CN100444177C - Method and apparatus for predicting bending life spans of electric wires and/or wire protecting members induced by vibrations, an d recording medium storing program - Google Patents

Method and apparatus for predicting bending life spans of electric wires and/or wire protecting members induced by vibrations, an d recording medium storing program Download PDF

Info

Publication number
CN100444177C
CN100444177C CNB200380104187XA CN200380104187A CN100444177C CN 100444177 C CN100444177 C CN 100444177C CN B200380104187X A CNB200380104187X A CN B200380104187XA CN 200380104187 A CN200380104187 A CN 200380104187A CN 100444177 C CN100444177 C CN 100444177C
Authority
CN
China
Prior art keywords
leads
flex life
finite element
wire
vibration
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CNB200380104187XA
Other languages
Chinese (zh)
Other versions
CN1717687A (en
Inventor
饭盛康生
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Yazaki Corp
Original Assignee
Yazaki Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Yazaki Corp filed Critical Yazaki Corp
Publication of CN1717687A publication Critical patent/CN1717687A/en
Application granted granted Critical
Publication of CN100444177C publication Critical patent/CN100444177C/en
Anticipated expiration legal-status Critical
Expired - Fee Related legal-status Critical Current

Links

Images

Abstract

In a method for predicting bending life spans of wires, the wires, temperatures, pre-vibration shapes, and constraint conditions are set, and finite element models of the electric wires are formed using a finite element method. Natural frequencies for the pre-vibration shapes are calculated, and stresses in individual finite elements of the finite element models which correspond to the n atural frequencies are calculated, and a maximum stress is retrieved. Predicting functions corresponding to the plural electric wires and the atmosphere temperatures, which are set, are read out. Abending life span corresponding to the maximum stress of each electric wire, is acquired while referring to the predicting functions read out, and a shortest bending life span is obtained from the bending life spans, and output.

Description

Be used to predict the method and apparatus of the flex life of the electrical lead that causes by vibration and/or wire-protecting parts
Technical field
The present invention relates to a kind of method and apparatus that is used to predict the flex life of a plurality of electrical leads and/or their wire-protecting parts; wherein these a plurality of electrical leads are clipped to predetermined portions at least two some places; this bending is caused by vibration, and relates to a kind of program that is used to predict this flex life.
Background technology
Usually, in vehicle etc., a plurality of electronic equipments are electrically connected mutually by a plurality of electrical leads (usually being called " lead " simply).These leads are single bundle by harnesses such as insulation locking strip, adhesive tapes, and as so-called wire harness, it is configured in the pre-position of automobile etc. in the extension mode.In some cases, these leads are subjected to the protection of wire-protecting parts, such as the sleeve pipe that is configured in the reservations office.In other cases, these conductor configurations are in the reservations office of vehicle etc., and harness does not become a line simultaneously, and/or be not subjected to the protection of wire-protecting parts.
Gross vehicle is to be in such environment, and promptly it is always vibrating owing to reasons such as engine driven.Especially, be distributed in the electrical lead bending repeatedly and the deformation of the direct reception engine luggine of engine room inside, and finally owing to vibration disconnects.Announced its experimental result.Thus, particularly importantly, predict the flex life of electrical lead and wire-protecting parts exactly.
Usually, by design iterations, trial-production and torture test, carry out the prediction of the flex life of electrical lead and wire-protecting parts.For example, in this torture test, vibrating on the substrate along the lead placement that the routing path of envisioning distributes.Make this vibration substrate with predetermined frequency and predetermined amplitude vibrations by Vib., and when making its vibration of having vibrated specific times, the flex life of prediction lead.
The document of quoting in this instructions is:
Non-patent literature 1
Brain Library Publishing Corp is in the B.Nasu of publication on August 10th, 1978 " Matrix Infinite Element Method ", pp7~15
Non-patent literature 2
Corona Corp is in the Kimihiko Yasuda of publication on November 10th, 1993 " Mode Analysis and Dynamic Design ", pp54~56
On the other hand, it is shorter and shorter that the R﹠D cycle of vehicle trends towards, but also has the requirement that increases the flex life prediction accuracy.In the case, the relevant flex life Forecasting Methodology that wherein repeats torture test shortens the R﹠D cycle unsatisfactorily, and satisfies the requirement that increases forecasting accuracy unsatisfactorily.
Summary of the invention
Therefore, in order to tackle problem mentioned above, the objective of the invention is to, a kind of method and apparatus that is used to predict the flex life of electrical lead is provided, in its environment that can vibrate therein, the requirement of satisfying pin-point accuracy ground prediction flex life and shortening the R﹠D cycle, and provide a kind of storage to be used for predicting the recording medium of the program of this flex life in this mode.
In order to realize purpose mentioned above, the invention is characterized in that it has following configuration.
(1) a kind of flex life Forecasting Methodology of predicting the flex life of a plurality of leads that cause by vibration, wherein at least two of each of these a plurality of leads points are restrained, this method may further comprise the steps:
The pre-stored step, wherein pre-stored is represented atmospheric temperature, each anticipation function about concerning between the stress of these a plurality of leads and the flex life about these a plurality of leads;
Step is set, the pre-vibration shape of these a plurality of leads, atmospheric temperature, these a plurality of leads and the constraint condition of these a plurality of leads wherein are set;
Finite element model forms step, wherein by using Finite Element Method, forms the finite element model of these a plurality of leads;
The vibration analysis step is wherein calculated the natural frequency about pre-vibration shape, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress searching step wherein in these a plurality of leads each, is retrieved maximum stress in the stress that calculates from the vibration analysis step;
The anticipation function reading step wherein reads the anticipation function corresponding to the atmospheric temperature that is provided with respectively in step is set;
The flex life prediction steps wherein under the situation with reference to the anticipation function read, obtain the flex life of maximum stress corresponding to each of these a plurality of leads, and this flex life obtains the shortest flex life certainly in the anticipation function reading step; With
The output step is wherein exported the shortest flex life that obtains in the flex life prediction steps.
(2) according to the method for (1), wherein in the vibration analysis step, it is that wherein these a plurality of leads and are calculated the natural frequency of these a plurality of leads respectively by the wire structures of harness that these a plurality of leads are used as.
(3) according to the method for (1), wherein these a plurality of lead harnesses are single bundle, and the bunchy of these a plurality of leads is set to be provided with one of constraint condition in the step.
(4) according to the method for (1), comprise that further the position limits step, wherein on lead, limit corresponding to the position of short flex life, the output of output step limits the position that step limits by this position.
(5) method of basis (1), wherein
In the vibration analysis step, calculate displacement corresponding to the finite element of the finite element model of natural frequency,
This method comprises the interference portion prediction steps, wherein based on the displacement of being calculated, predicts the interference portion on these a plurality of leads that caused by vibration, and
The interference portion of the output step prediction of output.
(6) method of basis (1), wherein use expression to be used for anticipation function at the curve of the lower confidence interval of PRF, wherein by using under a plurality of typical atmospheric temperatures at the stress of these a plurality of leads acquisitions and the data of relevant flexible life, this PRF of statistical computation.
(7) a kind of flex life Forecasting Methodology; it is predicted a plurality of electrical leads and is used to protect these a plurality of leads to prevent it is caused crooked wire-protecting parts by vibration flex life; wherein at least two of each of these a plurality of leads points are restrained, and this method may further comprise the steps:
The pre-stored step, wherein the pre-stored atmospheric temperature, about the relation between the flex life of the stress of these a plurality of leads and these wire-protecting parts and this a plurality of leads and these wire-protecting parts;
Step is set, the pre-vibration shape of these a plurality of leads, these wire-protecting parts, atmospheric temperature, these a plurality of leads and these wire-protecting parts and the constraint condition of this a plurality of leads and these wire-protecting parts wherein are set;
Finite element model forms step, wherein by using Finite Element Method, forms the finite element model of these a plurality of leads and these wire-protecting parts;
The vibration analysis step is wherein calculated the natural frequency about the pre-vibration shape of these a plurality of leads and these wire-protecting parts, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress searching step wherein for each and these wire-protecting parts in these a plurality of leads, is retrieved maximum stress in the stress that calculates from the vibration analysis step;
The anticipation function reading step wherein reads the anticipation function corresponding to the atmospheric temperature that is provided with in step is set;
The flex life prediction steps, wherein under situation with reference to the anticipation function of in the anticipation function reading step, reading, obtain flex life respectively, and obtain the shortest flex life from described flex life corresponding to the maximum stress of these a plurality of leads and these wire-protecting parts; With
The output step is wherein exported the shortest flex life that obtains in the flex life prediction steps.
(8) according to the method for (7), wherein in the vibration analysis step, it is that wherein these a plurality of leads and are calculated the natural frequency of these a plurality of leads respectively by the wire structures of harness that these a plurality of leads are used as.
(9) according to the method for (7), wherein these a plurality of lead harnesses are single bundle, and the bunchy of these a plurality of leads is set to be provided with one of constraint condition in the step.
(10) according to the method for (7), comprise that further the position limits step, wherein on lead or wire-protecting parts, limit corresponding to the position of short flex life, the output of output step limits the position that step limits by this position.
(11) method of basis (7), wherein
In the vibration analysis step, calculate displacement corresponding to the finite element of the finite element model of natural frequency,
This method comprises the interference portion prediction steps, wherein based on the displacement of being calculated, and these a plurality of leads that prediction is caused by vibration or the interference portion on the wire-protecting parts, and
The interference portion of the output step prediction of output.
(12) method of basis (7); wherein use expression to be used for anticipation function at the curve of the lower confidence interval of PRF; wherein by using under a plurality of typical atmospheric temperatures at these a plurality of leads and the stress of wire-protecting parts acquisition and the data of relevant flexible life, this PRF of statistical computation.
(13) a kind of flex life predict device that is used to predict the flex life of a plurality of leads that cause by vibration, wherein at least two of each of these a plurality of leads points are restrained, this equipment comprises:
The pre-stored unit is used for pre-stored and represents atmospheric temperature, each anticipation function about concerning between the stress of these a plurality of leads and the flex life about these a plurality of leads;
The unit is set, is used to be provided with the pre-vibration shape of these a plurality of leads, atmospheric temperature, these a plurality of leads and the constraint condition of these a plurality of leads;
Finite element model forms the unit, is used for by using Finite Element Method to form the finite element model of these a plurality of leads;
The vibration analysis unit is used to calculate the natural frequency about pre-vibration shape, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress retrieval unit is used for each at these a plurality of leads, retrieves maximum stress in the stress that calculates from the vibration analysis unit;
The anticipation function sensing element is used for reading respectively corresponding at the anticipation function that the atmospheric temperature that the unit is provided with is set;
The flex life predicting unit is used for reference under the situation of the anticipation function that the anticipation function sensing element is read, and obtain the flex life of maximum stress corresponding to each of these a plurality of leads, and this flex life obtains the shortest flex life certainly; With
Output unit is used for exporting the shortest flex life that obtains in the flex life predicting unit.
(14) equipment of basis (13), wherein
The vibration analysis unit calculates the displacement corresponding to the finite element of the finite element model of natural frequency,
This equipment comprises the interference portion predicting unit, and it is used for based on the displacement of being calculated, these a plurality of leads that prediction is caused by vibration or the interference portion on the wire-protecting parts, and
The interference portion of the output unit prediction of output.
(15) a kind of computer readable recording medium storing program for performing, its storage is used to predict the program of these a plurality of bending life spans of wires that caused by vibration, and wherein at least two of each of these a plurality of leads points are restrained, and this program is used as computing machine:
The pre-stored unit is used for pre-stored and represents atmospheric temperature, each anticipation function about concerning between the stress of these a plurality of leads and the flex life about these a plurality of leads;
The unit is set, is used to be provided with the pre-vibration shape of these a plurality of leads, atmospheric temperature, these a plurality of leads and the constraint condition of these a plurality of leads;
Finite element model forms the unit, is used for by using Finite Element Method to form the finite element model of these a plurality of leads;
The vibration analysis unit is used to calculate the natural frequency about pre-vibration shape, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress retrieval unit is used for each at these a plurality of leads, retrieves maximum stress in the stress that calculates from the vibration analysis unit;
The anticipation function sensing element is used for reading respectively corresponding at the anticipation function that the atmospheric temperature that the unit is provided with is set;
The flex life predicting unit is used for reference under the situation of the anticipation function that the anticipation function sensing element is read, and obtain the flex life of maximum stress corresponding to each of these a plurality of leads, and this flex life obtains the shortest flex life certainly; With
Output unit is used for exporting the shortest flex life that obtains in the flex life predicting unit.
Description of drawings
Fig. 1 shows the block diagram of basic configuration of the present invention.
Fig. 2 A shows the diagram of electrical lead when discretize of handling among the present invention.Fig. 2 B shows the beam element of the discretize electrical lead shown in Fig. 2 A and the diagram of node.
Fig. 3 shows the block diagram of the hardware configuration that makes up according to the present invention.
Fig. 4 A and 4B show the diagram of the flex life data in the memory device that is stored among Fig. 3.
Fig. 5 shows the process flow diagram of main processing procedure according to an embodiment of the invention.
Fig. 6 shows the process flow diagram of vibration analysis processing procedure shown in Figure 5.
Fig. 7 A, 7B and 7C show the diagram of the predicting shape of the electrical lead in first, second and the 3rd vibration mode respectively.
Be used to realize optimal mode of the present invention
Now by the preferred embodiments of the present invention are described with reference to the drawings.At first will be by describing prerequisite, theory and the basic formula that uses in an embodiment with reference to figure 2A and 2B.Fig. 2 A shows the diagram of the electrical lead of handling among the present invention that is in the discretize state.Fig. 2 B shows the beam element of the discrete electrical lead shown in Fig. 2 A and the diagram of node.
In the present invention, based on following hypothesis, utilized Finite Element Method:
(1) electrical lead comprises plastic components.
(2) electrical lead is the set of the beam element that is connected in series mutually.
(3) in each beam element, keep linear.
(4) cross section of electrical lead is circular.
Next step makes this electrical lead 1 discretize.Particularly, as shown in Fig. 2 A, electrical lead 1 divide (discretize) be a plurality of beam element C1, C2, C3 ....In other words, electrical lead 1 is taken as the set of a limited number of beam element that is connected in series mutually.
Therefore, electrical lead 1 can be considered to beam element C1, C2, C3 ... set, these beam elements C1, C2, C3 ... node N1, N2, N3 ... locate to be connected in series mutually, as shown in Fig. 2 B.Required attribute about this beam element is, for example, and length " l " (referring to Fig. 2 A), sectional area A (referring to Fig. 2 A), area inertia moment, area polar moment of inertia, density, modulus of direct elasticity, modulus of transverse elasticity or the like.These attributes can obtain by measuring or calculating in advance.Preferably, this attribute forms database, and can optionally obtain.In this application file, length and sectional area are set to geometric attribute, and area inertia moment, area polar moment of inertia, modulus of direct elasticity and modulus of transverse elasticity are set to material properties.
As is well known, and Hooke's law (Hook ' s Law) pass through the static(al) in the structural elasticity scope, the displacement that keeps this structure makes it not take place to vibrate.Similarly, Hooke's law also keep beam element C1, C2, C3 ..., as is known.Adjacent beam element C1, C2, C3 ... between, satisfied the condition of displacement continuity and dynamic balance.By utilizing these facts, connect these beam elements C1, C2, C3 ..., and the discrete bodies that is caused (electrical lead) is represented by following expression formula (1).
[K]{x}={F}(1)
In the superincumbent expression formula, [K] is the universe stiffness matrix, and it is combined by the stiffness matrix of beam element independently.In order to describe simply, the content class of universe stiffness matrix [K] is similar to the set of attribute.These values are to set in advance.{ x} is nodal displacement vector (perhaps being motion vector simply), and is the array of the displacement component of all nodes.{ component of x} comprises initialization vector (such as obligatory point) and unknown quantity to the nodal displacement vector.{ F} is clean outer force vector, and is the array of the outer force component at all node places.
Like this, formed the finite element model of discrete lead, it is divided into optional a limited number of beam element.For the formation of finite element model, can use a kind of technology, disclosed technology type is seemingly in the Japanese patent application No.2002-279503 that submitted on September 25th, 2002 for the applicant of itself and present patent application.For example, in non-patent literature mentioned above, general matrix Finite Element Method has been described.
In the present invention, in order to predict the flex life of the electrical lead that causes by vibration, be necessary to obtain natural frequency, displacement, stress or the like.To describe theory and the computing formula that is used to obtain natural frequency, displacement, stress etc. tout court below, set up expression formula (1) simultaneously.
Be used to predict its flex life in order dynamically to handle lead, inertial force [M] { x " } adds to by in the load item in the statically balanced expression formula of expression formula (1) expression, and considers damping [C] { x ' }, and then we have
[M]{x”}+[C]{x’}+[K]{x}={F(t)}(2)
Wherein
[M]: inertial matrix
[C]: ratio of damping matrix
X ' }: the motion vector { first order derivative of x}
X " }: the second derivative of motion vector
{x}
In the free vibration state, and if there is not damping (in expression formula (2), [C] { x ' }=0) in external force=0 (in expression formula (2), { F (t) }=0), then each point of lead mode of sentencing simple harmonic moving in fixing frequency is vibrated.In the time of in expression formula (2) that following expression formula (3) is replaced,
{x}={x 0}sinωt (3)
Then we have
[M]({x 0}sinωt)”+[K]({x 0}sinωt)=0
(-ω 2[M]+[K])singωt=0
([K]-ω 2[M]){x}=0 (4)
By expression formula (4), { x} is as latent vector can to obtain natural frequency ω and motion vector.Even { when x} multiply by fixed numbers, expression formula (4) was still effective at motion vector.So { x} is relative displacement to motion vector.Therefore, { stress of x} also is relative value to obtain the self-alignment amount of shifting to.The absolute value that obtains self-representation (4) only is natural frequency ω.In order to calculate actual displacement and stress, be necessary to import the loading condiction of actual vibration.
Be used for its flex life prediction in order dynamically to handle lead, be input to expression formula (2), then can calculate each displacement and stress basically about each unit interval if depend on the load { F (t) } of time.Therein by depending on that to expression formula (2) input the load { F (t) } of time finds the solution in the situation of this equation, in being attended by the phenomenon of periodic vibration, it is long being used to duplicate the VIBRATION ANALYSIS time, and the time that therefore is used to export analysis result is long especially.For fear of this problem, common practice is by Fourier (Fourier) conversion this expression formula to be transformed into frequency domain from time domain.When in frequency domain, carrying out expression formula calculating, that is, when carrying out Frequency Response Analysis, depend on that the load of frequency is input to expression formula, be used to calculate the displacement and the stress at each frequency place.For the load that depends on frequency, be applied to as the wire harness of flex life forecasting object or the power of the obligatory point on the wire-protecting parts and be set at optional value, this power participates in the expection vibration of engine, carbody or the like.Subsequently,, make this expression formula turn back to time domain, reduced calculated amount thus from frequency domain by inverse Fourier transform.This technology is known, and therefore will no longer provide its further description here.
By utilizing theory and the computing formula of describing up to now, can calculate natural frequency, displacement and stress, it will obtain describing hereinafter.For example, general eigenvalue analysis as indicated above has also been described in non-patent literature 2.
In the present invention, also carried out the vibration analysis that for example comprises as a plurality of electrical leads of the sleeve pipe of wire-protecting parts.For Finite Element Method being applied to the wire-protecting parts, these wire-protecting parts are divided into a plurality of triangular finite elements, and have obtained the stress at these finite element places.After the finite element model that comprises this finite element forms,, carry out the vibration analysis of these wire-protecting parts by the mode similar to the situation of electrical lead.
The hardware configuration that is used to realize processing procedure that makes up according to the present invention will be described below.Fig. 3 shows the block diagram of the hardware configuration that makes up according to the present invention.Fig. 4 A and 4B show the diagram of the flex life data in the memory device that is stored among Fig. 3.
As shown in Figure 3, in the present invention, for example, use personal computer, it has the basic configuration that is made of microcomputer 51, input equipment 52, display device 53, printing device 54, memory device 55, communication interface 56 and read/write device 57.RAM 51c that microcomputer 51 comprises CPU (CPU (central processing unit)) 51a, is used to store the ROM 51b of boot and other programs and is used for storing multiple result temporarily.Input equipment 52 is keyboard, computer mouse etc.; Display device 53 is LCD, the CRT etc. that are used for the display process result; And printing device 54 is the printers that are used for the print processing result.
Memory device 55 is, for example, and hard disk drive, and communication interface 56 is, for example, modem boards is used for being equal to external device communication by means of internet, LAN line.Read/write device 57 reads the flex life predictor 59a that makes up according to the present invention that is stored in the recording medium 59, and destination file 55c is written in the recording medium 59.These building blocks are by internal bus 58 interconnection.
In memory device 55, stored at least data file 55a, flex life data file 55b and destination file 55c have been set.Data file 55a is set is included as the data of predicting flex life and presetting.The type of this data representation electrical lead and wire-protecting parts, atmospheric temperature, vibrate shape, constraint condition etc. in advance, be provided with among its step S1 that describes hereinafter.This is provided with the positional information that data file 55a comprises barrier 2, such as stilt of estimating and electronic component (referring to Fig. 7).
Flex life data file 55b is the set of anticipation function y1, y2 and y3; it (for example is to use electrical lead 55a1 and 55a2 and wire-protecting parts; sleeve pipe) data of stress on the 55a3 and bending fatigue number of times carry out that statistical computation obtains; these data are to gather under different atmospheric temperatures; for example ,-40 ℃, 0 ℃ and 25 ℃.
For the PRF y21 that obtains by known regretional analysis, curve y22 represents upper confidence interval, and curve y23 represents the lower confidence interval, shown in Fig. 4 B.For anticipation function, used the curve y23 among these curves y22 and the y23.Fiducial interval is, for example, and 95%.This anticipation function is to obtain under such condition, and promptly electrical lead is placed under the different atmospheric temperatures with sleeve pipe.Therefore, under strict more statistical computation condition, predicted flex life.Obviously, considered given reliability of statistics, and the computation process of anticipation function is simple about anticipation function.As a result, under the situation of not adding complicated processing procedure, strictly predicted flex life.This helps further improving the quality and improving the routing path scheme.Mention in passing, use PRF, can obtain the bending fatigue number of times.
Destination file 55c comprises discrete lead in the finite element and whole stress of discrete sleeve pipe, and it carries out record by each natural frequency.Destination file 55c stores with text formatting, and can optionally export.Memory device 55 is corresponding to the anticipation function memory storage that illustrates in the claim.
By this configuration, microcomputer 51 has been installed flex life predictor 59a, and it is read in the memory device 55 by read/write device 57.After start, microcomputer 51 activates according to the boot that is stored among the ROM 51b, and beginning flex life predictor 59a.According to flex life predictor 59a; the electrical lead that microcomputer 51 prediction is caused by vibration and/or the flex life of wire-protecting parts; impel display device 53 and printing device 54 demonstrations and printing to predict the outcome, and this result is stored in the memory device 55.Flex life predictor 59a can be installed in another personal computer with identical configuration, and after installing, this computing machine is operated on it as the flex life predict device.Flex life predictor 59a can provide by communication line, such as internet, LAN etc., but not provides by recording medium 59.
Now will use the explanatory diagram of Fig. 7 A~7C and the process flow diagram of Fig. 5 and 6, describe processing procedure according to present embodiment of the present invention.Fig. 5 shows the process flow diagram of main processing procedure according to an embodiment of the invention.Fig. 6 shows the process flow diagram of vibration analysis processing procedure shown in Figure 5.Fig. 7 A, 7B and 7C show the diagram of the predicting shape of the electrical lead in first, second and the 3rd vibration mode respectively.
As shown in Figure 5, the required data predicted that is used for is set in step S1.Particularly, item to be provided be at least flex life a plurality of electrical leads to be predicted (being the type of electrical lead definitely), wire-protecting parts (sometimes not needing), atmospheric temperature are arranged, about the pre-vibration shape of each lead with about the constraint condition of each electrical lead.For the item of these necessity is set, the entr screen (not shown) on display device 53, occurred, and, the item of necessity has been logined entr screen by using input equipment 52.
The type of electrical lead is the type that flex life has electrical lead to be predicted.For electrical lead, geometric attribute and material properties are associated with the type of electrical lead.Particularly, geometric attribute comprises about the length of each lead and the information in cross section.Material properties is area inertia moment, area polar moment of inertia, density, modulus of direct elasticity and modulus of transverse elasticity.These data can be passed through, and for example, test in advance and obtain.The finite element of these relations on attributes in the stiffness matrix [K] of expression formula (1).Atmospheric temperature is electrical lead when carrying out the flex life prediction and/or the temperature around the wire-protecting parts, its typically-40 ℃, 0 ℃ and 25 ℃.
Pre-vibration shape is the shapes under static state such as electrical lead, is marked as the reference number 1a among Fig. 7 A.In explanation, carried out linear simplifiation and it has been illustrated.Pre-vibration shape 1a can login by using input equipment 52 artificiallies, perhaps can also use the pre-vibration shape that formed in advance before the flex life prediction.Preferably, calculated in advance satisfies the shape of vibration in advance of the minimum bending radius of given constraint condition and electrical lead, and it is used for vibrating in advance shape 1a.
For constraint condition, the information that constraint fully, rotation condition is set and discharges fully, it is corresponding to the coordinate information about the node n1~n5 among Fig. 7 A.Node n1~n5 is the tie point of the finite element that is divided into of electrical lead.Some this node corresponds respectively to the residing part of constraint component (such as connector and anchor clamps) on the position.In this case,, under complete or rotation condition condition, settle node n1 and n5, settling remaining node n2~n4 under the release conditions fully simultaneously by constraint component.The value of She Zhiing is related to the motion vector { value of the finite element among the x} in the expression formula (1) herein.
In some cases, by insulation locking strip, adhesive tape etc., be single bundle with a plurality of electrical lead harnesses that form wire harness, and in other situation, these electrical leads are not by harness.In the situation that electrical lead is bundled together, the lead bunchy is set to constraint condition therein.When the constraint condition of lead bunchy is set, preferably, be different from the processing that is positioned at those electrical leads on preceding a kind of electrical lead medial surface at processing with insulation locking strip or the contacted electrical lead of adhesive tape.By such operation, can predict the flex life of lead more exactly, this be because to the electrical lead of bunchy and not the electrical lead of bunchy handle individually.
In some cases, these electrical leads pass the wire-protecting parts such as sleeve pipe, and in other situation, arrange or this electrical lead that distributes under the situation of not using the wire-protecting parts.A plurality of electrical leads of wire-protecting parts are passed in use, and are as indicated above thus, and in some cases, these leads harness together are single bundle, and in other situation, not these leads of harness.Used therein in the situation of wire-protecting parts, remained to be provided with the constraint condition that is applicable to the wire-protecting parts.The step S1 of Miao Shuing is corresponding to " step is set " in the claim and " being provided with the unit " up to now.
Next step in step S2, forms the finite element model of electrical lead and/or wire-protecting parts.By the wire-protecting parts are divided into a plurality of rectangular finite elements, formed the finite element model of wire-protecting parts.The finite element model of electrical lead is formed and makes electrical lead be divided into a plurality of beam elements.Step S2 forms step corresponding to the finite element model in the claim and finite element model forms device.
Next step in step S3, at each finite element, is carried out vibration analysis and handles.Particularly, in step S301, based on such hypothesis, promptly the wire harness as the bundle of a plurality of electrical leads vibrates as object, and expression formula (4) is applied to this wire harness, in order to calculate the natural frequency of this wire harness.In this case, calculate geometric attribute and material properties as the independent element of stiffness matrix [K], this calculates based on such hypothesis, and promptly these attributes are to form each electrical lead and/or the geometric attribute of wire-protecting parts and the result of material properties.For natural frequency, shown in Fig. 7 A~7C, calculate corresponding to for example this natural frequency value of first, second and the 3rd vibration mode.There are the number and the natural frequency of vibration mode to be calculated to be not limited to illustrated situation.For example, first, second is set to default value with the 3rd vibration mode and can be changed by using input equipment 52.
After calculation on Natural Frequency; execution in step S302 and S303, wherein natural frequency is applied to by expression formula (2) is carried out the expression formula that Fourier transform obtains, and is as indicated above; at each electrical lead and/or wire-protecting parts, calculate the displacement and the stress of all finite elements thus.In this case, incorporated into about electrical lead whether harness be the information of single bundle and about whether having one or more specific electrical lead and insulation locking strip or the contacted information of adhesive tape (it is to be set to constraint condition in step S1), as the information that involves in inertial matrix [M] whole in the expression formula (2), ratio of damping matrix [C] and the external force { F (t) }.
In step S304, displacement of calculating about each each natural frequency and stress are associated with each electrical lead and/or wire-protecting position component (finite element) information as the flex life forecasting object, and are written in the destination file.These steps S3, S301~S304 are corresponding to vibration analysis step in the claim and vibration analysis unit.
Subsequently, in step S4, for each electrical lead and/or the wire-protecting parts in the flex life prediction, those stress retrieval maximum stresses that from destination file, write down.In step S5, sensing pin is to the electrical lead in the flex life prediction and/or the anticipation function of wire-protecting parts.Particularly, be stored in flex life data file 55b sensing pin in the memory device 55 certainly to the electrical lead in the flex life prediction and/or the anticipation function as atmospheric temperature set among the step S1 of wire-protecting parts.Step S4 is corresponding to maximum stress searching step in the claim and maximum stress retrieval element, and step S5 is corresponding to anticipation function reading step in the claim and anticipation function sensing element.
In next step S6, under situation, obtained each flex life in step S4 corresponding to each electrical lead and/or each wire-protecting parts maximum stress (it obtains) with reference to the anticipation function of in step S5, reading.By these flex life, obtained the shortest flex life.This shortest flex life can be, for example, and the bending fatigue number of times that the flex life function in Fig. 4 obtains, the tired time that perhaps can be based on the bending fatigue number of times and calculate corresponding to the former natural frequency.Step S6 is corresponding to flex life prediction steps in the claim and flex life predicting unit.
In step S7, limit by its finite element corresponding to the position of short flex life.When determining the position of the conductor part that lead wherein may disconnect, it is useful that this position limits.In step S8, position that limits in step S7 and the flex life of predicting in step S6 output to display device 53.Because except flex life, go back on output lead guard block and/or the electrical lead corresponding to the position of short flex life, therefore guaranteed flex life prediction more accurately.Step S7 limits step and position device for limiting corresponding to the position in the claim, and step S8 is corresponding to output step and output unit in the claim.
Can adopt following process: in step S9, the prediction interference portion, and in step S10, the interference portion of the prediction of output.Particularly, described in step S304, at the stress of each calculation on Natural Frequency with such state storage in destination file, promptly these stress are associated with the information of electrical lead and/or wire-protecting position component (finite element).Therefore, can generate predicting shape about each vibration mode by this destination file, as among the 1a2 among the 1a1 among Fig. 7 A, Fig. 7 B and Fig. 7 C 1a3 marked.As indicated above, the positional information of barrier 2 is stored in the memory device 55.Therefore, if this positional information includes the predicting shape about each vibration mode, then can see existing electrical lead will interfere the possibility of barrier 2 (referring to Fig. 7 C).On the contrary, might predict the electrical lead part that to interfere barrier 2.Step S9 is corresponding to the interference portion prediction steps in the claim.
If judge the order that has the output destination file in step S11, then in step S12, the content of destination file 55c is with the form output of text.This output content can be shown by display device 53, perhaps be printed on the paper by printing device 54.And, can specify content to be exported by input equipment 52.If do not need content output, then can end process sequence of steps (N among the step S11).
Therefore, embodiments of the invention successfully provide a kind of method and apparatus that is used to predict the flex life of electrical lead etc., it can predict the flex life of lead more exactly, and can satisfy the requirement that improves forecasting accuracy in the environment that vibration takes place therein satisfactorily, and a kind of program that is used for by this method prediction flex life is provided.Especially since the disconnection life-span of the electrical lead that causes of car engine machine vibration can in the short time, predict, and needn't carry out torture test.This is very favorable effect.And same gratifying is that flex life is to predict under the condition of strictness.Therefore, this embodiment helps further improving the quality and improving the routing path scheme.
Should be appreciated that and the invention is not restricted to embodiment mentioned above.For example, the wire-protecting parts are not limited to sleeve pipe.And, the invention is not restricted to automotive interior, but can be applied to the situation that vibration takes place in the factory.
According to the present invention, be provided with the pre-vibration shape of a plurality of electrical leads, atmospheric temperature, a plurality of electrical leads and the constraint condition of a plurality of electrical leads, and formed the finite element model of a plurality of electrical leads.Calculating is vibrated the natural frequency of shape about a plurality of electrical leads and in advance corresponding to the stress in the independent finite element of the finite element model of this natural frequency, and from about calculating of each electrical lead stress, the retrieval maximum stress.Read set anticipation function corresponding to a plurality of electrical leads and atmospheric temperature.Under situation with reference to the anticipation function of being read, obtain flex life, and this flex life obtains the shortest flex life certainly corresponding to the maximum stress of each electrical lead, and with its output.Therefore, under the situation of not carrying out torture test, can predict the flex life of a plurality of electrical leads exactly.As a result, provide a kind of flex life Forecasting Methodology, it can satisfy the requirement of shortening the R﹠D cycle and improving forecasting accuracy.
According to the present invention, be provided with the pre-vibration shape of a plurality of electrical leads and wire-protecting parts, atmospheric temperature, a plurality of electrical leads and the constraint condition of a plurality of electrical leads, and formed the finite element model of a plurality of electrical leads.Calculating is about the natural frequency of the pre-vibration shape of a plurality of electrical leads, and calculates corresponding to the stress in the independent finite element of the finite element model of this natural frequency, and from about calculating of each electrical lead stress, the retrieval maximum stress.Read set anticipation function corresponding to a plurality of electrical leads and atmospheric temperature.Under situation with reference to the anticipation function of being read, obtain flex life, and this flex life obtains the shortest flex life certainly corresponding to the maximum stress of each electrical lead, and with its output.Therefore, under the situation of not carrying out torture test, can predict the flex life of a plurality of electrical leads that comprise the wire-protecting parts exactly.As a result, provide a kind of flex life Forecasting Methodology, it can satisfy the requirement of shortening the R﹠D cycle fully.
According to the present invention, a plurality of electrical leads are taken as the structure of the similar lead of the bundle with a plurality of electrical leads, and calculate the natural frequency of these a plurality of electrical leads.This feature has caused the minimizing of calculated amount.Realized the further shortening that is used for the flex life predicted time that consumed.
According to the present invention, when a plurality of electrical lead harnesses are single bundle, and the bunchy of a plurality of electrical leads is set to a constraint condition in step is set.This has guaranteed flex life prediction more accurately.In fact, in some cases, a plurality of electrical lead harnesses are single bundle, and in other cases, they are not by harness.Although these situations are difference mutually clearly, still can predict flex life.
According to the present invention, together with flex life, limit step by the position, also on wire-protecting parts or electrical lead, define corresponding to the position of short flex life, and with its output.This feature has been guaranteed the prediction more accurately of flex life.
According to the present invention, also predict the interference portion that causes by vibration on each wire-protecting parts or each electrical lead.Therefore, by this feature,, can design the optimization routing path of avoiding lead to disconnect by the contact of lead.
According to the present invention; expression is used for this anticipation function at the curve of the lower confidence interval of PRF; wherein use under a plurality of typical atmospheric temperatures data, this PRF of statistical computation about the stress and the bending fatigue number of times of wire-protecting parts and electrical lead.Therefore, flex life is to predict under the statistical condition of strictness.Obviously, considered given reliability of statistics, and the computation process of anticipation function is simple about anticipation function.As a result, under the prerequisite of not adding complicated processing procedure, strictly predicted flex life.This helps further improving the quality and improving the routing path scheme.

Claims (14)

1. the flex life Forecasting Methodology of the flex life of a plurality of leads of causing by vibration of a prediction, wherein at least two of each of these a plurality of leads points are restrained, this method may further comprise the steps:
The pre-stored step, wherein pre-stored is represented atmospheric temperature, each anticipation function about concerning between the stress of these a plurality of leads and the flex life about these a plurality of leads;
Step is set, the pre-vibration shape of these a plurality of leads, atmospheric temperature, these a plurality of leads and the constraint condition of these a plurality of leads wherein are set;
Finite element model forms step, wherein by using Finite Element Method, forms the finite element model of these a plurality of leads;
The vibration analysis step is wherein calculated the natural frequency about pre-vibration shape, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress searching step wherein in these a plurality of leads each, is retrieved maximum stress in the stress that calculates from the vibration analysis step;
The anticipation function reading step wherein reads the anticipation function corresponding to the atmospheric temperature that is provided with respectively in step is set;
The flex life prediction steps wherein under the situation with reference to the anticipation function read, obtain the flex life of maximum stress corresponding to each of these a plurality of leads, and this flex life obtains the shortest flex life certainly in the anticipation function reading step; With
The output step is wherein exported the shortest flex life that obtains in the flex life prediction steps.
2. the process of claim 1 wherein that in the vibration analysis step it is that wherein these a plurality of leads and are calculated the natural frequency of these a plurality of leads respectively by the wire structures of harness that these a plurality of leads are used as.
3. the process of claim 1 wherein that with these a plurality of lead harnesses be single bundle, and the bunchy of these a plurality of leads is set to be provided with one of constraint condition in the step.
4. the method for claim 1 comprises that further the position limits step, wherein limits on lead corresponding to the position of short flex life, and the output of output step limits the position that step limits by this position.
5. the process of claim 1 wherein
In the vibration analysis step, calculate displacement corresponding to the finite element of the finite element model of natural frequency,
This method comprises the interference portion prediction steps, wherein based on the displacement of being calculated, predicts the interference portion on these a plurality of leads that caused by vibration, and
The interference portion of the output step prediction of output.
6. the method for claim 1, wherein use expression to be used for anticipation function at the curve of the lower confidence interval of PRF, wherein by using under a plurality of typical atmospheric temperatures at the stress of these a plurality of leads acquisitions and the data of relevant flexible life, this PRF of statistical computation.
7. flex life Forecasting Methodology; it is predicted a plurality of electrical leads and is used to protect these a plurality of leads to prevent it is caused crooked wire-protecting parts by vibration flex life; wherein at least two of each of these a plurality of leads points are restrained, and this method may further comprise the steps:
The pre-stored step, wherein the pre-stored atmospheric temperature, about the stress of these a plurality of leads and these wire-protecting parts with about the relation between the flex life of these a plurality of leads and these wire-protecting parts;
Step is set, the pre-vibration shape of these a plurality of leads, these wire-protecting parts, atmospheric temperature, these a plurality of leads and these wire-protecting parts and the constraint condition of this a plurality of leads and these wire-protecting parts wherein are set;
Finite element model forms step, wherein by using Finite Element Method, forms the finite element model of these a plurality of leads and these wire-protecting parts;
The vibration analysis step is wherein calculated the natural frequency about the pre-vibration shape of these a plurality of leads and these wire-protecting parts, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress searching step wherein for each and these wire-protecting parts in these a plurality of leads, is retrieved maximum stress in the stress that calculates from the vibration analysis step;
The anticipation function reading step wherein reads the anticipation function corresponding to the atmospheric temperature that is provided with in step is set;
The flex life prediction steps, wherein under situation with reference to the anticipation function of in the anticipation function reading step, reading, obtain flex life respectively, and obtain the shortest flex life from described flex life corresponding to the maximum stress of these a plurality of leads and these wire-protecting parts; With
The output step is wherein exported the shortest flex life that obtains in the flex life prediction steps.
8. the method for claim 7, wherein in the vibration analysis step, it is that wherein these a plurality of leads and are calculated the natural frequency of these a plurality of leads respectively by the wire structures of harness that these a plurality of leads are used as.
9. the method for claim 7 be single bundle with these a plurality of lead harnesses wherein, and the bunchy of these a plurality of leads is set to be provided with one of constraint condition in the step.
10. the method for claim 7 comprises that further the position limits step, wherein limits on this lead or this wire-protecting parts corresponding to the position of short flex life, and the output of output step limits the position that step limits by this position.
11. the method for claim 7, wherein
In the vibration analysis step, calculate displacement corresponding to the finite element of the finite element model of natural frequency,
This method comprises the interference portion prediction steps, wherein based on the displacement of being calculated, and these a plurality of leads that prediction is caused by vibration or the interference portion on this wire-protecting parts, and
The interference portion of the output step prediction of output.
12. the method for claim 7; wherein use expression to be used for anticipation function at the curve of the lower confidence interval of PRF; wherein use under a plurality of typical atmospheric temperatures at these a plurality of leads and the stress of this wire-protecting parts acquisition and the data of relevant flexible life, this PRF of statistical computation.
13. a flex life predict device that is used to predict the flex life of a plurality of leads that caused by vibration, wherein at least two of each of these a plurality of leads points are restrained, and this equipment comprises:
The pre-stored unit is used for pre-stored and represents atmospheric temperature, each anticipation function about concerning between the stress of these a plurality of leads and the flex life about these a plurality of leads;
The unit is set, is used to be provided with the pre-vibration shape of these a plurality of leads, atmospheric temperature, these a plurality of leads and the constraint condition of these a plurality of leads;
Finite element model forms the unit, is used for by using Finite Element Method to form the finite element model of these a plurality of leads;
The vibration analysis unit is used to calculate the natural frequency about pre-vibration shape, and calculates respectively corresponding to the stress in the independent finite element of the finite element model of this natural frequency;
The maximum stress retrieval unit is used for each at these a plurality of leads, retrieves maximum stress in the stress that calculates from the vibration analysis unit;
The anticipation function sensing element is used for reading respectively corresponding at the anticipation function that the atmospheric temperature that the unit is provided with is set;
The flex life predicting unit is used for reference under the situation of the anticipation function that the anticipation function sensing element is read, and obtain the flex life of maximum stress corresponding to each of these a plurality of leads, and this flex life obtains the shortest flex life certainly; With
Output unit is used for exporting the shortest flex life that obtains in the flex life predicting unit.
14. the equipment of claim 13, wherein
The vibration analysis unit calculates the displacement corresponding to the finite element of the finite element model of natural frequency,
This equipment comprises the interference portion predicting unit, and it is used for based on the displacement of being calculated, these a plurality of leads that prediction is caused by vibration or the interference portion on the wire-protecting parts, and
The interference portion of the output unit prediction of output.
CNB200380104187XA 2002-11-28 2003-11-25 Method and apparatus for predicting bending life spans of electric wires and/or wire protecting members induced by vibrations, an d recording medium storing program Expired - Fee Related CN100444177C (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
JP2002345220 2002-11-28
JP345220/2002 2002-11-28
JP364516/2003 2003-10-24

Publications (2)

Publication Number Publication Date
CN1717687A CN1717687A (en) 2006-01-04
CN100444177C true CN100444177C (en) 2008-12-17

Family

ID=35822574

Family Applications (1)

Application Number Title Priority Date Filing Date
CNB200380104187XA Expired - Fee Related CN100444177C (en) 2002-11-28 2003-11-25 Method and apparatus for predicting bending life spans of electric wires and/or wire protecting members induced by vibrations, an d recording medium storing program

Country Status (1)

Country Link
CN (1) CN100444177C (en)

Families Citing this family (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5248595B2 (en) * 2008-03-04 2013-07-31 新日鉄住金化学株式会社 Bending life prediction method for laminated body, bending life prediction apparatus for laminated body, bending life prediction program for laminated body, and recording medium
CN101995209B (en) * 2010-09-16 2012-05-23 上海电缆研究所 Aerial conductor bending amplitude sensor
CN102589992B (en) * 2012-02-28 2014-08-06 合肥工业大学 Method for forecasting residual service life of steel-cored aluminum strand overhead conductor
CN103077311B (en) * 2013-01-06 2016-05-11 广东电网公司电力科学研究院 The Forecasting Methodology of disconnected strand of rear remaining cross-section temperature rise peak value of high voltage overhead transmission pressure
CN103837343B (en) * 2014-03-19 2016-03-02 中国人民解放军镇江船艇学院 Based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis
CN105445126A (en) * 2015-11-18 2016-03-30 四川华西九方电缆有限公司 Fatigue resistance performance test method for cables
CN105784501B (en) * 2016-04-07 2018-06-12 北京航空航天大学 A kind of aging life-span appraisal procedure of carbon fiber composite core wire

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1236989A2 (en) * 2001-03-02 2002-09-04 Sumitomo Wiring Systems, Ltd. Flexure life estimating method, wire harness designing method and program thereof

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1236989A2 (en) * 2001-03-02 2002-09-04 Sumitomo Wiring Systems, Ltd. Flexure life estimating method, wire harness designing method and program thereof

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
VIBRATION THRESHOLDS FOR FRETTING CORROSIONIN ELECTRICAL CONNECTORS. FLOWERS G T EL AL.ELECTRICAL CONTACTS-2002.PROCEEDINGS OF THE 48TH. IEEE: HOLM CONFERENCE ON ELECTRICAL CONTACTS.. 2002
VIBRATION THRESHOLDS FOR FRETTING CORROSIONIN ELECTRICAL CONNECTORS. FLOWERS G T EL AL.ELECTRICAL CONTACTS.2002.PROCEEDINGS OF THE 48TH. IEEE: HOLM CONFERENCE ON ELECTRICAL CONTACTS. 2002 *

Also Published As

Publication number Publication date
CN1717687A (en) 2006-01-04

Similar Documents

Publication Publication Date Title
Sauter et al. On the hysteresis of wire cables in Stockbridge dampers
KR100696004B1 (en) Method and apparatus for predicting bending life spans of electric wires and/or wire protecting members induced by vibrations, and recording medium storing program
US7418677B2 (en) Method of calculating predictive shape of wire structure, calculation apparatus, and computer-readable recording medium
Steenackers et al. On the use of transmissibility measurements for finite element model updating
CN100444177C (en) Method and apparatus for predicting bending life spans of electric wires and/or wire protecting members induced by vibrations, an d recording medium storing program
Iga et al. Finite element modelling of turbine generator stator end windings for vibration analysis
KR100514706B1 (en) Method of assisting wiring design of wiring structure, its apparatus and its program
US7260811B2 (en) Method of calculating predictive shape of wiring structure, calculating apparatus, and computer-readable recording medium
JP4600912B2 (en) Wiring design support method, apparatus and program for wire-like structure
Kuether et al. Validation of nonlinear reduced order models with time integration targeted at nonlinear normal modes
CN1495072A (en) Method for predicating bundle conductor shift range, predicatin device and program
JP4516303B2 (en) WIRING DESIGN SUPPORT METHOD FOR LINE STRUCTURE, ITS DEVICE, AND ITS PROGRAM
WO2012038224A1 (en) A method, apparatus and computer program product for the finite element analysis of frequency dependent behaviour of nonlinear materials and contacts
JP4600913B2 (en) Wiring design support method, apparatus and program for wire-like structure
JP2005294195A (en) Method for assisting wiring design of wiring structure, its apparatus, and its program
JP4344204B2 (en) Method for predicting shape of wire-like structure, apparatus and program thereof
Bonisoli et al. A proposal of multi-dimensional modal reduction for nonlinear dynamic simulations
Xu et al. Correlation analysis of PCB and comparison of test-analysis model reduction methods
US20130179132A1 (en) Analysis Method, Apparatus and Software for a System With Frequency Dependent Materials
JP2004139568A (en) Method of assisting wiring design of wiring structure, its apparatus and its program
WO2023218570A1 (en) Assistance device, assistance method, and program
JPH11281522A (en) Method and device for analyzing vibration characteristic
Schneider et al. Digital validation of cable performance for vehicles in operation
Silva et al. Numerical analysis of wave propagation and vibration of overhead transmission cable
CN114707375A (en) Bolt pretightening force loading method and device, medium and electronic equipment

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
C14 Grant of patent or utility model
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20081217

Termination date: 20211125