CN114580237B - Method for analyzing and optimizing damage of cutter arm of web folding mechanism - Google Patents
Method for analyzing and optimizing damage of cutter arm of web folding mechanism Download PDFInfo
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Abstract
The invention provides a method for analyzing the damage of a chopper arm of a web folding mechanism and optimizing the structure, wherein the strength of the chopper arm is inspected by respectively establishing a dynamic mathematical model without a kinematic pair gap and a finite element dynamic model with a kinematic pair gap of the folding mechanism, so that the checking result is more accurate; the degree of freedom of the hacking knife arm is obtained by establishing a virtual prototype of the folding mechanism, and the constraint mode analysis of the hacking knife arm is carried out by taking the actual constraint condition of the hacking knife arm as a boundary condition, so that the calculation result is more practical; the topologically optimized removal material is filled through the truss structure, not only ensuring the strength of the chopper arm, but also changing the structural rigidity of the chopper arm by changing the bar width and the bar thickness of the truss triangle unit, so that the natural frequency of the chopper arm avoids the working frequency.
Description
Technical Field
The invention belongs to the field of printing machinery, and particularly relates to a method for analyzing the damage of a chopper arm of a web folding mechanism and optimizing the structure.
Background
The web paper folding machine is an indispensable unit on a web paper printing machine linkage line, folds paper for the first time through a triangular plate, and automatically folds a whole paper tape into eight-open or sixteen-open paper through the mutual matching of a cutting roller, a folding roller and a page discharging roller, so that the printing speed of newspapers or books and periodicals is greatly improved. In recent years, along with the continuous improvement of raw material cost and labor cost, in order to ensure profits, the requirements of various printing enterprises on printing speeds are higher and higher; but the increase in printing speed brings reliability and stability problems. For example, the knife folding mechanism of the N160 type printing machine set works stably under the working condition of 25000rph of rotating speed, but when the rotating speed is increased to 36000rph, the folding mechanism can be problematic, the root area of the chopper arm can be damaged in a short time, and the production benefit of printing enterprises is seriously affected.
In summary, how to find the reason why the chopper arm is damaged after the web folding machine is accelerated to 36000rph and provide a structure optimization method for the chopper arm, so that the optimized chopper arm structure meets the actual production requirement, and the problem to be solved is needed.
Disclosure of Invention
In order to overcome the drawbacks of the prior art, an object of the present invention is to provide a method for analyzing and optimizing the breakage of a chopper arm of a web folding mechanism, comprising the steps of:
step S1, establishing a dynamic mathematical model of the folding mechanism without a motion pair gap, and calculating the stress of each section of the hacking knife arm when the folding mechanism moves for one period;
s2, establishing a finite element dynamics model of the folding mechanism with a kinematic pair gap by utilizing a transient dynamics module of ANSYS software, and extracting the maximum equivalent stress of each section of the chopper arm when the folding mechanism moves for one period;
s3, selecting a minimum safety coefficient, comparing the stress value of each section of the hacking arm obtained in the steps S1 and S2 with the yield strength of the hacking arm material, and calculating the hacking arm strength safety coefficient; if the safety coefficient of a certain section is smaller than the selected minimum safety coefficient, the section is required to be thickened or widened correspondingly;
step S4, when the hacking knife arm meets the strength requirement, continuously examining the rigidity of the hacking knife arm:
examining the vibration of the chopper arm by utilizing constraint modal analysis, and extracting the natural frequency and vibration mode of the chopper arm;
setting up a vibration test system, testing the actual vibration condition under the operation of a chopper arm workshop, and collecting the vertical acceleration of the chopper arm;
obtaining the power spectrum density, namely the working frequency, of the hacking knife arm vibration signal by using a power spectrum analysis method;
s5, comparing the natural frequency of the chopper arm in the step S4 with the working frequency, and performing topological optimization on the chopper arm structure if the natural frequency can cause structural resonance in the range of the working frequency;
and S6, carrying out constraint mode analysis on the structure of the hacking knife arm after topological optimization, extracting the natural frequency of the hacking knife arm, comparing the natural frequency with the working frequency again, and if resonance conditions still occur, changing the structural rigidity of the hacking knife arm by increasing the rod unit until the natural frequency of the hacking knife arm is avoided from the working frequency and no resonance conditions occur.
Preferably, the step S1 specifically includes the following steps:
step S11, simplifying the folding mechanism into a four-bar mechanism, wherein the motion equation of the four-bar mechanism is as follows:
the above formula is a quadratic derivative of time, and the obtained acceleration relation is:
wherein L is 1 Is the length of the crank; phi (phi) 1 Is the included angle between the crank and the frame; l (L) 2 Is the length of the connecting rod; phi (phi) 2 Is the included angle between the connecting rod and the frame; phi (phi) 3 Is the included angle between the rocker and the frame; omega 1 Is the angular velocity of the crank, omega 2 Is the angular velocity of the connecting rod omega 3 Is the angular velocity of the rocker; alpha 1 Is the angular acceleration of the crank, alpha 2 Is the angular acceleration of the connecting rod, alpha 3 Is the angular acceleration of the rocker;
step S12, carrying out stress analysis on the rocker to obtain a kinetic equation:
the centroid acceleration vector equation of the rocker is:
wherein F is Dx And F Dy Is the acting force of the connecting rod to the rocker; f (F) Dx And F Dy Is the acting force of the frame to the rocker; m is m 3 Is the mass of the rocker; a, a 3x And a 3y Is a component of the centroid acceleration of the rocker; r is (r) 3 Is the distance from the center of mass of the rocker to the lower vertex of the rocker; j is the moment of inertia of the rocker to the lower vertex thereof;
step S13, stress of a certain section of the chopper arm is as follows:
wherein sigma is stress of the section of the chopper arm; a is the cross-sectional area of the hacking knife arm; l is the distance from the section to the cutter body seat; y is the height of the centroid, I is the moment of inertia of the cross section opposite to the centroid; l (L) m And m is the mass of the part below the section of the hacking arm.
Preferably, the step S2 specifically includes the following steps:
step S21, a three-dimensional model of the folding mechanism is imported into ANSYS software, material properties are set from a material library, and the material properties are given to each structure;
step S22, setting contact types of all structures;
step S23, unit type and grid division: the chopper arm is of a thin-wall structure, and the dimension in the thickness direction is far smaller than the dimension in the length and width directions, so that a shell181 unit is adopted for simulation analysis, commands are inserted into a Geometry, and the chopper arm is set through an APDL command; the rest part adopts a sol 186 unit; the method mainly comprises the steps of performing grid division based on a hexahedral grid filling principle;
s24, setting boundary conditions: applying system gravity, setting the rotating speed of a gear box shaft, setting a fixed support for a base, and setting an elastic support for a bearing position so as to represent micro deformation of the gear box shaft;
s25, selecting deformation and stress of the structure as an observation object to solve.
Preferably, in step S21, the material type is 45# steel;
in step S22, the contact type of each structure is set as: the connecting rod is connected with the top end of the hacking knife arm through a 20 multiplied by 42 multiplied by 22 needle roller bearing, the bottom end of the hacking knife arm is connected with the knife body seat through a 40 multiplied by 62 multiplied by 22 needle roller bearing, and a gap of 0.05mm is reserved between the bearing and the pin shaft; friction pair frictional is added between the bearing and the pin shaft to simulate a gap, and the friction coefficient is set to be 0.3; a total of 21 fixed pairs, 3 friction pairs and 4 rotating pairs were added.
Preferably, in step S3, the selected minimum safety factor is 1.3.
Preferably, in step S4, the vibration testing system includes a dynamic signal acquisition instrument, an acceleration sensor, signal acquisition and analysis software, a notebook computer, a wire and a connector.
Preferably, the step S4 specifically includes the following steps:
s41, establishing a virtual prototype of the folding mechanism in ADAMS software, wherein the top end of a hacking knife arm is hinged with a connecting rod, the bottom end of the hacking knife arm is hinged with a knife body seat, extracting the load of the hinged part of the hacking knife arm in a post-processor of the virtual prototype of the folding mechanism, and judging the degree of freedom of the hacking knife arm as a boundary condition for constraint mode analysis;
in the step S42, in the constraint mode analysis, a Block Lanczos algorithm is selected to extract the first 6 th order natural frequency and the vibration mode of the chopper arm.
Preferably, the step S5 specifically includes the following steps:
step S51, performing topology optimization by adopting a Shape Optimization module of ANSYS software, selecting a grid type SOLID95, and performing grid division by taking a hexahedral grid as a main material and a tetrahedral grid filling principle;
step S52, setting the percentage of the reduced material to 80%, taking the softness as an objective function and the volume as a constraint function;
and step S53, taking the load at the hinge position of the hacking knife arm extracted by the virtual prototype of the folding mechanism in the step S41 as an input condition of an optimization model, taking a group of load data at intervals to perform optimization calculation, and taking a collection of materials reserved in a plurality of optimization results as a final optimization model structure.
Preferably, the step S6 specifically includes the following steps:
step S61, filling the material removing part of the hacking knife arm by adopting a full-inclined web member truss structure;
and S62, selecting the triangular unit shape of the full-diagonal web member truss structure as an equilateral triangle, taking the rod width and the rod thickness of the triangular unit as test factors, taking the first 6-order mode natural frequency of the hacking knife arm as an evaluation index, and performing a 2-factor multi-level test to obtain the optimal rod width and the rod thickness of the triangular unit, so that the natural frequency and the working frequency of the hacking knife arm are avoided.
Compared with the prior art, the invention has the following beneficial effects:
1) According to the invention, the strength of the hacking knife arm is inspected by respectively establishing a dynamic mathematical model without a kinematic pair gap and a finite element dynamic model with a kinematic pair gap of the folding mechanism, so that the checking result is more accurate;
2) In the invention, the degree of freedom of the hacking knife arm is obtained by establishing the virtual prototype of the folding mechanism, and the constraint mode analysis of the hacking knife arm is performed by taking the actual constraint condition of the hacking knife arm as a boundary condition, so that the calculation result is more practical;
3) In the invention, the topological optimization removal material is filled through the truss structure, so that not only is the strength of the hacking knife arm ensured, but also the structural rigidity of the hacking knife arm is changed by changing the rod width and the rod thickness of the truss triangle unit, so that the natural frequency of the hacking knife arm avoids the working frequency.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic view of an N160 type blade folding four bar mechanism in accordance with a preferred embodiment of the present invention;
FIG. 3 is a block diagram of a chopper arm of an N160 type blade folding four bar mechanism in accordance with a preferred embodiment of the present invention;
FIG. 4 is an angular velocity of a four-bar hinge mechanism follower in a preferred embodiment of the present invention;
FIG. 5 is an angular acceleration of a four-bar hinge mechanism follower in a preferred embodiment of the present invention;
FIG. 6 shows the forces applied to the chopper arm at a crank speed of 25000rph in a preferred embodiment of the present invention;
FIG. 7 shows the force applied by a chopper arm with a crank speed of 36000rph in a preferred embodiment of the present invention;
FIG. 8 is a load on the top end of a chopper arm in a preferred embodiment of the invention;
FIG. 9 is a load on the bottom end of the chopper arm in a preferred embodiment of the present invention;
FIG. 10 is a chopper arm root vibration signal in a preferred embodiment of the present invention;
FIG. 11 is a power spectral density of a chopper arm root vibration signal in a preferred embodiment of the present invention;
FIG. 12 is a double arm hollow structure chopper arm in a preferred embodiment of the present invention;
fig. 13 is a full diagonal web truss structured chopper arm in accordance with a preferred embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention become more apparent, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, embodiments of the invention.
All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The embodiments described below, together with the words of orientation, are exemplary and intended to explain the invention and should not be taken as limiting the invention.
The invention will be described in further detail below with reference to the attached drawings, which illustrate preferred embodiments of the invention.
As shown in fig. 1, in an embodiment of the present invention, a method for analyzing and optimizing a chopper arm damage of a web folding mechanism includes the steps of:
step S1, establishing a dynamic mathematical model of the folding mechanism without a motion pair gap, and calculating the normal stress of each section of the hacking knife arm when the folding mechanism moves for one period;
step S11, the folding mechanism can be simplified into a four-bar mechanism, and the motion equation of the four-bar mechanism is as follows:
the above formula is a quadratic derivative of time, and the obtained acceleration relation is:
wherein L is 1 Is the length of the crank; phi (phi) 1 Is the included angle between the crank and the frame; l (L) 2 Is the length of the connecting rod; phi (phi) 2 Is the included angle between the connecting rod and the frame; phi (phi) 3 Is the included angle between the rocker and the frame; omega 1 Is the angular velocity of the crank, omega 2 Is the angular velocity of the connecting rod omega 3 Is the angular velocity of the rocker; alpha 1 Is the angular acceleration of the crank, alpha 2 Is the angular acceleration of the connecting rod, alpha 3 Is the angular acceleration of the rocker.
A schematic diagram of an N160 type knife folding four-bar mechanism is shown in FIG. 2, specific parameters of the mechanism are shown in Table 1, and a structure diagram of a chopper arm is shown in FIG. 3. Crank rotates at constant speed, rotational speed omega 1 25000 and 36000rph, respectively; the initial conditions are: phi (phi) 1 ＝70°，φ 2 ＝0°，φ 3 =151°. Programming solves the above equation to obtain the angular velocity and angular acceleration of the follower as shown in fig. 4 and 5.
Table 1 four bar hinge mechanism parameters
Step S12, carrying out stress analysis on the rocking bar (hacking knife arm) to obtain a kinetic equation:
the centroid acceleration vector equation of the rocker is:
wherein F is Dx And F Dy Is the acting force of the connecting rod to the rocker; f (F) Dx And F Dy Is the acting force of the frame to the rocker; m is m 3 Is the mass of the rocker; a, a 3x And a 3y Is a component of the centroid acceleration of the rocker; r is (r) 3 Is the distance from the center of mass of the rocker to the lower vertex of the rocker; j is the moment of inertia of the rocker to its lower apex.
The hacking knife arm is made of 45# steel, and the total mass m 3 =9.61 kg; distance r from center of mass to cutter body seat 3 = 152.32mm; moment of inertia j=m 3 ·L 3 2 /3＝0.6kg·m 2 。
Solving the problems simultaneously, and calculating to obtain the stress at the two ends of the hacking knife arm as shown in fig. 6 and 7.
Step S13, stress of a certain section of the chopper arm is as follows:
wherein sigma is stress of the section of the chopper arm; a is the cross-sectional area of the hacking knife arm; l is the distance from the section to the cutter body seat; y is the height of the centroid, I is the moment of inertia of the cross section opposite to the centroid; l (L) m And m is the mass of the part below the section of the hacking arm.
The minimum cross-sectional area of the chopper arm was 9.3X10 -4 m 2 A maximum cross-sectional area of 3.65X10 -3 m 2 For such a variable cross-section structure, we can easily obtain the centroid of the structure using the cross-section quality attribute function of creo softwareThe area of the position and the section, the height of the centroid and the moment of inertia. By using the calculation of the formula, the maximum stress of the hacking knife arm under the working condition of the rotating speed of 25000rph is 5.59Mpa, and the maximum stress of the hacking knife arm under the working condition of the rotating speed of 36000rph is 11.90Mpa, which are all positioned at the bending position of the hacking knife arm; the maximum stress of the hacking knife arm root area under two working conditions is 3.65MPa and 8.03MPa respectively. Theoretical calculation results find: the stress of the hacking knife arm is far smaller than the yield strength of the material, and it can be judged that the damage of the root of the hacking knife arm is not caused by the stress problem, and the hacking knife arm structure has enough strength.
S2, establishing a finite element dynamics model of the folding mechanism with a kinematic pair gap by utilizing a transient dynamics module of ANSYS software, and extracting the maximum equivalent stress of each section of the chopper arm when the folding mechanism moves for one period, wherein the specific steps comprise:
s21, importing a three-dimensional model of the folding mechanism into ANSYS software in an x-t format, setting material properties from a material library and giving the material properties to each structure, wherein the material type is 45# steel.
S22, setting contact types of the structures. The connecting rod is connected with the top end of the hacking knife arm through a 20 multiplied by 42 multiplied by 22 needle roller bearing, the bottom end of the hacking knife arm is connected with the knife body seat through a 40 multiplied by 62 multiplied by 22 needle roller bearing, and a gap of 0.05mm is reserved between the bearing and the pin shaft; friction pair frictional is added between the bearing and the pin shaft, and can be used for simulating a gap, and the friction coefficient is set to be 0.3. A total of 21 fixed pairs, 3 friction pairs and 4 rotating pairs were added.
S23, unit types and grid division. The chopper arm is of a thin-wall structure, the thickness is 8mm, and the dimension in the thickness direction is far smaller than the dimension in the length and width directions, so that a shell181 unit is adopted for simulation analysis, commands are inserted into a Geometry, and the chopper arm is set through an APDL command; the rest part adopts a sol 186 unit; the method is characterized in that the hexahedral grid is used as a main material, the tetrahedral grid is filled, the grid is divided, and the minimum unit size is 1mm.
S24, setting boundary conditions. And applying system gravity, setting the rotating speed of the gear box shaft, setting a fixed support for the base, and setting an elastic support for the bearing position so as to represent the micro deformation of the gear box shaft.
S25, selecting deformation and stress of the structure as an observation object to solve.
The finite element dynamics analysis result of the folding mechanism shows that: the maximum equivalent stress appears at the bending position of the chopper arm, the maximum equivalent stress of the chopper arm at 25000rph rotating speed is 5.94MPa, and the maximum equivalent stress of the chopper arm at 36000rph rotating speed is 12.71MPa; when the rotation speed of the output shaft of the gear box is increased from 25000rph to 36000rph, the deformation of each structure of the folding mechanism is obviously increased after the rotation speed is increased, but the deformation is smaller overall; the stress level is obviously increased, but the maximum equivalent stress is within 15MPa, which is far less than the yield strength of the material. The finite element dynamics result shows that when the folding mechanism contains a tiny kinematic pair gap, the hacking knife arm structure still has enough strength.
S3, taking 1.3 as a minimum safety coefficient, comparing the stress value of each section of the hacking knife arm obtained in the steps S1 and S2 with the yield strength of the hacking knife arm material, and calculating the intensity safety coefficient of the hacking knife arm; if the safety factor of a section is less than 1.3, the section needs to be thickened or widened correspondingly.
In this embodiment, the stress values of the sections of the hacking arm obtained in steps S1 and S2 are all far less than 355Mpa of the yield strength of the material, and the safety factor of the hacking arm is far greater than 1.3, so that the sections of the hacking arm do not need to be thickened or widened.
And S4, when the hacking knife arm meets the strength requirement, the hacking knife arm can bear a certain force and has the rigidity requirement. And (5) utilizing constraint mode analysis to inspect the vibration of the chopper arm, and extracting the natural frequency and the vibration mode of the chopper arm. Setting up a vibration test system, testing the actual vibration condition under the operation of a chopper arm workshop, and collecting the vertical acceleration of the chopper arm; and obtaining the power spectral density, namely the working frequency, of the hacking knife arm vibration signal by using a power spectral analysis method. The method comprises the following specific steps:
s41, establishing a virtual prototype of the folding mechanism in ADAMS software, wherein the top end of the hacking knife arm is hinged with the connecting rod, the bottom end of the hacking knife arm is hinged with the knife body seat, extracting the load of the hinged part of the hacking knife arm in a post-processor of the virtual prototype of the folding mechanism, and judging the degree of freedom of the hacking knife arm as a boundary condition of constraint modal analysis.
The three-dimensional model of the folding mechanism is led into an ADAMS in an x-t format, material properties (steel) are set, constraints (21 fixed pairs and 4 rotating pairs are added), friction and gravity of a kinematic pair are added, driving (the rotating speed of a flywheel is 36000 rph) is added, step length is selected for 1000 steps, and simulation analysis is carried out for 0.1s (one period of movement of a hacking knife arm). The top end of the hacking knife arm is hinged with the connecting rod, the bottom end of the hacking knife arm is hinged with the knife body seat, and the load at the hinged position of the hacking knife arm is extracted from the post processor of the virtual prototype of the folding mechanism, as shown in fig. 8 and 9. The top end and the bottom end of the chopper arm are subjected to forces in the directions of x, y and z axes and torques in the directions of the x axis and the y axis, and no torque in the direction of the z axis exists; therefore, the chopper arm has a degree of freedom of movement along the x, y, and z axes, a degree of freedom of rotation along the y, z axes, and no degree of freedom of rotation along the z axis.
S42, in constraint mode analysis, a Block Lanczos algorithm is selected to extract the first 6 th order natural frequency and the vibration mode of the chopper arm, and the specific values are shown in table 2.
TABLE 2 description of the values of the first 6 th order natural frequencies and modes of the chopper arms
S43, the vibration testing system comprises: dynamic signal acquisition instrument, acceleration sensor, signal acquisition and analysis software, notebook computer, wire and joint.
In this embodiment, the vibration test employs a test instrument: one INV3020 dynamic signal acquisition instrument adopts a full-shielding case, has better anti-interference capability, and is internally provided with an embedded computer module and a hard disk for storage; 1 acceleration sensor INV9824, the frequency range is 1-15 kHz, and the sensitivity is 5mV/g; the multichannel signal acquisition and real-time analysis software DASP V11 can conveniently analyze and process acquired data; one notebook computer; M5-BNC wire and BNC-BNC connects a plurality of.
The test object is the folding mechanism of the N160 type printing unit, and the test working condition is: the rotating speed of the folding mechanism is 25000rph; and (II) the rotating speed of the folding mechanism is 36000rph. And after the folding mechanism runs stably, data acquisition is started, the sampling frequency is 10kHz, and 30 seconds of data are acquired each time. The vibration time domain signals collected by the test under two working conditions of the root area of the hacking arm of the folding mechanism are shown in figure 10. For the vibration signal in fig. 10, the power spectrum analysis method can better highlight the main frequency component in the frequency spectrum, and in order to study the low-frequency vibration with larger influence on the vibration characteristics of the chopper arm in the vibration signal, the high-frequency interference signal with the frequency of more than 200Hz is filtered, and the power spectrum density of the vibration signal is obtained as shown in fig. 11.
And S5, comparing the natural frequency of the chopper arm in the step S4 with the working frequency, and if the natural frequency is in the range of the working frequency, causing structural resonance, topological optimization needs to be carried out on the structure of the chopper arm. The method comprises the following specific steps:
s51, performing topology optimization by adopting a Shape Optimization module of ANSYS software, selecting a grid type SOLID95, and performing grid division by taking a hexahedral grid as a main material and filling a tetrahedral grid.
S52, setting the percentage of the reduction material to 80%, taking flexibility as an objective function and taking volume as a constraint function.
And S53, taking the load at the hinge position of the hacking knife arm extracted by the virtual prototype of the folding mechanism in the step S41 as an input condition of an optimization model, taking a group of load data at intervals to perform optimization calculation, and taking a collection of materials reserved in a multi-time optimization result as a final optimization model structure.
In this example, the loading of the chopper arm in fig. 8 and 9 takes a set of data every 0.01s as the boundary condition for the optimization analysis, and performs 10 optimization calculations in total; the overlapping part of the material is removed after 10 times of results, namely the part of the optimization model, from which the material needs to be removed. And improving the hacking knife arm structure according to the topology optimization result. The sides of the hacking knife arm are mainly loaded by the upper side and the lower side, the material in the middle area is in interference, the material is removed, and the thickness of the arm is still 8mm; the back of the hacking knife arm is mainly loaded by two sides, the material in the middle area is in interference, the material is removed, the hacking knife arm is changed into a double-arm structure, and the width of each arm is 1/3 of the original structure, namely 16mm; the top of the hacking knife arm needs to keep the existing structure to install the knife blade, the cylindrical structure at the bottom is connected with the long shaft of the knife body seat through a bearing, and in order to ensure the safety and the cleanliness in the operation process, the material is reserved. The improved double-arm hollow structure hacking knife arm structure is shown in figure 12, the mass of the hacking knife arm structure is 5.21kg, and the mass of the hacking knife arm structure is reduced by 45.78% compared with that of the original structure.
And S6, carrying out constraint mode analysis on the structure of the hacking knife arm after topological optimization, extracting the natural frequency of the hacking knife arm, comparing the natural frequency with the working frequency again, and if resonance conditions still occur, changing the structural rigidity of the hacking knife arm by increasing the rod unit until the natural frequency of the hacking knife arm is avoided from the working frequency and no resonance conditions occur. The method comprises the following specific steps:
and (3) performing constraint mode calculation on the improved double-arm hollow structure hacking knife arm, and extracting the first 6 th order natural frequency and the matrix of the hacking knife arm, wherein the table 3 shows.
TABLE 3 description of the values of the first 6 th order natural frequencies and modes of the hollow structure chopper arms
The table shows that the natural frequency of each order mode of the improved double-arm hollow structure chopper arm is reduced, but is still far greater than the working main frequency under working conditions; the first-order natural frequency of the double-arm hollow structure hacking knife arm is close to the working main frequency 45.27Hz under the second working condition, the second-order natural frequency is close to the working main frequency 135.83Hz, and the structure still can resonate. For such longer arm structures with larger spans of chopper arms, we can use truss structures to properly increase stiffness to avoid the dominant frequency of operation.
And S61, filling the material removing part of the hacking knife arm by adopting a full-diagonal web member truss structure. And placing the truss structure on a symmetrical center plane of the hollow part of the hacking knife arm in the vertical direction, and establishing a hacking knife arm model of the full-inclined web member truss structure.
S62, the shape of the triangular unit of the full-diagonal web member truss is selected to be an equilateral triangle, the height of the equilateral triangle is equal to the height of the hollow part of the double-arm structure after topological optimization, and the value is 26mm; the width of each arm is 16mm, so the rod width of the triangular unit is not more than 16mm; the rod width is equally divided into 4 levels, the rod thickness is half of the rod width, the rod width is equally divided into 4 levels, the natural frequency of the first 6-order mode of the chopper arm is used as an evaluation index, and a 2-factor 4-level test is carried out to determine the optimal parameters of the triangle unit rod width and the rod thickness. The test factor levels are shown in table 4.
Table 4 test factors and levels
In total, 16 groups of constraint modal analysis tests are carried out, and compared results find that: when the thickness of the triangle unit is 4mm and the width of the triangle unit is 8mm, the first-order natural frequency of the cutter arm of the full-diagonal web member truss structure is 87.481Hz, the resonance area is 65.61-109.35Hz, working main frequencies 45.27Hz and 135.83Hz under the second working condition are avoided, the second-order natural frequency is 424.29Hz, the second-order natural frequency is far greater than each working main frequency, the structure cannot resonate, and the structure still has enough strength. The final three-dimensional model of the full-diagonal web member truss structure hacking knife arm is shown in fig. 13, and the first 6 th order inherent frequency value and the vibration mode are shown in table 5.
TABLE 5 description of the values of the first 6 th order natural frequencies and modes of the chopper arms
Preliminary workshop tests are carried out on the full-diagonal web member type double-arm truss structure hacking knife arm, and the hacking knife arm operates stably under the working conditions of 24000rph and 36000rph of rotating speed of the folding mechanism, and no abnormality is seen.
Finally, it should be pointed out that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting. Although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (9)
1. The method for analyzing the damage of the chopper arm and optimizing the structure of the web folding mechanism is characterized by comprising the following steps:
step S1, establishing a dynamic mathematical model of the folding mechanism without a motion pair gap, and calculating the stress of each section of the hacking knife arm when the folding mechanism moves for one period;
s2, establishing a finite element dynamics model of the folding mechanism with a kinematic pair gap by utilizing a transient dynamics module of ANSYS software, and extracting the maximum equivalent stress of each section of the chopper arm when the folding mechanism moves for one period;
s3, selecting a minimum safety coefficient, comparing the stress value of each section of the hacking arm obtained in the steps S1 and S2 with the yield strength of the hacking arm material, and calculating the hacking arm strength safety coefficient; if the safety coefficient of a certain section is smaller than the selected minimum safety coefficient, the section is required to be thickened or widened correspondingly;
step S4, when the hacking knife arm meets the strength requirement, continuously examining the rigidity of the hacking knife arm:
examining the vibration of the chopper arm by utilizing constraint modal analysis, and extracting the natural frequency and vibration mode of the chopper arm;
setting up a vibration test system, testing the actual vibration condition under the operation of a chopper arm workshop, and collecting the vertical acceleration of the chopper arm;
obtaining the power spectrum density, namely the working frequency, of the hacking knife arm vibration signal by using a power spectrum analysis method;
s5, comparing the natural frequency of the chopper arm in the step S4 with the working frequency, and performing topological optimization on the chopper arm structure if the natural frequency can cause structural resonance in the range of the working frequency;
and S6, carrying out constraint mode analysis on the structure of the hacking knife arm after topological optimization, extracting the natural frequency of the hacking knife arm, comparing the natural frequency with the working frequency again, and if resonance conditions still occur, changing the structural rigidity of the hacking knife arm by increasing the rod unit until the natural frequency of the hacking knife arm is avoided from the working frequency and no resonance conditions occur.
2. The method for analyzing and optimizing the structure of a chopper arm of a web folding mechanism according to claim 1, wherein the step S1 comprises the steps of:
step S11, simplifying the folding mechanism into a four-bar mechanism, wherein the motion equation of the four-bar mechanism is as follows:
the above formula is a quadratic derivative of time, and the obtained acceleration relation is:
wherein L is 1 Is the length of the crank; phi (phi) 1 Is the included angle between the crank and the frame; l (L) 2 Is the length of the connecting rod; phi (phi) 2 Is the included angle between the connecting rod and the frame; phi (phi) 3 Is the included angle between the rocker and the frame; omega 1 Is the angular velocity of the crank, omega 2 Is the angular velocity of the connecting rod omega 3 Is the angular velocity of the rocker; alpha 1 Is the angular acceleration of the crank, alpha 2 Is the angular acceleration of the connecting rod, alpha 3 Is the angular acceleration of the rocker;
step S12, carrying out stress analysis on the rocker to obtain a kinetic equation:
the centroid acceleration vector equation of the rocker is:
wherein F is Dx And F Dy Is the acting force of the connecting rod to the rocker; f (F) Dx And F Dy Is the acting force of the frame to the rocker; m is m 3 Is the mass of the rocker; a, a 3x And a 3y Is a component of the centroid acceleration of the rocker; r is (r) 3 Is the distance from the center of mass of the rocker to the lower vertex of the rocker; j is the moment of inertia of the rocker to the lower vertex thereof;
step S13, stress of a certain section of the chopper arm is as follows:
wherein sigma is stress of the section of the chopper arm; a is the cross-sectional area of the hacking knife arm; l is the distance from the section to the cutter body seat; y is the height of the centroid, I is the moment of inertia of the cross section opposite to the centroid; l (L) m And m is the mass of the part below the section of the hacking arm.
3. The method for analyzing and optimizing the structure of a chopper arm of a web folding mechanism according to claim 1, wherein the step S2 comprises the steps of:
step S21, a three-dimensional model of the folding mechanism is imported into ANSYS software, material properties are set from a material library, and the material properties are given to each structure;
step S22, setting contact types of all structures;
step S23, unit type and grid division: the chopper arm is of a thin-wall structure, and the dimension in the thickness direction is far smaller than the dimension in the length and width directions, so that a shell181 unit is adopted for simulation analysis, commands are inserted into a Geometry, and the chopper arm is set through an APDL command; the rest part adopts a sol 186 unit; the method mainly comprises the steps of performing grid division based on a hexahedral grid filling principle;
s24, setting boundary conditions: applying system gravity, setting the rotating speed of a gear box shaft, setting a fixed support for a base, and setting an elastic support for a bearing position so as to represent micro deformation of the gear box shaft;
s25, selecting deformation and stress of the structure as an observation object to solve.
4. A web folding mechanism chopper arm damage analysis and structure optimization method in accordance with claim 3, wherein in step S21, the material type is 45# steel;
in step S22, the contact type of each structure is set as: the connecting rod is connected with the top end of the hacking knife arm through a 20 multiplied by 42 multiplied by 22 needle roller bearing, the bottom end of the hacking knife arm is connected with the knife body seat through a 40 multiplied by 62 multiplied by 22 needle roller bearing, and a gap of 0.05mm is reserved between the bearing and the pin shaft; friction pair frictional is added between the bearing and the pin shaft to simulate a gap, and the friction coefficient is set to be 0.3; a total of 21 fixed pairs, 3 friction pairs and 4 rotating pairs were added.
5. The method for web folding mechanism chopper arm damage analysis and structure optimization of claim 1, wherein in step S3, the selected minimum safety factor is 1.3.
6. The method for analyzing the damage to the chopper arm and optimizing the structure of a web folding mechanism according to claim 1, wherein in step S4, the vibration testing system comprises a dynamic signal acquisition instrument, an acceleration sensor, signal acquisition and analysis software, a notebook computer, wires and connectors.
7. The method for analyzing and optimizing the structure of a chopper arm of a web folding mechanism according to claim 1, wherein the step S4 comprises the steps of:
s41, establishing a virtual prototype of the folding mechanism in ADAMS software, wherein the top end of a hacking knife arm is hinged with a connecting rod, the bottom end of the hacking knife arm is hinged with a knife body seat, extracting the load of the hinged part of the hacking knife arm in a post-processor of the virtual prototype of the folding mechanism, and judging the degree of freedom of the hacking knife arm as a boundary condition for constraint mode analysis;
in the step S42, in the constraint mode analysis, a Block Lanczos algorithm is selected to extract the first 6 th order natural frequency and the vibration mode of the chopper arm.
8. The method for analyzing and optimizing the structure of a chopper arm of a web folding mechanism according to claim 1, wherein the step S5 comprises the steps of:
step S51, performing topology optimization by adopting a Shape Optimization module of ANSYS software, selecting a grid type SOLID95, and performing grid division by taking a hexahedral grid as a main material and a tetrahedral grid filling principle;
step S52, setting the percentage of the reduced material to 80%, taking the softness as an objective function and the volume as a constraint function;
and step S53, taking the load at the hinge position of the hacking knife arm extracted by the virtual prototype of the folding mechanism in the step S41 as an input condition of an optimization model, taking a group of load data at intervals to perform optimization calculation, and taking a collection of materials reserved in a plurality of optimization results as a final optimization model structure.
9. The method for analyzing and optimizing the structure of a chopper arm of a web folding mechanism according to claim 1, wherein the step S6 comprises the steps of:
step S61, filling the material removing part of the hacking knife arm by adopting a full-inclined web member truss structure;
and S62, selecting the triangular unit shape of the full-diagonal web member truss structure as an equilateral triangle, taking the rod width and the rod thickness of the triangular unit as test factors, taking the first 6-order mode natural frequency of the hacking knife arm as an evaluation index, and performing a 2-factor multi-level test to obtain the optimal rod width and the rod thickness of the triangular unit, so that the natural frequency and the working frequency of the hacking knife arm are avoided.
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