CN116955915B - Method and device for measuring and calculating falling stone collision recovery coefficient - Google Patents
Method and device for measuring and calculating falling stone collision recovery coefficient Download PDFInfo
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- 238000011084 recovery Methods 0.000 title claims abstract description 182
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- 239000004575 stone Substances 0.000 title claims abstract description 22
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- 229910000831 Steel Inorganic materials 0.000 claims description 23
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- 239000004579 marble Substances 0.000 description 2
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- NIXOWILDQLNWCW-UHFFFAOYSA-N acrylic acid group Chemical group C(C=C)(=O)O NIXOWILDQLNWCW-UHFFFAOYSA-N 0.000 description 1
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Abstract
The invention provides a method and a device for measuring and calculating a falling stone collision recovery coefficient. The method comprises the following steps: based on a collision experiment of the rock sphere and the plane, a plurality of experimental results including normal incidence speed and experimental normal collision recovery coefficient are obtained; determining the contact yield stress corresponding to each normal incidence speed by a dichotomy, and calculating three average values of all the contact yield stresses; calculating three corresponding groups of normal collision recovery coefficients based on three average values of each normal incidence speed and contact yield stress; respectively calculating the mean square error of each group of normal collision recovery coefficients and experimental normal collision recovery coefficients; determining a contact yield stress value corresponding to the minimum mean square error as a fitting contact yield stress; based on the fitted contact yield stress, a collision recovery coefficient corresponding to the known incident speed and incident angle is obtained. The method provided by the invention can calculate the collision recovery coefficients under different incident speeds and incident angles.
Description
Technical Field
The invention belongs to the technical field of geotechnical engineering, and particularly relates to a method and a device for measuring and calculating a falling stone collision recovery coefficient.
Background
The falling rock disaster is one of common geological disasters, the falling rock movement track is complex and changeable, and particularly the movement track can be obviously influenced by collision in the movement process, so that the falling rock movement track can be accurately estimated by accurately analyzing the collision movement, and the falling rock protection design is assisted.
The collision recovery coefficient is a physical quantity representing the energy loss of a collision body before and after collision, and the physical quantity is influenced by a plurality of factors such as material quality, incident angle, impact speed and the like. The normal collision recovery coefficient under a certain working condition can only be calculated by a single frontal collision experiment, and in the falling stone movement process, the movement speed and the incident angle are changed at any time, so that the movement tracks of all falling stones in geological disasters cannot be known through the experiment, and therefore, a method for calculating the collision recovery coefficient of the falling stones with any incident speed and incident angle is needed.
Disclosure of Invention
The invention aims to provide a method for measuring and calculating a falling stone collision recovery coefficient, which can calculate normal and tangential collision recovery coefficients under different incident speeds and incident angles by using a calculation formula after determining the key parameter contact yield stress influencing the normal recovery collision coefficient.
In order to achieve the above object, the present invention provides a method for measuring and calculating a collision recovery coefficient of a falling stone, wherein the falling stone is a rock sphere, and the method comprises the following steps:
step (1), based on experiments that rock spheres do free falling body motion at a plurality of different heights and collide with a plane, a plurality of experimental results are obtained, wherein each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
determining the contact yield stress corresponding to each normal incidence speed by a dichotomy method by utilizing a first formula and a second formula, and calculating the average value of all the contact yield stresses, wherein the average value comprises three average values, namely an arithmetic average value, a geometric average value and a harmonic average value;
step (3), based on each normal incidence speed and each average value, calculating three groups of normal collision recovery coefficients corresponding to the three average values one by utilizing the second formula and the first formula, wherein each group of normal collision recovery coefficients comprises a plurality of calculated normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
step (4), respectively calculating the mean square error of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients, and obtaining a first mean square error corresponding to the arithmetic mean value, a second mean square error corresponding to the geometric mean value and a third mean square error corresponding to the harmonic mean value;
Step (5), determining an average value corresponding to a target mean square error as a fitting contact yield stress, wherein the target mean square error is the smallest mean square error among the first mean square error, the second mean square error and the third mean square error;
and (6) acquiring a normal collision recovery coefficient and a tangential collision recovery coefficient corresponding to known incident speed and incident angle by using the first formula, the second formula and the third formula based on the fitting contact yield stress.
In a specific embodiment, the first formula is:
wherein V is n Is the normal incidence speed;
V y is the yield rate;
k n is the normal collision recovery coefficient;
the second formula is:
wherein V is y Is the yield rate;
σ y is the contact yield stress;
ρ is the density of the rock spheres;
E * is the equivalent Young's modulus of a rock sphere.
In a specific embodiment, the step (2) includes:
determining yield speeds corresponding to the normal incidence speeds by using the first formula through a dichotomy, wherein the absolute error between a theoretical normal collision recovery coefficient corresponding to each yield speed and an experimental normal collision recovery coefficient with a corresponding relation is smaller than a first preset value;
Calculating a plurality of contact yield stresses based on each yield speed and a second formula, wherein the contact yield stresses correspond to the yield speeds one by one;
the average of all contact yield stresses was calculated and included three averages, arithmetic, geometric, and harmonic, respectively.
In a specific embodiment, the step (6) includes:
calculating to obtain a fitting yield speed corresponding to the fitting contact yield stress by using a second formula;
based on the known incident speed and incident angle, calculating the obtained normal incident speed to be calculated;
based on the fitting yield speed and the normal incidence speed to be measured and calculated, calculating a normal collision recovery coefficient corresponding to the known incidence speed by using a first formula;
and calculating a tangential collision recovery coefficient corresponding to the known incident speed based on the normal collision recovery coefficient by using a third formula.
In a specific embodiment, the step (1) includes:
step (a), providing an experimental set-up comprising:
a rock sphere, wherein the rock sphere is an experimental object;
the base comprises a bottom plate and a rock plate arranged on the upper side of the bottom plate;
The ball release mechanism comprises a guide rail, a ball release assembly and a distance measuring assembly, wherein the guide rail is installed at one end of the bottom plate, the ball release assembly is installed on the guide rail and can slide up and down along the guide rail, the distance measuring assembly is used for measuring the distance between the bottom of the rock ball and the surface of the rock plate far away from the bottom plate, and the rock ball is installed on the ball release assembly and is located right above the center position of the rock plate;
the camera shooting mechanism comprises a transparent grid plate arranged on one side of the bottom plate, a high-speed camera which is arranged opposite to the central axis of the transparent grid plate in the vertical direction, and a light supplementing lamp with the illumination direction facing to the falling area of the rock sphere, wherein the transparent grid plate is used for calibrating the position of the rock sphere;
step (b), fixing the ball release assembly with the rock ball at a first height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball;
step (c), fixing the release assembly with the rock ball mounted on a second height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball, wherein the second height position is different from the first height position;
Repeating the step (d) for a plurality of times to obtain dynamic images corresponding to the rock spheres when the rock spheres do free falling body movement at a plurality of different heights;
and (e) respectively processing all dynamic images to obtain a plurality of experimental results, wherein the number of the experimental results is the same as the number of experiments, and each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed.
In a specific embodiment, the step of obtaining each of the plurality of test results includes:
determining the distance between the bottom of the rock sphere and the rock plate based on the distance measured by the distance measuring assembly, and calculating to obtain the theoretical incident speed of the rock sphere;
based on the dynamic image shot by the high-speed camera, acquiring an experimental incidence speed and an experimental rebound speed corresponding to the free falling body movement of the rock ball;
and when the absolute error between the experimental incident speed and the theoretical incident speed is smaller than a second preset value, taking the ratio of the experimental rebound speed to the experimental incident speed as an experimental normal collision recovery coefficient, wherein the experimental incident speed is the normal incident speed in an experimental result, and the experimental normal collision recovery coefficient has a corresponding relation with the normal incident speed.
In a specific embodiment, the step of obtaining the experimental incident speed and the experimental rebound speed corresponding to the free falling motion of the rock ball based on the dynamic image shot by the high-speed camera includes:
acquiring a dynamic image shot by the high-speed camera, and selecting a first frame image and a second frame image of a rock sphere before collision with the rock plate, and a third frame image and a fourth frame image of a rock sphere after collision with the rock plate, wherein the shooting time of the first frame image, the shooting time of the second frame image, the shooting time of the third frame image and the shooting time of the fourth frame image are sequentially increased;
acquiring a first shooting time of the first frame image and a first position of the rock sphere on the transparent grid plate based on the first frame image; acquiring a second shooting time of the second frame image and a second position of the rock sphere on the transparent grid plate based on the second frame image; based on the absolute value of the difference value between the first position and the second position and the difference between the second shooting time and the first shooting time, acquiring the experimental incidence speed of the rock sphere;
Acquiring a third shooting time of the third frame image and a third position of the rock sphere on the transparent grid plate based on the third frame image; acquiring a fourth shooting time of the fourth frame image and a fourth position of the rock sphere on the transparent grid plate based on the fourth frame image; and acquiring the experimental rebound speed of the rock sphere based on the absolute value of the difference value between the fourth position and the third position and the difference between the fourth shooting time and the third shooting time.
In a specific embodiment, the sphere releasing assembly comprises a locking sliding block which is installed on the guide rail and can slide along the guide rail, a steel shell which is fixedly connected with the locking sliding block and is positioned right above the rock plate, a mounting hole which penetrates through the steel shell and is far away from one end of the guide rail, a motor which is fixed on the steel shell, and an electric expansion plate which is positioned in the steel shell and can expand and contract along the length direction of the steel shell, wherein the electric expansion plate is connected with the motor, and when the electric expansion plate is positioned at a limit position, the electric expansion plate is accommodated in the mounting hole, and the rock sphere is installed on the electric expansion plate; the range finding assembly comprises a laser range finder arranged at one end, far away from the guide rail, of the steel shell.
In a specific embodiment, the sphere releasing assembly comprises a first sliding block which is arranged on the guide rail and can slide along the guide rail, a first telescopic hollow rod which is fixedly connected with the first sliding block and is arranged vertically to the guide rail, a mechanical claw for placing a rock sphere, a connecting piece with one end connected with the first telescopic hollow rod and the other end connected with the mechanical claw, and a motor which is fixed at the non-telescopic end of the first telescopic hollow rod, wherein the output end of the motor is connected with the mechanical claw hand and can control the mechanical claw hand to open so as to release the rock sphere; the range unit is including installing in the guide rail and can follow the second slider that the guide rail slided, with second slider fixed connection and with the scalable hollow pole of the perpendicular setting of guide rail, be fixed in the scalable hollow pole of second is kept away from the laser range finder of guide rail one end, laser range finder is located the coplanar with the spheroidal bottom of ground.
The invention also provides a device for measuring and calculating the falling stone collision recovery coefficient, which comprises:
the first acquisition module is used for acquiring a plurality of experimental results based on experiments that the rock ball makes free falling motion at a plurality of different heights and collides with a plane, wherein each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
The first calculation module is used for determining the contact yield stress corresponding to each normal incidence speed through a dichotomy by utilizing a first formula and a second formula, and calculating the average value of all the contact yield stresses, wherein the average value comprises three average values, namely an arithmetic average value, a geometric average value and a harmonic average value;
the second calculation module is used for calculating three groups of normal collision recovery coefficients corresponding to the three average values one by one based on each normal incidence speed and each average value by utilizing the second formula and the first formula, and each group of normal collision recovery coefficients comprises a plurality of calculated normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
the third calculation module is used for respectively calculating the mean square error of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients to obtain a first mean square error corresponding to the arithmetic mean value, a second mean square error corresponding to the geometric mean value and a third mean square error corresponding to the harmonic mean value;
the determining module is used for determining an average value corresponding to a target mean square error as a fitting contact yield stress, wherein the target mean square error is the smallest mean square error among the first mean square error, the second mean square error and the third mean square error;
And the second acquisition module is used for acquiring a normal collision recovery coefficient and a tangential collision recovery coefficient corresponding to known incident speed and incident angle by using the first formula, the second formula and the third formula based on the fitting contact yield stress.
The beneficial effects of the invention at least comprise:
the invention provides a method for measuring and calculating a falling stone collision recovery coefficient, wherein the falling stone is a rock sphere, a plurality of experimental results comprising normal incidence speeds and experimental normal collision recovery coefficients corresponding to the normal incidence speeds are obtained through experiments of collision of a plurality of rock spheres and planes, then contact yield stress corresponding to the normal incidence speeds is reversely calculated through a dichotomy by utilizing a first formula and a second formula, arithmetic average values, geometric average values and harmonic average values of all the contact yield stress are calculated, the three average values are respectively substituted into the second formula to be calculated to obtain three yield speeds corresponding to the three average values one by one, and under the condition that the normal incidence speeds and the yield speeds are known, three calculation normal collision recovery coefficients corresponding to the normal incidence speeds can be calculated by utilizing the first formula; respectively calculating the mean square error of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients to obtain a first mean square error corresponding to the arithmetic mean value, a second mean square error corresponding to the geometric mean value and a third mean square error corresponding to the harmonic mean value; the average value corresponding to the smallest mean square error in the first mean square error, the second mean square error and the third mean square error is used as the fitting contact yield stress, the fitting yield speed can be calculated according to the obtained fitting contact yield stress, the fitting yield speed is substituted into the first formula, in this way, if the normal incidence speed is known, the normal collision recovery coefficient corresponding to the normal incidence speed can be calculated, then the normal collision recovery coefficient can be calculated by substituting into the third formula, and therefore the normal rebound speed and the tangential rebound speed after collision, namely the movement state of a sphere after collision, can be calculated, the result can directly help to determine the collision characteristics of a sphere particle system under complex topography, and help researchers to assist in analyzing the movement situation of a falling stone disaster.
In addition to the objects, features and advantages described above, the present invention has other objects, features and advantages. The present invention will be described in further detail with reference to the drawings.
Drawings
Fig. 1 is a schematic structural diagram of an experimental apparatus for collision between a ball drop and a plane according to embodiment 1 of the present invention;
FIG. 2 is an enlarged view of portion A of FIG. 1;
fig. 3 is a schematic structural diagram of an experimental apparatus for collision between a ball drop and a plane according to embodiment 2 of the present invention;
FIG. 4 is a flowchart showing the steps of a method for measuring and calculating the falling stone collision recovery coefficient according to embodiment 3 of the present invention;
FIG. 5 is a graph comparing the experimental normal crash recovery coefficient with the calculated normal crash recovery coefficient calculated based on the fitted contact yield stress
Fig. 6 is a block diagram of a measuring device for measuring and calculating the coefficient of restitution of a falling rock collision according to embodiment 3 of the present invention.
Detailed Description
The embodiments of the invention are described in detail below with reference to the attached drawings, but the invention can be defined and covered in a number of different embodiments according to the claims.
Example 1
Referring to fig. 1 and 2, the invention provides an experimental device 100 for collision between a ball falling and a plane, wherein the experimental device 100 captures images of the ball before and after collision by a high-speed camera, determines the movement distance of the ball within an interval time by the shooting time and the position of the images, thereby calculating the incident speed and the rebound speed of the ball, and then calculates the ratio of the rebound speed to the incident speed of the ball to obtain a normal collision recovery coefficient.
It should be noted that, in the device 100 provided by the present invention, the ball performs free falling motion, the normal incidence speed is equal to the incidence speed, and the rebound speed is equal to the normal rebound speed, so that the normal collision recovery coefficient=rebound speed/incidence speed.
In this embodiment, the rock sphere is used as the falling stone for the experiment, and in other embodiments, the experiment may be performed by using spheres made of other materials, which is different in that in the calculation process, the basic data related to the materials needs to be changed correspondingly.
The device 100 comprises a base 11, a sphere releasing mechanism 12, a camera shooting mechanism 13 and a rock sphere 14 arranged on the sphere releasing mechanism 12, wherein the sphere releasing mechanism 12 is used for releasing the rock spheres at different heights and colliding with the base 11 to generate rebound, and the camera shooting mechanism 13 is used for shooting dynamic images of falling and rebound of the rock spheres so as to accurately capture the motion states of the rock spheres before and after collision.
The base 11 includes a bottom plate 111, a rock plate 112 disposed on the bottom plate 111, and a plurality of guide wheels 113 mounted on a lower end of the bottom plate 111.
In this embodiment, the bottom plate 111 is a rectangular solid steel plate having dimensions of 1m (length) ×1m (width) ×10cm (height). The bottom plate 111 is used to carry the weight of other objects and to ensure that the whole experimental device is not deformed.
The rock plate 112 is made of a material to be measured, and in this embodiment, the dimensions of the rock plate 112 are 50cm (length) ×50cm (width) ×20cm (height), and the height of 20cm is used to ensure that the loss of collision energy in the collision test is all provided by the rock plate 112, irrespective of the steel material making the bottom plate 111.
In this example, the rock plates 112 are of the same material as the rock spheres 14, and are all marble.
In this embodiment, the number of the guide wheels 113 is four, and the four guide wheels 113 are respectively mounted at four corners of the bottom plate 111.
By providing the guide wheels 113, the experimental set-up 100 is conveniently moved.
Preferably, the base 11 further includes a first groove, a second groove, and a third groove formed by recessing inward from an upper surface of the bottom plate 111, the first groove is located at one end of the bottom plate 111, the second groove is located at one side of the bottom plate 111, a size of the first groove is smaller than a size of the second groove, and a central axis of the first groove in a width direction is perpendicular to a central axis of the second groove in the width direction; the third groove is located at the middle position of the bottom plate, the shape of the third groove is matched with the shape of the rock plate 112, and the rock plate 112 is partially embedded in the third groove.
The sphere release mechanism 12 comprises a guide rail 121 mounted in the first groove and detachably connected with the bottom plate 111, a sphere release assembly mounted on the guide rail 121 and capable of sliding up and down along the guide rail 121, and a distance measuring assembly 123 for measuring the distance between the bottom of the rock sphere 14 and the surface of the rock plate 112 away from the bottom plate 111, wherein the rock sphere 14 is mounted on the sphere release assembly and located right above the center position of the rock plate 112.
In this embodiment, the guide rail 121 is an SBR guide rail, and the height thereof is 2m; the guide rail 121 is disposed perpendicular to the plane of the rock plate 112.
In this embodiment, the guide rail 121 is connected to the bottom plate 111 by bolts.
The ball release assembly comprises a locking slide block 1221 mounted on the guide rail 121 and capable of sliding along the guide rail 121, a steel shell 1222 fixedly connected with the locking slide block 1221 and positioned right above the rock plate 112, a mounting hole formed through the steel shell 1222, a motor 1223 fixed on the steel shell 1222, and an electric telescopic plate 1224 positioned in the steel shell 1222 and capable of stretching along the length direction of the steel shell 1222, wherein the electric telescopic plate 1224 is connected with the motor 1223 and capable of retracting into the steel shell 1222 under the drive of the motor 1223, and the rock ball 14 is mounted on the electric telescopic plate 1224.
Before the experiment, the electric expansion plate 1124 is located at the limit position, at this time, the electric expansion plate is accommodated in the mounting hole, the rock mass ball 14 is placed on the electric expansion plate 1124, during the experiment, the motor 1223 drives the electric expansion plate 1124 to retract into the steel shell 1222 in a very short time, and no longer supports the rock mass ball 14, and the rock mass ball 14 moves in a free falling manner towards the direction of the rock plate 112, and rebounds after colliding with the rock plate 112.
In this embodiment, the steel case 1222 has a size of 40cm (length) ×5cm (width) ×3cm (height).
Preferably, the motorized expansion plates 1124 have detents thereon on which the rock ball 14 is placed.
In this embodiment, on the one hand, the positioning groove plays a role of positioning to ensure that the rock ball 14 is placed at the same position before being released, and on the other hand, by providing the positioning groove, the rock ball 14 can be stably placed on the electric expansion plate 1124 without rolling thereon.
In this embodiment, the cross-sectional shape of the positioning groove is a circle.
Preferably, the detent is directly opposite the central location of the rock plate, such that the rock sphere 14 falls right down to the central location of the rock plate after free fall.
It will be appreciated that the cross-sectional dimensions of the detent and the depth thereof are small, and that the rock ball 14 can be quickly disengaged from the detent as the motor-operated extension plate is retracted.
The distance measuring assembly 123 includes a laser distance measuring device mounted to an end of the steel casing 1222 remote from the rail.
The camera mechanism 13 includes a transparent grid plate 131, a camera support 132, a high-speed camera 133, a light supplementing lamp support 134 and a light supplementing lamp 135, wherein the transparent grid plate 131 is installed in the second groove and detachably connected with the bottom plate 111, the high-speed camera 133 is installed on the camera support 132 and is opposite to the central axis of the vertical direction of the transparent grid plate 131, the light supplementing lamp 135 is installed on the light supplementing lamp support 134, the lighting direction of the light supplementing lamp 135 faces the falling area of the rock ball 14, and the transparent grid plate 131 is used for calibrating the position of the rock ball 14.
In this embodiment, the transparent grid plate 121 is composed of a 75cm×150cm×2cm transparent acrylic plate, and the grid distributed thereon is 5cm×5cm, and this grid plate will be used as a reference system for acquiring the speed before and after the collision based on the image in the later stage.
In the present embodiment, the frame rate of the high-speed camera 133 is 200 to 1000fps.
In this embodiment, the light supplement lamp 135 is located at one side of the high-speed camera 133, so as to ensure that the image is clear and free of sharpening through soft light.
In this embodiment, the falling rocks are rock spheres, specifically marble, and the Young's modulus of the material E=22Gpa, and Poisson's ratio v=0.16, namely equivalent Young's modulus E * = 11.289Gpa. Density ρ=2842 kg/m 3 。
Preferably, the diameter of the rock sphere is 5-8 cm, in this embodiment the diameter of the rock sphere is 6 cm.
In other embodiments, the falling rocks can be spheres made of other materials, and the function of the device is not affected.
Example 2
Referring to fig. 1 to 3 in combination, the present invention further provides an experimental apparatus 200 for ball falling and plane collision, the structure of the experimental apparatus 200 is substantially the same as that of the experimental apparatus 100 provided in embodiment 1, and the experimental apparatus also includes a base 21, a ball release mechanism 22, a camera 23, and a rock ball 24 mounted on the ball release mechanism 22, wherein the base 21 of the experimental apparatus 200 is the same as that of the base 11 of the experimental apparatus 100, the camera 23 of the experimental apparatus 200 is the same as that of the camera 13 of the experimental apparatus 100, and the rock ball 24 of the experimental apparatus 200 is the same as that of the rock ball 14 of the experimental apparatus 100; the main difference is that the structure of the ball release mechanism 22 of the experimental set-up 200 is different from the structure of the ball release mechanism 12 of the experimental set-up 100. The structures of the base 21, the imaging mechanism 23, and the rock mass ball 24 of the experimental apparatus 200 will not be described in detail with reference to embodiment 1.
The sphere release mechanism 22 comprises a guide rail 221 installed at one end of the bottom plate 211, a sphere release assembly 222 installed on the guide rail 221 and capable of sliding up and down along the guide rail 221, and a distance measuring assembly 223 installed on one side of the sphere release assembly 222 close to the bottom plate 211, wherein the sphere release assembly 222 is located above the rock plate 212, and the distance measuring assembly 223 is used for measuring the distance between the bottom of the rock sphere 24 installed on the sphere release assembly 222 and the surface of the rock plate 212 far away from the bottom plate 211.
The ball release assembly 222 includes a first slider 2221 mounted on the guide rail 221 and capable of sliding along the guide rail 221, a first telescopic hollow bar 2222 fixedly connected with the first slider 2221 and vertically arranged with the guide rail 221, a gripper 2223 for mounting the rock ball 24, a connecting piece 2224 with one end connected with the first telescopic hollow bar 2222 and the other end connected with the gripper 2223, and a motor 2225 fixed on the non-telescopic end of the first telescopic hollow bar 2222, wherein the output end of the motor 2225 is connected with the gripper 2223 and can control the gripper 2223 to open so as to release the rock ball 24.
It should be noted that, the mechanical claw 2223 is a structure in the prior art, and is directly obtained by commercial purchasing, and the structure of the component is not in the scope of the invention, and the mechanical claw 2223 may include a claw main body portion, a connecting arm hinged to the claw main body portion, and a connecting shaft mounted on the connecting piece, where the motor is connected to the mechanical arm through the connecting shaft, so as to control the opening or closing of the mechanical claw. The structure of the mechanical claw 2223 may also be referred to the structure disclosed in patent CN 110593331B.
The distance measuring assembly 223 includes a second slider 2231 mounted on the guide rail 221 and capable of sliding along the guide rail 221, a second retractable hollow rod 2232 fixedly connected with the second slider 2231 and vertically disposed on the guide rail 221, and a laser distance meter 2233 fixedly disposed on one end of the second retractable hollow rod 2232 far away from the guide rail 221, where the laser distance meter 2233 and the bottom of the rock sphere 24 are located on the same plane.
In this way, the gripper 2223 is released, the rock ball 24 performs free-falling motion, and an image of the free-falling motion is acquired by the image capturing mechanism 23, so as to determine the collision recovery coefficient of the free-falling motion.
Example 3
Referring to fig. 4 in combination, the present invention further provides a method for measuring and calculating a coefficient of restitution of a falling stone, wherein the falling stone is a rock sphere, and the method comprises the following steps:
s10, based on experiments that rock spheres do free falling body motion at a plurality of different heights and collide with a plane, a plurality of experimental results are obtained, and each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
the method comprises the following steps:
step 1), providing an experimental device;
in this embodiment, the experimental apparatus is the experimental apparatus provided in embodiment 1 or embodiment 2, and the detailed structure is described above, which is not repeated here.
Step 2), fixing the ball release assembly provided with the rock ball at a first height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball;
step 3), fixing the release assembly provided with the rock ball at a second height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball, wherein the second height position is different from the first height position;
Step 4), repeating the step 3) for a plurality of times to obtain dynamic images corresponding to the rock spheres when the rock spheres do free falling movement at a plurality of different heights;
and 5) respectively processing all the dynamic images to obtain a plurality of experimental results, wherein the number of the experimental results is the same as the number of the experiments, and each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed.
In this embodiment, the experimental device is used to perform multiple rock sphere and plane collision experiments specifically: and changing the position of the ball release assembly on the guide rail, so that the rock ball can freely fall at different heights, and continuously shooting by the high-speed camera to obtain images of each free falling movement of the rock ball.
In this example, a total of 25 rock sphere and plane collision experiments were performed using the experimental apparatus 100 provided in example 1, and the collision experiment was repeated five times at the same height to reduce human errors caused by experimental observation, and the collision experiment data (incident speed and rebound speed) at the same height were averaged.
It is to be understood that only one experiment of 5 experiments corresponding to the same height will be described hereinafter, and the experimental data in the actual table 1 is the average data of 5 experiments. The experimental results are shown in table 1:
TABLE 1 Collision test data at different heights
| Sequence number | Drop height (m) | Incident speed (m/s) | Rebound speed (m/s) | Coefficient of restitution of collision |
| 1 | 0.084 | 1.28256 | 1.05231 | 0.82048 |
| 2 | 0.128 | 1.58323 | 1.27898 | 0.80783 |
| 3 | 0.195 | 1.95415 | 1.57157 | 0.80422 |
| 4 | 0.309 | 2.45991 | 1.96052 | 0.79699 |
| 5 | 0.493 | 3.10716 | 2.46513 | 0.79337 |
For the convenience of understanding, the data in table 1 are illustrated by way of example, each row in table 1 represents an experiment, the experiment corresponding to the serial number 1, the falling height, which is the height between the rock sphere and the rock plate measured by the laser range finder, is 0.084m, the dynamic image obtained by the high-speed camera is processed, the calculated incident speed and rebound speed are 1.28552 and 1.05231m/s respectively, and then the collision recovery coefficient is 0.82048 according to the formula normal collision recovery coefficient=normal rebound speed/normal incident speed.
The experimental device is used for experiments, and the rock spheres do free falling body movement, and the rebound speed is normal rebound speed, and the incidence speed is normal incidence speed.
The step of obtaining each of the plurality of experimental results includes:
step (1), determining the distance between the rock sphere and the rock plate based on the distance measured by the laser range finder, and calculating to obtain the theoretical incidence speed of the rock sphere;
for example, when the distance displayed by the laser range finder is 2.000m, the distance h=2m between the rock sphere and the rock plate can be calculated to obtain the theoretical incident velocity v= (2 gh) according to the calculation formula of free falling body motion 1/2 Theoretical incident velocity v= 6.25827m/s.
Step (2), based on the dynamic image shot by the high-speed camera, acquiring an experimental incidence speed and an experimental rebound speed corresponding to the free falling body movement of the rock ball;
specifically, the method comprises the following steps:
step (a), acquiring all images shot by the high-speed camera, and selecting a first frame image and a second frame image of a rock sphere before collision with the rock plate, and a third frame image and a fourth frame image of the rock sphere after collision with the rock plate, wherein the shooting time of the first frame image, the shooting time of the second frame image, the shooting time of the third frame image and the shooting time of the fourth frame image are sequentially increased;
in this embodiment, the high-speed camera records dynamic images of the falling of the rock sphere and rebound after collision with the rock plate at a speed of 200 to 1000 frames per second, wherein the higher the falling height is, the larger the camera frame rate should be. Selecting two images nearest to the collision time with the rock plate from the images before the collision with the rock plate as a first frame image and a second frame image; and selecting two images nearest to the collision time with the rock plate from the images after the collision with the rock plate as a third frame image and a fourth frame image. For ease of understanding, it is assumed that the interval photographing time of two adjacent images constituting a moving image is t 1 The shooting time of the image of the collision of the rock sphere and the rock plate is t p Then the shooting time corresponding to the first frame image is t p -2t 1 The shooting time corresponding to the second frame image is t p -t 1 The shooting time corresponding to the third frame image is t p +t 1 The shooting time corresponding to the fourth frame image is t p +2t 1 。
Step (b), based on the first frame image, acquiring a first shooting time of the first frame image and a first position of the rock sphere on the transparent grid plate; acquiring a second shooting time of the second frame image and a second position of the rock sphere on the transparent grid plate based on the second frame image; based on the absolute value of the difference value between the first position and the second position and the difference between the second shooting time and the first shooting time, acquiring the experimental incidence speed of the rock sphere;
in this embodiment, the photographing time of the first frame image and the second frame image and the position thereof on the transparent grid plate may be directly obtained from the images.
According to the formula speed = distance/time, dividing the absolute value of the difference between the first position and the second position by the difference between the second shooting time and the first shooting time, and obtaining the experimental incidence speed of the rock sphere.
Step (c), based on the third frame image, acquiring a third shooting time of the third frame image and a third position of the rock sphere on the transparent grid plate; acquiring a fourth shooting time of the fourth frame image and a fourth position of the rock sphere on the transparent grid plate based on the fourth frame image; and acquiring the experimental rebound speed of the rock sphere based on the absolute value of the difference value between the fourth position and the third position and the difference between the fourth shooting time and the third shooting time.
In this embodiment, the photographing time of the third frame image and the fourth frame image and the position thereof on the transparent grid plate may be directly obtained from the images.
And dividing the absolute value of the difference between the fourth position and the third position by the difference between the fourth shooting time and the third shooting time according to the formula speed = distance/time, and calculating to obtain the experimental rebound speed of the rock sphere.
And (3) taking the ratio of the experimental rebound speed to the experimental incidence speed as an experimental normal collision recovery coefficient when the absolute value of the error between the experimental incidence speed and the theoretical incidence speed is smaller than a second preset value.
In order to ensure the accuracy of the normal collision recovery coefficient of the experiment, the accuracy of the incident speed of the experiment is judged by taking the theoretical incident speed as a reference, so that the accuracy of the rebound speed of the experiment and the normal collision recovery coefficient of the experiment is ensured.
In this example, the second preset value is 1% of the theoretical incident speed, and when the absolute value of the difference between the experimental incident speed and the theoretical incident speed is smaller than the second preset value, it is indicated that the accuracy of the experimental data is higher, and the experimental data can be used; when the absolute value of the difference between the experimental incident speed and the theoretical incident speed is larger than a second preset value, the experimental data do not meet the requirements, and the experiment is conducted again.
S20, determining the contact yield stress corresponding to each normal incidence speed by a dichotomy by utilizing a first formula and a second formula, and calculating the average value of all the contact yield stress, wherein the average value comprises three average values, namely an arithmetic average value, a geometric average value and a harmonic average value;
the method comprises the following steps:
determining yield speeds corresponding to the normal incidence speeds by a dichotomy by using a first formula, wherein the absolute error of a theoretical normal collision recovery coefficient corresponding to each yield speed and an experimental normal collision recovery coefficient with a corresponding relation is smaller than a first preset value;
The first formula is:
wherein V is n For normal incidenceA speed;
V y is the yield rate;
k n is normal collision recovery coefficient
It should be noted that since the first formula is too complex, even if V is known n And k n Nor can V be directly calculated y In this application, therefore, the optimal solution is approximated by a dichotomy, i.e., V is continuously adjusted y Value calculation k n Up to the calculated k n The difference value between the normal collision recovery coefficient and the experiment is smaller than a first preset value, and the corresponding V y The value is the optimal solution.
The first preset value is 1×10 -6 。
In this step, the normal incidence speed is the corresponding normal incidence speed in the experimental result, i.e., column 3 data in table 1; and the yield rate is determined by dichotomy. For ease of understanding, it is illustrated how the yield speed corresponding to the incident speed 1.28552m/s is determined, specifically, first, the range of yield speeds can be determined to be (0, V) based on the first formula n ]Then, when the first calculation is performed, V n = 1.28552m/s and V y Substitution of = (0+1.28552)/2= 0.64276m/s into the first formula can calculate k n1 If k n1 >0.82048 (Experimental normal Collision recovery coefficient corresponding to incident Rate), then when performing the second calculation, V will be n = 1.28552m/s and V y Substitution of = (0+0.64276)/2= 0.32138m/s into the first equation can calculate k n2 The method comprises the steps of carrying out a first treatment on the surface of the If k n1 <0.82048 (Experimental normal Collision recovery coefficient corresponding to incident Rate), then when performing the second calculation, V will be n = 1.28552m/s and V y Substitution of = (1.28552+0.64276)/2= 0.96414m/s into the first equation can calculate k n2 The method comprises the steps of carrying out a first treatment on the surface of the That is, the value of the yield speed calculated next time is determined based on the magnitude relation between the calculated normal collision recovery coefficient and the experimental normal collision recovery coefficient, the optimal solution is approximated according to the dichotomy, when V is calculated y And V n = 1.28552m/s substituted into the first equation, and the absolute difference between the calculated normal collision recovery coefficient and the experimental normal collision recovery coefficientA value of less than 1X 10 -6 Corresponding V at this time y The value is the optimal solution.
According to the method described above, yield speeds corresponding to the other 4 incident speeds are sequentially calculated to obtain 5 yield speeds in total, and it is understood that the 5 yield speeds have a one-to-one correspondence with the 5 incident speeds.
Step (2), calculating a plurality of contact yield stresses based on each yield speed and a second formula, wherein the contact yield stresses are in one-to-one correspondence with the yield speeds;
the second formula is:
Wherein V is y Is the yield rate;
σ y is the contact yield stress;
ρ is the density of the rock spheres;
E * is the equivalent Young's modulus of a rock sphere.
Wherein,
e is the Young's modulus of the rock mass sphere,
v is the poisson's ratio of the rock sphere.
In this embodiment, the young's modulus e=22gpa, poisson ratio v=0.16, i.e. the equivalent young's modulus E of the material * 11.289Gpa, density ρ=2842 kg/m 3 。
It should be noted that young's modulus, poisson's ratio and density of a material are all understood as known data, and can be obtained by the prior art.
And (3) substituting the 5 yield speeds calculated in the step (1) into a second formula respectively, and calculating 5 contact yield stresses, wherein the 5 contact yield stresses and the 5 yield speeds have a one-to-one correspondence, and the 5 contact yield stresses and the 5 normal incidence speeds have a one-to-one correspondence as the yield speeds and the incidence speeds have a one-to-one correspondence.
And (3) calculating the average value of all the contact yield stress, wherein the average value comprises three average values, namely an arithmetic average value, a geometric average value and a harmonic average value.
For ease of understanding, it is assumed by way of example that step (2) calculates 5 contact yield stresses, σ, respectively 1 、σ 2 、σ 3 、σ 4 、σ 5 Arithmetic mean sigma A ＝(σ 1 +σ 2 +σ 3 +σ 4 +σ 5 ) 5 geometric mean sigma G ＝(σ 1 *σ 2 *σ 3 *σ 4 *σ 5 ) 1/5 Harmonic mean sigma H ＝5/(1/σ 1 +1/σ 2 +1/σ 3 +1/σ 4 +1/σ 5 )。
S30, based on each normal incidence speed and each average value, calculating three groups of normal collision recovery coefficients corresponding to the three average values one by utilizing the second formula and the first formula, wherein each group of normal collision recovery coefficients comprises a plurality of calculated normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
specifically, the method comprises the following steps:
calculating a yield speed corresponding to the arithmetic average value by using a second formula based on the arithmetic average value, and calculating a first group of calculation algorithm collision recovery coefficients by using a first formula based on the normal incidence speed and the yield speed in each experimental result, wherein the first group of calculation algorithm collision recovery coefficients comprise a plurality of first calculation normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
when the first group of calculation algorithms are used for calculating the normal collision recovery coefficients, the yield speeds are the same, the normal incidence speeds are respectively substituted into the first group of calculation algorithms, the first calculated normal collision recovery coefficients are obtained through calculation, and at the moment, the normal incidence speeds and the first calculated normal collision recovery coefficients have corresponding relations.
Based on the geometric average, obtaining yield speed corresponding to the harmonic average by using a second formula, and based on the normal incidence speed and the yield speed in each experimental result, calculating by using a first formula to obtain a second group of calculation algorithm normal collision recovery coefficients, wherein the second group of calculation algorithm normal collision recovery coefficients comprise a plurality of second calculation normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
when the first formula is used for calculating the second group of calculation algorithms to the collision recovery coefficients, the yield speeds are the same, the normal incidence speeds are respectively substituted into the first formula, the second calculation normal collision recovery coefficients are calculated, and at the moment, the normal incidence speeds and the second calculation normal collision recovery coefficients have corresponding relations.
Based on the harmonic mean value, obtaining yield speed corresponding to the harmonic mean value by utilizing a second formula, and based on the normal incidence speed and the yield speed in each experimental result, calculating to obtain a third group of calculation algorithm collision recovery coefficients by utilizing a first formula, wherein the third group of calculation algorithm collision recovery coefficients comprise a plurality of third calculation algorithm collision recovery coefficients which are in one-to-one correspondence with a plurality of normal incidence speeds;
When the first formula is used for calculating the third group of calculation algorithm collision recovery coefficients, the yield speeds are the same, a plurality of normal incidence speeds are respectively substituted into the first formula, the plurality of third calculation algorithm collision recovery coefficients are obtained through calculation, and at the moment, the plurality of normal incidence speeds and the plurality of third calculation algorithm collision recovery coefficients have corresponding relations.
In this embodiment, the number of normal incidence speeds is 5, each corresponding group of normal collision recovery coefficients includes 5 calculated normal collision recovery coefficients, and the 5 calculated normal collision recovery coefficients have a one-to-one correspondence with the 5 experimental normal collision recovery coefficients, and it is understood that the calculated normal collision recovery coefficients calculated based on the same normal incidence speed have a one-to-one correspondence with the experimental normal collision recovery coefficients.
For ease of understanding, the mean sigma of the sum of the illustrations and arithmetic A The corresponding group of normal collision recovery coefficients are calculated by the following steps: first, the arithmetic mean sigma A Substituting into a second formula to obtain a sum arithmetic mean sigma A Corresponding yield speed V yA Then the incident velocity in the first row and the yield velocity V calculated by the second formula yA Substituting the first formula, the calculated normal collision recovery coefficient corresponding to the incident speed of the first row can be obtained; then calculating a normal collision coefficient corresponding to the incident speed of the second row, wherein the calculation method is the same as the calculation method for calculating the normal collision recovery coefficient corresponding to the incident speed of the first row, and the difference is only that the data of the incident speeds are different; and substituting different incident speeds into the first formula in sequence to obtain a first group of normal collision coefficients.
The calculation process of a group of normal collision recovery coefficients corresponding to the geometric mean value specifically comprises the following steps: first, the geometric mean sigma is calculated G Substituting into a second formula to obtain a geometric mean sigma G Corresponding yield speed V yG Then the incident velocity in the first row and the yield velocity V calculated by the second formula yG Substituting the first formula, the calculated normal collision recovery coefficient corresponding to the incident speed of the first row can be obtained; then calculating a normal collision coefficient corresponding to the incident speed of the second row, wherein the calculation method is the same as the calculation method for calculating the normal collision recovery coefficient corresponding to the incident speed of the first row, and the difference is only that the data of the incident speeds are different; and substituting different incident speeds into the first formula in sequence to obtain a second group of normal collision coefficients.
The calculation process of a group of normal collision recovery coefficients corresponding to the harmonic mean value specifically includes: first, the harmonic mean sigma H Substituting into a second formula to obtain a harmonic mean sigma H Corresponding yield speed V yH Then the incident velocity in the first row and the yield velocity V calculated by the second formula yH Substituting the first formula, the calculated normal collision recovery coefficient corresponding to the incident speed of the first row can be obtained; then calculating the normal collision coefficient corresponding to the incident speed of the second row, wherein the calculation method is the normal of the calculation corresponding to the incident speed of the first row The calculation method of the collision recovery coefficient is the same, and the difference is only that the incident speed data are different; and substituting different incident speeds into the first formula in sequence to obtain a third group of normal collision coefficients.
S40, respectively calculating the mean square error of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients, and obtaining a first mean square error corresponding to the arithmetic mean value, a second mean square error corresponding to the geometric mean value and a third mean square error corresponding to the harmonic mean value;
according to a plurality of experimental normal collision recovery coefficients corresponding to a plurality of normal incidence speeds and a plurality of first calculation normal collision recovery coefficients, calculating to obtain a first mean square error, wherein the first mean square error has a corresponding relation with the arithmetic mean value; according to a plurality of experimental normal collision recovery coefficients corresponding to a plurality of normal incidence speeds and a plurality of second calculated normal collision recovery coefficients, calculating to obtain a second mean square error, wherein the second mean square error has a corresponding relation with the geometric mean value; and calculating a third mean square error according to a plurality of experimental normal collision recovery coefficients corresponding to the normal incidence speeds and a plurality of third calculation algorithm normal collision recovery coefficients, wherein the third mean square error has a corresponding relation with the harmonic mean value.
Specifically, according to a calculation formula of mean square error, calculating the mean square error of 5 first calculation normal collision coefficients and 5 experimental normal collision recovery values in the first group of normal collision coefficients to obtain a first mean square error; calculating the mean square error of 5 second calculated normal collision coefficients in the second group of normal collision coefficients and 5 experimental normal collision recovery values to obtain a second mean square error; and calculating the mean square error of 5 third calculation algorithm directional collision coefficients in the third group of normal collision coefficients and 5 experimental normal collision recovery values to obtain a third mean square error.
S50, determining an average value corresponding to a target mean square error as a fitting contact yield stress, wherein the target mean square error is the smallest mean square error among the first mean square error, the second mean square error and the third mean square error;
in this embodiment, the first mean square error is 0.00205285, the second mean square error is 0.00204377, and the third mean square error is 0.00204543.
Comparing the three mean square deviations to obtain that the second mean square deviation is minimum, and the geometric mean value corresponding to the second mean square deviation is the fitting contact yield stress; in this example, the fit contact yield stress = 335.451Mpa.
Table 2 comparison table of the experimental normal crash recovery coefficient and the normal crash recovery coefficient calculated by fitting
| Incident speed (m/s) | Average value of collision recovery coefficient (experiment) | Collision recovery coefficient (fitting) |
| 1.28256 | 0.82048 | 0.88039 |
| 1.58323 | 0.80783 | 0.84373 |
| 1.95415 | 0.80422 | 0.80675 |
| 2.45991 | 0.79699 | 0.76668 |
| 3.10716 | 0.79337 | 0.72692 |
The second column of the average value of the collision recovery coefficients in table 2 is the average value of the collision recovery coefficients calculated based on the experimental data, which are all average values obtained by 5 experiments, and the third column in table 2 is the calculated normal collision recovery coefficient calculated by the determined fit contact yield stress calculation.
Referring to fig. 5 in combination, fig. 5 is a comparison chart of an experimental normal collision recovery coefficient and a calculated normal collision recovery coefficient calculated based on a fitted contact yield stress, and as can be seen from fig. 5, the fitting effect is better.
S60, based on the fitting contact yield stress, a normal collision recovery coefficient and a tangential collision recovery coefficient corresponding to the known incidence speed are obtained by using the first formula, the second formula and the third formula.
The fitting contact yield stress is substituted into the second formula, the value of the yield speed can be calculated, the value of the yield speed is substituted into the first formula, the first formula is simplified into a formula related to the normal incidence speed and the normal collision recovery coefficient, the known normal incidence speed is substituted into the first formula, the normal collision recovery coefficient corresponding to the normal incidence speed can be obtained, and therefore the normal rebound speed is further calculated, and therefore the movement state of the ball falling at different heights is not required to be determined through experiments.
Whereas normal incidence can be calculated from known incident speeds and angles of incidence.
And substituting the calculated normal collision recovery coefficient into a third formula to calculate the tangential collision recovery coefficient.
The third formula is:
wherein,
k t is the tangential collision recovery coefficient; θ is the angle of incidence of the incident sphere; kappa is the stiffness ratio; mu is the equivalent friction coefficient of the friction coefficient,μ 1 sum mu 2 Is the coefficient of friction of two impacting objects; g 1 And G 2 Is the shear modulus, v, of two impacting objects 1 And v 2 Poisson's ratio for two collision objects; here two collision objects, one referring to the incident rock sphere and the other to the plane being impacted.
The normal rebound velocity can be calculated by knowing the normal incidence velocity and the normal collision recovery coefficient, and the tangential rebound velocity can be calculated by knowing the tangential incidence velocity and the tangential collision recovery coefficient, so that the movement state of the ball body meeting the real situation after collision can be calculated without a test, the result can directly help to determine the collision characteristics of the ball body particle system under the complex terrain, and help researchers to assist in analyzing the movement situation of the falling stone disaster.
Example 4
Referring to fig. 6 in combination, the present invention further provides a measuring device 300 for measuring and calculating a coefficient of restitution of a falling stone collision, where the device 300 includes:
The first obtaining module 310 is configured to obtain a plurality of experimental results based on experiments that the rock sphere performs free falling motion at a plurality of different heights and collides with a plane, where each experimental result includes a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
a first calculation module 320, configured to determine, by using a first formula and a second formula, a contact yield stress corresponding to each normal incidence speed by a dichotomy, and calculate an average value of all the contact yield stresses, where the average value includes three average values, that is, an arithmetic average value, a geometric average value, and a harmonic average value;
the second calculation module 330 is configured to calculate, based on each normal incidence speed and each average value, three sets of normal collision recovery coefficients corresponding to the three average values one to one by using the second formula and the first formula, where each set of normal collision recovery coefficients includes a plurality of calculated normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one to one;
a third calculation module 340, configured to calculate, respectively, mean square deviations of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients, to obtain a first mean square deviation corresponding to the arithmetic mean value, a second mean square deviation corresponding to the geometric mean value, and a third mean square deviation corresponding to the harmonic mean value;
A determining module 350, configured to determine an average value corresponding to a target mean square error as a fitted contact yield stress, where the target mean square error is a smallest mean square error among the first mean square error, the second mean square error, and the third mean square error;
and a second obtaining module 360, configured to obtain a normal collision recovery coefficient and a tangential collision recovery coefficient corresponding to a known incident speed and incident angle, using the first formula, the second formula, and a third formula, based on the fitted contact yield stress.
It will be clear to those skilled in the art that, for convenience and brevity of description, the specific working process of the apparatus and module described above may refer to the content of the method embodiment corresponding to embodiment 3, which is not described herein again.
The foregoing is a further detailed description of the invention in connection with specific preferred embodiments, and is not intended to limit the practice of the invention to such description. It will be apparent to those skilled in the art that several simple deductions and substitutions can be made without departing from the spirit of the invention, and these are considered to be within the scope of the invention.
Claims (7)
1. A method for measuring and calculating the collision recovery coefficient of falling rocks which are rock spheres, comprising the following steps:
step (1), based on experiments that rock spheres do free falling body motion at a plurality of different heights and collide with a plane, a plurality of experimental results are obtained, wherein each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
the step (1) comprises:
step (a), providing an experimental set-up comprising:
a rock sphere, wherein the rock sphere is an experimental object;
the base comprises a bottom plate and a rock plate arranged on the upper side of the bottom plate;
the ball release mechanism comprises a guide rail, a ball release assembly and a distance measuring assembly, wherein the guide rail is installed at one end of the bottom plate, the ball release assembly is installed on the guide rail and can slide up and down along the guide rail, the distance measuring assembly is used for measuring the distance between the bottom of the rock ball and the surface of the rock plate far away from the bottom plate, and the rock ball is installed on the ball release assembly and is located right above the center position of the rock plate;
the camera shooting mechanism comprises a transparent grid plate arranged on one side of the bottom plate, a high-speed camera which is arranged opposite to the central axis of the transparent grid plate in the vertical direction, and a light supplementing lamp with the illumination direction facing to the falling area of the rock sphere, wherein the transparent grid plate is used for calibrating the position of the rock sphere;
Step (b), fixing the ball release assembly with the rock ball at a first height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball;
step (c), fixing the release assembly with the rock ball mounted on a second height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball, wherein the second height position is different from the first height position;
repeating the step (d) for a plurality of times to obtain dynamic images corresponding to the rock spheres when the rock spheres do free falling body movement at a plurality of different heights;
step (e), processing all dynamic images respectively to obtain a plurality of experimental results, wherein the number of the experimental results is the same as the number of experiments, and each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
determining the contact yield stress corresponding to each normal incidence speed by a dichotomy method by utilizing a first formula and a second formula, and calculating the average value of all the contact yield stresses, wherein the average value comprises three average values, namely an arithmetic average value, a geometric average value and a harmonic average value;
The step of determining the contact yield stress corresponding to each of the normal incidence speeds by a dichotomy using the first formula and the second formula comprises:
determining yield speeds corresponding to the normal incidence speeds by using the first formula through a dichotomy, wherein the absolute error between a theoretical normal collision recovery coefficient corresponding to each yield speed and an experimental normal collision recovery coefficient with a corresponding relation is smaller than a first preset value;
calculating a plurality of contact yield stresses based on each yield speed and a second formula, wherein the contact yield stresses correspond to the yield speeds one by one;
wherein,
the first formula is:
wherein V is n Is the normal incidence speed;
V y is the yield rate;
k n is the normal collision recovery coefficient;
the second formula is:
wherein V is y Is the yield rate;
σ y is the contact yield stress;
ρ is the density of the rock spheres;
E * is the equivalent Young's modulus of a rock sphere;
step (3), based on each normal incidence speed and each average value, calculating three groups of normal collision recovery coefficients corresponding to the three average values one by utilizing the second formula and the first formula, wherein each group of normal collision recovery coefficients comprises a plurality of calculated normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
Step (4), respectively calculating the mean square error of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients, and obtaining a first mean square error corresponding to the arithmetic mean value, a second mean square error corresponding to the geometric mean value and a third mean square error corresponding to the harmonic mean value;
step (5), determining an average value corresponding to a target mean square error as a fitting contact yield stress, wherein the target mean square error is the smallest mean square error among the first mean square error, the second mean square error and the third mean square error;
and (6) acquiring a normal collision recovery coefficient and a tangential collision recovery coefficient corresponding to known incident speed and incident angle by using the first formula, the second formula and the third formula based on the fitting contact yield stress.
2. The method for measuring and calculating a clashing recovery coefficient according to claim 1, wherein said step (6) comprises:
calculating to obtain a fitting yield speed corresponding to the fitting contact yield stress by using a second formula;
calculating to obtain the normal incidence speed to be calculated based on the known incidence speed and incidence angle;
based on the fitting yield speed and the normal incidence speed to be measured and calculated, calculating a normal collision recovery coefficient corresponding to the known incidence speed by using a first formula;
And calculating a tangential collision recovery coefficient corresponding to the known incident speed based on the normal collision recovery coefficient by using a third formula.
3. The method for measuring and calculating a clashing recovery coefficient of a falling rock according to claim 1, wherein the step of obtaining each of the plurality of experimental results comprises:
determining the distance between the bottom of the rock sphere and the rock plate based on the distance measured by the distance measuring assembly, and calculating to obtain the theoretical incident speed of the rock sphere;
based on the dynamic image shot by the high-speed camera, acquiring an experimental incidence speed and an experimental rebound speed corresponding to the free falling body movement of the rock ball;
and when the absolute error between the experimental incident speed and the theoretical incident speed is smaller than a second preset value, taking the ratio of the experimental rebound speed to the experimental incident speed as an experimental normal collision recovery coefficient, wherein the experimental incident speed is the normal incident speed in an experimental result, and the experimental normal collision recovery coefficient has a corresponding relation with the normal incident speed.
4. The method for measuring and calculating a falling rock collision recovery coefficient according to claim 3, wherein the step of acquiring the experimental incident speed and the experimental rebound speed corresponding to the free falling body movement of the rock ball based on the dynamic image photographed by the high-speed camera comprises the steps of:
Acquiring a dynamic image shot by the high-speed camera, and selecting a first frame image and a second frame image of a rock sphere before collision with the rock plate, and a third frame image and a fourth frame image of a rock sphere after collision with the rock plate, wherein the shooting time of the first frame image, the shooting time of the second frame image, the shooting time of the third frame image and the shooting time of the fourth frame image are sequentially increased;
acquiring a first shooting time of the first frame image and a first position of the rock sphere on the transparent grid plate based on the first frame image; acquiring a second shooting time of the second frame image and a second position of the rock sphere on the transparent grid plate based on the second frame image; based on the absolute value of the difference value between the first position and the second position and the difference between the second shooting time and the first shooting time, acquiring the experimental incidence speed of the rock sphere;
acquiring a third shooting time of the third frame image and a third position of the rock sphere on the transparent grid plate based on the third frame image; acquiring a fourth shooting time of the fourth frame image and a fourth position of the rock sphere on the transparent grid plate based on the fourth frame image; and acquiring the experimental rebound speed of the rock sphere based on the absolute value of the difference value between the fourth position and the third position and the difference between the fourth shooting time and the third shooting time.
5. The method for measuring and calculating a falling stone collision recovery coefficient according to claim 1, wherein the sphere releasing assembly comprises a locking slide block which is mounted on the guide rail and can slide along the guide rail, a steel shell which is fixedly connected with the locking slide block and is positioned right above the rock plate, a mounting hole which is formed through one end of the steel shell far away from the guide rail, a motor which is fixed on the steel shell, and an electric expansion plate which is positioned in the steel shell and can expand and contract along the length direction of the steel shell, the electric expansion plate is connected with the motor, and when the electric expansion plate is positioned at a limit position, the electric expansion plate is accommodated in the mounting hole, and the rock sphere is mounted on the electric expansion plate; the range finding assembly comprises a laser range finder arranged at one end, far away from the guide rail, of the steel shell.
6. The method for measuring and calculating a falling rock collision recovery coefficient according to claim 1, wherein the sphere releasing assembly comprises a first sliding block which is installed on the guide rail and can slide along the guide rail, a first telescopic hollow rod which is fixedly connected with the first sliding block and is arranged vertically to the guide rail, a mechanical claw for placing a rock sphere, a connecting piece with one end connected with the first telescopic hollow rod and with the other end connected with the mechanical claw, and a motor which is fixed at the non-telescopic end of the first telescopic hollow rod, wherein the output end of the motor is connected with the mechanical claw and can control the mechanical claw to open so as to release the rock sphere; the range finding subassembly including install in the guide rail and can follow the second slider that the guide rail slided, with second slider fixed connection and with the scalable hollow pole of the perpendicular setting of guide rail, be fixed in the scalable hollow pole of second is kept away from the laser range finder of guide rail one end, laser range finder is located the coplanar with the spheroidal bottom of ground.
7. A measuring and calculating device for measuring and calculating a falling stone collision recovery coefficient, characterized in that the measuring and calculating device comprises:
the first acquisition module is used for acquiring a plurality of experimental results based on experiments that the rock ball makes free falling motion at a plurality of different heights and collides with a plane, wherein each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
the step of obtaining a plurality of experimental results based on experiments that the rock ball makes free falling body movement at a plurality of different heights and collides with a plane comprises the following steps:
step (a), providing an experimental set-up comprising:
a rock sphere, wherein the rock sphere is an experimental object;
the base comprises a bottom plate and a rock plate arranged on the upper side of the bottom plate;
the ball release mechanism comprises a guide rail, a ball release assembly and a distance measuring assembly, wherein the guide rail is installed at one end of the bottom plate, the ball release assembly is installed on the guide rail and can slide up and down along the guide rail, the distance measuring assembly is used for measuring the distance between the bottom of the rock ball and the surface of the rock plate far away from the bottom plate, and the rock ball is installed on the ball release assembly and is located right above the center position of the rock plate;
The camera shooting mechanism comprises a transparent grid plate arranged on one side of the bottom plate, a high-speed camera which is arranged opposite to the central axis of the transparent grid plate in the vertical direction, and a light supplementing lamp with the illumination direction facing to the falling area of the rock sphere, wherein the transparent grid plate is used for calibrating the position of the rock sphere;
step (b), fixing the ball release assembly with the rock ball at a first height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball;
step (c), fixing the release assembly with the rock ball mounted on a second height position of the guide rail, releasing the rock ball to make free falling motion, and simultaneously, shooting by the high-speed camera to obtain a dynamic image of the free falling motion of the rock ball, wherein the second height position is different from the first height position;
repeating the step (d) for a plurality of times to obtain dynamic images corresponding to the rock spheres when the rock spheres do free falling body movement at a plurality of different heights;
Step (e), processing all dynamic images respectively to obtain a plurality of experimental results, wherein the number of the experimental results is the same as the number of experiments, and each experimental result comprises a normal incidence speed and an experimental normal collision recovery coefficient corresponding to the normal incidence speed;
the first calculation module is used for determining the contact yield stress corresponding to each normal incidence speed through a dichotomy by utilizing a first formula and a second formula, and calculating the average value of all the contact yield stresses, wherein the average value comprises three average values, namely an arithmetic average value, a geometric average value and a harmonic average value;
the step of determining the contact yield stress corresponding to each of the normal incidence speeds by a dichotomy using the first formula and the second formula comprises:
determining yield speeds corresponding to the normal incidence speeds by using the first formula through a dichotomy, wherein the absolute error between a theoretical normal collision recovery coefficient corresponding to each yield speed and an experimental normal collision recovery coefficient with a corresponding relation is smaller than a first preset value;
calculating a plurality of contact yield stresses based on each yield speed and a second formula, wherein the contact yield stresses correspond to the yield speeds one by one;
Wherein:
the first formula is:
wherein V is n Is the normal incidence speed;
V y is the yield rate;
k n is the normal collision recovery coefficient;
the second formula is:
wherein V is y Is the yield rate;
σ y is the contact yield stress;
ρ is the density of the rock spheres;
E * is the equivalent Young's modulus of a rock sphere;
the second calculation module is used for calculating three groups of normal collision recovery coefficients corresponding to the three average values one by one based on each normal incidence speed and each average value by utilizing the second formula and the first formula, and each group of normal collision recovery coefficients comprises a plurality of calculated normal collision recovery coefficients corresponding to a plurality of normal incidence speeds one by one;
the third calculation module is used for respectively calculating the mean square error of a plurality of calculated normal collision coefficients and a plurality of experimental normal collision recovery coefficients in each group of normal collision recovery coefficients to obtain a first mean square error corresponding to the arithmetic mean value, a second mean square error corresponding to the geometric mean value and a third mean square error corresponding to the harmonic mean value;
the determining module is used for determining an average value corresponding to a target mean square error as a fitting contact yield stress, wherein the target mean square error is the smallest mean square error among the first mean square error, the second mean square error and the third mean square error;
And the second acquisition module is used for acquiring a normal collision recovery coefficient and a tangential collision recovery coefficient corresponding to known incident speed and incident angle by using the first formula, the second formula and the third formula based on the fitting contact yield stress.
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| CN107589069A (en) * | 2017-07-10 | 2018-01-16 | 同济大学 | A kind of contactless measurement of object collision recovery coefficient |
| CN113128022A (en) * | 2021-03-12 | 2021-07-16 | 中国海洋大学 | Algorithm for predicting recovery coefficient after collision between particles and wall surface |
| CN114169053A (en) * | 2021-12-03 | 2022-03-11 | 中铁第一勘察设计院集团有限公司 | Method for calculating maximum impact force of falling rocks |
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| CN107589069A (en) * | 2017-07-10 | 2018-01-16 | 同济大学 | A kind of contactless measurement of object collision recovery coefficient |
| CN113128022A (en) * | 2021-03-12 | 2021-07-16 | 中国海洋大学 | Algorithm for predicting recovery coefficient after collision between particles and wall surface |
| CN114169053A (en) * | 2021-12-03 | 2022-03-11 | 中铁第一勘察设计院集团有限公司 | Method for calculating maximum impact force of falling rocks |
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| 岩石球砾弹塑性碰撞能耗分析及数值模拟;王珂 等;粉煤灰综合利用(第02期);13-20 * |
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