Analysis Method for the Rigid-Flexible Coupling Dynamic Characteristics of a Web Knife-Folding Mechanism

Abstract

The present invention discloses a method for analyzing the rigid-flexible coupling dynamic characteristics of a web knife folding mechanism, which includes: establishing a three-dimensional rigid model of the folding mechanism and importing it into the multi-body dynamics analysis software ADAMS; establishing a flexible machete arm model of the folding mechanism by using the ANSYS rigid region method, establishing a flexible paper model by using the ANSYS rigid region method, and placing the flexible paper on the paper feeding table of the folding mechanism model; adding constraints, loads, contacts, and drives to each component of the folding mechanism model according to the actual working state of the folding mechanism to generate a rigid-flexible coupling dynamic model of the folding mechanism; establishing the kinematic equation of the folding mechanism and comparing the kinematic analytical values with the calculated values of the rigid-flexible coupling model; determining the maximum rotational speed of the folding mechanism when ensuring the folding accuracy. When modeling the present invention, the paper and the machete arm are treated as flexible bodies, and other components are still rigid bodies, which can more accurately reflect the dynamic characteristics of the folding mechanism.

Description

Technical Field

[0001] The invention belongs to the technical field of computer-aided design optimization using finite element algorithms, and specifically relates to a method for analyzing the rigid-flexible coupling dynamic characteristics of a web-fed knife-type folding mechanism. Background Technique

[0002] For a web-fed knife-type folding mechanism, the paper is a typical flexible body; the chopping knife arm is a long-arm thin-wall structure with a large span. When the folding mechanism operates at high speed, the chopping knife arm will undergo a certain degree of flexible deformation under the influence of its own weight, load, and inertia moment. Therefore, it is an inevitable choice to study the web-fed knife-type folding mechanism as a rigid-flexible coupling multi-body system. However, in the current related research on web-fed knife-type folding mechanisms, they are usually simplified as rigid systems, ignoring the deformation of weak components.

[0003] Since it is difficult to obtain the dynamic contact force between the chopping knife and the paper through experimental means, there is no exact design value for the working load. In the conventional dynamic analysis of folding mechanisms, the working load is often ignored, resulting in a large calculation error; the deformation of the chopping knife arm is positively correlated with the rotational speed. The deformation of the chopping knife arm will cause a slight change in the motion trajectory of the chopping knife head, which will directly affect the folding accuracy. Ignoring the deformation of the chopping knife arm leads to the problem that the determination of the maximum rotational speed of the folding mechanism relies on experience and is inaccurate. Summary of the Invention

[0004] Aiming at the problems existing in the background technique, the invention provides a method for analyzing the rigid-flexible coupling dynamic characteristics of a web-fed knife-type folding mechanism, which is characterized by including:

[0005] Step S1, establishing a three-dimensional rigid body model of the folding mechanism and importing it into the multi-body dynamics analysis software ADAMS; establishing three-dimensional rigid models of each component of the folding mechanism in three-dimensional modeling software, and assembling each component according to the actual mating relationship of the folding mechanism to obtain a three-dimensional multi-rigid body model; then saving it in parasolid format and importing it into the multi-body dynamics analysis software ADAMS;

[0006] Step S2, replacing the rigid chopping knife arm in the rigid body model in Step S1 with a flexible chopping knife arm, where the generation process of the flexible chopping knife arm is: using the ANSYS rigid region method to establish a flexible chopping knife arm model of the folding mechanism, generating an mnf modal neutral file, and finally importing it into the three-dimensional rigid body model of the folding mechanism in ADAMS and replacing the rigid chopping knife arm;

[0007] Step S3, using the ANSYS rigid region method to establish a flexible paper model, generating an mnf modal neutral file and importing it into ADAMS, and placing the flexible paper on the paper feeding table of the folding mechanism model in Step S2;

[0008] Step S4: According to the actual working state of the folding mechanism, add constraints, loads, contacts, and drives to each component of the folding mechanism model in Step S3 to generate a rigid-flexible coupling dynamic model of the folding mechanism;

[0009] Step S5: Establish the kinematic equation of the folding mechanism in Step S1, compare the kinematic analytical values with the calculated values of the rigid-flexible coupling model in Step S4, and verify the rationality of the rigid-flexible coupling model modeling and constraint relationship of the folding mechanism;

[0010] Step S6: Analyze the influence of the flexible machete arm deformation on the folding accuracy, and determine the maximum rotation speed of the folding mechanism when ensuring the folding accuracy;

[0011] Step S7: Conduct a dynamic analysis of the rigid-flexible coupling model of the folding mechanism, calculate the dynamic contact excitation between the machete and the flexible paper, and obtain the working load of the machete;

[0012] Step S8: Establish the dynamic equation of the folding mechanism in Step S1, compare the dynamic analytical values with the calculated values of the rigid-flexible coupling model in Step S4, and determine the influence of the flexible machete arm deformation on the support reaction force.

[0013] The said Step 2 includes:

[0014] Step S21: Import the three-dimensional solid model of the machete arm into ANSYS software, set the element type, material properties, and perform structured mesh division.

[0015] Step S22: Select the central nodes at the two hinge joints of the machete arm respectively to generate two tiny mass elements. The element type is selected as mass21, and the element attribute is mass21p. In order not to affect the mass distribution of the machete arm, then use the central node as the master node to form a rigid region with the surrounding slave nodes. The rigid region is the non-deformable region where the flexible body is connected to the outside world in ADAMS; through the GUI command Preprocessor>Coupling / Ceqn>Rigid Region, first select the central master node, and then select the nodes around this node to connect with it;

[0016] Step S23: Generate the modal neutral file of the flexible machete arm through the macro command adams.mac of ANSYS software, generate the mnf file through the GUI command Solution>ADAMS Connection>Export to ADAMS, and create the master node of the rigid region as an interface node; in ADAMS, when it is necessary to associate a kinematic pair with the machete arm, the corresponding constraint will be added to the interface node;

[0017] Step S24, importing the modal neutral file of the flexible chopper arm into ADAMS through the Flex module, a data exchange interface of ADAMS, and replacing the rigid chopper arm in the three-dimensional rigid body model imported into ADAMS in step S1 with the flexible chopper arm.

[0018] The knife arm material is 45# steel, the Young's modulus is 209Gpa, the Poisson's ratio is 0.269, the material density is 7850kg / m3, the unit type is set to solid186, the number of grid units after division is 64666, and the number of nodes is 18199; the mass21 mass unit attribute is set to 10-6.

[0019] The step 3 comprises:

[0020] Step S31, establishing a paper model in ANSYS software, using shell181 shell elements for meshing, after which the number of mesh elements is 2491 and the number of nodes is 2477;

[0021] Step S32, generating four tiny mass units at the nodes of the four corners of the paper model, selecting the unit type as mass21 and the unit attribute as mass21p; then using them as master nodes to form a rigid region with their surrounding slave nodes;

[0022] Step S33, generate a modal neutral file of the flexible paper model through the macro command adams.mac of the ANSYS software, generate an mnf file through the GUI command Solution>ADAMS Connection>Export to ADAMS, and create the main nodes of the rigid area of the paper as interface nodes; in ADAMS, add force vectors to the main nodes of the four rigid areas to simulate the friction force of the conveyor belt of the paper feeder on the paper;

[0023] Step S34, importing the modal neutral file of the flexible paper into ADAMS through the Flex module, a data exchange interface of ADAMS, and placing it on the paper feeding table of the folding mechanism model generated in step S24.

[0024] The material type of the paper is linear elastic orthotropic, the paper is a thin sheet structure and has a small bending stiffness, and the shell181 shell unit is used for grid division, the side length of the paper unit is 1mm, and the shell thickness is 0.1mm; the mass21 mass unit attribute is set to 10-6.

[0025] The step 5 comprises:

[0026] Step S51, the knife-type folding mechanism is a crank rocker mechanism. Through the closed vector equation of the planar four-bar mechanism, the motion equation of the four-bar mechanism is obtained as follows:

[0027]

[0028] Taking the derivative of Equation (1) with respect to time, the angular velocity relationship can be obtained as follows:

[0029]

[0030] Taking the derivative of Equation (2) with respect to time, the angular acceleration relationship can be obtained as follows:

[0031]

[0032] Wherein, l1 is the length of the crank; θ1 is the angle between the crank and the frame; l2 is the length of the connecting rod; θ2 is the angle between the connecting rod and the frame; l3 is the length of the rocker; l4 is the length of the frame; θ3 is the angle between the rocker and the frame.

[0033] The length parameters of the components of the folding four-bar mechanism are shown in Table 3. The crank rotates at a constant speed, and the rotational speed ω1 is 36000 rph; the initial conditions are: θ1 = 70°, θ2 = 0°, θ3 = 29°. Substituting the data into Equations (1) to (3) to obtain the analytical values of the motion characteristics of the four-bar mechanism.

[0034] The said step 6 includes:

[0035] Step S61: Establish the geometric position relationship between the machete head of the rigid folding mechanism in S1 and each rod, and solve to obtain the lateral displacement of the machete head at different rotational speeds of the folding mechanism; the position (x E , y E ) of point E of the machete head and the geometric position relationship of each rod can be expressed as:

[0036]

[0037] Wherein, β is the angle between the machete arm and the machete, and its size is 80.25°.

[0038] Step S62: Perform kinematic solution on the rigid-flexible coupling model of the folding mechanism in step S4 to obtain the lateral displacement of the machete head of the flexible machete arm at different rotational speeds of the folding mechanism;

[0039] Step S63: Compare the lateral displacement deviation of the machete head in step S61 and S62 at different rotational speeds to obtain the limit working rotational speed of the folding mechanism..

[0040] The said step 7 includes:

[0041] Step S71: Determine the machete and the paper of the rigid-flexible coupling model of the folding mechanism;

[0042] Step S72, add point tensile forces on the master nodes of the four rigid regions of the flexible paper model using the Step function to simulate the friction between the paper and the conveyor belt of the paper feeding table. The function formula is Step(time, 0, 0, 0.01, -2.15) + step(time, 0.01, 0, 0.055, 0) + step(time, 0.055, 0, 0.072, 2.15);

[0043] Step S73, set the flywheel speed to 36000 rph, the solution time to 0.1 s, and the number of steps to 1000 steps. Perform dynamic solution on the rigid-flexible coupling model of the folding mechanism to calculate the dynamic contact excitation between the chopper and the paper during one revolution of the folding mechanism, and obtain the working load of the chopper, as Figure 6 shown; within the time of 0 - 0.072 s, the paper moves along the paper feeding table under the action of the point tensile force. At 0.072 s, the paper moves directly below the chopper and contacts the chopper; within the time of 0.072 s - 0.092 s, the paper makes dynamic contact with the chopper, and the paper undergoes elastic deformation under the action of the chopper; at 0.092 s, the chopper reaches the bottom and then rises to separate from the paper, and the paper finally completes the paper folding action under the rolling action of the roller; at the crank angle of 336.82° (0.072 s), the chopper makes impact contact with the paper, and the impact force in the x direction is 120.78 N. Then the chopper makes dynamic contact with the paper, and the acting force changes continuously. At the crank angle of 67.9° (0.092 s), the chopper separates from the paper, and the contact force returns to 0; it is calculated that the average value of the amplitude of the acting force in the x direction between the chopper and the 16 - opening flexible paper is 39.6 N, and the average value of the amplitude of the acting force in the y direction is 3.2 N; the determination of this acting force can provide mechanical boundary data for the kinematic analysis model of the folding mechanism.

[0044] The said Step 8 includes:

[0045] Step S81, obtain the structural parameters of each component of the four - bar folding mechanism through calculation;

[0046] Step S82, set up the equilibrium equation and calculate the support reaction force of the rigid chopper arm:

[0047] The structural parameters of each component of the folding mechanism are as follows: The mass of the crank disc is m1, the moment of inertia is J s1 , the coordinates of the centroid S1 are (x s1 , y s1 ), and the distance from point A is l s1 ; the mass of the connecting rod is m2, the moment of inertia is J s2 , the coordinates of the centroid S2 are (x s2 , y s2 ), and the distance from point B is l s2 ; the mass of the chopper arm is m3, the moment of inertia is Js3 , the coordinates of the centroid S3 are (x s3 , y s3 ), and the distance from point D is l s3 ; F Ax , F Ay are the components of the constraint reaction force at hinge A in the x and y directions; F Bx , F By are the components of the constraint reaction force at hinge B in the x and y directions; F Cx , F Cy are the components of the constraint reaction force at hinge C in the x and y directions; F Dx , F Dy are the components of the constraint reaction force at hinge D in the x and y directions; F Ex and F Ey are the components of the resistance of the paper to the machete in the x and y directions when the machete folds the paper; M is the moment acting on the crank disc;

[0048] The following equilibrium equations can be listed for the crank disc:

[0049]

[0050] The following equilibrium equations can be listed for the connecting rod:

[0051]

[0052] The following equilibrium equations can be listed for the machete arm:

[0053]

[0054] Combine the equations and the parameters in step S81 to calculate the support reaction force of the rigid machete arm;

[0055] Step S83, at the same rotational speed of the folding mechanism as in step S82, perform a dynamic solution on the rigid-flexible coupling model of the folding mechanism in step S4, and analyze to obtain the support reaction force of the flexible machete arm.

[0056] The maximum rotational speed of the crank disc obtained in step S83 that ignores the deformation of the machete arm.

[0057] The beneficial effects of the present invention are as follows:

[0058] 1. According to the working characteristics of each component of the folding mechanism, when modeling, the paper and the machete arm are treated as flexible bodies, and other components remain rigid bodies, thereby establishing a rigid-flexible coupling dynamics model, which can more accurately reflect the dynamic characteristics of the folding mechanism and can calculate the dynamic contact excitation between the machete and the paper that cannot be obtained by the rigid body model. Description of the Drawings

[0059] Figure 1Schematic diagram of the process of the method for analyzing the rigid-flexible coupling dynamic characteristics of a web-fed knife-type folding mechanism according to the present invention;

[0060] Figure 2 Schematic diagram of the structure of the web-fed knife-type folding mechanism in the embodiment of the present invention;

[0061] Figure 3 Front view schematic diagram of the web-fed knife-type folding mechanism in the embodiment of the present invention;

[0062] Figure 4 Kinetic diagram of the folding mechanism in the embodiment of the present invention;

[0063] Figure 5 Comparison between the simulated value and the analytical value of the angular acceleration of the follower of the rigid-flexible coupling model in the embodiment of the present invention;

[0064] Figure 6 Contact force between the chopping knife and the paper in the embodiment of the present invention;

[0065] Figure 7 Structural diagram of the crank disc of the folding mechanism in the embodiment of the present invention;

[0066] Figure 8 Structural diagram of the connecting rod of the folding mechanism in the embodiment of the present invention;

[0067] Figure 9 Structural diagram of the chopping knife arm of the folding mechanism in the embodiment of the present invention;

[0068] Figure 10 Force analysis diagram of the folding mechanism in the embodiment of the present invention;

[0069] Figure 11 Bar chart of the deviation of the reaction force of the chopping knife arm support in the embodiment of the present invention.

[0070] Wherein: 1. Gearbox, 2. Connecting rod, 3. Chopping knife, 4. Pair of rollers, 5. Crank disc, 6. Chopping knife arm, 7. Knife body seat, 8. Sheet feeding table, 9. Machine frame. Detailed implementation manner

[0071] The present invention will be further described in detail below with reference to the accompanying drawings.

[0072] As Figure 1 shown in the embodiment of the present invention, a rigid-flexible coupling modeling and dynamic characteristic analysis are performed on the knife-type folding mechanism of the N160 web-fed printing press, including the following steps:

[0073] Step S1, establish a 3D rigid body model of the folding mechanism and import it into the multi-body dynamics analysis software ADAMS; establish 3D rigid models of the components of the folding mechanism in a 3D modeling software, and assemble the components according to the actual mating relationship of the folding mechanism to obtain a 3D multi-rigid body model; then save it in parasolid format and import it into the multi-body dynamics analysis software ADAMS; among them, as Figure 2 and Figure 3 shown, the folding mechanism includes: a gearbox 1, a pair of rollers 4, a crank disc 5, a connecting rod 2, a machete arm 6, a machete 3, a frame 9, a sheet feeder 8, a tool body seat 7 and other components. The horizontally arranged sheet feeder 8 is installed in the middle of the frame 9. A pair of rollers 4 arranged below the sheet feeder 8 are opposite to the opening of the sheet feeder 8. The machete 3 is opposite to the middle of the pair of rollers 4. The machete 3 is fixedly installed below one end of the machete arm 6. The other end of the machete arm 6 is hinged to the tool body seat 7. The tool body seat 7 is fixedly connected to the outer wall of the wall panel on one side of the frame 9. Above the end of the machete arm 6 where the machete 3 is installed, it is hinged to one end of the connecting rod 2. The other end of the connecting rod 2 is rotatably connected to the opening on the circular surface of the crank disc 5. The opening at the center of the crank disc 5 is fixedly connected to the output shaft of the gearbox 1. The gearbox 1 is fixedly connected to the wall panel of the frame 9.

[0074] Step S2, replace the rigid machete arm in the rigid body model in Step S1 with a flexible machete arm. The generation process of the flexible machete arm is as follows: use the ANSYS rigid region method to establish a flexible machete arm model of the folding mechanism, generate an mnf modal neutral file, and finally import it into the 3D rigid body model of the folding mechanism in ADAMS; specifically, it is further divided into:

[0075] Step S21, import the 3D solid model of the machete arm into the ANSYS software, set the element type, material properties and perform structured mesh division. The material of the machete arm is selected as 45# steel, the Young's modulus is 209 GPa, the Poisson's ratio is 0.269, the material density is 7850 kg / m3, the element type is set to solid186, and the number of mesh elements after division is 64666, and the number of nodes is 18199.

[0076] Step S22, respectively select the central nodes at the two hinge joints of the machete arm to generate two tiny mass elements. The element type is selected as mass21, and the element attribute is mass21p. In order to make its mass not affect the mass distribution of the machete arm, the mass attribute of the mass21 mass element is taken as a very small value, such as 10-6; then use the central node as the master node to form a rigid region with the surrounding slave nodes. The rigid region is the non-deformable region where the flexible body is connected to the outside world in ADAMS; through the GUI command Preprocessor>Coupling / Ceqn>Rigid Region, first select the central master node, and then select the nodes around this node to connect to it;

[0077] Step S23: Generate the modal neutral file of the flexible machete arm through the macro command adams.mac of ANSYS software. Generate the mnf file through the GUI command Solution>ADAMS Connection>Export to ADAMS, and create the master nodes of the rigid region as interface nodes. In ADAMS, when it is necessary to associate kinematic pairs with the machete arm, the corresponding constraints will be added to the interface nodes.

[0078] Step S24: Import the modal neutral file of the flexible machete arm into ADAMS through the Flex module of the ADAMS data exchange interface, and replace the rigid machete arm in the 3D rigid body model imported into ADAMS in Step S1 with the flexible machete arm.

[0079] Step S3: Establish a flexible paper model using the ANSYS rigid region method, generate the mnf modal neutral file and import it into ADAMS, and place the flexible paper on the paper feeding table of the folding mechanism model in Step S2. Specifically, it is further divided into:

[0080] Step S31: Establish a paper model in ANSYS software. The paper type is the 16mo standard size 787 paper, the material type of the paper is linear elastic orthotropic, and the material properties of the paper are shown in Table 1. The paper belongs to a thin sheet structure and has a small bending stiffness. The shell181 shell element is used for mesh division. The side length of the paper element is 1 mm, and the shell thickness is 0.1 mm. After division, the number of mesh elements is 2491, and the number of nodes is 2477.

[0081] Table 1 Material properties of the paper

[0082]

[0083] Step S32: Generate four tiny mass elements at the nodes at the four corners of the 16mo paper model. The element type is selected as mass21, and the element property is mass21p. Take an extremely small value for the mass21 mass element property. Then use it as the master node to form a rigid region with the surrounding slave nodes respectively.

[0084] Step S33: Generate the modal neutral file of the flexible paper model through the macro command adams.mac of ANSYS software. Generate the mnf file through the GUI command Solution>ADAMS Connection>Export to ADAMS, and create the master nodes of the paper rigid region as interface nodes. In ADAMS, add force vectors to the master nodes of the four rigid regions to simulate the friction force of the paper feeding table conveyor belt on the paper.

[0085] Step S34: Import the modal neutral file of the flexible paper into ADAMS through the Flex module of the ADAMS data exchange interface, and place it on the paper feeding table of the folding mechanism model generated in Step S24.

[0086] Step S4: According to the actual working state of the folding mechanism, add constraints, loads, contacts, and drives to each component of the folding mechanism model in Step S3 to generate a rigid-flexible coupling dynamic model of the folding mechanism; to improve the analysis efficiency, hide the components that do not affect the transmission. The constraint relationships of the components of the simplified folding mechanism are shown in Table 2;

[0087] Table 2 Constraint relationships between components

[0088]

[0089] Step S5: Establish the kinematic equation of the folding mechanism in Step S1, compare the kinematic analysis values with the calculated values of the rigid-flexible coupling model in Step S4, and verify the rationality of the modeling and constraint relationships of the rigid-flexible coupling model of the folding mechanism;

[0090] Step S51: The knife-type folding mechanism is essentially a crank-rocker mechanism, and its kinematic diagram and coordinate system are as shown in Figure 3 and Figure 4 ; Through the closed vector equation of the planar four-bar mechanism, the motion equation of this four-bar mechanism is obtained as follows:

[0091]

[0092] Taking the derivative of Equation (1) with respect to time, the angular velocity relationship can be obtained as:

[0093]

[0094] Taking the derivative of Equation (2) with respect to time, the angular acceleration relationship can be obtained as:

[0095]

[0096] Among them, l1 is the length of the crank; θ1 is the angle between the crank and the frame; l2 is the length of the connecting rod; θ2 is the angle between the connecting rod and the frame; l3 is the length of the rocker; l4 is the length of the frame; θ3 is the angle between the rocker (connecting rod 2) and the frame;

[0097] The length parameters of each component of the folding four-bar mechanism are shown in Table 3. The crank rotates at a constant speed, and the rotational speed ω1 is 36000 rph; the initial conditions are: θ1 = 70°, θ2 = 0°, θ3 = 29°. Substitute the data into Equations (1) to (3) to obtain the kinematic characteristic analysis values of the four-bar mechanism;

[0098] Table 3 Four-bar mechanism length parameters

[0099]

[0100] Step S52: At the same rotational speed of the folding mechanism as in Step S51, perform kinematic solution on the rigid-flexible coupling model of the folding mechanism in Step S4; extract the displacement, velocity, angular velocity, and angular acceleration of the follower, and compare them with the analytical values in Step S51; the analytical solutions of the motion characteristic curves such as the displacement and velocity of point C at the hinge joint between the connecting rod and the machete arm, and the angular velocity of the connecting rod and the machete arm are in good agreement with the simulation values, verifying the rationality of the rigid-flexible coupling modeling and constraint relationship of the folding mechanism; in Figure 5 comparison between the analytical value of the angular acceleration of the connecting rod and the solution result of the rigid-flexible coupling model, the average deviation between the two is 9.6 rad / s², and the average deviation rate is 1.2%; in comparison between the analytical value of the angular acceleration of the machete arm and the solution result of the rigid-flexible coupling model, the average deviation between the two is 0.38 rad / s², and the average deviation rate is 1.56%; the deformation of the machete arm has a certain degree of influence on the angular acceleration.

[0101] Step S6: Analyze the influence of the deformation of the flexible machete arm on the folding accuracy, and determine the maximum rotational speed of the folding mechanism when ensuring the folding accuracy;

[0102] Step S61: Establish the geometric position relationship between the machete head and each rod of the rigid folding mechanism in S1, and solve the lateral displacement of the machete head at different rotational speeds of the folding mechanism; the position (x E , y E ) of point E of the machete head and the geometric position relationship of each rod can be expressed as:

[0103]

[0104] where β is the angle between the machete arm and the machete, and its magnitude is 80.25°;

[0105] Step S62: Perform kinematic solution on the rigid-flexible coupling model of the folding mechanism in Step S4 to obtain the lateral displacement of the machete head of the flexible machete arm at different rotational speeds of the folding mechanism;

[0106] Step S63: Compare the lateral displacement deviations of the machete head in Steps S61 and S62 at different rotational speeds, as shown in Table 4. Practical experience of the folding mechanism shows that to ensure a high folding accuracy, the lateral deformation of the machete head must be controlled within 0.1 mm. As can be seen from Table 4, when the crank rotational speed is less than or equal to 41000 rph, the lateral deformation of the machete head is within the allowable range, and the folding mechanism can meet the working requirements; when the crank rotational speed reaches 42000 rph, the maximum lateral deformation deviation of the machete arm exceeds the allowable value; when the crank rotational speed is increased to 43000 rph, both the maximum deviation and the average deviation of the lateral deformation of the machete arm exceed the allowable value, and the folding accuracy cannot be guaranteed. Considering that the possible clearances and wear of the kinematic pairs will increase the deformation of the machete head to a certain extent, it is recommended that the maximum working rotational speed of the N160 type knife folding mechanism does not exceed 41000 rph.

[0107] Table 4 Relationship between Lateral Displacement Deviation of Machete Head and Rotational Speed

[0108]

[0109] Step S7: Conduct a dynamic analysis of the rigid-flexible coupling model of the folding mechanism, calculate the dynamic contact excitation between the machete and the flexible paper, and obtain the working load of the machete.

[0110] Step S71: Refer to the collision parameter table of various materials for the contact force in ADAMS to determine the contact parameters between the machete and the paper, and between the paper feeding table and the paper in the rigid-flexible coupling model of the folding mechanism, as shown in Table 5.

[0111] Table 5 Contact Parameters

[0112]

[0113] Step S72: Add a point-to-point tensile force to the main nodes of the four rigid regions of the flexible paper model using the Step function to simulate the friction force between the paper and the conveyor belt of the paper feeding table. Its function formula is Step(time,0,0,0.01,- 2.15)+step(time,0.01,0,0.055,0)+step(time,0.055,0,0.072,2.15); time is the time to be solved.

[0114] Step S73: Set the flywheel rotational speed to 36000 rph, the solution time to 0.1 s, and the number of steps to 1000 steps. Conduct a dynamic solution for the rigid-flexible coupling model of the folding mechanism, calculate the dynamic contact excitation between the machete and the paper during one rotation of the folding mechanism, and obtain the working load of the machete, as Figure 6As shown in the figure; within the time range of 0 - 0.072 s, the paper moves along the paper feeding table under the action of the pulling force at the point. At 0.072 s, the paper moves directly below the machete and comes into contact with the machete. During the time range of 0.072 s - 0.092 s, the paper has dynamic contact with the machete, and the paper undergoes elastic deformation under the action of the machete. At 0.092 s, the machete reaches the bottommost position and then rises to separate from the paper. The paper finally completes the paper folding action under the rolling action of the roller. When the crank angle is 336.82° (0.072 s), the machete has impact contact with the paper, and the impact force in the x - direction is 120.78 N. Then, the machete has dynamic contact with the paper, and the acting force continuously changes. When the crank angle is 67.9° (0.092 s), the machete separates from the paper, and the contact force returns to 0. It is calculated that the average value of the amplitude of the x - direction acting force between the machete and the 16 - opening flexible paper is 39.6 N, and the average value of the amplitude of the y - direction acting force is 3.2 N. The determination of this acting force can provide mechanical boundary data for the kinematic analysis model of the folding mechanism.

[0115] Step S8: Establish the dynamic equation of the folding mechanism in Step S1, compare the dynamic analysis values with the calculated values of the rigid - flexible coupling model in Step S4, and determine the influence of the deformation of the flexible machete arm on the support reaction force.

[0116] Step S81: Analyze the structural parameters of the main components of the folding mechanism in Step S1. The structures of components such as the crank disc, connecting rod, and machete arm are as Figures 7 - 9 shown. The structure of the crank disc is as Figure 7 shown; the crank length l1 = 63.5 mm, the outer diameter of the crank disc D1 = 180 mm, the thickness H1 = 54 mm, and the material density ρ = 7800 kg / m 3 . Then the formula for calculating its mass is: m1 = π·D1 2 ·H1·ρ1 / 4 = 10.72 mm; through static balance testing, its mass eccentricity distance l s1 = 0.05l1 = 3.17 mm, and the moment of inertia J s1 = 1 / 12·m1·D1 2 + m1·l s1 2 = 2.90×10 4 kg·mm 2 ; the acceleration and angular acceleration of the crank can be obtained from the above kinematic solution results. The structure of the connecting rod is as Figure 8 shown; the structure of the connecting rod can be regarded as a square rod with a constant cross - section. The connecting rod length l2 = 160.5 mm, the width B2 = 40 mm, the thickness H2 = 20 mm, and the material density is ρ = 7800 kg / m3. Then the formula for calculating its mass is: m2 = ρ·(B2·H2·l2 + π·B2 2·H2 / 4); Its centroid is located at the center of the rod, and the distance from the centroid to the center of hinge B or C is l s2 = 0.5·l2; The formula for calculating the moment of inertia Js2 is: J s2 = 1 / 12·m2·l2 2 ; The acceleration of the connecting rod angular acceleration can be obtained from the above kinematic solution results. The structure of the machete arm is as Figure 9 shown. Due to the complex structure of the machete arm, its mass m3 and the centroid position are both obtained by on-site physical measurement. The measured mass of the machete arm m3 = 9.61 kg, and the distance from the centroid to point D is l s3 = 0.41·l3, and the formula for calculating the moment of inertia J s3 is: J s3 = 0.135·m3·l3 2 + m3·l s3 2 . The acceleration of the machete arm angular acceleration can be obtained from the above kinematic solution results; the resistance F Ex and F Ey of the paper to the machete during folding can be obtained from Figure 6 ; The structural parameters of each component of the folding four-bar mechanism are calculated as shown in Table 6.

[0117] Table 6 Basic parameters of each component of the folding mechanism

[0118]

[0119] Step S82, for the folding mechanism, its force analysis diagram is as Figure 7 shown; The structural parameters of each component of the folding mechanism are as follows: The mass of the crank disc is m1, the moment of inertia is J s1 , and the coordinates of the centroid S1 are (x s1 , y s1 ), and the distance from point A is l s1 ; The mass of the connecting rod is m2, the moment of inertia is J s2 , and the coordinates of the centroid S2 are (x s2 , y s2 ), and the distance from point B is l s2 ; The mass of the machete arm is m3, the moment of inertia is J s3 , and the coordinates of the centroid S3 are (x s3 , y s3 ), and the distance from point D is l s3 ; F Ax , F Ay are the components of the constraint reaction force at hinge A in the x and y directions; F Bx , F Byare the x- and y-components of the reaction force at hinge B; F Cx and F Cy are the x- and y-components of the reaction force at hinge C; F Dx and F Dy are the x- and y-components of the reaction force at hinge D; F Ex and F Ey are the x- and y-components of the resistance force of the paper on the machete when the machete folds; M is the moment acting on the crank disc;

[0120] The following equilibrium equations can be listed for the crank disc:

[0121]

[0122] The following equilibrium equations can be listed for the connecting rod:

[0123]

[0124] The following equilibrium equations can be listed for the machete arm:

[0125]

[0126] By combining the equations and the parameters in step S81, the reaction forces at the supports of the rigid machete arm are calculated.

[0127] Step S83: At the same rotational speed of the folding mechanism as in step S82, perform dynamic solution on the rigid-flexible coupling model of the folding mechanism in step S4 to analyze and obtain the reaction forces at the supports of the flexible machete arm;

[0128] Step S84: When the rotational speed of the crank disc is 36000 rph, compare and analyze the reaction forces at the supports of the rigid machete arm and the flexible machete arm. The comparison results are as Figure 11 shown; for the reaction force at the support of point C in the x-direction at the hinge joint ( Figure 11 (a) of ), when comparing the solution result of the rigid-flexible coupling model with the analytical value, it is found that: the maximum deviation between the two is 37.95 N, occurring when the crank disc rotation angle is 36°, the average deviation is 16.49 N, the maximum deviation rate between the two is 8.25%, occurring when the crank disc rotation angle is 116.36°, and the average deviation rate is 3.87%; for the reaction force at the support of point C in the y-direction at the hinge joint ( Figure 11 (b) of ), when comparing the solution result of the rigid-flexible coupling model with the analytical value, it is found that: the maximum deviation between the two is 13.79 N, occurring when the crank disc rotation angle is 83.63°, the average deviation is 10.11 N, the maximum deviation rate between the two is 10.01%, occurring when the crank rotation angle is 109.09°, and the average deviation rate is 3.34%; for the reaction force at the support of point D in the x-direction at the hinge joint ( Figure 11In (c)), by comparing the solution results of the rigid-flexible coupling model with the analytical values, it is found that: the maximum deviation between the two is 3.38 N, which occurs when the crank angle is 330.91°, the average deviation is 1.24 N, the maximum deviation rate between the two is 6.16%, which occurs when the crank disc angle is 341.82°, and the average deviation rate is 0.78%; for the support reaction force in the y-direction at point D of the hinge joint ( Figure 11 In (d)), by comparing the solution results of the rigid-flexible coupling model with the analytical values, it is found that: the maximum deviation between the two is 4.79 N, which occurs when the crank disc angle is 334.54°, the average deviation is 1.94 N, the maximum deviation rate between the two is 6.94%, which occurs when the crank disc angle is 272.73°, and the average deviation rate is 0.85%; from the above analysis, it can be seen that the deformation of the machete arm has a certain influence on the angular acceleration and a greater influence on the constraint reaction forces of each kinematic pair; further comparative analysis shows that: as the rotational speed of the folding mechanism increases, the deviation between the solution results of the rigid-flexible coupling model and the analytical values becomes more significant. However, when the rotational speed of the folding mechanism is less than or equal to 25000 rph, the average deviation rates of the support reaction forces in the x-direction and y-direction at point C are both less than 1%, and the average deviation rates of the support reaction forces in the x-direction and y-direction at point D are both less than 0.2%. The solution results of the rigid-flexible coupling model are approximately equal to the analytical values, and the deformation of the machete arm can be ignored.

Claims

1. A method for analyzing the rigid-flexible coupling dynamic characteristics of a web knife folding mechanism, characterized in that Including: Step S1: Establish a three-dimensional rigid body model of the folding mechanism and import it into the multi-body dynamics analysis software ADAMS; Establish a three-dimensional rigid model of each component of the folding mechanism in the three-dimensional modeling software. According to the actual mating relationship of the folding mechanism, assemble each component to obtain a three-dimensional multi-rigid body model; then save it in parasolid format and import it into the multi-body dynamics analysis software ADAMS; Step S2: Replace the rigid machete arm of the rigid body model in Step S1 with a flexible machete arm. The generation process of the flexible machete arm is as follows: Use the ANSYS rigid region method to establish a flexible machete arm model of the folding mechanism, generate an mnf modal neutral file, and finally import it into the three-dimensional rigid body model of the folding mechanism in ADAMS and replace the rigid machete arm; Step S3: Use the ANSYS rigid region method to establish a flexible paper model, generate an mnf modal neutral file and import it into ADAMS, and place the flexible paper on the paper feeding table of the folding mechanism model in Step S2; Step S4: According to the actual working state of the folding mechanism, add constraints, loads, contacts, and drives to each component of the folding mechanism model in Step S3 to generate a rigid-flexible coupling dynamic model of the folding mechanism; Step S5: Establish the kinematic equation of the folding mechanism in Step S1, compare the kinematic analytical value with the calculated value of the rigid-flexible coupling model in Step S4, and verify the rationality of the modeling and constraint relationship of the rigid-flexible coupling model of the folding mechanism; Step S6: Conduct an analysis of the influence of the deformation of the flexible machete arm on the folding accuracy, and determine the maximum rotational speed of the folding mechanism when ensuring the folding accuracy; Step S7: Conduct a dynamic analysis of the rigid-flexible coupling model of the folding mechanism, calculate the dynamic contact excitation between the machete and the flexible paper, and obtain the working load of the machete; Step S8: Establish the dynamic equation of the folding mechanism in Step S1, compare the dynamic analytical value with the calculated value of the rigid-flexible coupling model in Step S4, and determine the influence of the deformation of the flexible machete arm on the support reaction force; The said Step S6 includes: Step S61, establish the geometric position relationship between the chopping head and each rod of the rigid folding mechanism in S1, and solve to obtain the lateral displacement of the chopping head at different rotation speeds of the folding mechanism; the position of point E of the chopping head (x E ,y E ) and the geometric position relationship of each rod is expressed as: Wherein, β is the angle between the machete arm and the machete, and its size is 80.25°; Step S62: Conduct kinematic solution on the rigid-flexible coupling model of the folding mechanism in Step S4 to obtain the lateral displacement of the machete head of the flexible machete arm at different rotational speeds of the folding mechanism; Step S63: Compare the lateral displacement deviation of the machete head in Step S61 and S62 at different rotational speeds to obtain the limit working rotational speed of the folding mechanism.

2. The analysis method for the rigid-flexible coupling dynamic characteristics of a web-fed knife-type folding mechanism according to claim 1, wherein The said Step S2 includes: Step S21: Import the three-dimensional solid model of the machete arm into the ANSYS software, set the element type, material properties and conduct structured mesh division; Step S22: Respectively select the central nodes at the two hinge points of the machete arm to generate two tiny mass elements. The element type is selected as mass21, and the element attribute is mass21p. To ensure that their mass does not affect the mass distribution of the machete arm, then use the central nodes as master nodes to form a rigid region with the surrounding slave nodes. The rigid region is the non-deformable region where the flexible body is connected to the outside world in ADAMS. Through the GUI command Preprocessor>Coupling / Ceqn>Rigid Region, first select the central master node, and then select the nodes around this node to connect to it. Step S23: Generate the modal neutral file of the flexible machete arm through the macro command adams.mac of ANSYS software. Generate the mnf file through the GUI command Solution>ADAMS Connection>Export to ADAMS, and create the master nodes of the rigid region as interface nodes. In ADAMS, when it is necessary to associate a kinematic pair with the machete arm, the corresponding constraints will be added to the interface nodes. Step S24: Import the modal neutral file of the flexible machete arm into ADAMS through the Flex module of the ADAMS data exchange interface, and replace the rigid machete arm in the 3D rigid body model imported into ADAMS in Step S1 with the flexible machete arm.

3. The method for analyzing the rigid-flexible coupling dynamic characteristics of a web knife folding mechanism according to claim 2, characterized in that, The material of the knife arm is selected as 45# steel, with a Young's modulus of 209 GPa, a Poisson's ratio of 0.269, and a material density of 7850 kg / m3. The element type is set as solid186, and the number of mesh elements after division is 64666, and the number of nodes is 18199. The mass unit attribute of mass21 is taken as 10-6.

4. A method for analyzing the rigid-flexible coupling dynamic characteristics of a web knife folding mechanism according to claim 2, characterized in that The said Step S3 includes: Step S31: Establish a paper model in ANSYS software, and use shell181 shell elements for mesh division. The number of mesh elements after division is 2491, and the number of nodes is 2477. Step S32: Generate four tiny mass elements at the nodes at the four corners of the paper model. The element type is selected as mass21, and the element attribute is mass21p. Then use them as master nodes to form a rigid region with the surrounding slave nodes. Step S33: Generate the modal neutral file of the flexible paper model through the macro command adams.mac of ANSYS software. Generate the mnf file through the GUI command Solution>ADAMS Connection>Export to ADAMS, and create the master nodes of the paper rigid region as interface nodes. In ADAMS, add force vectors to the master nodes of the four rigid regions to simulate the friction force of the paper feeding table conveyor belt on the paper. Step S34: Import the modal neutral file of the flexible paper into ADAMS through the Flex module of the ADAMS data exchange interface, and place it on the paper feeding table of the folding mechanism model generated in Step S24.

5. A method for analyzing the rigid-flexible coupling dynamic characteristics of a web-fed knife folding mechanism according to claim 4, characterized in that The material type of the paper is linearly elastic orthotropic. The paper belongs to a thin sheet structure and has a small bending stiffness. The shell181 shell element is used for mesh division. The side length of the paper element is 1 mm, and the shell thickness is 0.1 mm. The mass21 mass element attribute is taken as 10-6.

6. The method for analyzing the rigid-flexible coupling dynamic characteristics of a web knife folding mechanism according to claim 1, characterized in that The said step S5 includes: Step S51, the guillotine folding mechanism is a crank-rocker mechanism. By using the closed vector equation of the planar four-bar mechanism, the motion equation of the four-bar mechanism is obtained as: Taking the derivative of Equation (1) with respect to time, the angular velocity relationship is obtained as: Taking the derivative of Equation (2) with respect to time, the angular acceleration relationship is obtained as: Where, l1 is the length of the crank; θ1 is the angle between the crank and the frame; l2 is the length of the connecting rod; θ2 is the angle between the connecting rod and the frame; l3 is the length of the rocker; l4 is the length of the frame; θ3 is the angle between the rocker and the frame; The crank rotates at a constant speed, and the rotational speed ω1 is 36000 rph. The initial conditions are: θ1 = 70°, θ2 = 0°, θ3 = 29°. Substituting the data into Equations (1) to (3), the analytical values of the motion characteristics of the four-bar mechanism are obtained.

7. A method for analyzing the rigid-flexible coupling dynamic characteristics of a web-fed knife-type folding mechanism according to claim 1, characterized in that The said step S7 includes: Step S71, determining the guillotine and the paper of the rigid-flexible coupling model of the folding mechanism; Step S72, adding point tensile forces on the main nodes of the four rigid regions of the flexible paper model by using the Step function to simulate the friction force between the paper and the conveyor belt of the paper feeding table. The function formula is Step(time, 0, 0, 0.01, -2.15) + step(time, 0.01, 0, 0.055, 0) + step(time, 0.055, 0, 0.072, 2.15); Step S73, setting the flywheel rotational speed to 36000 rph, the solution time to 0.1 s, and the number of steps to 1000 steps. Conducting a dynamic solution for the rigid-flexible coupling model of the folding mechanism, calculating the dynamic contact excitation between the guillotine and the paper during one rotation of the folding mechanism, obtaining the working load of the guillotine. Within the time of 0 - 0.072 s, the paper moves along the paper feeding table under the action of the point tensile force. At 0.072 s, the paper moves to directly below the guillotine and contacts the guillotine. During the time of 0.072 s - 0.092 s, the paper and the guillotine have dynamic contact, and the paper undergoes elastic deformation under the action of the guillotine. At 0.092 s, the guillotine reaches the bottommost position and then rises to separate from the paper. The paper finally completes the paper folding action under the rolling action of the rollers. At the crank angle of 336.82°, that is, at 0.072 s, the guillotine and the paper have impact contact, and the impact force in the x direction is 120.78 N. Then, the guillotine and the paper have dynamic contact, and the acting force continuously changes. At the crank angle of 67.9° (0.092 s), the guillotine and the paper separate, and the contact force returns to 0. The average value of the amplitude of the x-direction acting force between the guillotine and the 16-opening flexible paper is calculated to be 39.6 N, and the average value of the amplitude of the y-direction acting force is 3.2 N. The determination of this acting force provides mechanical boundary data for the kinematic analysis model of the folding mechanism.

8. The method for analyzing the rigid-flexible coupling dynamic characteristics of a web-fed knife folding mechanism according to claim 1, wherein The said step S8 includes: Step S81, obtaining the structural parameters of each component of the folding four-bar mechanism through calculation; Step S82, setting the equilibrium equation and calculating the support reaction force of the rigid chopper arm: The structural parameters of each component of the folding mechanism are as follows: The mass of the crank disc is m1, and the moment of inertia is J. s1 , and the coordinates of the center of mass S1 are (x s1 , y s1 ), and the distance from point A is l s1 ; The mass of the connecting rod is m2, and the moment of inertia is J s2 , and the coordinates of the center of mass S2 are (x s2 , y s2 ), and the distance from point B is l s2 ; The mass of the machete arm is m3, and the moment of inertia is J s3 , and the coordinates of the center of mass S3 are (x s3 , y s3 ), and the distance from point D is l s3 ; F Ax , F Ay are the components of the constraint reaction force at hinge A in the x and y directions; F Bx , F By are the components of the constraint reaction force at hinge B in the x and y directions; F Cx , F Cy are the components of the constraint reaction force at hinge C in the x and y directions; F Dx , F Dy are the components of the constraint reaction force at hinge D in the x and y directions; F Ex and F Ey are the components of the resistance force of the paper on the machete in the x and y directions when the machete folds the paper; M is the torque acting on the crank disc. The following equilibrium equation is given for the crank disk: The equilibrium equation for the connecting rod is as follows: The following equilibrium equation is given for the machete arm: The equations are combined with the parameters in step S81 to calculate the support reaction force of the rigid chopper arm; Step S83, the rotation speed of the folding mechanism is the same as that of step S82, and the rigid-flexible coupling model of the folding mechanism in step S4 is dynamically solved to analyze and obtain the support reaction force of the flexible chopper arm.

9. The analysis method for the rigid-flexible coupling dynamic characteristics of a web knife folding mechanism according to claim 8, wherein In step S83, the maximum rotation speed of the crank disc ignoring the deformation of the chopper arm is obtained.

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