JP6362510B2 - Contact state analysis method, contact state analysis apparatus, and program - Google Patents

Description

  The present invention relates to a contact state analysis method, a contact state analysis apparatus, and a program, and more specifically, analyzes a slip state as to whether or not a slip has occurred in each part of a contact surface of two members, and each part of a contact surface of two members. Contact state analysis method for analyzing contact state whether contact is made, contact state analysis device for performing contact state analysis using such contact state analysis method, and causing computer to function as contact state analysis device Regarding the program.

  Conventionally, as this kind of contact state analysis method, a method for analyzing the damping characteristics of a flat plate structure having a bolt joint by using a finite element method has been proposed (for example, see Non-Patent Document 1). In this paper, finite element method analysis is used for contact state analysis. First, linear vibration analysis is performed, and the difference in damping characteristics for each mode is considered based on the vibration mode shape. And the static contact analysis which made the vibration mode shape the forced displacement part is performed, and the attenuation characteristic for each mode is evaluated by calculating the energy dissipated by friction.

"Damping characteristics of flat structures with bolted joints", Takaro Hirai, Fumiho Sugaya, Ichiro Kido, Japan Society of Mechanical Engineers [No.12-12] Dynamics and Design Conference 2012 USB Proceedings [2012,9,18-21 ,Yokohama]

  However, since the finite element method analysis of the linear portion is repeatedly incorporated in the technique of the above-mentioned paper, it takes a long time to obtain the analysis result. The finite element method analysis is effective for the analysis of the linear part, but is not suitable for iterative processing because of the large computation and the large amount of processing. In order to deal with these problems, it has been proposed to introduce the slip ratio and determine it appropriately so that the theoretical value matches the experimental value. However, which part of the contact surface is fixed and which part It is not possible to determine whether or not slipping, nor to predict the amount of slipping, and it cannot be determined as an essential solution.

  A contact state analysis method, a contact state analysis apparatus, and a program according to the present invention are mainly intended to more accurately identify a slip state and a contact state and to shorten the analysis process.

  The contact state analysis method, contact state analysis apparatus, and program of the present invention employ the following means in order to achieve the main object described above.

The first contact state analysis method of the present invention includes:
It is a state analysis method for analyzing a slip state as to whether or not slip has occurred in each part of the first surface of the first member and the second surface of the second member, which are contact surfaces of the first member and the second member. And
The relationship between the force acting on each part of the first member and the second member and the displacement thereof is stored as linear data,
When a relative displacement or a relative force is applied to the first member and the second member in the sliding direction on the first surface and the second surface,
Using the linear data, for each fixing portion assumed to belong to a fixing region where no slip occurs among the corresponding portions of the first surface and the second surface, the first member and the second member A slip region in which the generated displacement is known to be equal to the sum of the displacements of each member and the shear force in the slip direction is unknown, and a slip occurs in the corresponding portions of the first surface and the second surface. For each slip part assumed to belong to the equation, an equation is made in which the displacement is unknown and the shear force in the slip direction is known. A solution finding step for solving the displacement of each sliding portion;
In the solution obtained by the solution finding step, at least a part of the fixed portions having a contradiction that the shear force exceeds the static friction force among the fixed portions is changed to a member belonging to the slip region, and A change step of changing at least a part of the slip portion having a contradiction that the displacement does not become a slip displacement in the slip direction to belong to the fixing region;
By repeating until the contradiction does not occur in the fixing part and the sliding part in the changing step, to identify the fixing part and the sliding part,
It is characterized by that.

  In this contact state analysis method of the present invention, first, the relationship between the force acting on each part of the first member and the second member and the displacement thereof is stored as linear data. That is, linear data is stored in a database. Next, when a relative displacement or a relative force is applied to the first member and the second member in the sliding direction on the first surface and the second surface, linear data is used as a solution finding step, For each fixed portion assumed to belong to a fixed region where slip does not occur among the corresponding portions of the second surface, the displacement generated in the first member and the second member is known to be equal to the sum of the displacement of each member. In addition to creating an equation that makes the shear force in the slip direction unknown, the displacement is unknown for each slip part assumed to belong to the slip region where slip occurs among the corresponding parts of the first and second surfaces. Create an equation with a known shear force in the slip direction, and solve the shear force of each fixed part and the displacement of each slip part that are made unknown by connecting the created equations. In this solution, at least a part of the fixed parts having the contradiction that the shear force exceeds the static friction force among the fixed parts is changed to belong to the slip region, and the displacement of each slip part is the slip displacement in the slip direction. At least a part of the slip portion having the contradiction that it does not become is changed to belong to the fixed region. Then, until such a contradiction does not occur, the solution by the solution step and the change of the region by the change step are repeatedly executed. When no contradiction is caused by such repeated processing, each fixing portion belonging to the fixing region at that time and each sliding portion belonging to the sliding region are specified. Since linear data is stored in a database, linear problems are not analyzed (linear data is solved) during repetitive processing. For this reason, the analysis time can be shortened as compared with the case where the linear problem is analyzed during the iterative process. Moreover, since it analyzes on the assumption that each part which respond | corresponds to a 1st surface and a 2nd surface belongs to a sticking | fixed area | region, a sticking part and a slip part can be specified more correctly. It is also possible to determine the shearing force and displacement distribution in the sliding direction at the corresponding portions of the first surface and the second surface, or the history, deformation and stress distribution of each portion within each member. Here, the linear data may be actually measured, may be analyzed by a finite element method, or may be analyzed by a difference method or a boundary element method. Moreover, the dynamic friction force obtained by the product of a friction coefficient and a drag can be used for the shearing force in the sliding direction of each sliding portion.

  In the first contact state analysis method of the present invention, the relative displacement or the relative force is changed by a minute amount to identify the respective fixed portions and the respective slip portions for each relative displacement or each relative force; You can also In this way, each time the relative displacement or relative force changes by a small amount, the fixed portion and the sliding portion are specified, so how the fixed portion and the sliding portion change in the process of relative displacement and relative force change. Can be identified. In this case, the amount of work for calculating the work amount before and after the change as the sum of the product of the amount of change in the slip displacement and the shear force in each slip portion before and after the change of the relative displacement or the relative force by a minute amount. It can also have a calculation step. In this way, the friction loss work is calculated every time the relative displacement or relative force changes by a small amount, so it is possible to calculate how the friction loss work changes in the process of the relative displacement or relative force change. . If the equivalent attenuation coefficient is obtained using this result, a more appropriate equivalent attenuation coefficient can be obtained.

  In the contact state analysis method of the present invention, the first member and the second member may be rotated relative to each other using the force as torque, the displacement as rotational displacement, the relative displacement as relative rotational displacement, and the relative force as relative torque. The fixed portions and the sliding portions in motion or relative rotational vibration may be specified. In this way, it can be used for analysis of the sliding state of the rotating system.

The second contact state analysis method of the present invention is:
A contact state analysis method for analyzing a contact state as to whether or not each part of the first surface of the first member and the second surface of the second member, which are contact surfaces of the first member and the second member, is in contact. And
The relationship between the force acting on each part of the first member and the second member and the displacement thereof is stored as linear data,
Using the linear data, for each contact portion assumed to belong to the contact region among the corresponding portions of the first surface and the second surface, the displacement generated in the first member and the second member is Each non-contact portion assumed to belong to the non-contact region among the corresponding portions of the first surface and the second surface is created by making an equation that is known to be equal to the sum of the displacements of the members and that the contact force is unknown. For, create an equation in which the displacement is unknown and the contact force is 0, and solve the contact force of each contact portion and the displacement of each non-contact portion that are made unknown by combining the created equations Solving step to
In the solution obtained by the solving step, at least a part of the contact parts having a contradiction that the contact force is negative among the contact parts is changed to belong to the non-contact area, A change step of changing to at least a part of the non-contact portion having a contradiction that it becomes a displacement that bites into each other, to belong to the contact area;
In the changing step, the contact parts and the non-contact parts are identified by repeating until no contradiction occurs in the contact parts and the non-contact parts,
It is characterized by that.

  In the second contact state analysis method of the present invention, first, the relationship between the force acting on each corresponding part of the first surface of the first member and the second surface of the second member and the displacement thereof is stored as linear data. Keep it. That is, linear data is stored in a database. Next, as the solving step, using linear data, the displacement generated in the first member and the second member for each contact portion assumed to belong to the contact region among the corresponding portions of the first surface and the second surface Each non-contact portion assumed to belong to the non-contact region among the corresponding portions of the first surface and the second surface by creating an equation in which the contact force is unknown and the contact force is unknown Create an equation with unknown displacement and contact force value of 0, and solve the contact force of each contact part and the displacement of each non-contact part that were made unknown by connecting the created equations. As a step, in the solution obtained by the solution step, at least a part of the contact parts having a contradiction that the contact force becomes negative among the contact parts is changed to belong to the non-contact area, The displacement that bites into each other For at least some of the non-contact portion having a contradiction it is changed to belong to the contact area. Then, until such a contradiction does not occur, the solution finding by the solution finding step and the region changing by the region changing step are repeatedly executed. Then, when no contradiction occurs, each contact part belonging to the contact area at that time and each non-contact part belonging to the non-contact area are specified. Since linear data is stored in a database, linear problems are not analyzed (linear data is solved) during repetitive processing. For this reason, the analysis time can be shortened as compared with the case where the linear problem is analyzed during the iterative process. Moreover, since each part corresponding to the first surface and the second surface is analyzed on the assumption that it belongs to the contact area or the non-contact area, the contact part and the non-contact part can be more accurately identified. It is also possible to obtain the distribution of contact force and displacement in each corresponding part of the first surface and the second surface, or the deformation and stress distribution of each part in each member. Here, the linear data may be actually measured, may be analyzed by a finite element method, or may be analyzed by a difference method or a boundary element method.

The contact state analysis apparatus of the present invention is a contact state analysis method of the present invention according to any one of the above-described aspects, that is, basically,
(1) State analysis for analyzing whether or not slip occurs in each part of the first surface of the first member and the second surface of the second member, which are contact surfaces of the first member and the second member. A method,
The relationship between the force acting on each part of the first member and the second member and the displacement thereof is stored as linear data, and the first surface and the first member with respect to the first member and the second member are stored. When a relative displacement or a relative force is applied in the sliding direction on two surfaces, it is assumed that the linear data belongs to a fixed region where no slip occurs among corresponding parts of the first surface and the second surface. For each of the fixed portions, an equation is prepared in which the displacement generated in the first member and the second member is known to be equal to the sum of the displacements of the members and the shear force in the sliding direction is unknown. For each slip part assumed to belong to the slip region where the slip occurs among the corresponding parts of the surface and the second surface, an equation was created to make the displacement unknown and the shear force in the slip direction known. The equation In the solution step obtained by solving the shearing force of each of the fixed portions and the displacement of each of the sliding portions that are made unknown by standing, and in the solution obtained by the solution step, the shear force of each of the fixed portions is a static friction force At least a part of the fixed part having a contradiction that exceeds that of the slip region is changed to one belonging to the slip region, and at least a part of the slip part having a contradiction that the displacement does not become a slip displacement in the slip direction among the slip parts. Is determined by repeating the change step to change to those belonging to the fixed region, until the contradiction does not occur in the fixed portion and the slip portion in the change step, to identify each fixed portion and each slip portion, A first contact state analysis method according to the present invention,
(2) Contact state analysis for analyzing whether or not each part of the first surface of the first member and the second surface of the second member which are contact surfaces of the first member and the second member are in contact with each other. In the method, a relationship between a force acting on each part of the first member and the second member and a displacement thereof is stored as linear data, and the first surface and the first member are stored using the linear data. For each contact portion assumed to belong to the contact area among the corresponding portions of the two surfaces, the displacement generated in the first member and the second member is assumed to be equal to the sum of the displacement of each member and the contact force is An unknown equation is created, and for each non-contact portion assumed to belong to a non-contact region among the corresponding portions of the first surface and the second surface, the displacement is unknown and the contact force is 0. To create an equation that is In the solution step obtained by solving the contact force of each contact part and the displacement of each non-contact part, and in the solution obtained by the solution finding step, the contact part having a contradiction that the contact force becomes negative among the contact parts. At least a part of the non-contact part is changed to belong to the non-contact area, and at least a part of the non-contact part having a contradiction that each of the non-contact parts bites into each other is changed to belong to the contact area. And identifying the contact parts and the non-contact parts by repeating the change step until the contradiction does not occur in the contact part and the non-contact part in the change step. The second contact state analysis method of
It is an apparatus which performs a contact state analysis using.

  Since the contact state analysis apparatus of the present invention uses the first contact state analysis method of the present invention, the effect exhibited by the first contact state analysis method of the present invention, that is, the linear problem is analyzed during repetitive processing. The analysis time can be shortened compared to what is to be achieved, the fixing part and the sliding part can be specified more accurately, the shearing force in the sliding direction at the corresponding parts of the first surface and the second surface, The displacement distribution, the history thereof, the deformation of each part in each member, and the stress distribution can also be obtained. In addition, since the second contact state analysis method of the present invention is used, the effect of the second contact state analysis method of the present invention, that is, the analysis time compared with the case where the linear problem is analyzed during the repeated processing. The effect that the contact portion and the non-contact portion can be specified more accurately, the contact force and the distribution of displacement in the corresponding portions of the first surface and the second surface, or each portion in each member It is possible to obtain the effect that the deformation and the stress distribution can be obtained.

  The program of the present invention causes a computer to perform the contact state analysis apparatus of the present invention, that is, an apparatus that basically performs contact state analysis using the first contact state analysis method of the present invention, or the second of the present invention. It functions as a device that performs contact state analysis using the contact state analysis method. Therefore, since the program of the present invention uses the first contact state analysis method of the present invention or the second contact state analysis method of the present invention, the effects exhibited by the first contact state analysis method of the present invention and the The effect of the second contact state analysis method, that is, the effect that the analysis time can be shortened as compared with the case where the analysis of the linear problem is performed during the repetitive processing, and the fixing portion and the sliding portion more accurately. It is possible to obtain an effect such as specifying or more accurately specifying the contact portion and the non-contact portion.

It is a block diagram which shows the outline of a structure of the slip condition analysis apparatus 20 as one Example of this invention. It is a flowchart which shows an example of the slip state analysis program which analyzes the slip state in a fastening surface when the rotational relative displacement which vibrates centering on a bolt axis | shaft is made to act on two bolt fastening members. It is explanatory drawing which shows the example which made the relative rotational displacement (torque) and the relative displacement (relative force) which vibrate act on two members of bolt fastening. 5 is an explanatory diagram showing an example of a distribution of stress (contact stress) generated on the second surface 52 of the second member 50 with respect to the fastening force of the bolt 60. FIG. Is an explanatory view showing the relationship between the distance r _j and the stress sigma _j from the central axis of the bolt 60 when allowed to act unit clamping force to the bolt 60. It is explanatory drawing which shows typically relative displacement (phi) when the lower surface 54 of the 2nd member 50 when making unit torque act on the 2nd surface 52 of the 2nd member 50 is made into a reference | standard. It is explanatory drawing which shows typically rotational displacement (PSI) when giving a relative rotational displacement using a sticking area | region and a sliding area | region. It is explanatory drawing which shows typically the torque T when giving a relative rotational displacement using the adhering area | region and a slip area | region. It is explanatory drawing which shows typically the friction loss work Wi when giving a relative rotational displacement. It is explanatory drawing which shows typically the friction loss work W in case the relative rotational displacement (omega | ohm) vibrates. It is a block diagram which shows an example of the experimental apparatus with which relative rotational displacement (ohm) vibrates. It is explanatory drawing which displayed the list and the specification and conditions of the analysis example by an experiment apparatus and an Example. It is explanatory drawing which shows the result of the relationship between the rotational displacement (ohm) by the example of an analysis, and experiment of an experiment apparatus, and the torque T. FIG. It is explanatory drawing which shows the result of the relationship between the rotational displacement (ohm) by the example of an analysis, and experiment of an experiment apparatus, and the friction loss work W. FIG. It is explanatory drawing which shows the result of the relationship between the rotational displacement (ohm) by experiment of an analysis example and an experiment apparatus, and the equivalent damping coefficient De. It is a flowchart which shows an example of the generalized slip condition analysis program. It is a flowchart which shows an example of a contact state analysis program.

  Next, the form for implementing this invention is demonstrated using an Example.

  FIG. 1 is a configuration diagram showing an outline of a configuration of a slip state analysis apparatus 20 as an embodiment of the present invention. As shown in the figure, the slip state analysis apparatus 20 according to the embodiment is configured such that a general state computer 22 is installed with a slip state analysis program 30 as application software. The slip state analysis program 30 includes a linear data solution module 32, a solution module 34, a region change module 36, and a friction loss work calculation module 38.

  The linear data solution module 32 determines the relationship between the force and torque within the linear deformation range and the stress acting on each part and the displacement of each node with respect to each part (each node) fastened by a bolt or the like. It is a module that finds solutions using analysis, the difference method, the boundary element method, etc., and stores the obtained solutions in a database as linear data.

  The solution module 34 uses linear data to prevent slippage when a relative displacement, a relative rotational displacement, a relative force or a relative torque (hereinafter abbreviated as “relative displacement, etc.”) is applied to two members. For a node assumed to belong to a region, a slip region where slip occurs where the displacement generated in the two members is known equal to the sum of the displacements of each node and the shear force (torque) in the slip direction is unknown. For the nodes assumed to belong to the equation, an equation is created in which the displacement of the corresponding nodes on the fastening surface of the two members is unknown and the shear force (torque) in the sliding direction is known, and the equations for each node in the fixed region This is a module that finds a solution by combining the equations for each node in the slip region.

  In the solution obtained by the solution finding module 34, the region change module 36 changes at least a part of the nodes whose shear force (torque) exceeds the static friction force among the nodes belonging to the fixed region to belong to the slip region, In this module, at least some of the nodes whose displacement does not become the slip displacement in the slip direction among the nodes belonging to the slip region are changed to those belonging to the fixed region. For example, among the nodes belonging to the fixed region, the node having the largest shear force (torque) among the nodes whose shear force (torque) exceeds the static friction force is changed to the one belonging to the slip region, and each node belonging to the slip region Of the nodes whose displacement does not become the slip displacement in the slip direction, the one having the maximum slip displacement different from the slip direction may be changed to belong to the fixing region. The nodes belonging to the fixed region are obtained by repeating the solution by the solution module 34 for each node after the region change and the region change by the change module 36 until the change of the node region in the change module 36 is not performed. And nodes belonging to the slip region can be specified. Then, the relative displacement is increased or decreased by a minute amount, and the nodes belonging to the fixed region and the nodes belonging to the slip region are specified in the same manner, so that the fixed region slides against the change of the relative displacement. Region variations can be identified.

  The friction loss work calculation module 38 calculates the friction loss work of the nodes by the product of the sliding displacement between the nodes belonging to the slip region and the dynamic friction force, and calculates the friction loss work on the fastening surface of the two members with respect to the relative displacement etc. by the sum. This is a module to calculate. In other words, the relative displacement is increased or decreased by a minute amount, and the friction loss work at each node for each minute displacement, such as relative displacement, is similarly obtained. The total friction loss work such as relative displacement can be calculated by obtaining the total friction loss work when the total friction loss work is reduced or reduced, and further adding up the total friction loss work. When the relative displacement or the like vibrates, this total friction loss work becomes vibration damping energy.

  FIG. 2 is a flowchart showing an example of a slip state analysis program for analyzing a slip state on the fastening surface when a rotational relative displacement (torque) that vibrates about the bolt axis is applied to two bolt fastening members. FIG. 3 is an explanatory view showing an example in which a relative rotational displacement (torque) and a relative displacement (relative force) are applied to two bolt-fastened members. As shown in FIG. 3, the first member 40 is attached to the second member 50 by a bolt 60 so that the first surface 42 of the lower surface in the drawing contacts the second surface 52 of the upper surface of the second member 50 as the base plate. It is concluded. The fastening surface corresponds to the first surface 42 of the first member 40 and the second surface 52 of the second member 50. FIG. 3A is an explanatory diagram for explaining a state in which a rotational relative displacement (torque) that vibrates about the axis of the bolt 60 acts on the first member 40 and the second member 50 fastened by the bolt 60. FIG. 3B is an explanatory diagram for explaining a state in which a relative displacement (relative force) that vibrates in parallel acts on the first member 40 and the second member 50, and FIG. ) Is an explanatory view illustrating a state in which a vertical relative vibrating force is acting on the first member 40 and the second member 50. The slip analysis program of FIG. 2 is a program for analyzing the slip state when the rotational relative displacement (torque) of FIG. The slip state analysis method of FIG. 3A will be described below along the processing of the slip state analysis program of FIG.

In the slip state analysis program of FIG. 2, first, linear data is obtained using the finite element method, and the linear data is stored in a database (step S100). Specifically, the stress generated on the first surface 42 of the first member 40 and the second surface 52 of the second member 50 with respect to the fastening force (clamping force) of the bolt 60, or the torque about the axis of the bolt 60 Analyzing linear problems such as the displacement of each part of the first surface 42 of the first member 40 and the second surface 52 of the second member 50 when acting, and database the results (linear data) obtained by the analysis To do. FIG. 4 shows an example of the distribution of stress (contact stress) generated on the second surface 52 of the second member 50 with respect to the fastening force of the bolt 60, and FIG. 5 shows the bolt when a unit clamping force is applied to the bolt 60. The relationship between the distance r _j from the central axis of 60 and the stress σ _j is shown. Therefore, when the clamping force P is applied to the bolt 60, the stress of P × σ _j is applied to the j-th radial position from the inner peripheral side within the linear range. FIG. 6 schematically shows the relative displacement φ with reference to the lower surface 54 of the second member 50 when unit torque is applied to the second surface 52 of the second member 50. FIG. 6 shows the displacement φ _{j, k} of the _jth radial position from the inner peripheral side when the unit torque is applied to the kth radial position from the inner peripheral side. For this reason, when the torque T is applied to the k-th radial position from the inner circumferential side _, a displacement of T × φ _{j, k} occurs at the j-th radial position from the inner circumferential side within the linear range. Since the rotational displacement at the j-th radial position from the inner circumferential side is the sum of displacements due to torque acting on all radial positions from the innermost circumferential side to the outermost circumferential side, Σ (T _i × φ _{j, i} ) Can be calculated by: In step S100, the stress σ _j of the distance r _j from the central axis of the bolt 60 when the unit clamping force is applied to the bolt 60 of FIG. 5, the first surface 42 of the first member 40 and the second member 50 The displacement θ _{j, k} and the displacement φ _{j, k of the} j-th radial position from the inner peripheral side when a unit torque is applied to the second surface 52 at the k-th radial position from the inner peripheral side are _defined as finite elements. It is obtained by the method and stored as linear data as a database.

  Next, the coefficient of friction μ between the first surface 42 of the first member 40 and the second surface 52 of the second member 50 and the clamping force P of the bolt 60 are input (step S110). Here, the friction coefficient μ may be a static friction coefficient or a dynamic friction coefficient, or the friction coefficient may be a function of the friction speed, but a single one is used for convenience. Also good. Then, based on the linear data obtained in step S100 on the first surface 42 of the first member 40, an area where the contact stress is not 0 is assumed to be a fixed area where no slip occurs (step S120). When torque about the axis of the bolt 60 is applied to the upper surface 44 of the first member 40, the first surface 42 is fixed to the second surface 52 of the second member 50 without slipping. (Fixed region), a region where a slip occurs with respect to the second surface 52 of the second member 50 (slip region), and a non-contact with a contact stress of 0 on the second surface 52 of the second member 50 However, in the slip state analysis program of the embodiment, it is assumed that all areas of the first surface 42 that are not non-contact areas are fixed areas as initial values. Since this is an assumption, it is assumed that the nth radial position from the inner peripheral side of the first surface 42 is the fixed region as an initial value, and the n + 1 and subsequent radial positions from the inner peripheral side are the slip regions. It may be assumed.

Assuming the region in this way, the relative rotational displacement Ω _i as a rotational displacement given relative to the lower surface 54 of the second member 50 relative to the upper surface 44 of the first member 40 is increased by a minute amount ΔΩ (step S130). Steps S140 to S210 are repeated until the maximum relative rotational displacement is reached. When step S130 is executed for the first time, the initial value of the relative rotational displacement Ω ₀ is 0, so the relative rotational displacement Ω ₁ is a minute amount ΔΩ. The i-th relative rotational displacement Ω _i can be calculated as a product of a minute amount ΔΩ and i. When the relative rotational displacement Ω _i is given in this way, the rotational displacement φ on the second surface 52 of the second member 50 relative to the lower surface 54 of the second member 50 and the first displacement are assumed to belong to the fixed region by assumption. An equation is prepared in which the rotational displacement Ψ obtained as the sum of the rotational displacement θ on the first surface 42 of the first member 40 with respect to the upper surface 44 of the member 40 is known and the torque T is unknown (step S140). . FIG. 7 is an explanatory diagram schematically showing the rotational displacement Ψ when a relative rotational displacement is given to the upper surface 44 of the first member 40 with respect to the lower surface 54 of the second member 50 using a fixed region and a slip region. FIG. 8 is an explanatory diagram schematically showing the torque T when a relative rotational displacement is given to the upper surface 44 of the first member 40 with respect to the lower surface 54 of the second member 50 using a fixing region and a sliding region. It is. In the figure, the horizontal axis r _x represents the lower surface 54 of the second member 50 of the origin of the absolute rotational displacement (zero), the oblique line r _Omega about 30 degrees absolute rotational displacement around the upper surface 44 of the first member 40 Show. 8 shows for a schematic diagram, the angle of the oblique line r _Omega in the figure illustrates schematically. The horizontal axis r _x and the left and right upper from a branch from the branching of the branch to a thick solid line (a portion broken line) between the diagonal line r _Omega absolute rotational displacement at each radius of the first surface 42 of the first member 40 The left side of the thick solid line (partially broken line) branch and the lower right part of the branch indicate the absolute rotational displacement at each radius of the second surface 52 of the second member 50. The left side of the thick solid line (partially broken line) branch is a fixing region, and the right side of the branch is a slip region and a non-contact region. In the lower part of the figure, the contact stress σ _k is shown. As shown in FIG. 7, the rotational displacement Ψ _{k at} the k-th radial position from the inner peripheral side is the displacement θ _k of the first surface 42 of the first member 40 and the displacement φ _k of the second surface 52 of the second member 50. And defined as the sum of In the fixed region, the given relative rotational displacement Ω is equal to the rotational displacement ψ and can be known.

On the other hand, for a node that is assumed to belong to the slip region by assumption, an equation for making the rotational displacement Ψ unknown and the torque T known is created (step S150). In the slip region, the j-th torque T _j from the inner circumference side can be calculated as the product of the frictional force q _j and the distance r _j from the rotation center. Here, the frictional force q _j is expressed by the following equation (1) as a product of the friction coefficient μ, the contact stress σ _j, and the area 2πr _j · Δr at the j-th radial position from the inner circumference side, and therefore should be known. Can do. When step S150 is first executed by this program, it is assumed in step S120 that all areas that are not non-contact areas of the first surface 42 of the first member 40 are fixed areas that do not slip. Therefore, no equation is created.

In this way, when the equation for the node belonging to the fixed region and the equation for the node belonging to the slip region are created, the created equation is combined into the simultaneous equation of the following equation (2), and the unknown torque T in the fixed region and the slip region An unknown rotational displacement Ψ is obtained as a solution (step S160). In the expression (2), the stk region from the inner periphery side is the fixed region, and the stk number from the inner periphery side to the sld region is the slip region. Therefore, from the rotational displacement on the left side, ψ _{1 to} ψ _stk are known, and from ψ _stk to ψ _sld are unknown. Further, T _{1 to} T _stk of the torque on the right side is unknown, and from T _stk to T _sld is known. For this reason, since the number of unknowns and the number of equations are the same, a solution can be obtained as a simultaneous linear equation. For the nodes belonging to the non-contact region, an equation may be created with the torque T as a value of 0, and the equations may be combined with the equations for the nodes belonging to the fixed region and the slip region to form simultaneous equations. In this case, the displacement of the node belonging to the non-contact area can be obtained.

When the simultaneous equations are solved in this manner, it is determined whether or not the torque T _stk is less than or equal to the product of the friction force q _stk and the distance r _stk from the rotation center at the outermost peripheral node among the nodes belonging to the fixed region. When T _stk is larger than the product of the frictional force q _stk and the distance r _stk , the region to which the outermost node of the fixed region belongs is changed from the fixed region to the slip region (step S170). Then, a negative determination is made with respect to the determination that there is no change in the area (step S180), and the process returns to step S140, and the simultaneous equations of expression (2) are created based on the assumption of the new fixed area and the slip area. Then, a solution is obtained, and it is determined again whether or not the torque T _stk is less than or equal to the product of the frictional force q _stk and the distance r _stk at the outermost peripheral node among the nodes belonging to the fixed region.

If it is determined in step S180 that there is no change in the region with respect to the outermost peripheral node of the fixed region, the fixed region and the slip region assumed at that time are specified as the fixed region and the slip region at the relative rotational displacement Ωi ( Step S190). Then, the friction loss work W _i is calculated with respect to the relative rotational displacement Ω _i at each node of the slip region (step S200). The friction loss work W _i is expressed by the following equation (3). U _{i, j} in equation (3) is expressed by equation (4). The friction loss work W _i is shown in an explanatory diagram schematically showing the friction loss work W _i when the maximum relative rotational displacement Ω ^amp and the maximum relative rotational displacement −Ω ^amp on the opposite side are given in FIG. The product of the contact stress, the area of the minute ring element (area 2πr _j · Δr at the j-th radial position from the inner circumference side), the friction coefficient, and the slip amount at each node in the slip region indicated by the hatched region (each node) Of friction loss work).

When the friction loss work W _i is calculated in this way, it is determined whether or not the relative rotational displacement Ω has reached the maximum relative rotational displacement Ω ^amp (step S210), and when the relative rotational displacement Ω has not reached the maximum relative rotational displacement Ω ^amp , relative rotational displacement Omega is up to the maximum relative rotational displacement Omega ^{# 038,} repeats the processing of steps S130~ step S210 of increasing the relative rotational displacement Omega _i minute amount ΔΩ returns to step S130. That is, the relative rotational displacement Ω is increased by a minute amount ΔΩ to identify the fixed region and the slip region at each relative rotational displacement Ω and calculate the friction loss work Wi. When the relative rotational displacement Ω reaches the maximum relative rotational displacement Ω ^amp , the program is terminated on the assumption that the slip state analysis has been completed.

Consider the case where the relative rotational displacement Ω vibrates. In this case, since the friction loss work causes a damping force, the equivalent damping coefficient De is given by the following equation (5). Here, the friction loss work W is the friction loss work dissipated in one vibration cycle of the vibration amplitude Ω ^amp . FIG. 10 schematically shows the friction loss work W when the relative rotational displacement Ω vibrates. As shown in the drawing, the relationship between the rotational displacement Ω and the torque T is as follows. First, from the point A, the rotational displacement Ω and the torque T reach the point B along the arrow line. A hysteresis is drawn from point B to point C along the lower arrow line and from point C to point B along the upper arrow line. The friction loss work W can be expressed as the area of this hysteresis region (a hatched region surrounded by an upper arrow line and a lower arrow line). Dissipating W _i by the relationship between the rotational displacement Ω and the torque T reaches the point A to the point B as a friction loss work WA-B shown in Figure 9 (a). Since the point C is symmetrical with the point B, the state shown in FIG. 9B is obtained, and therefore 2W _i is dissipated as the friction loss work WB-C from the point B to the point C. Similarly, 2W _i is dissipated from point C to point B as friction loss work WC-B. As a result, in one cycle, the friction loss work W is 4W _i . Therefore, the friction loss work W can be expressed as four times the friction loss work WA-B from the point A to the point B (W = 4WA-B). In order to obtain the equivalent damping coefficient De, analysis from the point A to the point B, that is, the relative rotational displacement Ω from the value 0 to the maximum relative rotational displacement Ω ^amp is analyzed by the slip state analysis program illustrated in FIG. You can do it. Note that these are established by a simple solution in which the friction coefficient is constant, and strictly speaking, they are not established when the friction coefficient is a function of the friction speed.

  FIG. 11 is a configuration diagram illustrating an example of an experimental apparatus in which the relative rotational displacement Ω vibrates. FIG. 11A shows the front of the experimental apparatus, and FIG. 11B shows the side of the experimental apparatus. FIG. 12 is an explanatory diagram showing a list of specifications and conditions of an analysis example according to an experimental apparatus and an example. In the experimental apparatus, a square plate with a side of 130 mm and a thickness of 30 mm formed of cast iron is used as the second member, and a square of 80 mm × 175 mm formed of steel (SS400) as the first member with a thickness of 10 mm. Plates were used. The first member and the second member are formed with φ10 mm at the center as fastening bolt holes. As shown in FIG. 11, a weight is attached to the first member by a plate spring, and the piano wire is cut in a state where the weight is pulled to the right side in FIG. The relative rotational displacement Ω is vibrated by vibrating left and right inside. This apparatus is adjusted so that the vibration period of the weight is 25 Hz and the angular velocity ω is 50π [rad / s].

  On the other hand, in the analysis example, a circular plate having a diameter of 130 mm and a thickness of 30 mm formed of a material having an elastic modulus of 110 GPa and a Poisson's ratio of 0.3 is used as the second member, and the elastic modulus is 200 GPa as the first member. A circular plate having a diameter of 80 mm and a thickness of 10 mm made of a material having a Poisson's ratio of 0.3 was used. The first member and the second member are formed with φ10 mm at the center as fastening bolt holes. As analysis conditions, the vibration period and the angular velocity ω are set to 25 Hz and 50π [rad / s] so as to be the same as the experimental apparatus, the minute amount ΔΩ that increases the relative rotational displacement Ω is 0.4 [μrad], and the radial direction The increase Δr of the radial position was 0.5 [mm], and the friction coefficient μ was 0.17.

  The analysis result by an analysis example and the experiment result by an experimental apparatus are shown in FIGS. FIG. 13 shows the result of the relationship between the rotational displacement Ω and the torque T, FIG. 14 shows the result of the relationship between the rotational displacement amplitude Ω and the friction loss work W, and FIG. 15 shows the rotational displacement amplitude Ω and the equivalent damping coefficient De. The result of the relationship is shown. In the drawing, each curve of P = 10 kN, 20 kN, 30 kN, and 40 kN shows an analysis example when the clamping force P is 10 kN, 20 kN, 30 kN, and 40 kN. In the figure, circles, triangles, squares, and rhombuses indicate the experimental results of the experimental apparatus when the clamping force P is 10 kN, 20 kN, 30 kN, and 40 kN. In FIG. 13, the straight line “No slip” is an analysis example when it is assumed that all are fixed areas and no slip occurs. It can be said that the analysis example is comparatively well matched with the experimental result by the experimental apparatus. Therefore, it can be said that the analysis result by the slip state analysis apparatus 20 of the embodiment is sufficiently practical.

In the slip state analysis apparatus 20 of the embodiment described above, first, the finite element is only once for the clamping force P of the first member 40 and the second member 50 fastened by the bolt 60 and the torque around the axis of the bolt 60. The linear data is solved by the method and stored in a database. As a solving step, using linear data, an equation is created with the rotational displacement ψ known and torque T unknown for nodes belonging to the fixed region, and the rotational displacement ψ unknown for nodes belonging to the slip region. At the same time, an equation is created assuming that the torque T is known, and an unknown rotational displacement ψ and an unknown torque T are obtained by simultaneous creation of the created equations. As a region change step, when the torque T _stk is larger than the product of the friction force q _stk and the distance r _stk from the rotation center at the outermost peripheral node among the nodes belonging to the fixed region, the outermost peripheral node of the fixed region belongs. Change the area from the fixed area to the sliding area. By repeating the solution finding step and the region changing step until the change of the region is not performed, the fixed region and the slip region can be specified as the fixed region and the slip region at the relative rotational displacement Ω _i . As described above, since the finite element method analysis is not included in the iterative process, the iterative process can be completed quickly. In addition, since all regions are fixed regions as initial values, whether or not the torque T _stk is larger than the product of the friction force q _stk and the distance r _stk from the rotation center only at the outermost peripheral node of the fixed region. Therefore, the calculation amount can be greatly reduced, and the analysis time can be shortened.

  In the slip state analysis apparatus 20 of the embodiment, the friction coefficient μ is used without distinguishing between the static friction coefficient and the dynamic friction coefficient. However, the static friction coefficient and the dynamic friction coefficient may be used separately. May be treated as a function of speed. Further, in the slip state analysis apparatus 20 of the embodiment, all the regions that are not the non-contact region in the first surface 42 are assumed as the fixed regions as the initial values, but the inner periphery of the regions that are not the non-contact regions as the initial values. It is also possible to assume the fixing region and the sliding region as appropriate, assuming that the region from the side to 3/4 in the radial direction is the fixing region and the outer peripheral side thereof is the sliding region.

  In the slip state analyzing apparatus 20 of the embodiment, the slip analysis program of FIG. 2 is used to analyze the slip state when the rotational relative displacement (torque) of FIG. When the relative displacement (relative force) which vibrates in parallel with respect to the 1st surface 42 and 2nd surface 52 of b) is acting, or with respect to the 1st surface 42 and 2nd surface 52 of FIG.3 (c). In order to analyze the slip state in the case where the relative displacement (relative force) that vibrates vertically is acting (however, the contact area does not change), the slip state analysis program of FIG. 16 may be used. The slip state analysis program shown in FIG. 16 is a generalized version of the slip state analysis program shown in FIG. Therefore, in order to avoid redundant descriptions, descriptions of similar processing are omitted to the extent that they can be fully understood. In order to easily understand that the processing is the same, the step number of the slip state analysis program in FIG. 16 includes the same step number for the same processing as each processing of the slip state analysis program in FIG. 1000 was added. Therefore, a completely new process in the slip state analysis program of FIG. 16 is step S1175. Hereinafter, the analysis of the slip state in the case of FIG. 3B or 3C will be described using the slip state analysis program of FIG.

  In the slip state analysis program of FIG. 16, first, linear data is obtained using the finite element method, and the resulting linear data is stored in a database (step S1100). As the linear data, each node on the boundary surface of each member on which relative displacement such as relative displacement, relative force, relative rotational displacement, and torque acts, and the first surface of the first member that is the fastening surface or Among the nodes on the second surface of the second member, a unit displacement is given only in a certain direction of a certain node, and a force generated in each node and each direction when all the other node displacements are fixed. Subsequently, the friction coefficient μ and the acting force P acting in a fixed manner are input (step S1110). The acting force acting fixedly is not limited to the clamping force of the bolt, but means all forces acting fixedly. Then, a fixed region and a slip region are assumed with respect to the first surface of the first member and the second surface of the second member (step S1120). Here, any region may be assumed as the fixed region and the slip region, but it is preferable to assume a region that is considered appropriate for reducing the repetitive processing and shortening the analysis time.

  Subsequently, the relative displacement or the like is increased or decreased by a minute amount (step S1130), and the processing of steps S1140 to S1210 is repeated until the maximum relative displacement or the like is reached. In the iterative process, first, for a node that is assumed to belong to the fixed region, an equation is prepared in which the displacement ψ is known to be equal to the relative displacement given between the two members and the shear force F is unknown (step). S1140) For the nodes that are assumed to belong to the slip region by assumption, an equation for making the displacement ψ unknown and the shearing force F known is created (step S1150), and these equations are coupled to the unknown displacement ψ. A shearing force F is obtained (step S1160). The reason why the displacement ψ is known at the node of the fixed region is that the relative displacement given between the two members is the sum of the relative displacements of each member (the amount of deformation of each member). In addition, the fact that the shear force F is known at the nodes of the slip region can be obtained based on the dynamic friction force.

  When the simultaneous equations are solved in this way, among the nodes belonging to the fixed region, at least some of the nodes whose shear force is greater than the static friction force, the region is changed from the fixed region to the slip region (step S1170). At least a part of the nodes where the displacement ψ does not become the slip displacement in the slip direction is changed from the slip region to the fixed region (step S1180). The area change from the fixed area to the sliding area is the same as in the embodiment. Since the nodes belonging to the slip region are displaced in the slip direction, it is contradictory that the nodes not displaced in the slip direction belong to the slip region. In addition, when the angle formed between the assumed shear force direction (the reverse direction of the slip) and the slip displacement direction is small (less than 90 degrees), the slip region is contradictory, and the angle formed is large (greater than 90 degrees). Therefore, it is necessary to correct the slip direction. In order to avoid such a contradiction, among the nodes belonging to the slip region, for some of the nodes where the displacement Ψ does not become the slip displacement in the slip direction, the region is changed from the slip region to the fixed region and the slip direction is corrected. The process from step S1140 to step S1180 is repeated based on the changed area until the area change from the fixing area to the sliding area or the area change from the sliding area to the fixing area is not performed. If the change in the opposite direction) is not performed, the fixing region and the sliding region assumed at that time are specified as the fixing region and the sliding region in the relative displacement or the like (step S1190). Then, the friction loss work is calculated with respect to the relative displacement at each node in the slip region (step S1200), and the process returns to step S1130 and the relative displacement is increased by a minute amount until the relative displacement becomes the maximum relative displacement. Steps S1210 to S1210 are repeated.

  By executing the slip state analysis program of FIG. 16 described above, the relative displacement between the fixed region and the slip region on the contact surface when relative displacement, relative rotational displacement, relative force, and torque are applied to the two members is performed. Etc. can be specified by varying each minute amount. Moreover, since the friction loss work due to the slip region is also calculated, the damping phenomenon can be analyzed. Of course, since the solution of linear data by the finite element method is not included in the iterative process, the iterative process can be completed quickly, and the slip state can be analyzed in a short time.

  In the embodiment, the slip state is analyzed whether each node on the contact surface is fixed or slipped, but the contact state is analyzed whether each node on the contact surface is in contact or not in contact. It is good. FIG. 17 is a flowchart showing an example of a contact state analysis program installed in the computer of FIG. 1 instead of the slip state analysis program. Therefore, the computer in which the contact state analysis program of FIG. 17 is installed functions as a contact state analysis device. The contact state analysis program shown in FIG. 17 is basically the same process because the slip state analysis program shown in FIG. 16 is simplified and slightly modified. Therefore, in order to avoid redundant descriptions, descriptions of similar processing are omitted to the extent that they can be fully understood. In order to easily understand that the processing is the same, the step number of the contact state analysis program in FIG. 17 is set to the 2000s for the same processing as each processing of the slip state analysis program in FIG. . The contact state analysis will be described below using the contact state analysis program of FIG.

  In the contact state analysis program of FIG. 17, first, linear data is analyzed using the finite element method and the linear data is stored in a database (step S2100). The linear data includes the nodes on the boundary surface of each member to be analyzed, the nodes on which relative displacement such as relative displacement, relative force, relative rotational displacement, and torque acts, and the first member that is the contact surface. Among the nodes on one surface or the second surface of the second member, the unit displacement is given only to a certain direction of a certain node, and the forces generated in each node and each direction when all other node displacements are fixed. . Subsequently, the acting force acting in a fixed manner is input (step S2110), and the contact area that is in contact with the first surface of the first member and the second surface of the second member is not in contact. A contact area is assumed (step S2120). Here, regarding the contact area and the non-contact area, any area may be assumed, but it is preferable to assume an area that is considered appropriate in order to reduce the repetitive processing and shorten the analysis time.

  Subsequently, for a node that is assumed to belong to the contact region, an equation is prepared in which the displacement ψ is known to be equal to the relative displacement given between the two members and the contact force F is unknown (step S2140). With respect to the nodes belonging to the non-contact region by the above, the displacement ψ is made unknown and a known equation with a contact force F of 0 is created (step S2150). The contact force F is obtained (step S2160). The fact that the displacement ψ is equal to the relative displacement applied between the two members for the nodes in the contact area and that the contact force F is 0 for the nodes in the non-contact area originates from contact or non-contact.

  When the simultaneous equations are solved in this way, at least a part of the nodes having a negative contact surface normal direction component of the contact force F among the nodes belonging to the contact area is changed from the contact area to the non-contact area (step) In step S2170, at least a part of the nodes having the displacement ψ that bite into each other among the nodes belonging to the non-contact area is changed from the non-contact area to the contact area (step S2180). Since a positive contact force is generated even slightly at the nodes of the contact region, it is a contradiction that the contact surface normal direction component of the contact force F becomes a negative value. Further, since the nodes in the non-contact region are not in contact with each other, the mutual displacements ψ do not bite into each other, and therefore it is contradictory to become the biting displacements ψ. In order to avoid such a contradiction, the area is changed. Until the area change from the contact area to the non-contact area or the area change from the non-contact area to the contact area is not performed, the processes from step S2140 to S2180 are repeated based on the changed area, and the area change is not performed. Then, the contact area and the non-contact area assumed at that time are specified as the contact area and the non-contact area (step S2190), and the process is terminated. When the positions of the nodes facing each other through the contact surface are shifted due to the deformation, or when the position is shifted from the beginning, the displacement or force of the opposing positions may be obtained by interpolation.

  The contact state analysis apparatus obtained by installing the contact state analysis program of FIG. 17 described above solves linear data using the finite element method, stores the linear data obtained as a database, and stores the data. For the nodes belonging to the contact area in the state where the force is applied, an equation for making the displacement Ψ known to be equal to the relative displacement given between the two members and making the contact force F unknown is created. Creates a known equation with unknown displacement Ψ and a contact force F value of 0, and solves them by solving them simultaneously, and the contact surface normal of the contact force F among the nodes belonging to the contact region Displacement Ψ that changes at least some of the nodes whose direction component is negative from the contact area to the non-contact area and bites each other among the nodes belonging to the non-contact area The contact region and the non-contact region on the contact surface of the two members are identified by repeating the region changing step for changing from the non-contact region to the contact region for at least a part of the nodes, until the region change is not performed. can do. Naturally, since the finite element method analysis is not included in the iterative process, the iterative process can be completed quickly, and the slip state can be analyzed in a short time.

  As mentioned above, although the form for implementing this invention was demonstrated using the Example, this invention is not limited at all to such an Example, In the range which does not deviate from the summary of this invention, it is with various forms. Of course, it can be implemented.

  The present invention can be used in the machine manufacturing industry.

  20 slip state analysis device, 22 computer, 30 slip state analysis program, 32 linear data solution module, 34 solution module, 36 region change module, 38 friction loss work calculation module, 40 first member, 42 first surface, 44 upper surface, 50 second member, 52 second surface, 54 lower surface, 60 bolts.

Claims (9)

It is a state analysis method for analyzing a slip state as to whether or not slip has occurred in each part of the first surface of the first member and the second surface of the second member, which are contact surfaces of the first member and the second member. And
The relationship between the force acting on each part of the first member and the second member and the displacement thereof is stored as linear data,
When a relative displacement or a relative force is applied to the first member and the second member in the sliding direction on the first surface and the second surface,
Using the linear data, for each fixing portion assumed to belong to a fixing region where no slip occurs among the corresponding portions of the first surface and the second surface, the first member and the second member An equation is created in which the generated displacement is known to be equal to the sum of the displacements of each member and the shearing force in the sliding direction is unknown, and the slip region where the slip occurs among the corresponding portions of the first surface and the second surface is generated. For each slip portion assumed to belong, an equation is made in which the displacement is unknown and the shear force in the slip direction is known, and the shear force of each of the fixed portions made unknown by combining the prepared equations and the above A solution step for solving the displacement of each sliding portion;
In the solution obtained by the solution finding step, at least a part of the fixed portions having a contradiction that the shear force exceeds the static friction force among the fixed portions is changed to a member belonging to the slip region, and A change step of changing at least a part of the slip portion having a contradiction that the displacement does not become a slip displacement in the slip direction to belong to the fixing region;
By repeating until the contradiction does not occur in the fixing part and the sliding part in the changing step, to identify the fixing part and the sliding part,
The contact state analysis method characterized by this. The contact state analysis method according to claim 1,
Changing each of the relative displacement or the relative force by a minute amount to identify the fixing portion and the sliding portion with respect to each relative displacement or each relative force;
Contact state analysis method. The contact state analysis method according to claim 2,
A work amount calculating step of calculating a sum of products of the amount of change of the slip displacement and the shear force in each of the slip portions before and after the change of the relative displacement or the relative force by a minute amount as a work amount before and after the change; Have
Contact state analysis method. The contact state analysis method according to any one of claims 1 to 3,
The linear data is data analyzed by a finite element method.
Contact state analysis method. The contact state analysis method according to any one of claims 1 to 4,
The shearing force in the sliding direction of each sliding part is a dynamic frictional force obtained by the product of the friction coefficient and the drag,
Contact state analysis method. The contact state analysis method according to any one of claims 1 to 5,
Each of the fixing portions in the relative rotational motion or relative rotational vibration of the first member and the second member, wherein the force is torque, the displacement is rotational displacement, the relative displacement is relative rotational displacement, and the relative force is relative torque. Identify each of the sliding parts,
Contact state analysis method. A contact state analysis method for analyzing a contact state as to whether or not each part of the first surface of the first member and the second surface of the second member, which are contact surfaces of the first member and the second member, is in contact. And
The relationship between the force acting on each part of the first member and the second member and the displacement thereof is stored as linear data,
Using the linear data, for each contact portion assumed to belong to the contact region among the corresponding portions of the first surface and the second surface, the displacement generated in the first member and the second member is Each non-contact portion assumed to belong to the non-contact region among the corresponding portions of the first surface and the second surface is created by making an equation that is known to be equal to the sum of the displacements of the members and that the contact force is unknown. For, create an equation in which the displacement is unknown and the contact force is 0, and solve the contact force of each contact portion and the displacement of each non-contact portion that are made unknown by combining the created equations Solving step to
In the solution obtained by the solving step, at least a part of the contact parts having a contradiction that the contact force is negative among the contact parts is changed to belong to the non-contact area, A change step of changing to at least a part of the non-contact portion having a contradiction that it becomes a displacement that bites into each other, to belong to the contact area;
In the changing step, the contact parts and the non-contact parts are identified by repeating until no contradiction occurs in the contact parts and the non-contact parts,
The contact state analysis method characterized by this.   A contact state analysis device that performs a contact state analysis using the contact state analysis method according to claim 1.   A program for causing a computer to function as the contact state analyzing apparatus according to claim 8.