 22 The radial deformation at point 2 when force is applied at point 2. S 21 , S 23 … S 2n When applying force to point 2, the area around point 2... j Radial deformation of a point S 22 Measured by the first laser displacement sensor, S 21 , S 23 … S 2n Measured by the second laser displacement sensor; S nn The radial deformation at point n when force is applied is given. S n1 , S n2 , S n3 …when applying force to point n, the areas surrounding point n… j Radial deformation of a point S nn Measured by the first laser displacement sensor, S n1 , S n2 , S n3 …measured by the second laser displacement sensor.

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