CN117407995A - Semi-autogenous mill grinding medium dynamics modeling method - Google Patents
Semi-autogenous mill grinding medium dynamics modeling method Download PDFInfo
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Abstract
The patent introduces a semi-autogenous mill grinding medium dynamics modeling method, establishes a theoretical model capable of accurately calculating the disengaging angle, the falling back angle and the normal impact energy and tangential grinding energy of a grinding medium under the lifting action of a lining plate according to different structural parameters of a cylinder lining plate and working parameters of a mineral mill, and can deepen understanding of the dynamic characteristics of the grinding medium by carrying out numerical simulation and simulation after programming the mathematical theoretical model, thereby providing theoretical guidance for design and optimization of the cylinder lining plate structure of the mineral mill.
Description
Technical Field
The invention relates to the technical field of mill dynamics modeling and simulation, in particular to a semi-autogenous mill grinding medium dynamics modeling method.
Background
The dynamic modeling is taken as an important content of dynamic analysis and research of the grinding medium of the mineral mill, and is the basis of dynamic characteristic analysis of the grinding medium, structural design of a liner plate of a mill cylinder and optimization research; because the number of grinding media in the mineral mill is numerous, the motion characteristics of the mineral mill are complex, the modeling steps are complex, and the calculated amount is large; therefore, in the field of actual engineering, a designer can complete structural design work of the barrel lining plate through reference design according to engineering experience accumulated for many years and based on similar mineral mill specifications and similar ore properties; the designer can also complete the optimization work of the structure of the cylinder liner plate according to the feedback information of the actual running condition and the actual ore treatment effect of the mineral mill on site; the designer can verify the rationality of the structural design and optimization of the barrel lining plate by simulating the motion trail of the grinding medium in the barrel by means of professional commercial software, but the process needs to complete the establishment of a mineral mill model and the setting of commercial software parameters, so that the time consumption is serious, the designer needs to master the operation and application knowledge of related software, the capability requirement on the designer is high, and in combination, the structural design and optimization of the barrel lining plate of the mineral mill is disjointed in the mathematical theory level; in particular, the establishment of a dynamic model of a grinding medium of a semi-autogenous mill is always a difficult problem which needs to be solved by a plurality of researchers and engineering fields.
In the field of mine crushing and grinding, a liner plate of a semi-autogenous mill cylinder body is generally in a trapezoid structure, as shown in figure 2, a cross-sectional schematic view of the semi-autogenous mill cylinder body provided with the liner plate,the top width of the trapezoid lining board is the top width;is the face angle of the trapezoid lining plate;the thickness of the trapezoid liner plate base plate is subtracted from the effective radius of the semi-autogenous mill cylinder, namely the cylinder radius,for the rate of rotation of the mineral mill,is the angular velocity of the cylinder body itself,；the height of the trapezoid liner plate is the height from the upper plane of the trapezoid liner plate to the upper part of the trapezoid liner plate base plate; the ore grinding medium directly receiving the lifting action of the cylinder liner plate is mainly used for impacting the ore, and the ore grinding medium not directly receiving the lifting action of the cylinder liner plate or the ore grinding medium close to the central layer of the cylinder is mainly used for grinding the ore, so that the semi-autogenous mill has the functions of crushing and grinding; because the motion trail of the outermost layer grinding medium is an outer wrapping line of the motion trail of all the grinding mediums, the motion scope of other grinding mediums is determined, and if the working parameters of the mineral mill and the structural parameters of the cylinder liner are improperly selected, the outermost layer grinding medium is most likely to be thrown to the cylinder liner to cause equipment damage and influence on-site work; it is therefore extremely important to study the kinetics of the outermost grinding media during the process from low start-up operation to normal rotation of the mill.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a semi-autogenous mill grinding medium dynamics modeling method which can accurately and effectively solve the problems of design and lack of theoretical guidance in optimization of a mineral mill cylinder liner plate structure.
The technical scheme adopted by the invention is that the semi-autogenous mill grinding medium dynamics modeling method comprises the following specific steps:
step 1: based on geometrical characteristics of the semi-autogenous mill, establishing a mechanical structure mathematical model of the semi-autogenous mill;
step 2: establishing a grinding medium kinematic model based on the motion characteristics of the grinding medium of the semi-autogenous mill directly subjected to the lifting action of the lining plate;
step 3: solving the disengaging angle of the ore grinding medium directly subjected to lifting action of the lining plate based on the step 1 and the step 2；
Step 4: solving the falling back angle of the grinding medium directly subjected to lifting action of the lining plate based on the differential equation of motion of the grinding medium；
Step 5: solving normal impact energy of ore grinding medium directly subjected to lifting action of lining plate based on step 3, step 4 and energy equationTangential grinding energyAnd based on the ore processing effect evaluation index functionAnd guiding the design and optimization of the lining plate structure of the cylinder body of the mineral mill.
Specifically, the specific steps of establishing the mathematical model of the mechanical structure of the semi-autogenous mill in the step 1 are as follows:
1a: the ore grinding medium is directly lifted by the lining plate and is atWhen the axial direction reaches the stress balance state,included angle between shaft and gravity direction of grinding medium：
；
1b: barrel center when ore grinding medium is lifted by lining boardOre grinding media centerIs connected with the line of (a)Included angle of axes：
；
1c: the ore grinding medium moves to the vertex of the trapezoid lining plateWhen, i.e. the centre of the grinding mediumPoint of attachmentAt this point when overlappingTo the center of the cylinderDistance of (2)：
；
1d: maximum distance of movement of grinding medium on material facing surface of trapezoid lining plate：
；
1e: the ore grinding medium moves to the vertex of the trapezoid lining plateWhen, i.e. the centre of the grinding mediumPoint of attachmentWhen overlapping, the center of the cylinder bodySum pointIs connected with the line of (a)And (3) withIncluded angle of axes：
The method comprises the steps of carrying out a first treatment on the surface of the Wherein,the top width of the trapezoid lining board is the top width;is the radius of the grinding medium;is the face angle of the trapezoid lining plate;is the effective radius of the semi-autogenous mill cylinder;the height of the trapezoid lining plate is equal to that of the trapezoid lining plate;the shaft is the center of the overgrinding mediumAnd the axis is parallel to the material facing surface of the lining plate;for the angular velocity of the cylinder body,；gravitational acceleration;
the specific steps of establishing the grinding medium kinematic model in the step 2 are as follows:
2a: based on the motion and stress characteristics of the grinding medium, establishing a coordinate system XOY by taking the center of the cylinder as a coordinate origin;
2b: the ore grinding medium is directly lifted by the lining plate and isBalance angle when axial direction reaches stress balance state：
；
2c: the ore grinding medium moves to the top point of the lining boardWhen, i.e. the centre of the grinding mediumPoint of attachmentWhen the materials are in a state of coincidence,included angle between shaft and gravity direction of grinding medium：
；
Wherein,for the ore grinding medium to lift from the lining plateThe axial force begins to move to the top point of the lining board when the axial force is balancedTime elapsed.
Specifically, the step 3 is characterized in that the disengaging angle of the grinding medium is directly lifted by the lining plateThe solving method of (2) is as follows:
。
specifically, in the step 4, according to the differential equation of motion of the grinding medium, solving the falling angle of the grinding medium directly subjected to lifting action of the lining plateThe method specifically comprises the following steps:
4a: during this process, the ore grinding medium is displaced with timeFunctional expression of (2)：
；
4b: during this process, the grinding medium is lifted from the lining plate and is in contact withThe axial force begins to move to the top point of the lining board when the axial force is balancedTime of elapsed time：
；
4c: the ore grinding medium moves to the top point of the lining boardDuring the process, the grinding medium is alongSpeed of shaft；
4d: the ore grinding medium moves to the top point of the lining boardDuring the process, the grinding medium is alongThe speed of the shaft isThe angular velocity of the cylinder body isObtaining the vertex of the lining board separated from the grinding mediumVelocity along X axisAnd velocity along Y axis：
；
；
4e: the grinding medium is separated from the vertex of the lining boardThen, parabolic motion is carried out until the grinding medium contacts the lining plate, and the falling angle of the grinding medium is obtained according to a motion equationWith respect to the angle of separation of the grinding mediaIs a hidden function expression of (2):
。
specifically, in the step 5, the grinding medium is separated from the top point of the lining plateThen, parabolic motion is carried out until the lining plate is contacted, and according to the step 3 and the step 4, the normal impact energy of the ore grinding medium directly lifted by the lining plate is solved by establishing an energy equationMeasuring amountTangential grinding energyThe method comprises the steps of carrying out a first treatment on the surface of the And based on the ore processing effect evaluation index functionGuiding the design and optimization of the lining plate structure of the cylinder body of the mineral mill; the method comprises the following specific steps:
5a: separating from the apex of the lining board according to the grinding mediumKinetic energy at the time, and potential energy in the built coordinate system, energy in the X-axis direction of the grinding medium when the grinding medium falls back to the linerEnergy in Y-axis direction：
；
The method comprises the steps of carrying out a first treatment on the surface of the Wherein,is the mass of the ore grinding medium;
5b: falling back angle obtained based on solving in step 4eObtaining the normal impact energy of the grinding mediumTangential grinding energy：
；
；
5c: establishing an ore processing effect evaluation index function according to the calculation result of the step 5b，The design and optimization of the lining plate structure of the cylinder body of the mineral mill are guided; aiming at different barrel lining plate structural parameters and mineral mill working parameters, evaluating index functionThe closer the value is to 1, namely, the larger the value is, the larger the impact energy of the ore grinding medium is, namely, the ore treatment effect is the best when the structural parameter is selected by the barrel lining plate under the working parameter of the mineral mill.
By adopting the technical scheme, the invention has the following advantages:
aiming at different structural parameters of a cylinder liner plate and working parameters of a mineral mill, the invention establishes a disengaging angle which can accurately calculate the disengaging angle of a grinding medium under the lifting action of the liner plateAngle of falling backNormal impact energyTangential grinding energyThe theoretical model is programmed and then numerical simulation and simulation are carried out, so that the understanding of the dynamics characteristics of the grinding medium can be enhancedProvides theoretical guidance for the design and optimization of the lining plate structure of the cylinder body of the mineral mill.
Drawings
Fig. 1 is a technical block diagram of the present invention.
Fig. 2 is a cross-section of a semi-autogenous mill cylinder equipped with a liner plate provided by an embodiment of the invention.
Fig. 3 is a schematic diagram of parameters related to movement of the grinding medium along the trapezoidal lining board according to the embodiment of the invention.
Fig. 4 is a schematic diagram of the movement state of each layer of medium of the mineral mill according to the embodiment of the invention.
FIG. 5 is a schematic diagram of a motion model of a medium directly lifted by a lining plate according to an embodiment of the invention.
FIG. 6 is a schematic diagram of a stress model when the motion of the outermost medium is balanced by lifting the liner plate directly according to the embodiment of the invention.
Fig. 7 is a schematic diagram of a motion state of an outermost medium t moment directly subjected to lifting action of a lining plate according to an embodiment of the present invention.
Fig. 8 is a numerical simulation diagram of changing the face angle of a liner plate of a cylinder and the disengaging angle and the falling angle of a grinding medium at different rotating speeds of a semi-autogenous mill according to the embodiment of the invention.
Fig. 9 is a numerical simulation diagram of a grinding medium release angle and a falling angle at different rotation speeds of a semi-autogenous mill by changing the height of a lifting bar of a barrel liner plate according to an embodiment of the invention.
Fig. 10 is a numerical simulation diagram of the separation angle and the falling angle of the grinding medium at different rotation speeds of the semi-autogenous mill by changing the top width of the liner plate of the cylinder body according to the embodiment of the invention.
Fig. 11 is a numerical simulation diagram of the separation speed of the grinding medium at different rotation speeds of the semi-autogenous mill, which is provided by the embodiment of the invention, by changing the face angle of the lining plate of the cylinder.
Fig. 12 is a numerical simulation diagram of the separation speed of grinding media at different rotation speeds of the semi-autogenous mill with the change of the height of the lifting bars of the cylinder liner provided by the embodiment of the invention.
Fig. 13 is a numerical simulation diagram of the separation speed of the grinding medium at different rotation speeds of the semi-autogenous mill with the change of the top width of the liner plate provided by the embodiment of the invention.
FIG. 14 is a graph showing a numerical simulation of an evaluation index function of the ore treatment effect at a semi-autogenous mill angular velocity of 1.4rad/s with varying barrel liner face angle provided in an embodiment of the present invention.
FIG. 15 is a graph of a numerical simulation of an ore processing effect evaluation index function provided by an embodiment of the present invention with varying barrel liner lifting bar height and at a semi-autogenous mill angular velocity of 1.4 rad/s.
FIG. 16 is a graph of a numerical simulation of an evaluation index function of ore processing effect at a semi-autogenous mill angular velocity of 1.4rad/s with varying barrel liner top width provided in an embodiment of the present invention.
FIG. 17 is a graph of simulation results of a speed field of a grinding medium provided by an embodiment of the invention using EDEM software simulation to change the face angle of a barrel liner and at a semi-autogenous mill angular velocity of 1.4 rad/s.
FIG. 18 is a graph of simulation results of a speed field of a grinding medium provided by an embodiment of the present invention using EDEM software simulation with varying barrel liner lifting bar height and at a semi-autogenous mill angular velocity of 1.4 rad/s.
FIG. 19 is a graph of simulation results of a speed field of a grinding medium provided by an embodiment of the present invention with varying top width of the barrel liner and simulated using EDEM software at a semi-autogenous mill angular velocity of 1.4 rad/s.
FIG. 20 is a graph showing the comparison of results of changing the face angle of a barrel liner and calculating the disengaging angle and the falling angle by using a kinetic theory model and EDEM simulation software when the angular speed of a semi-autogenous mill is 1.4rad/s, provided by the embodiment of the invention.
FIG. 21 is a graph comparing the results of changing the height of a lifting bar of a barrel liner and calculating the disengaging angle and the falling angle by using a kinetic theory model and EDEM simulation software when the angular speed of a semi-autogenous mill is 1.4rad/s, provided by the embodiment of the invention.
FIG. 22 is a graph showing the comparison of the results of the change in top width of the liner plate of the cylinder provided by the embodiment of the invention and the calculation of the disengaging angle and the falling angle by the kinetic theory model and the EDEM simulation software at the angular speed of the semi-autogenous mill of 1.4 rad/s.
Description of the embodiments
The present invention is further explained below with reference to the drawings and examples, which are not to be construed as limiting the scope of the invention, and the purpose of the present invention is to protect all technical improvements within the scope of the invention.
As shown in fig. 5, a coordinate system XOY is established with the center of the cylinder as the origin of coordinates; the grinding medium is subjected to kinematic and dynamic analysis, the friction between the grinding medium and the cylinder lining plate is negligible, as shown in figure 6, when the rotation angular velocity of the cylinder of the mineral mill isWhen the radius isWhen the grinding medium moves to the position shown in fig. 6, the gravity and the centrifugal force of the grinding medium are applied toThe axial balance, namely:（1）；
wherein,for centrifugal forces to which the grinding medium is subjected, i.e.The method comprises the steps of carrying out a first treatment on the surface of the Bringing it into formula (1) yields:included angle between shaft and gravity direction of grinding medium：（2）。
Barrel center when ore grinding medium is lifted by lining boardOre grinding media centerIs connected with the line of (a)Included angle of axes The solving process of (1) is as follows:
inIn (C) due toThen；
Taking outThen；
Thereby making it；
InIn,，
i.e.；
Further:；
inIn taking out，
Further:；
due to，
Further:（3）。
based on the theoretical analysis described above, mathematical modeling was performed on a semi-autogenous mill structure equipped with a barrel liner:
first, when the grinding medium moves to the apex of the lining plate, the grinding medium is centeredPoint of attachmentOverlapping; point(s)To the center of the cylinderDistance ofThe solving process of (1) is as follows:
due to，，，
InIn (1) byBasic theorem of Euclidean plane geometry-cosine theorem
，
Obtaining:；
again with sine theorem，
Obtaining:；
and is further composed ofAnd (2) and，
therefore, the spleen and stomach are in the middle energizerIn,
from the cosine theorem，
Obtaining:（4）。
secondly, the grinding medium moves at the maximum distance on the material facing surface of the trapezoid lining plateThe solving process of (1) is as follows:
when the grinding medium moves to the top point of the lining plate, the grinding medium is centeredPoint of attachmentThe two parts are overlapped together,
due to，Taking out，
InIn,
from the cosine theorem，
Obtaining the product
（5）；
At this time, from the center point of the cylinderTo the point ofThe axis is perpendicular, and the foot is the point，
It is known that:，，，，
combined standAnd;
obtaining:，
i.e.Expressed as:
（6）；
thus, the mathematical modeling of the mechanical structure of the semi-autogenous mill equipped with the cylinder liner is completed.
As shown in FIG. 6, the grinding medium is directly lifted by the lining plate and is thenBalance angle when axial direction reaches stress balance state：
（7）。
As shown in FIG. 7, according to the geometric relationship, the grinding medium moves to the apex of the lining plateWhen, i.e. the centre of the grinding mediumPoint of attachmentWhen the materials are in a state of coincidence,included angle between shaft and gravity direction of grinding medium：
（8）；
As shown in fig. 7, based on the geometric relationship, the disengaging angle of the ore grinding medium directly subjected to the lifting action of the lining plate is solved based on the theoretical basis：
（9）。
To the disengaging angle of the ore grinding medium directly acted by the lifting of the lining plateThe specific solving process of (1) is as follows:
as shown in FIG. 7, when the grinding medium is inAfter the stress in the axial direction is balanced, the lining plate starts to move along the material facing surface until the lining plate moves to the top point of the lining plateThe method comprises the steps of carrying out a first treatment on the surface of the In this process, assuming that a time t has elapsed, the grinding medium moves to a pointEstablishing a differential equation of motion of the grinding medium:
（10）；
wherein,is the center of the cylinder bodyOre grinding medium center at time tThe distance between the two points is chosen to be the same,is the center of the cylinder bodyOre grinding medium center at time tConnection of two pointsThe angle of the axes, and the boundary condition of formula (10) is:
，（11）；
as can be seen from fig. 7, andfrom the foregoing theoretical analysis, it is known that,for ore grinding medium to be lifted by the lining plateThe balance angle of stress balance in the axial direction relates to the working parameters of a mineral mill, the structural parameters of the mineral mill and the radius of a grinding mediumAnd a function of structural parameters of the barrel liner;is the center of the cylinder bodyOre grinding media centerIs connected with the line of (a)The included angle of the axes relates to the structural parameter of the mineral mill and the radius of the grinding mediumAnd a function of structural parameters of the barrel liner; thus (2)、All independent of time t;
wherein the working parameter of the mineral mill is the rotation angular velocityThe method comprises the steps of carrying out a first treatment on the surface of the The structural parameter of the mineral mill is the effective radius of the cylinderThe method comprises the steps of carrying out a first treatment on the surface of the The structural parameters of the cylinder lining plate are as follows: angle of attackHeight of trapezoid lining boardSum of top width。
For the center of the cylinderOre grinding medium center at time tDistance between two points：
Due toTaking out，，
Therefore, the spleen and stomach are in the middle energizerIn,
from the cosine theorem，
Obtaining:（12）；
wherein the method comprises the steps ofThe distance that the grinding medium moves on the feed surface of the barrel liner at time t is a function of time t.
For the center of the cylinderOre grinding medium center at time tConnection of two pointsIncluded angle of axes：
Due toThen；
InIn,
from the cosine theorem，
Obtaining:；
bringing formula (12) into the availability:
（13）；
taking equation (13) into equation (10), the differential equation of motion can be reduced to:
（14）；
obviously, when working parameters of a mineral mill, structural parameters of the mineral mill and radius of grinding mediaWhen the structural parameters of the cylinder liner plate are determined, the equation (14) is a second-order constant-coefficient non-homogeneous linear differential equation, and the boundary condition equation (11) and the equation (14) are combined to obtain the general solution of the second-order constant-coefficient non-homogeneous linear differential equation:
（15）；
the speed of the grinding medium moving along the material facing surface of the cylinder liner plate at the moment t can be obtained by deriving the (15):
（16）；
the ore grinding medium is lifted from the lining plate and is inThe axial force begins to move to the top point of the lining board when the axial force is balancedTime of elapsed timeI.e. whenWhen solving for time：
（17）；
Obtaining the disengaging angle of the grinding medium from the cylinder liner：
（18）。
The ore grinding medium starts to move to the top point of the lining plate and then makes parabolic motion, and the speed in the X-axis direction is set asThe Y-axis has a speed ofUnder the coordinate system XOY, the parabolic motion equation is:
（19）；
wherein the grinding medium breaks away from the pointIs the coordinates of (a)：
（20）；
The ore grinding medium falls back to the cylinder liner after parabolic motion, and the track of the falling back point is set to meet the following equation:
（21）；
all the speed values when the grinding medium is separated from the cylinder lining plate are decomposed to the X axis and the Y axis respectively, so that the speed of the grinding medium along the positive direction of the X axis when the grinding medium is separated from the cylinder lining plateAnd velocity in the positive Y-axis direction：
（22）；
The simultaneous type (19) (21) eliminates the time t to obtain the falling angleWith respect to the angle of disengagementIs hidden in (1)The functional expression:
（23）；
so far, the ore grinding medium is directly lifted by the cylinder liner plate to take off the angleAnd falling back angleAll are solved.
Starting from the time when the ore grinding medium is separated from the barrel lining plate, and returning to the barrel lining plate, according to the energy conservation theorem, returning the energy in the X-axis direction when the ore grinding medium is returned to the barrel lining plateAnd Y-axis direction energyIs converted into impact energy perpendicular to the tangential velocity direction of the cylinderAnd grinding energy parallel to the tangential velocity direction of the cylinderAnd grinding energyThe kinetic energy of the rotation of the cylinder body is removedThe method comprises the following steps:
（24）；
（25）；
based on the theoretical basis, establishing an ore treatment effect evaluationPrice index functionI.e. the ratio of impact energy to total energy:（26）。
1. dynamic model numerical simulation
Taking a phi 6.1 multiplied by 7.5m single-section semi-autogenous mill as an example, programming the mathematical theory model, and carrying out numerical simulation on a semi-autogenous mill grinding medium dynamics model; the numerical simulation related parameters of the dynamic model of the semi-autogenous mill with the specification are shown in Table 1.
| Parameter name | (symbol) | Value taking | Remarks |
| Radius of grinding medium | r | 50mm | |
| Quality of ore grinding medium | m | 4.11Kg | |
| Rotation rate of semi-autogenous mill | φ | 55%/60%/65%/70%/75%/80%/85% | Numerical simulation is carried out on the grinding medium dynamic model under different rotation speeds |
| Effective radius of semi-autogenous mill | R | 2954mm | |
| Face angle of cylinder lining board | δ | 16°/24°/32°/40° | Lifting bar height h=200 mm lifting bar top width b=100 mm |
| Height of lifting strip of cylinder liner | H | 100mm/150mm/200mm/250mm | Head-on angle δ=32° lifting bar top width b=100 mm |
| Top width of lifting strip for cylinder liner | B | 50mm/100mm/150mm/200mm | Head-on angle δ=32° lifter height h=200mm |
Table 1 numerical simulation parameters table of semi-autogenous mill dynamics model.
Wherein the rotation rate of the mineral mill。
Structural parameters of the cylinder liner: face angle of cylinder lining boardLifting bar height of cylinder linerAnd the top width of lifting strip of cylinder lining boardThe method comprises the steps of carrying out a first treatment on the surface of the Aiming at the description of the selection of multiple groups of structural parameters of the cylinder liner plate: because of more variable parameters and larger calculated amount, the embodiment adopts a single variable method to analyze the dynamic model of the grinding medium, such as: when researching the influence of the angle of attack of the cylinder liner plate on the motion behavior of the grinding medium, keeping the height and the top width of the lifting bar unchanged; the same principle as the study on the height and top width of the lifting strip of the cylinder liner is shown in the remarks of table 1.
Numerical simulation is carried out on the semi-autogenous mill grinding medium dynamic model according to the information in table 1, the numerical simulation results are shown in fig. 8-16, and the influence of different barrel lining plate structural parameters and semi-autogenous mill working parameters on the grinding medium motion and impact energy is briefly described below:
as can be seen from fig. 8: under the lifting action of the cylinder liner plate with the same face angle, the disengaging angle and the falling angle of the grinding medium are reduced along with the increase of the rotation rate of the semi-autogenous mill, namely, the lower the rotation speed of the mineral mill is, the closer the throwing distance of the grinding medium is; under the same rotation speed of the semi-autogenous mill, the grinding medium release angle and the grinding medium falling angle are increased along with the increase of the facing angle of the barrel lining plate, namely the larger the facing angle of the barrel lining plate is, the closer the grinding medium throwing distance is.
As can be seen from fig. 9: under the lifting action of the cylinder liner plates with the same lifting bar height, the grinding medium release angle and the grinding medium falling angle are reduced along with the increase of the rotation rate of the semi-autogenous mill, namely the lower the rotation speed of the mineral mill is, the closer the grinding medium throwing distance is; under the same rotation speed of the semi-autogenous mill, as the height of the lifting bar of the barrel lining plate is increased, the disengaging angle and the falling angle of the grinding medium are reduced, namely, the larger the height of the lifting bar of the barrel lining plate is, the farther the throwing distance of the grinding medium is.
As can be seen from fig. 10: under the lifting action of the cylinder liner plate with the same lifting strip top width, the grinding medium release angle and the grinding medium falling angle are reduced along with the increase of the rotation rate of the semi-autogenous mill, namely the lower the rotation speed of the mineral mill is, the closer the grinding medium throwing distance is; under the same rotation speed of the semi-autogenous mill, as the top width of the lifting strip of the barrel lining plate is increased, the disengaging angle and the falling angle of the grinding medium are reduced, namely, the larger the top width of the lifting strip of the barrel lining plate is, the farther the grinding medium is thrown.
As can be seen from fig. 14: when the rotation speed of the semi-autogenous mill increases along with the increase of the face angle of the liner plate of the cylinder body, the impact energy of the ore grinding medium can be kept the maximum, namely the ore treatment effect is optimal.
As can be seen from fig. 15: when the rotation speed of the semi-autogenous mill is reduced along with the increase of the height of the lifting strip of the cylinder liner plate, the impact energy of the ore grinding medium can be kept to be maximum, namely the ore treatment effect is optimal.
As can be seen from fig. 16: when the rotation speed of the semi-autogenous mill is reduced along with the increase of the top width of the lifting strip of the cylinder liner plate, the impact energy of the ore grinding medium can be kept the maximum, namely the ore treatment effect is optimal.
From the above analysis, the influence of structural parameters of the cylinder liner on the motion and impact energy of the grinding medium is as follows: face angle of cylinder lining boardLifting bar height of cylinder linerLifting strip top width of cylinder liner。
2. Discrete element professional software EDEM simulation
Taking phi 6.1 multiplied by 7.5m single-section semi-autogenous mill as an example, special discrete element simulation software EDEM is utilized to simulate the dynamics of the ore grinding medium in the semi-autogenous mill cylinder under the lifting action of a cylinder liner plate, and the angular speed of the semi-autogenous mill during operationThe results are shown in detail in FIGS. 17, 18 and 19.
Calculating the disengaging angle and the falling angle of the grinding medium respectively through discrete meta-software and the proposed dynamic model of the grinding medium, and comparing the disengaging angle and the falling angle, wherein the results are shown in figures 20, 21 and 22; by combining the numerical simulation results of figures 8-13 and the discrete element EDEM simulation results of figures 17-18, the proposed dynamic model can effectively explain the motion behavior and dynamic characteristics of the grinding medium on the mathematical theory level; and the accuracy and the effectiveness of the grinding medium dynamic model are verified through discrete element simulation software EDEM.
Those of ordinary skill in the art will appreciate that: all or part of the steps for implementing the above method embodiments may be implemented by hardware associated with program instructions, and the above program may be stored in a computer-readable storage medium, which when executed, performs steps including the above method embodiments; and the aforementioned storage medium includes: various media that can store program code, such as ROM, RAM, magnetic or optical disks.
The invention is not described in detail in the prior art.
The embodiments selected herein for the purposes of disclosing the present invention are presently considered to be suitable, however, it is to be understood that the present invention is intended to include all such variations and modifications as fall within the spirit and scope of the present invention.
Claims (5)
1. A semi-autogenous mill grinding medium dynamics modeling method is characterized by comprising the following specific steps:
step 1: based on geometrical characteristics of the semi-autogenous mill, establishing a mechanical structure mathematical model of the semi-autogenous mill;
step 2: establishing a grinding medium kinematic model based on the motion characteristics of the grinding medium of the semi-autogenous mill directly subjected to the lifting action of the lining plate;
step 3: solving the disengaging angle of the ore grinding medium directly subjected to lifting action of the lining plate based on the step 1 and the step 2；
Step 4: solving grinding medium directly subjected to lifting action of lining plate based on grinding medium motion differential equationAngle of fall back of matter；
Step 5: solving normal impact energy of ore grinding medium directly subjected to lifting action of lining plate based on step 3, step 4 and energy equationTangential grinding energy->And based on the ore treatment effect evaluation index function +.>And guiding the design and optimization of the lining plate structure of the cylinder body of the mineral mill.
2. The semi-autogenous mill grinding medium dynamics modeling method of claim 1, wherein: the specific steps for establishing the mathematical model of the mechanical structure of the semi-autogenous mill in the step 1 are as follows:
1a: the ore grinding medium is directly lifted by the lining plate and is atWhen the axial direction reaches the stress balance state, the valve is opened or closed>The included angle between the shaft and the gravity direction of the grinding medium is +.>：
；
1b: barrel center when ore grinding medium is lifted by lining boardAnd grinding media center->Is connected with->Included angle of shaft->：
；
1c: the ore grinding medium moves to the vertex of the trapezoid lining plateAt the moment, i.e. grinding media center->And (4) point->At this point +.>To the center of the cylinder->Distance of->：
；
1d: maximum distance of movement of grinding medium on material facing surface of trapezoid lining plate：
；
1e: the ore grinding medium moves to the vertex of the trapezoid lining plateAt the moment, i.e. grinding media center->And (4) point->When the two parts are overlapped, the center of the cylinder body is->And (4) point->Is->And->Included angle of shaft->：
The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>The top width of the trapezoid lining board is the top width; />Is the radius of the grinding medium; />Is the face angle of the trapezoid lining plate; />Is the effective radius of the semi-autogenous mill cylinder; />The height of the trapezoid lining plate is equal to that of the trapezoid lining plate; />The axis is the center of the ore grinding medium>And the axis is parallel to the material facing surface of the lining plate; />For the angular velocity of the cylinder>；/>Gravitational acceleration;
the specific steps of establishing the grinding medium kinematic model in the step 2 are as follows:
2a: based on the motion and stress characteristics of the grinding medium, establishing a coordinate system XOY by taking the center of the cylinder as a coordinate origin;
2b: the ore grinding medium is directly lifted by the lining plate and isBalance angle +.>：
；
2c: the ore grinding medium moves to the top point of the lining boardAt the moment, i.e. grinding media center->And (4) point->When coincident, the head is (are)>The included angle between the shaft and the gravity direction of the grinding medium is +.>：
The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>For the ore grinding medium to lift up from the lining plate and in +.>Starting to move to the top of the lining board when the stress in the axial direction is balanced>Time elapsed.
3. The semi-autogenous mill grinding medium dynamics modeling method according to claim 2, wherein: the step 3 is characterized in that the disengaging angle of the ore grinding medium directly subjected to lifting action of the lining plateThe solving method of (2) is as follows:
。
4. a semi-autogenous mill grinding media dynamics modeling method according to claim 3, wherein: in the step 4, according to the differential equation of motion of the grinding medium, solving the falling angle of the grinding medium directly subjected to lifting action of the lining plateThe method specifically comprises the following steps:
4a: during this process, the ore grinding medium is displaced with timeFunctional expression +.>：
；
4b: during this process, the grinding medium is lifted from the lining plate and is in contact withStarting to move to the top of the lining board when the stress in the axial direction is balanced>Time of going through->：
；
4c: the ore grinding medium moves to the top point of the lining boardDuring this time, the grinding media is ∈ ->Speed of shaft
；
4d: the ore grinding medium moves to the top point of the lining boardDuring this time, the grinding media is ∈ ->The speed of the shaft is +.>The angular velocity of the cylinder body is ∈>Obtaining the grinding medium which is separated from the vertex of the lining plate>Speed along X axis>And speed along Y-axis>：
；
；
4e: the grinding medium is separated from the vertex of the lining boardThen, parabolic motion is carried out until the grinding medium contacts the lining plate, and the grinding medium falling angle is obtained according to a motion equation>About the grinding media release angle->Is a hidden function expression of (2):
。
5. the method for modeling the dynamics of the grinding medium of the semi-autogenous mill according to claim 4, wherein the method comprises the following steps: in the step 5, the grinding medium is separated from the vertex of the lining plateThen, parabolic motion is carried out until the lining plate is contacted, and according to the step 3 and the step 4, the normal impact energy of the ore grinding medium directly lifted by the lining plate is solved by establishing an energy equation>Tangential grinding energy->The method comprises the steps of carrying out a first treatment on the surface of the And based on the ore treatment effect evaluation index function +.>Guiding the design and optimization of the lining plate structure of the cylinder body of the mineral mill; the method comprises the following specific steps:
5a: separating from the apex of the lining board according to the grinding mediumKinetic energy in the time and potential energy in the built coordinate system, when the grinding medium falls back to the lining plate, the energy in the X-axis direction of the grinding medium is +.>Energy in Y-axis direction +.>：
；
The method comprises the steps of carrying out a first treatment on the surface of the Wherein (1)>Is the mass of the ore grinding medium;
5b: falling back angle obtained based on solving in step 4eObtaining the normal impact energy of the grinding medium>Tangential grinding energy：
；
；
5c: establishing an ore processing effect evaluation index function according to the calculation result of the step 5b，The design and optimization of the lining plate structure of the cylinder body of the mineral mill are guided; aiming at different structural parameters of a cylinder lining plate and working parameters of a mineral mill, an evaluation index function is +.>The closer the value is to 1, namely, the larger the value is, the larger the impact energy of the ore grinding medium is, namely, the ore treatment effect is the best when the structural parameter is selected by the barrel lining plate under the working parameter of the mineral mill.
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Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106216077A (en) * | 2016-07-28 | 2016-12-14 | 洛阳矿山机械工程设计研究院有限责任公司 | A kind of detection method of grinding machine intelligence automatic speed regulation system grinding machine energy distribution |
| CN109201221A (en) * | 2018-09-18 | 2019-01-15 | 中冶沈勘工程技术有限公司 | A kind of drum's speed of rotation control method based on steel ball pulverization in ball mill |
| CN112347689A (en) * | 2020-10-30 | 2021-02-09 | 昆明理工大学 | Discrete element method-based semi-autogenous mill lining plate shape optimization method |
| CN115138447A (en) * | 2022-07-21 | 2022-10-04 | 玉溪矿业有限公司 | Method for determining size of steel ball of semi-automatic mill based on collision energy of steel ball and ore |
| WO2022216219A1 (en) * | 2021-04-09 | 2022-10-13 | S.P.M. Instrument Ab | Method and system for operating a comminution process in a ball mill |
| CN116796492A (en) * | 2023-02-09 | 2023-09-22 | 昆明理工大学 | Method for determining shape and parameters of lining plate of ball mill |
| CN117034635A (en) * | 2023-08-21 | 2023-11-10 | 昆明理工大学 | Method for predicting relative sizes of lining plate abrasion rates under different grinding parameters based on discrete element method |
-
2023
- 2023-12-14 CN CN202311720496.5A patent/CN117407995B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106216077A (en) * | 2016-07-28 | 2016-12-14 | 洛阳矿山机械工程设计研究院有限责任公司 | A kind of detection method of grinding machine intelligence automatic speed regulation system grinding machine energy distribution |
| CN109201221A (en) * | 2018-09-18 | 2019-01-15 | 中冶沈勘工程技术有限公司 | A kind of drum's speed of rotation control method based on steel ball pulverization in ball mill |
| CN112347689A (en) * | 2020-10-30 | 2021-02-09 | 昆明理工大学 | Discrete element method-based semi-autogenous mill lining plate shape optimization method |
| WO2022216219A1 (en) * | 2021-04-09 | 2022-10-13 | S.P.M. Instrument Ab | Method and system for operating a comminution process in a ball mill |
| CN115138447A (en) * | 2022-07-21 | 2022-10-04 | 玉溪矿业有限公司 | Method for determining size of steel ball of semi-automatic mill based on collision energy of steel ball and ore |
| CN116796492A (en) * | 2023-02-09 | 2023-09-22 | 昆明理工大学 | Method for determining shape and parameters of lining plate of ball mill |
| CN117034635A (en) * | 2023-08-21 | 2023-11-10 | 昆明理工大学 | Method for predicting relative sizes of lining plate abrasion rates under different grinding parameters based on discrete element method |
Non-Patent Citations (3)
| Title |
|---|
| STEFAN VÖTH ET AL: "Mechanics of the grinding media in ball mills with longitudinal and transverse motion of the grinding media", 《ZKG INTERNATIONAL》, 30 June 2019 (2019-06-30) * |
| 侯亚娟: "基于离散元与有限元耦合的大型球磨机衬板性能研究", 《中国硕士学位论文全文数据库电子期刊 工程科技I辑》, vol. 2015, no. 8, 15 August 2015 (2015-08-15) * |
| 梁曼 等: "正多边形角螺旋衬板对球磨机粉磨效率影响的数值分析", 《机械工程学报》, 30 September 2015 (2015-09-30) * |
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