A method for recording and analyzing the dynamics of mill media using a sensor ball

Abstract

A method for recording and analyzing mill medium dynamics by using an inductive ball, which specifically comprises: 1) grinding experiment and data collection: placing the inductive ball in the mill, setting the corresponding mill parameters, the inductive ball running with the mill when the mill rotates, taking out the storage card in the acceleration recorder after the experiment is completed, and extracting the relative spatial three-dimensional acceleration data in the storage card; 2) data analysis: repeating the step 1) under different mill parameters to obtain multiple groups of relative spatial three-dimensional acceleration data, then processing and analyzing each group of relative spatial three-dimensional acceleration data to obtain the dynamics of the inductive ball under different mill parameters. Through analyzing the data recorded by the inductive ball and combining the grinding theory, an efficient mill operation parameter can be found, so that a specific and quantified scheme for saving energy consumption and reducing production cost can be provided for the grinding enterprise.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of grinding medium dynamics research, and particularly relates to a method for recording and analyzing grinding mill medium dynamics by using inductive balls. BACKGROUND

[0002] The grinding mill (also known as a ball mill) is a key equipment in the mineral processing process, and is suitable for grinding various ores and other materials due to its large crushing ratio and good grinding effect, and is also widely used in the building materials and chemical industries in addition to the mineral processing industry. However, the grinding mill also has problems such as low energy efficiency, large consumption of steel balls, and easy wear of the liner. Therefore, the research on the grinding factors of the grinding mill has great scientific research significance for improving the energy efficiency of the grinding mill, reducing the consumption of steel balls, and saving resources. The grinding factors of the grinding mill mainly include the rotational speed of the grinding mill, the type of the liner, the filling ratio, and the ratio of the grinding medium. Among them, the influence of the grinding medium on the grinding factors of the grinding mill is the most complex. In the grinding process, the grinding medium (iron balls or iron rods, etc.) impacts and grinds the ore under the driving of the liner through the action of throwing and falling. The grinding medium is the carrier of energy, and its movement characteristics determine the amount of energy it carries and the way it breaks the ore. Therefore, the size, quantity ratio, and movement behavior of the grinding medium in the grinding mill largely determine the operating power of the grinding mill, the consumption of the grinding medium, and the grinding efficiency. However, due to the extremely complex movement process of the medium, researchers have not yet fundamentally mastered the movement rules and specific influencing factors of the medium inside the grinding mill. In addition, there is no mathematical model for quantitatively evaluating the dynamic characteristics of the medium. Therefore, it is necessary to carry out research on the dynamic behavior of the grinding medium of the grinding mill, to explore the specific movement behavior and rules of the grinding medium under different grinding factors, to use the specific movement behavior and rules of the grinding medium to find the best grinding condition factors, and to provide basic theory and technical support for improving the grinding efficiency of the grinding mill.

[0003] Due to the extremely complex movement process of the medium, researchers have not yet fundamentally mastered the movement rules and specific influencing factors of the medium inside the grinding mill. In addition, there is no mathematical model for quantitatively evaluating the dynamic characteristics of the medium. Therefore, it is necessary to carry out research on the dynamic behavior of the grinding medium of the grinding mill, to explore the specific movement behavior and rules of the grinding medium under different grinding factors, to use the specific movement behavior and rules of the grinding medium to find the best grinding condition factors, and to provide basic theory and technical support for improving the grinding efficiency of the grinding mill. In addition, because the medium collides violently inside the grinding mill, the absolute coordinates and medium speed and position information obtained by using quaternions and integral methods have very large errors, so the current methods for analyzing the movement state of the medium inside the grinding mill have large errors and cannot effectively reflect the grinding efficiency of the grinding mill. SUMMARY

[0004] Based on this, the application provides a method for recording and analyzing the dynamics of the medium in a mill by using an inductive ball, so as to solve the technical problem of the large error of the method for analyzing the motion state of the medium in the mill in the prior art and the inability to effectively reflect the grinding efficiency of the mill.

[0005] To achieve the above object, the application provides a method for recording and analyzing the dynamics of the medium in a mill by using an inductive ball, wherein the inductive ball comprises a hollow ball, an acceleration recorder and a balancing body, the acceleration recorder is arranged inside the hollow ball and is used for recording the relative spatial three-dimensional acceleration data generated when the hollow ball moves, the acceleration recorder is integrated with a storage card used for storing the relative spatial three-dimensional acceleration data, the balancing body is arranged inside the hollow ball, the material density of the balancing body is greater than that of the hollow ball, the weight of the inductive ball is equal to that of a solid ball with the same volume and material as the hollow ball, and the center of gravity of the inductive ball falls on the position of the center of the hollow ball.

[0006] The method for recording and analyzing the dynamics of the medium in a mill by using the inductive ball comprises the following steps:

[0007] 1) Milling experiment and data collection:

[0008] The inductive ball is placed in the mill, the corresponding mill parameters are set, the inductive ball runs with the mill when the mill rotates, the storage card in the acceleration recorder is taken out after the experiment is completed, and the relative spatial three-dimensional acceleration data in the storage card is extracted;

[0009] 2) Data analysis:

[0010] Step 1) is repeated under different mill parameters to obtain a plurality of groups of relative spatial three-dimensional acceleration data, and then each group of relative spatial three-dimensional acceleration data is processed and analyzed to obtain the dynamics of the inductive ball under different mill parameters, and the specific steps are as follows:

[0011] 2.1) The extracted relative spatial three-dimensional acceleration data is calculated by using the formula of resultant acceleration (a X 2 +a Y 2 +a Z 2 ) 1 / 2 , the resultant acceleration value a 合 at different times is calculated, a time-acceleration two-dimensional coordinate data graph is established, and the specific values of the three-dimensional component accelerations a X , a Y , a Z and the resultant acceleration a 合 at different times are obtained;

[0012] 2.2) According to the data rule shown by the time-acceleration two-dimensional coordinate data graph, the dynamics of the sensing ball in the mill is identified, which includes the sensing ball being static, the sensing ball rolling and rotating, the sensing ball being relatively static with the cylinder and rotating with the cylinder, the sensing ball falling, and the sensing ball colliding, and the specific identification strategies of each dynamics are as follows:

[0013] I. The sensing ball is static

[0014] If the values of the component accelerations a X , a Y , and a Z remain unchanged and the resultant acceleration a 合 is always 1g (g is the acceleration of gravity) in a certain period of time, it is determined that the sensing ball is in a static state in the period of time;

[0015] II. The sensing ball is rolling and rotating

[0016] If the time-acceleration two-dimensional coordinate data graph presents a positive sine wave graph and the wave period is much smaller than the cylinder rotation period in a certain period of time, it can be determined that the sensing ball is rolling and rotating in the period of time, and each wave period represents that the sensing ball rolls one circle;

[0017] III. The sensing ball is relatively static with the cylinder and rotates with the cylinder or centrifugal

[0018] If the time-acceleration two-dimensional coordinate data graph is an interrupted positive sine function curve and the wave period is consistent with the cylinder rotation period in a certain period of time, it is indicated that the sensing ball is relatively static with the cylinder and rotates with the cylinder, and if the time-acceleration two-dimensional coordinate data graph presents a complete positive sine function curve and the wave period is consistent with the cylinder rotation period, it is indicated that the sensing ball is in centrifugal motion in the cylinder;

[0019] IV. The sensing ball is falling

[0020] If the component accelerations and the resultant acceleration are both 0 in the time-acceleration two-dimensional coordinate data graph in a certain period of time, it can be determined that the sensing ball is in a falling state in the period of time, and the longitudinal falling height s of the sensing ball can be calculated according to Newton's second law through the time t during which the acceleration is 0, s = V0t + 1 / 2V1t = 1 / 2gt 2 , wherein the longitudinal initial velocity V0 of the sensing ball is 0, and the longitudinal final velocity V1 is gt;

[0021] V. The sensing ball collides and the impact force

[0022] If, within a certain period of time, the component acceleration data and the resultant acceleration data in the time-acceleration two-dimensional coordinate data graph change drastically in a short time, it reflects that the sensing ball has undergone collision behavior at this time, and according to the acceleration formula F=ma... 合 The instantaneous impact force on the sensing ball during the collision can be calculated, where m is the mass of the sensing ball.

[0023] As a further preferred embodiment of the present invention, the hollow sphere is a hollow iron sphere, and the balancing body is a tungsten block with a density of 19.35 kg / m³. 3 .

[0024] As a further preferred embodiment of the present invention, the hollow sphere is composed of a detachable upper hemisphere and a lower hemisphere. The upper hemisphere has a first receiving groove near the center of the sphere and a second receiving groove away from the center of the sphere. The lower hemisphere has a third receiving groove near the center of the sphere and a fourth receiving groove away from the center of the sphere. When the upper hemisphere and the lower hemisphere are connected as a whole, the first receiving groove and the third receiving groove are connected to form a receiving cavity. The receiving cavity is used to place the accelerometer. The second receiving groove and the fourth receiving groove are each used to place a piece of the balancing body.

[0025] As a further preferred embodiment of the present invention, when the sensing sphere is stationary, the accelerometer inside the sensing sphere can only detect the effect of gravity. At this time, the value of the three-dimensional component acceleration relative to space remains constant, and the resultant acceleration satisfies the following formula:

[0026] a 合 =(a X 2 +a Y 2 +a Z 2 ) 1 / 2 = 1g.

[0027] As a further preferred technical solution of the present invention, when the induction ball rolls and rotates, the X, Y, and Z axes of the accelerometer inside the induction ball all form a certain angle with the rotation axis of the induction ball, and the rotation axis of the induction ball is perpendicular to the gravity line. Let the angle between the X-axis of the accelerometer and the rotation plane be α; when the X-axis rotates to its highest point, the component acceleration of gravitational acceleration on the X-axis is gcosα; when the X-axis rotates around the rotation axis by an angle θ, the component acceleration of gravitational acceleration on the X-axis is gcosαcosθ. Since the angle α between the X-axis and the rotation plane is a constant, gcosα is also a constant. Therefore, when the X-axis rotates around the rotation axis by an angle θ, let ω be the angular velocity of the induction ball rolling, then the component acceleration of gravitational acceleration on the X-axis can be expressed as the following sine and cosine functions with time as the independent variable:

[0028] a X(t) = gcosαcosθ = gcosαcosωt

[0029] Similarly, let the angles between Y-axis and Z-axis and the rotating surface be β and Ψ, and the components of gravitational acceleration on Y-axis and Z-axis be as follows:

[0030] a Y (t) = gcosβcosθ = gcosβcosωt

[0031] a Z (t) = gcosΨcosθ = gcosΨcosωt.

[0032] As a further preferred technical solution of the present application, when the inductive ball is relatively stationary with the mill barrel wall and rotates or centrifugates with the barrel, the X, Y and Z axes of the acceleration recorder in the inductive ball all form a certain angle with the direction of centrifugal acceleration;

[0033] Let the angle between the X-axis of the acceleration recorder and the direction of centrifugal acceleration be γ, the rotating radius be r, and the angular velocity of the mill be ω, then the component of centrifugal acceleration on the X-axis is ω 2 rcosγ, and when the X-axis rotates by an angle θ around the barrel rotating axis, the component of gravitational acceleration on the X-axis is gcosθ, since the angle γ between the X-axis and the centrifugal acceleration is a constant value, ω 2 rcosγ is also a constant value, so the acceleration value when the X-axis rotates by an angle θ around the barrel rotating axis is as follows:

[0034] a X (t) = ω 2 rcosγ + gcosθ = ω 2 rcosγ + gcosωt

[0035] Similarly, let the angles between Y-axis and Z-axis and the rotating surface be δ and ε, and the acceleration values of Y-axis and Z-axis be as follows:

[0036] a Y (t) = ω 2 rcosδ + gcosθ = ω 2 rcosδ + gcosωt

[0037] a Z (t) = ω 2 rcosε + gcosθ = ω 2 rcosε + gcosωt

[0038] Since ω 2 rcosγ, ω 2 rcosδ, and ω 2Rcosε are constant values, so the acceleration data of X, Y and Z axes are positive cosine functions with time as the independent variable, and the rotating radius of the sensing ball can be calculated according to the relative spatial three-dimensional acceleration data and the rotating speed of the cylinder.

[0039] As a further preferred technical solution of the present application, when the sensing ball is in the state of falling, the whole acceleration recorder is in the state of weightlessness, i.e. the relative spatial three-dimensional acceleration data are all zero, and the resultant acceleration (a X 2 +a Y 2 +a Z 2 ) 1 / 2 is also zero.

[0040] As a further preferred technical solution of the present application, when the sensing ball collides, the speed of the sensing ball changes, and the change of the speed must be caused by the acceleration, and the force must act. According to the momentum impulse formula:

[0041] Ft=mat=mV1-mV2

[0042] a 合 =(V1-V2) / t

[0043] wherein a 合 is the resultant acceleration (a X 2 +a Y 2 +a Z 2 ) 1 / 2 Once the sensing ball collides, and the shorter the collision time is, the greater the speed change before and after the collision is, the greater the resultant acceleration and the component acceleration of the sensing ball change.

[0044] The method for recording and analyzing the dynamics of the mill medium by using the sensing ball according to the present application can achieve the following beneficial effects by using the above technical solution:

[0045] 1) The sensing ball according to the present application loses mass due to the hollowing, and the large-density tungsten block is added to make the sensing ball have the same mechanical properties as the ordinary medium iron ball, so that the dynamics of the medium ball in the mill can be truly restored.

[0046] 2) According to the present application, the acceleration recorder is placed in the hollow ball body simulating the medium iron ball to form the sensing ball based on the principle of relative spatial three-dimensional acceleration, so that the relative spatial three-dimensional acceleration data of the medium ball can be recorded more directly, and the dynamics of the sensing ball can be quantitatively analyzed, including the static state, the rotating state, the relative static state with the cylinder (centrifugal state), the falling state, the collision state and the impact force, etc.

[0047] 3) The method used in the present application is based on the relative coordinate system of relative spatial three-dimensional acceleration, without quaternion operation, without cumulative error and error caused by collision, not affected by medium collision, and can truly and accurately record the motion state of the medium ball in the mill, effectively reflecting the grinding efficiency of the mill;

[0048] 4) The present application can find a set of high-efficiency mill operation parameters by analyzing the data recorded by the induction ball combined with the grinding theory, so as to provide specific quantitative schemes for saving energy and reducing production cost for grinding enterprises. BRIEF DESCRIPTION OF DRAWINGS

[0049] The present application will be further described in detail below in combination with the drawings and specific embodiments.

[0050] Figure 1 It is a front view of the induction ball of the present application.

[0051] Figure 2 It is a top view of the upper half iron ball of the induction ball of the present application.

[0052] Figure 3 It is a top view of the lower half iron ball of the induction ball of the present application.

[0053] Figure 4 It is a time-acceleration two-dimensional coordinate data graph of the induction ball placed in a mill with a 25cm barrel diameter and without starting the mill.

[0054] Figure 5 It is a time-acceleration two-dimensional coordinate data graph of a single induction ball placed in an unloaded mill with a 25cm barrel diameter and 20% critical speed.

[0055] Figure 6 It is a time-acceleration two-dimensional coordinate data graph of the induction ball placed in a mill with 30% filling rate, 40cm barrel diameter and 15% critical speed.

[0056] Figure 7 It is a time-acceleration two-dimensional coordinate data graph of the induction ball placed in a mill with 40% filling rate, 25cm barrel diameter and 120% critical speed.

[0057] Figure 8 It is a time-acceleration two-dimensional coordinate data graph of the induction ball placed in a mill with 30% filling rate, 25cm barrel diameter and 80% critical speed.

[0058] In the figure: 1, upper half iron ball, 2, lower half iron ball, 3, fourth accommodating groove, 4, third accommodating groove, 5, first accommodating groove, 6, second accommodating groove, 7, accommodating cavity.

[0059] The object, function, feature and advantage of the present application will be further described in conjunction with embodiments, with reference to the drawings. DETAILED DESCRIPTION

[0060] The present application will be further described in conjunction with the drawings and specific embodiments. The terms such as "upper", "lower", "left", "right", "middle" and "one" used in the preferred embodiments are only for the convenience of clear description, and are not used to limit the scope of the present application. The change or adjustment of the relative relationship without substantial change of the technical content is also considered as the scope of the present application.

[0061] As shown in Figure 1 , Figure 2 and Figure 3 , an inductive ball capable of recording the dynamics of mill media includes a hollow iron ball, tungsten blocks arranged in the hollow iron ball as balancing bodies, and an acceleration recorder for recording the relative spatial three-dimensional acceleration data generated when the hollow iron ball moves. The hollow iron ball is divided into an upper half iron ball 1 and a lower half iron ball 2, and the upper half iron ball 1 and the lower half iron ball 2 are combined using screws. The upper half iron ball 1 has a first accommodating groove 5 close to the center of the ball and a second accommodating groove 6 away from the center of the ball, and the lower half iron ball 2 has a third accommodating groove 4 close to the center of the ball and a fourth accommodating groove 3 away from the center of the ball. When the upper half ball and the lower half ball are connected into a whole, the first accommodating groove 5 and the third accommodating groove 4 are connected to form an accommodating cavity 7 for placing the acceleration recorder, and the second accommodating groove 6 and the fourth accommodating groove 3 each are used for placing a tungsten block. The tungsten blocks are used to balance the mass lost inside the inductive ball due to hollowing, so that the density of the inductive ball remains consistent with the density of the solid medium iron ball, and the center of gravity of the inductive ball falls on the center of the ball, so that the inductive ball and the solid medium iron ball have consistent mechanical properties. The acceleration recorder is embedded in the hollow iron ball and can be used to record the relative spatial three-dimensional acceleration data of the inductive ball changing with time, and the data exists in a storage card. By establishing a time-acceleration two-dimensional coordinate data graph from the obtained relative spatial three-dimensional acceleration data, mechanical analysis and calculation can be performed, and the dynamics of the inductive ball in the mill can be obtained.

[0062] The inductive ball is assembled by the following steps:

[0063] 1) The two tungsten blocks are embedded and fixed in the second accommodating groove and the fourth accommodating groove of the hollow iron ball.

[0064] 2) The acceleration recorder is wrapped with a buffer pad and waterproof material, placed in the accommodating cavity formed by the connection of the first accommodating groove and the third accommodating groove, and the upper half iron ball and the lower half iron ball are fixed and combined using screws to form the inductive ball.

[0065] In order for those skilled in the art to better understand and implement the technical solutions of the present application, the following will make further detailed description on the method for recording and analyzing the dynamics of the mill medium based on the above induction ball through specific examples.

[0066] Example 1

[0067] The induction ball is placed in a mill with a cylinder diameter of 25 cm, the mill is not started, and after waiting for 20 seconds, the storage card inside the induction ball is taken out, the relative spatial three-dimensional acceleration data in the storage card is read out, and the resultant acceleration is calculated according to the formula (a X 2 +a Y 2 +a Z 2 ) 1 / 2 . Finally, the time- acceleration two-dimensional coordinate data graph is drawn with time as the horizontal coordinate and acceleration value as the vertical coordinate, as shown in Figure 4 .

[0068] As can be seen from Figure 4 , when the mill is not started, the induction ball is in a static state, the X, Y and Z axial acceleration data are constant values, and the resultant acceleration value is always maintained at 1g.

[0069] Therefore, if the X, Y and Z axial acceleration data are constant values and the resultant acceleration value is always 1g in the time- acceleration two-dimensional coordinate data graph within a certain period of time, it can be determined that the induction ball is in a static state in the mill within the period of time.

[0070] Example 2

[0071] A single induction ball is placed in a mill with a cylinder diameter of 25 cm, the mill is started, and after the speed is stabilized, the speed is adjusted to 20% of the critical speed of the mill (low speed), and the mill is continuously operated for 30 seconds, then the mill is stopped, the storage card inside the induction ball is taken out, the relative spatial three-dimensional acceleration data in the storage card is read out, and the resultant acceleration is calculated according to the formula (a X 2 +a Y 2 +a Z 2 ) 1 / 2 . Finally, the time- acceleration two-dimensional coordinate data graph is drawn with time as the horizontal coordinate and acceleration value as the vertical coordinate, as shown in Figure 5 .

[0072] As can be seen from Figure 5It can be seen that the barrel of the mill at low speed (20% of the critical speed), the X, Y, Z axis acceleration data presents a regular positive cosine curve, and the waveform period is much smaller (at least 5 times difference) than the barrel rotation period (can be determined according to the set mill parameters).

[0073] When the X axis rotates to the highest point, the component acceleration of the gravitational acceleration on the X axis is gcosα, and when the X axis rotates θ angle around the rotation axis, the component acceleration of the gravitational acceleration on the X axis is gcosαcosθ. Since the intersection angle α of the X axis and the rotation surface is a constant value, gcosα is also a constant value. Therefore, when the X axis rotates θ angle around the rotation axis, and ω is the angular velocity of the inductive ball rolling, the component acceleration of the gravitational acceleration on the X axis can be written as:

[0074] a X (t) = gcosαcosθ = gcosαcosωt

[0075] Similarly, let the intersection angle of the Y axis and the rotation surface be β, and the intersection angle of the Z axis and the rotation surface be Ψ, the component accelerations of the gravitational acceleration on the Y axis and the Z axis are as follows:

[0076] a Y (t) = gcosβcosθ = gcosβcosωt

[0077] a Z (t) = gcosΨcosθ = gcosΨcosωt

[0078] Therefore, if the data graph is a positive cosine waveform graph, and the waveform period is much smaller (at least 5 times difference) than the barrel rotation period, it means that the inductive ball is rolling and rotating in the mill during this period, and one period in the waveform data graph represents that the inductive ball has rolled one circle.

[0079] Based on the above analysis, it is shown that the inductive ball is rolling in the mill.

[0080] Example 3

[0081] A single inductive ball is placed in a mill with a medium filling rate of 30% and a barrel diameter of 40 cm. The mill is started, the speed is adjusted to 15% of the critical speed of the mill (low speed), and after the speed is stable, the mill is continuously run for 30 seconds, then the mill is stopped, the storage card inside the inductive ball is taken out, the relative space three-dimensional acceleration data in the storage card is read out, and the resultant acceleration is calculated according to the formula (a X 2 +a Y 2 +a Z 2 1 / 2 ​The acceleration values are calculated. Finally, a time-acceleration two-dimensional coordinate data graph is plotted with time as the horizontal coordinate and the acceleration values as the vertical coordinate, as shown in FIG. 3. Figure 6

[0082] It should be noted that the above-mentioned medium refers to the iron grinding ball used in the mill, and the induction ball of the present application is used to simulate the iron grinding ball. Compared with the ordinary iron grinding ball, the induction ball increases the acceleration recorder, has the same volume and mass, and the center of gravity is located at the center of the ball. Therefore, the induction ball has the same mechanical behavior as the ordinary iron grinding ball. In addition, the medium filling rate will affect the experimental data. Because the difference in medium filling rate is large, the dynamics of the medium in the mill will be very different. In this example, a medium filling rate of 30% and a critical speed of 15% are selected only for example, in order to verify that under the parameters of the present application, the induction ball can record the dynamics of the medium relative to the static rotation of the cylinder.

[0083] As can be seen from FIG. 3, Figure 6 under the conditions of 30% filling rate and 15% critical speed, the XYZ axial acceleration data of the medium ball in the mill appears an interrupted and incomplete sine curve, and the waveform period is basically consistent with the cylinder rotation period.

[0084] Let the angle between the X-axis of the relative space three-dimensional acceleration recorder and the centrifugal acceleration direction be γ, the rotation radius be r, and the angular velocity of the mill be ω. Then the component acceleration of the centrifugal acceleration on the X-axis is ω 2 rcosγ, when the X-axis rotates by an angle θ around the cylinder rotation axis, the component acceleration of the gravitational acceleration on the X-axis is gcosθ. Since the angle γ between the X-axis and the centrifugal acceleration is a constant value, ω 2 rcosγ is also a constant value, so the acceleration value when the X-axis rotates by an angle θ around the cylinder rotation axis can be written as:

[0085] a X (t)=ω 2 rcosγ+gcosθ=ω 2 rcosγ+gcosωt

[0086] Similarly, let the angles between the Y-axis and the rotation plane be δ, and between the Z-axis and the rotation plane be ε. Then the acceleration values of the Y-axis and the Z-axis are as follows:

[0087] a Y (t)=ω 2 rcosδ+gcosθ=ω 2 rcosδ+gcosωt

[0088] a Z (t)=ω 2 rcosε+gcosθ=ω 2 rcosε+gcosωt

[0089] ​Because ω 2 rcosγ, ω 2 rcosδ, ω 2 rcosεare constant values, the XYZ axis data are all acceleration-time functions and are positive cosine functions.

[0090] In this example, the XYZ axis component acceleration data appears as an incomplete positive cosine curve with discontinuity, and the waveform period is basically consistent with the rotation period of the cylinder. This indicates that the sensing ball and the cylinder are relatively stationary and the sensing ball rotates with the cylinder. After rising to a certain height, the sensing ball slides back to the bottom of the cylinder under the action of gravity, and the process repeats.

[0091] In addition, the XYZ axis component acceleration and the combined acceleration data appear a cluster of fluctuations at the end of each positive cosine curve.

[0092] Because the sensing ball collides, the velocity of the sensing ball will change, and the change in velocity will be caused by acceleration. According to the momentum impulse formula:

[0093] Ft = mat = mV1 - mV2

[0094] a = (V1 - V2) / t

[0095] where a is the three-dimensional combined acceleration (a X 2 + a Y 2 + a Z 2 ) 1 / 2 Once the sensing ball collides, and the shorter the collision time, the greater the change in velocity before and after the collision, the greater the change in the combined acceleration of the sensing ball and the three-dimensional component acceleration.

[0096] Therefore, the fluctuations in the XYZ axis component acceleration and the combined acceleration data at the end of each positive cosine curve, i.e., the relative spatial three-dimensional component acceleration data and the combined acceleration data of the sensing ball change dramatically in a short time, indicating that the sensing ball collides during this stage. According to the acceleration formula F = ma, the instantaneous impact force on the sensing ball during the collision can be calculated. In this example, the mass m of the sensing ball is 0.51 kg. Referring to the original data in Figure 6 , the maximum collision combined acceleration a is 3.6g in 30 seconds, i.e., the maximum impact force on the sensing ball during this period is 1.8N.

[0097] Example 4

[0098] The single sensing ball is placed in a mill with a medium filling rate of 40% and a cylinder diameter of 25 cm, the mill is started, the rotating speed is adjusted to 120% of the critical rotating speed of the mill (high rotating speed), after the rotating speed is stable, the mill is continuously run for 20 seconds, then the mill is stopped, the storage card in the sensing ball is taken out, the relative spatial three-dimensional acceleration data in the storage card is read out, and the resultant acceleration is calculated according to the formula (a X 2 +a Y 2 +a Z 2 ) 1 / 2 . Finally, the time- acceleration two-dimensional coordinate data graph is drawn with time as the horizontal coordinate and acceleration value as the vertical coordinate, as shown in Figure 7

[0099] It can be seen from Figure 7 that under the condition of 40% filling rate and 120% critical rotating speed, the XYZ axial acceleration data and the resultant acceleration of the medium ball in the mill all appear obvious and complete cosine curves.

[0100] Let the angle between the X axis of the relative spatial three-dimensional acceleration recorder and the centrifugal acceleration direction be γ, the rotating radius be r, and the angular velocity of the mill be ω, then the component acceleration of the centrifugal acceleration on the X axis is ω 2 rcosγ, when the X axis rotates by an angle θ around the cylinder rotating axis, the component acceleration of the gravitational acceleration on the X axis is gcosθ. Since the angle γ between the X axis and the centrifugal acceleration is a constant value, ω 2 rcosγ is also a constant value, so the acceleration value when the X axis rotates by an angle θ around the cylinder rotating axis can be written as:

[0101] a X (t)=ω 2 rcosγ+gcosθ=ω 2 rcosγ+gcosωt

[0102] Similarly, let the angles between the Y axis and the rotating surface and between the Z axis and the rotating surface be δ and ε respectively, then the acceleration values of the Y axis and the Z axis are as follows:

[0103] a Y (t)=ω 2 rcosδ+gcosθ=ω 2 rcosδ+gcosωt

[0104] a Z (t)=ω 2 rcosε+gcosθ=ω 2 rcosε+gcosωt

[0105] Because ω 2 rcosγ, ω 2 ​rcosδ, ω 2 rcosε are constant, so the XYZ axis data are all acceleration-time functions which are positive cosine functions.

[0106] In this example, the XYZ axial component acceleration data all appear obvious complete positive cosine curve waveforms, and the waveform period is basically consistent with the rotation period of the cylinder, indicating that the induction ball and the cylinder are relatively stationary and the induction ball rotates with the cylinder centrifugally in this time period, which is consistent with the principle that the medium is in a centrifugal state when the mill speed is greater than the critical speed.

[0107] Moreover, the combined acceleration data also have obvious periodic rules, and the period is basically consistent with the rotation period of the cylinder. This is because when centrifuged, the induction ball receives different centrifugal accelerations at the cylinder bottom and the cylinder top. At the cylinder top, the gravitational acceleration cancels out part of the centrifugal acceleration, and the combined acceleration value reaches a minimum; at the cylinder bottom, the combined acceleration superimposes the gravitational acceleration and the centrifugal acceleration, and the combined acceleration value reaches a maximum.

[0108] Therefore, when the XYZ axial component acceleration data all appear obvious complete positive cosine curve waveforms in a certain time period, the waveform period is basically consistent with the rotation period of the cylinder, and the combined acceleration data also have obvious periodic rules and are basically consistent with the rotation period of the cylinder, it can be determined that the induction ball is in a centrifugal state in the mill in this time period.

[0109] Example 5

[0110] A single induction ball was placed in a mill with a medium filling rate of 30% and a cylinder diameter of 25 cm, the mill was started, the speed was adjusted to 80% of the critical speed of the mill, after the speed was stable, the mill was continuously run for 30 seconds, then the mill was stopped, the storage card inside the induction ball was taken out, the relative spatial three-dimensional acceleration data in the storage card were read out, and the combined acceleration was calculated according to the formula (a X 2 +a Y 2 +a Z 2 ) 1 / 2 . Finally, a time-acceleration two-dimensional coordinate data graph was drawn with time as the horizontal coordinate and acceleration value as the vertical coordinate, as shown in Figure 8 .

[0111] It can be seen from Figure 8 that when the cylinder speed reaches 80% of the critical speed, the combined acceleration appears a smooth and stable data segment equal to 0g, indicating that the entire relative spatial three-dimensional accelerometer is in a weightless state, i.e., the relative spatial three-dimensional acceleration data are all zero, and the combined acceleration (a X 2 +a Y 2 +aZ 2 ) 1 / 2 Also for zero, and can be calculated by the acceleration for zero time t, according to Newton's second law can be calculated the longitudinal ball drop height:

[0112] The longitudinal initial velocity V0 is 0, the longitudinal final velocity V1 is gt, and the longitudinal drop height s = V0t + 1 / 2V1t = 1 / 2gt 2 .

[0113] View Figure 8 The original time data in each period of weightlessness is about 0.2s, indicating that the longitudinal drop height is about 0.2m.

[0114] In addition, at the end of each drop, there is a sharp change in acceleration. This is because the inductive ball collides at the end of the drop, and the inductive ball collides, and the speed must change, and the change in speed must be caused by acceleration, according to the momentum impulse formula:

[0115] Ft = mat = mV1 - mV2

[0116] a = (V1 - V2) / t

[0117] Where a is the three-dimensional acceleration (a X 2 +a Y 2 +a Z 2 ) 1 / 2 Once the inductive ball collides, and the shorter the collision time, the greater the speed change before and after the collision, the greater the change in the inductive ball's acceleration and three-dimensional component acceleration. And according to the acceleration formula F = ma, the instantaneous impact force of the inductive ball during the collision can be calculated. In this example, the mass m of the inductive ball is 0.51kg, and the original data in Figure 8 View

[0118] In summary, the application uses the inductive ball equipped with a relative space three-dimensional acceleration recorder to carry out grinding experiments under different mill parameters, records multiple sets of relative space three-dimensional acceleration data, and then processes and analyzes each set of relative space three-dimensional acceleration data, which can accurately and effectively obtain the dynamics of the inductive ball under different mill parameters, so as to explore the specific dynamics of the grinding medium under different grinding factors and provide specific quantitative schemes for saving energy and reducing production cost for grinding enterprises.

[0119] Although the specific embodiments of the present application have been described above, it is understood by those skilled in the art that these are merely illustrative and various changes or modifications can be made to the present embodiments without departing from the principles and the spirit of the present application, and the scope of protection of the present application is defined only by the appended claims.

Claims

1. A method for recording and analyzing the dynamics of mill media using a sensing ball, characterized by, The inductive ball comprises a hollow sphere, an acceleration recorder and a balancing body, the acceleration recorder is arranged inside the hollow sphere for recording relative spatial three-dimensional acceleration data generated when the hollow sphere moves, the acceleration recorder is integrated with a storage card for storing the relative spatial three-dimensional acceleration data, the balancing body is arranged inside the hollow sphere, the material density of the balancing body is greater than that of the hollow sphere, the weight of the inductive ball is equal to that of a solid sphere with the same material and volume as the hollow sphere, and the center of gravity of the inductive ball is located at the center of the hollow sphere; The method for recording and analyzing the medium dynamics of a mill by using the inductive ball comprises the following steps: 1) Milling experiment and data collection: The inductive ball is placed in the mill, the corresponding mill parameters are set, the inductive ball moves with the mill when the mill rotates, the storage card in the acceleration recorder is taken out after the experiment is completed, and the relative spatial three-dimensional acceleration data in the storage card is extracted; 2) Data analysis: Step 1) is repeated under different mill parameters to obtain multiple sets of relative spatial three-dimensional acceleration data, and then each set of relative spatial three-dimensional acceleration data is processed and analyzed to obtain the dynamics of the inductive ball under different mill parameters, and the specific steps are as follows: 2.1) Using the formula of the resultant acceleration (a X 2 +a Y 2 +a Z 2 ) 1 / 2 , the resultant acceleration value a 合 at different time is calculated, the time-acceleration two-dimensional coordinate data graph is established, and the specific values of three-dimensional component accelerations a X , a Y , a Z and the resultant acceleration a 合 at different time are obtained; 2.2) According to the data rule shown in the time-acceleration two-dimensional coordinate data graph, the dynamics of the inductive ball in the mill is identified, which includes the inductive ball being static, the inductive ball rolling and rotating, the inductive ball being relatively static with the cylinder of the mill and rotating with the cylinder, the inductive ball falling, and the inductive ball colliding.

2. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 1, wherein, The hollow sphere is a hollow iron sphere, and the counterpoise is a tungsten block with a density of 19.35 kg / m 3 .

3. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 1, wherein, The hollow sphere is composed of a detachable upper half sphere and a lower half sphere, the first accommodating groove close to the center of the sphere and the second accommodating groove away from the center of the sphere are arranged in the interior of the upper half sphere, the third accommodating groove close to the center of the sphere and the fourth accommodating groove away from the center of the sphere are arranged in the interior of the lower half sphere; when the upper half sphere and the lower half sphere are connected into a whole, the first accommodating groove and the third accommodating groove are connected to form an accommodating cavity for placing the acceleration recorder, and the second accommodating groove and the fourth accommodating groove are each used for placing a balancing body.

4. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 1, wherein, According to the data rule shown in the time-acceleration two-dimensional coordinate data graph, the specific identification strategy for each dynamics of the inductive ball in the mill is as follows: Ⅰ, the inductive ball is static When the values of the component accelerations a X , a Y , a Z remain unchanged and the resultant acceleration a 合 is always 1g in a certain period of time, it is determined that the inductive ball is in a stationary state in the period of time. Ⅱ, the inductive ball rolls and rotates If the time-acceleration two-dimensional coordinate data graph presents a positive sine wave graph in a certain period of time, and the wave period is much smaller than the cylinder rotation period, it can be determined that the inductive ball rolls and rotates in this period of time, and each wave period represents that the inductive ball rolls one circle; Ⅲ, the inductive ball is relatively static with the cylinder of the mill and rotates with the cylinder or centrifugal If the time-acceleration two-dimensional coordinate data graph is an intermittent positive sine function curve in a certain period of time, and the wave period is consistent with the cylinder rotation period, it indicates that the inductive ball is relatively static with the cylinder and rotates with the cylinder; if the obtained relative spatial three-dimensional acceleration data is a complete positive sine function curve, and the wave period is consistent with the cylinder rotation period, it indicates that the inductive ball makes centrifugal motion in the cylinder. Ⅳ, the induction ball falls When the component acceleration and the resultant acceleration are both 0 in the time-acceleration two-dimensional coordinate data graph within a certain period of time, it can be judged that the inductive ball is in the state of free fall within the period of time, and the longitudinal free fall height s of the inductive ball can be calculated according to Newton's second law through the time t during which the acceleration is 0, that is, s = V0t + 1 / 2V1t = 1 / 2gt 2 wherein the longitudinal initial velocity V0 of the throw is 0. Ⅴ, the induction ball collision and impact force When the component acceleration data and the resultant acceleration data in the time-acceleration two-dimensional coordinate data graph change dramatically in a short time, it reflects that the sensing ball has a collision behavior at this time, and according to the acceleration formula F=ma 合 , the instantaneous impact force suffered by the sensing ball at the time of collision can be calculated, where m is the mass of the sensing ball.

5. A method of recording and analyzing the dynamics of the mill media using the inductive ball as claimed in claim 4, characterized in that, When the induction ball is static, the acceleration recorder inside the induction ball can only detect the effect of gravity, at this time the value of the relative space three-dimensional component acceleration remains unchanged, and the resultant acceleration satisfies the following formula: a 合 = (a X 2 + a Y 2 + a Z 2 ) 1 / 2 = 1g.

6. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 4, wherein, When the induction ball rolls and rotates, the X, Y, Z axes of the acceleration recorder inside the induction ball are at a certain angle with the rotation axis of the induction ball, and the rotation axis of the induction ball is perpendicular to the gravity line. Set the angle between the X axis of the acceleration recorder and the rotation surface as α. When the X axis rotates to the highest point, the component acceleration of the gravitational acceleration on the X axis is gcosα. When the X axis rotates θ angle around the rotation axis, the component acceleration of the gravitational acceleration on the X axis is gcosαcosθ. Since the intersection angle α between the X axis and the rotation surface is a constant value, gcosα is also a constant value. Therefore, when the X axis rotates θ angle around the rotation axis, set ω as the angular velocity of the induction ball rolling, then the component acceleration of the gravitational acceleration on the X axis can be expressed as the following sine and cosine functions with time as the independent variable: a X (t) = g cos a cos Q = g cos a cos cot Similarly, set the angles between the Y and Z axes and the rotation surface as β and Ψ, and the component accelerations of the gravitational acceleration on the Y and Z axes are as follows: a Y (t) = g cos β cos θ = g cos β cos ωt a Z (t) = g cos Ψ cos θ = g cos Ψ cos ωt.

7. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 4, wherein, When the induction ball is relatively static with the mill cylinder wall and rotates or centrifugates with the cylinder body, the X, Y, Z axes of the acceleration recorder inside the induction ball are at a certain angle with the direction of the centrifugal acceleration; Let the angle between the X axis of the accelerometer and the centrifugal acceleration direction be γ, the radius of rotation be r, and the angular velocity of the mill be ω, then the component of the centrifugal acceleration on the X axis is ω 2 rcosγ, and when the X axis rotates by an angle θ about the cylinder rotation axis, the component of the gravitational acceleration on the X axis is gcosθ. Since the angle γ between the X axis and the centrifugal acceleration is a constant value, ω 2 rcosγ is also a constant value, so the calculation formula of the acceleration value when the X axis rotates by an angle θ about the cylinder rotation axis is as follows: a X (t) = ω 2 rcosγ+gcosθ=ω 2 rcosγ+gcosωt Similarly, set the angles between the Y and Z axes and the rotation surface as δ and ε, and the acceleration values of the Y and Z axes are as follows: a Y (t) = ω 2 rcosδ + gcosθ = ω 2 rcosδ + gcosωt a Z (t) = ω 2 rcosε+gcosθ = ω 2 rcosε+gcosωt Because ω 2 r cos γ, ω 2 r cos δ, ω 2 r cos ε are constant values, the acceleration data of X, Y, Z axes are all positive cosine functions with time as the independent variable, and the rotating radius of the inductive ball can be calculated according to the relative spatial three-dimensional acceleration data and the speed of the cylinder rotation, that is, the height position of the inductive ball in the mill cylinder is obtained.

8. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 4, wherein, When the sensing ball is in the state of falling, the whole accelerometer is in the state of weightlessness, i.e. the relative three-dimensional acceleration data are all zero, and the resultant acceleration (a X 2 +a Y 2 +a Z 2 ) 1 / 2 is also zero.

9. The method of recording and analyzing mill media dynamics using a sensing ball as claimed in claim 4, wherein, When the induction ball collides, the velocity of the induction ball changes, and the change in velocity must be caused by acceleration, and force must act. According to the momentum impulse formula: Ft = mat = mV1 - mV2 a 合 = (V1-V2) / t Where a 合 The resultant acceleration (a) X 2 +a Y 2 +a Z 2 ) 1 / 2 Once the sensing ball collides, the shorter the collision time and the greater the change in velocity before and after the collision, the greater the change in the resultant acceleration and component acceleration of the sensing ball.

Images