JPH0981595A - Contact analysis method for two contacting members - Google Patents

Abstract

PROBLEM TO BE SOLVED: To more accurately perform the contact analysis or two contacting members on a computer by combining forcible displacement type and load type finite element methods to perform the contact analysis. SOLUTION: When the distance between axes of a blanket roll 10 for print and a metallic roll 12 is shortened and initial forcible displacement is given, an extent of pressing-in is given to a blanket 13 for print. Then, the blanket 13 for print is elastically deformed to come into face contact with the metallic roll 12. Positions and the number of nodal points in this contact part are detected. Next, the extent of deviation in the forcible displacement direction between corresponding nodal points of the blanket 13 for print and the metallic roll 12 is calculated in accordance with distances between contacting nodal points. As the result of elastic deformation of the blanket 13 for print, the reaction force of deformation of the blanket 13 for print is exerted on the metallic roll 12. Then, FEM analysis is performed which gives forcible displacement to overlapping nodal points on one side of the contact face so that the extent of contact face mis-matching of overlapping nodal points is 0, and an initial nodal point reaction force is obtained. The vertical drag of the contact part and the extent of contact face mismatching are calculated, based on this reaction force.

Description

Detailed Description of the Invention

[0001]

TECHNICAL FIELD The present invention relates to an analysis method for analyzing a mechanical behavior acting on a contact 2 member.

[0002]

2. Description of the Related Art In order to analyze the mechanical behavior acting on two contact members, a structural analysis program called a design support system, for example, by the finite element method is generally used. However, the conventional structural analysis program cannot analyze the mechanical behavior of a nonlinear elastic body (rubber, plastic, carbon fiber, etc.) and a different material, or a composite material in which nonlinear elastic bodies are combined. This is because these non-linear elastic bodies take into consideration many parameters such as non-linearity of property values, anisotropy, homogenization, deformation due to contact with other structures, magnitude of applied load, generation of frictional force, etc. This is because it is impossible to grasp the mechanical behavior such as the generated deformation and stress by inserting it. It is impossible to carry out experiments on all of these factors in the laboratory as well because of too many parameters. For this reason, conventionally, there has been no choice but to adopt a method of successively producing finished products, measuring the characteristics thereof, and feeding back the results, and repeating the design.

More specifically, for example, in order to evaluate the mechanical characteristics of a printing blanket, it is essential to know the mechanical behavior of the blanket roll during contact rotation, that is, the state of deformation and stress. However, the printing blanket is a composite material having a laminated structure of rubber, sponge, cloth and the like, and the printing rolls rotate at high speed while being in contact with each other, so that it is difficult to analyze its behavior. Therefore, it is very difficult to design a blanket that satisfies the required characteristics, and no systematic design method has been established so far. Specifically, there are contact length, contact pressure distribution, stress distribution (lamination direction stress and circumferential direction stress), etc. as blanket design parameters, but proper evaluation of printing blanket considering these variables is performed by numerical simulation. Construction of a design support system is desired.

[0004]

SUMMARY OF THE INVENTION It is an object of the present invention to provide a contact analysis method capable of more accurately performing contact analysis of two contact members on a computer. Another object of the present invention is to obtain a contact analysis method that can reduce the number of trial iterations through more accurate prediction. Another object of the present invention is to obtain an analysis method capable of analyzing deformation and stress generated in a printing blanket.

[0005]

SUMMARY OF THE INVENTION The present invention performs more accurate contact analysis of two contact members by combining a method using the finite element method called the forced displacement type and a method using the finite element method called the load type. It was completed based on the idea that it is possible.

According to the method of the present invention, a step of setting a forced displacement amount in the contact direction given to the contact 2 member; a finite amount existing on the contact surface of the contact 2 member based on the forced displacement amount set in the displacement amount setting step. Step of detecting the number of nodes by the element method; Step of calculating displacement amount in the direction of forced displacement between corresponding contact nodes of two contact members caused by forced displacement by forced displacement type finite element analysis; Based on this displacement amount A step of calculating a reaction force of each contact node; a step of recalculating a displacement amount in the forced displacement direction between the corresponding contact nodes of the two contact members caused by the reaction force of each contact node by a load-type finite element analysis; The calculation of each node reaction force by the above forced displacement finite element analysis and the calculation of the displacement amount in the forced displacement direction between the corresponding contact nodes of the contact 2 members by the load type finite element analysis are performed. Repeated until the deviation amount falls within the tolerance range, the step of detecting the position of each contact node; and,
And a step of detecting a mechanical behavior of the contact 2 member based on the position information of each contact node, which is a contact analysis method for the contact 2 member.

According to the method of the present invention, when the contact surface of the contact 2 member is a cylindrical surface, in order to obtain more accurate position information of the contact node, the contact surface is further separated by the normal force of each contact node. Determining whether or not a directional force is included; and, if the normal force of each contact node includes a force in the direction in which the contact surface separates, contact nodes at both ends of the contact node group. It is preferable to recalculate the position information except for the position information of. The fact that the reaction force value includes a value that is opposite in sign to the compression force is likely to mean that the nodes indicating the reaction force value are distant from each other. It is appropriate to perform the calculation excluding the information on the nodes. Further, according to the method of the present invention, when the contact surfaces of the contact 2 members are cylindrical surfaces that rotate while contacting each other, the contact surfaces of the two cylindrical surfaces during rotation are further analyzed. It is preferable to include the step; A more accurate contact surface analysis (prediction) can be performed by considering the frictional force when alternately applying the load type and displacement type finite element methods.

In the method of the present invention, for example, one of the contact 2 members is a printing blanket wound on a metal roll,
It is applicable when the other is a metal roll. The mechanical behavior of the printing blanket detected by the method of the present invention includes at least the deformation state of the printing blanket, the stress state, the contact length, and the frictional force acting between the two contact members.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS A contact analysis method for two contact members according to the present invention will be described below with reference to the drawings. The illustrated embodiment is one in which the present invention is applied to the behavior analysis of a printing blanket.
FIG. 1 shows an arrangement model of a printing blanket roll 10 to which the method of the present invention is applied and a metal roll 12.
The printing blanket roll 10 includes a printing blanket (composite material) to be analyzed on the surface of the metal roll 11.
It is a roll of 13. Blanket roll for printing 1
The axes of 0 and the metal roll 12 are parallel to each other, and the distance between the central axes can be changed. Printing blanket 1
The initial forced displacement amount (pushing amount) in the contact direction can be set by the reduction amount of the distance between the central axes from the state where the wire 3 and the metal roll 12 are in line contact without being compressed. In the following analysis, the printing blanket 13 is regarded as a homogeneous anisotropic material, and its thickness is 2 mm, the elastic modulus in the rotation direction is 773.6 MPa, and the elastic modulus in the radial direction is 5.7 MP.
a, the Poisson's ratio of thickness change during in-plane tension was 0.4, and the Poisson's ratio of circumferential shrinkage during out-of-plane tension was 2.9 × 10 ^-3 . The material of the metal rolls 11 and 12 is isotropic, and the elastic modulus was 205.8 MPa and the Poisson's ratio was 0.3.

2 and 3 show finite element models to be analyzed. FIG. 2 shows a printing blanket roll 10.
And an overall view of the finite element mesh of the metal roll 12 (calculation is performed on the half on the contact side), and FIG. 3 is an enlarged view of the III portion (contact portion) of FIG. The total number of meshes was 4,884, and the number of nodes was 2,552.

According to the method of the present invention, after the finite element model is set as described above, the steps shown in FIGS.
Finite element analysis (FEM analysis) is performed to analyze the mechanical behavior of the printing blanket 13. First, the distance between the central axes of the printing blanket roll 10 and the metal roll 12 is shortened to give an initial forced displacement (step S1). By this initial forced displacement, the pressing amount is given to the printing blanket 13. One of the features of the present invention is the next contact analysis 20 (step S2) performed based on this initial forced displacement amount (push amount).

FIG. 5 shows the specific contents of this contact analysis. When the initial forced displacement amount is given, the printing blanket 13 elastically deforms and comes into surface contact with the metal roll 12. Therefore, the position of the node and the number n of the surface-contacting portion are detected (steps S10 and S12). Next, the shift amount δ in the forced displacement direction between the corresponding nodes (overlapping nodes) of the printing blanket 13 and the metal roll 12
₀ is calculated from the distance between contact nodes (step S13).
The amount of displacement (overlap amount or gap amount) in the forced displacement direction between the contact nodes is called the contact surface irregularity amount. As a result of the elastic deformation of the printing blanket 13, the deformation reaction force of the printing blanket 13 is exerted on the metal roll 12. Therefore, a forced displacement type FEM analysis is performed in which a forced displacement is applied to the overlapping node on one side of the contact surface (the metal roll 12 side) so that the contact surface irregularity amount of the overlapping node becomes zero.
The initial nodal reaction force f ₀ generated at this time is obtained (step S14). That is, the nodal reaction force f ₀ that causes the displacement required to set the contact surface irregularity amount of the overlapping nodes to 0 is obtained. This initial nodal reaction force f ₀ is totaled and the normal force F of the contact portion is
₁ is calculated (steps S15 and S16). From this normal force F ₁ , a load type FEM analysis is performed, and the contact surface irregularity δ ₁ is calculated again (step S1).
7). That is, the displacement generated as a result of applying the normal force F ₁ is obtained, and the contact surface irregularity amount is recalculated. Next, it is determined whether or not the recalculated contact surface irregularity amount δ ₁ is less than a predetermined allowable value δ _e (step S
18). If it is not less than the allowable value, the forced displacement is given by the forced displacement type FEM analysis similar to step S14 to calculate the nodal reaction force at that time (step S19). Find F ₂ (Step S2
0, S16, S17), a load type FEM analysis is performed on the basis of this normal force F _2, and the contact surface irregularity amount δ ₂ is calculated again (step S17). That is, the position of the overlapping node is corrected while repeatedly obtaining the load based on the displacement and the displacement based on the load. The above load-type and forced displacement-type FEM analyzes are repeated until the contact surface irregularity amount δ _N becomes less than the allowable value δ _e, and when it becomes less than the allowable value, all normal forces at each node used for calculation are compressed. It is determined whether the direction is the direction (step S21). When this determination is NO, there is a high possibility that the nodes at both ends of the contact surface forming a part of the cylindrical surface are separated (the force in the direction of opening the contact surface is acting), so the nodes at both ends are high. The information related to is excluded from the calculation, and the same calculation is repeated until the normal forces of all the nodes are in the compression direction (steps S22, S12 to S21). The normal force F _i is the sum of the nodal reaction forces calculated in each step, and in the illustrated example,
The normal force in the compression direction has a negative value in the upper printing blanket roll 10 and a positive value in the lower metal roll 12.

By the above calculation, the coordinates of each node on the contact surface,
That is, the contact surface shape is determined. Therefore, returning to FIG. 4 again, based on this contact surface shape, the deformation amount, the stress state,
It is possible to know the mechanical behavior such as the contact length (step S3).

The above analysis is an analysis in the case where the printing blanket roll 10 and the metal roll 12 do not rotate, but when they rotate, a frictional force acts between them. Is hitting the frictional force analysis of the rotating cylinder, based on the above analysis, the frictional force at the contact node j R _j, the normal force F _j, as the friction coefficient mu, can be obtained by R _j = μF _j (Step S4). However, since the frictional force acts in the direction along the roll (the direction orthogonal to the normal force), the step analysis is performed so that the frictional force always occurs in the direction orthogonal to the normal force at each overlapping node. That is, the shape of the contact node is updated every step so that the contact surface irregularity is not generated, and the analysis is performed while searching the friction direction in the next step (step S5). More specifically, when the contact node j receives the frictional force R _j , in order to perform the analysis in m steps, the contact shape is changed for each step so that the contact surface irregularity does not occur, and the stress is reduced. While adding (friction force ∝ stress), the direction of the friction force in the next step is searched for, and the friction force R ′ _j is added for analysis. Number of steps m
Is arbitrary (R ' _j = R _j / m). Furthermore, by comprehensively analyzing the above, it is possible to grasp the mechanical behavior such as deformation and stress due to the contact pressure and the frictional force (step S6).

FIG. 6 shows the calculation result when the displacement between the central axes of the printing blanket roll 10 and the metal roll 12 (initial forced displacement amount) is 0.3 mm, and no rotation occurs. FIG. 7 shows the calculation result when the rotation in the arrow direction is simulated under the same conditions. In both figures, a is a deformation diagram of the contact portion, b is a stress distribution in the radial direction, and c is a stress distribution in the circumferential direction. In the analysis without rotation in FIG. 6,
It can be seen that the stress distributions in the radial direction and the circumferential direction are bilaterally symmetrical. On the other hand, in the analysis involving rotation in FIG. 7, it is found that the stress is asymmetrical, and compressive (− sign) stress is generated on the front side in the rotation direction and expansion (+ sign) stress is generated on the rear side.

FIG. 8 shows the contact length analyzed by the analysis method according to the present invention and the actual measurement value of the contact length by the experiment with different amounts of displacement of the central axis. From this graph, it can be seen that the predicted value and the measured value of the contact length match well at each center axis displacement.

In the above analysis, the printing blanket 13 made of a laminated material was macroscopically regarded as a homogeneous anisotropic material. Since the thickness of the printing blanket 13 is very thin compared to the diameter of the entire roll, this assumption is valid. Since the material, physical constants, thickness, etc. of each layer of the printing blanket 13 are known, those skilled in the art can easily design a laminate structure based on the above analysis of the mechanical behavior of the printing blanket. You can If at least the above analysis results are used, the number of trial productions when producing a laminate-structured printing blanket can be significantly reduced.

Although the present invention is applied to the case where the contact 2 members are the printing blanket roll and the metal roll, the present invention is particularly suitable for the contact analysis of the contact 2 members including the nonlinear elastic body, Furthermore, regardless of the material, it can be widely used for contact analysis of two contact members.

[0019]

As described above, according to the present invention, the contact analysis of the contact 2 member can be performed more accurately on a computer, and the number of times of trial production can be reduced through more accurate prediction. The present invention is suitable for use in, for example, analysis of deformation and stress occurring in a printing blanket.

[Brief description of drawings]

FIG. 1 is a model diagram of an analysis target to which the method of the present invention is applied.

FIG. 2 is a diagram showing an entire finite element model of the analysis target.

FIG. 3 is a diagram showing a finite element model showing an enlarged part III of FIG.

FIG. 4 is a flowchart of a contact analysis method according to the present invention.

FIG. 5 is a flowchart of a contact analysis method according to the present invention.

FIG. 6 is a graph showing a mechanical behavior of a printing blanket obtained by a contact analysis method according to the present invention when the printing blanket is not rotated.

FIG. 7 is a graph showing a mechanical behavior of a printing blanket, which is obtained by a contact analysis method according to the present invention, when the printing blanket rotates.

FIG. 8 is a graph showing a comparison result of the contact length of the contact 2 member obtained by the method of the present invention and the actual measurement value.

[Explanation of symbols]

 10 Printing blanket roll 11 12 Metal roll 13 Printing blanket

Claims (6)

[Claims] 1. A step of setting a forced displacement amount in the contact direction given to the contact 2 member; based on the forced displacement amount set in the displacement amount setting step, existing on the contact surface of the contact 2 member by the finite element method. Step of detecting the number of nodes; Step of calculating the displacement amount in the direction of forced displacement between the corresponding contact nodes of the contact 2 member, which is generated as a result of the forced displacement, by the forced displacement type finite element analysis; Each contact based on the displacement amount Steps for calculating the reaction force of the nodes; Steps for recalculating the amount of displacement in the forced displacement direction between the corresponding contact nodes of the contact 2 members caused by the reaction force of each contact node by the load type finite element analysis; Calculation of each node reaction force by forced displacement type finite element analysis and calculation of displacement amount in forced displacement direction between corresponding contact nodes of two contact members by load type finite element analysis Repeat until is within tolerance,
And a step of detecting the position of each contact node; and a step of detecting the mechanical behavior of the contact 2 member based on the position information of each contact node. 2. The contact surface of the contact 2 member according to claim 1, wherein the contact surface is a cylindrical surface, and the normal force of each contact node includes a force in the contact surface separating direction. And, when the normal force of each contact node includes a force in the contact surface opening direction, the step of recalculating the contact nodes except for the position information of the contact nodes at both ends of the contact node group; Contact analysis method. 3. The contact surface of the contact 2 member according to claim 1 or 2, wherein the contact surface is a cylindrical surface that rotates while contacting. Further, in order to analyze the contact surfaces of the two cylindrical surfaces during rotation,
A method for analyzing contact between two contact members, including a step of considering a frictional force generated on both cylindrical surfaces. 4. The method for analyzing the contact 2 member according to claim 1, wherein one of the contact 2 members is a printing blanket wound on a metal roll and the other is a metal roll. 5. The method according to claim 4, wherein in the step of detecting the mechanical behavior of the contact 2 member, at least the deformation state, stress state, contact length, and contact 2 of the printing blanket are included.
A contact analysis method for two contact members in which a frictional force acting between the members is detected. 6. A contact analysis method for two contact members, wherein the shape is determined by alternately applying displacement type and load type finite element methods when performing the shape analysis of the contact surface of the two contact members.