JP2004084908A

JP2004084908A - Friction evaluating method of sliding bearing

Info

Publication number: JP2004084908A
Application number: JP2002250304A
Authority: JP
Inventors: Hiroshi Hibino; 日比野　浩; Masami Takagi; 高木　政美; Shoji Katsuta; 勝田　庄二; Shinya Nishimoto; 西本　信哉
Original assignee: Taisei Corp
Current assignee: Taisei Corp
Priority date: 2002-08-29
Filing date: 2002-08-29
Publication date: 2004-03-18
Anticipated expiration: 2022-08-29
Also published as: JP4251532B2

Abstract

<P>PROBLEM TO BE SOLVED: To provide a friction evaluating method of a sliding bearing for improving evaluation accuracy by evaluating friction of the sliding bearing so as to approach an actual sliding state. <P>SOLUTION: When evaluating the friction of the sliding bearing in a sliding state, a friction coefficient in the optional time or a predictor of frictional force is expressed as a function shape of a load, a speed and a repetition index. [Formula 1] μ(t) = f<SB>R</SB>(N(t),v(t),R(t)) R(t) is an index by numerically expressing a repetition progress degree. The load N(t) is a load acting at a right angle on a sliding bearing surface, and the speed v(t) is a sliding speed in the parallel direction to the sliding bearing surface. A repetition frequency, a surface temperature of a sliding material or a sliding plate and cumulative sliding displacement from a start of sliding are used as the repetition index. <P>COPYRIGHT: (C)2004,JPO

Description

【０００１】
【発明の属する技術分野】
本発明は、建築物や橋梁等の構造物に用いられる免震装置のための滑り支承の摩擦を評価するための方法に関する。
【０００２】
【従来の技術】
建物や橋梁など構造物の免震手段として用いられる滑り支承は、滑り材の低い摩擦係数を利用して、支承材と滑り材があたかも分離されたような挙動を示し、構造物と地盤（基礎）を絶縁する役割を果たしている。
【０００３】
この滑り支承の摩擦を評価するための方法として、従来、以下に述べる荷重・速度・繰り返しに関する第１の評価方法と、静摩擦・動摩擦に関する第２の評価方法が知られている。
【０００４】
［第１の評価方法］
滑り材には、低摩擦、低摩耗、高強度などの特徴を有しかつ化学的に安定した材料が用いられるが、滑り材として頻繁に使用されるＰＴＦＥ（ポリ四フッ化エチレン）などの高分子材料の場合、摩擦係数は荷重と速度に依存する傾向が認められる他、往復運動の繰り返しに伴う摩擦係数の変化、すなわち繰り返し依存性を持つことが知られている。これらの荷重・速度・繰り返しに関する依存性は、従来、各影響因子を独立に評価するのが一般的で、各影響因子の変動幅に対応する摩擦係数（摩擦力）の変化量をばらつきとして考慮し、設計に用いることが多い。
【０００５】
［第２の評価方法］
滑り支承が停止状態から滑り状態に移行する際、支承に作用する摩擦力が瞬間的に大きくなり、その後滑り状態が続くと摩擦力が次第に安定するといった現象が滑り支承の載荷実験により確認されており、前者は静摩擦、後者は動摩擦に相当する現象と考えられる。すべり支承を適用した構造物の時刻歴応答解析において滑り状態の摩擦力を想定する際には、従来、常に動摩擦状態を仮定するか、または滑り開始時（ｔ＝０）のみ静摩擦としてその直後の計算時刻点（ｔ＝Δｔ）以降は動摩擦状態を仮定するのが一般的である。
【０００６】
【発明が解決しようとする課題】
［第１の評価方法について］
地震時において滑り状態にある滑り支承では、速度・荷重が非定常に変動する他、非定常的に繰り返し往復載荷を受けるため、摩擦係数（摩擦力）の変化は相当に複雑なものとなる。したがって、滑り支承を適用した免震構造物について地震応答解析により時々刻々の応答を精度良く評価するためには、滑り状態下の摩擦係数を荷重・速度・繰り返しの各状態量より推定する必要がある。
【０００７】
［第２の評価方法について］
弾性すべり支承の実験結果より、静摩擦状態から動摩擦状態に至る摩擦力の遷移過程をみると、図６に示されているように、ある時間をかけて連続的かつ滑らかに移行する傾向がみられる。
【０００８】
一方、滑り開始時（ｔ＝０）および滑り開始後（ｔ≧Δｔ）における静摩擦係数、動摩擦係数の予測値をμ_ｓ、μ_ｄとすれば、一般に
【数１】

となるので、ある時刻における摩擦係数がμ_ｓ、μ_ｄのうちいずれか一方の値をとるものとすれば、停止状態（ｔ＝０）から滑り状態（ｔ＝Δｔ）に移る瞬間、図７に示されているように、摩擦係数の予測値はμ_ｓからμ_ｄに瞬時に移行され、評価摩擦力は急変することになる。μ_ｓおよびμ_ｄがともに時刻ｔに依存する場合も、
【数２】

の関係があるので、同様の問題が生じる。
【０００９】
本発明の目的は、滑り支承の摩擦を、実際の滑り状態に近づけて評価でき、評価精度の向上を図ることができる滑り支承の摩擦評価方法を提供するところにある。
【００１０】
【課題を解決するための手段】
本発明に係る第１の滑り支承の摩擦評価方法は、滑り状態にある滑り支承の摩擦を評価する方法であって、任意の時刻における摩擦係数または摩擦力の予測値を、荷重と速度と繰り返し指標との関数形として表現することを特徴とするものである。
【００１１】
すなわち、この滑り支承の摩擦評価方法では、滑り状態にある滑り支承の任意の時刻における摩擦係数または摩擦力の予測値が、荷重と速度と繰り返し指標との関数形として表現されることになり、この予測値に基づき滑り支承の摩擦の評価を行う。
【００１２】
この滑り支承の摩擦評価方法において、定常滑り状態にある滑り支承については、前記繰り返し指標として、繰り返し回数を用いることができる。また、定常滑り状態にある滑り支承と非定常滑り状態にある滑り支承について、繰り返し指標は、相手部材との間で滑りが生じている部材である滑り材または滑り板の表面温度でもよく、滑り始めからの累積滑り変位でもよい。
【００１３】
本発明に係る第２の滑り支承の摩擦評価方法は、停止と滑りを繰り返す滑り支承の摩擦を評価する方法であって、停止状態から滑り状態に移る過程の摩擦係数または摩擦力を、静摩擦係数および動摩擦係数の評価式に重み関数を適用して、滑り始めからの時刻に関して連続的に表現することを特徴とするものである。
【００１４】
すなわち、この滑り支承の摩擦評価方法では、停止と滑りを繰り返す滑り支承の摩擦を評価するにあたり、先ず、停止状態から滑り状態に移る過程の摩擦係数または摩擦力を、静摩擦係数および動摩擦係数の評価式に重み関数を適用して、滑り始めからの時刻に関して連続的に表現する。この後、これらの摩擦係数または摩擦力に基づき滑り支承の摩擦についての評価を行う。
【００１５】
以上の本発明に係る滑り支承の摩擦評価方法は、各種の用途に用いることができる。その一例は、建物や橋梁等の構造物に適用される滑り支承式免震装置の性能試験時に、滑り支承の摩擦を正確に把握（算出）し、免震装置の動特性を表現する力学モデルの構築に用いることである。また、他の例は、滑り支承式免震装置が実際に適用された既設の構造物に地震等による揺れが生じたときに、その揺れの大きさを正確に算出するために用いることである。
【００１６】
【発明の実施の形態】
［第１の実施形態］
この実施形態は、建物や橋梁等の構造物と地盤（基礎）との間に配置される滑り支承に適用され、この滑り支承は、ＰＴＦＥ等による滑り面を有する支承材と、ステンレス等による滑り材または滑り板とにより形成される。
【００１７】
この実施形態では、滑り状態下の摩擦係数を予め、滑り始めからの時刻ｔにおける各支承の摩擦係数μ（ｔ）を、荷重Ｎ（ｔ）と速度ｖ（ｔ）と繰り返し指標Ｒ（ｔ）の関数形として次式のように表現する。
【数３】

Ｒ（ｔ）は繰り返しの進行度を数値化した指標である。荷重Ｎ（ｔ）は、滑り支承面に直角に作用する荷重で、速度ｖ（ｔ）は、滑り支承面と平行方向の滑り速度である。この（１）式により各時刻ステップで摩擦係数を予測することが出来る。また、（１）式の両辺に荷重Ｎ（ｔ）を乗ずれば摩擦力の定式となる。（１）式はまた、荷重Ｎ（ｔ）を支承のみかけ面積Ａで除したみかけの面圧σ（ｔ）を用いて
【数４】

のように表現してもよい。（１）式または（１）’式は実測データの重回帰分析により経験式として得ることができる。
【００１８】
（繰り返し指標としての繰り返し回数の使用）
滑り変位が振幅一定の定常波（たとえば正弦波や三角波など）である場合に限定すれば、同条件下の摩擦係数を表す場合、（１）、（１）’式の繰り返し指標Ｒ（ｔ）として繰り返しサイクル数ｎ（ｔ）を用いることができる。すなわち、
【数５】

【数６】

（繰り返し指標としての温度の使用）
滑り状態が継続する場合、滑り材表面はクローン摩擦により温度上昇を始める。滑り材料や摩擦係数、支承およびその周辺の伝熱性が等しいものとすれば、（１）、（１）’式の繰り返し指標Ｒ（ｔ）として滑り材表面温度または滑り板表面温度Ｔ（ｔ）を用いることができる。すなわち、
【数７】

【数８】

これらの（３）、（３）’式は地震動が作用する場合など、非定常な載荷に対しても適用可能である。
【００１９】
（繰り返し指標としての累積滑り変位量の利用）
実際には、滑り材表面の正確な温度測定は難しいことから、（３）、（３）’式を温度Ｔ（ｔ）に関する回帰分析から求めることには困難を伴う。また、摩擦熱による滑り材の温度上昇率は荷重Ｎ、速度ｖ、摩擦係数μの積に比例するが、実際の温度上昇は摺動部分の伝熱性にも依存するので温度Ｔ（ｔ）を与条件として定めることも難しい。
【００２０】
しかし、滑り状態が継続する場合、摩擦熱の総量Ｑは摩擦の総仕事量に比例する。即ち、
【数９】

が成立する。ここに、Ｓ（ｔ）は、滑り始めから時刻ｔまでの累積滑り変位である。
【００２１】
従って、荷重・摩擦係数・摺動部分の伝熱性が同等とみなせる場合、時刻ｔにおける各支承の摩擦係数μ（ｔ）は、（３）、（３）’式および（４）式より
【数１０】

【数１１】

となり、摩擦係数μ（ｔ）を、荷重（またはみかけの面圧）と速度と累積滑り変位という力学的に明確な物理量で表現することができる。
【００２２】
（実施例）
以下に、面圧一定のもとで行った滑り支承の往復連続載荷試験結果について、繰り返し指標を取り入れて滑り支承の摩擦を評価した実施例を示す。
【００２３】
（２）’式、（３）’式、（５）’式について、標準面圧σ_０を用いて以下のように変形する。
【数１２】

【数１３】

【数１４】

ここに、αは、面圧の変化に伴う摩擦係数の増減係数で、α（σ＝σ_０）＝１となる。ｈ_ｎ（またはｈ_Ｔ、ｈ_Ｓ）について適当な関数を仮定し、ｎ（ｔ）（またはＴ（ｔ）、Ｓ（ｔ））およびｖ（ｔ）を変数とする重回帰分析を行うことで、速度と繰り返し指標に関する摩擦係数の近似式を得ることができる。
【００２４】
以下に、模型支承の載荷試験による摩擦係数の回帰結果から、（６）〜（８）式に相当する近似式を求めた例を示す。試験データは、滑り面にＰＴＦＥ材を使用した直径１５０ｍｍの弾性滑り支承材と滑り板（ステンレス製）について、面圧９．８Ｎ／ｍｍ^２（鉛直荷重１７３ｋＮ）のもとで往復連続載荷試験を行い、各繰り返しサイクル毎の摩擦係数（動摩擦係数の平均値）を求めたものである。図１は速度ｖ−摩擦係数μの関係、図２は繰り返しサイクル数ｎ−摩擦係数μの関係、図３はすべり材表面温度Ｔ−摩擦係数μの関係、図４は累積すべり変位Ｓ−摩擦係数μの関係関係をそれぞれ示している。これらの図中に示す回帰曲線は、ｎ（またはＴ、Ｓ）およびｖを変数とする重回帰分析により求められた以下の近似式による値である。
【数１５】

【数１６】

【数１７】

面圧９．８Ｎ／ｍｍ^２における摩擦係数μの近似式（９）〜（１１）は、速度および繰り返し指標の変動に伴う摩擦係数の変化を良く捉えている。これらの近似式により、同支承の摩擦係数を任意の速度、繰り返しサイクル数、滑り材温度に対して求めることが出来る。
【００２５】
［第２の実施形態］
この実施形態も、建物や橋梁等の構造物と地盤（基礎）との間に配置される滑り支承に適用され、この滑り支承は、ＰＴＦＥ等による滑り面を有する支承材と、ステンレス等による滑り材または滑り板とにより形成される。
前述の発明が解決しようとする課題の［第２の評価方向について］で述べた理由から、予測式上では静摩擦から動摩擦への移行を連続的かつ滑らかに表現する方が実現象との対応が良い。そこでこれを解決するために、滑り変位量ｓを変数とする重み関数Ｗ（ｓ）を導入し、次式で表される修正摩擦係数を定義する（図５参照）。
【数１８】

ここに、ｓは、滑り距離（一旦停止した場合は０にリセットされる）で、ａは、静摩擦保持区間距離である。すなわち、滑り変位量ｓは、滑り支承面と平行方向への移動量である。
【００２６】
重み関数は、０≦Ｗ（ｓ）≦１（０≦ｓ≦ａ）、Ｗ（０）＝１、Ｗ（ａ）＝０を満足する任意の関数とする。
【００２７】
【発明の効果】
本発明によると、滑り支承の摩擦を、実際の滑り状態に近づけて評価でき、評価精度の向上を図ることができるという効果を得られる。
【図面の簡単な説明】
【図１】本発明の第１の実施形態に関する載荷試験結果に係る速度ｖ−摩擦係数μの関係を示した図である。
【図２】同載荷試験結果に係る繰り返しサイクル数ｎ−摩擦係数μの関係を示した図である。
【図３】同載荷試験結果に係るすべり材表面温度Ｔ−摩擦係数μの関係を示した図である。
【図４】同載荷試験結果に係る累積すべり変位Ｓ−摩擦係数μの関係を示した図である。
【図５】本発明の第２の実施形態に関する摩擦力の表現を示した図である
【図６】静摩擦力から動摩擦力への遷移過程を示した図である。
【図７】静摩擦から動摩擦へ瞬時に移行されたときに評価摩擦力が急変することを示した図である。[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a method for evaluating the friction of a sliding bearing for a seismic isolation device used for a structure such as a building or a bridge.
[0002]
[Prior art]
Sliding bearings, which are used as seismic isolation means for structures such as buildings and bridges, use the low coefficient of friction of the sliding material to behave as if the bearing material and the sliding material are separated from each other. Plays the role of insulating).
[0003]
Conventionally, as a method for evaluating the friction of the sliding bearing, a first evaluation method for load, speed, and repetition and a second evaluation method for static friction and dynamic friction described below are known.
[0004]
[First evaluation method]
As the sliding material, a material having characteristics such as low friction, low wear, and high strength and being chemically stable is used, but high sliding materials such as PTFE (polytetrafluoroethylene) which is frequently used as the sliding material are used. In the case of molecular materials, it is known that the friction coefficient tends to depend on the load and the speed, and that the friction coefficient changes due to repetition of reciprocating motion, that is, it has repetition dependence. Conventionally, these dependencies regarding load, speed, and repetition are generally evaluated independently for each influential factor, and the amount of change in the friction coefficient (friction force) corresponding to the fluctuation range of each influential factor is considered as a variation. They are often used for design.
[0005]
[Second evaluation method]
When the sliding bearing shifts from the stopped state to the sliding state, the frictional force acting on the bearing increases instantaneously, and then the frictional force gradually stabilizes as the sliding state continues. The former is considered to be a phenomenon corresponding to static friction, and the latter is a phenomenon corresponding to dynamic friction. Conventionally, when assuming a frictional force in a sliding state in a time history response analysis of a structure to which a sliding bearing is applied, a dynamic frictional state is always assumed, or static friction is assumed only at the start of sliding (t = 0). After the calculation time point (t = Δt), it is general to assume a dynamic friction state.
[0006]
[Problems to be solved by the invention]
[About the first evaluation method]
In a sliding bearing that is in a sliding state during an earthquake, the speed and load fluctuate unsteadily, and also undergo repetitive reciprocal loading in an unsteady manner, so that the change in friction coefficient (friction force) is considerably complicated. Therefore, in order to accurately evaluate the moment-to-moment response of seismically isolated structures to which sliding bearings are applied by seismic response analysis, it is necessary to estimate the friction coefficient under sliding conditions from the load, speed, and repetitive state quantities. is there.
[0007]
[About the second evaluation method]
From the experimental results of the elastic sliding bearing, the transition process of the frictional force from the static frictional state to the dynamic frictional state shows that the transition tends to be continuous and smooth over a period of time, as shown in FIG. .
[0008]
On the other hand, if the predicted values of the static friction coefficient and the dynamic friction coefficient at the start of sliding (t = 0) and after the start of sliding (t ≧ Δt) are μ _s and μ _d , generally

Since the, if the friction coefficient at a time mu _s, and shall take one of the values of mu _d, instant move the sliding state (t = Δt) from the stop state (t = 0), FIG. 7 as shown in, the predicted value of the friction coefficients are migrated instantaneously mu _d from mu _s, so that the evaluation frictional force is suddenly changed. When both μ _s and μ _d depend on time t,
(Equation 2)

A similar problem arises.
[0009]
SUMMARY OF THE INVENTION An object of the present invention is to provide a method of evaluating friction of a sliding bearing, which can evaluate the friction of the sliding bearing close to an actual sliding state and can improve the evaluation accuracy.
[0010]
[Means for Solving the Problems]
The first method for evaluating the friction of a sliding bearing according to the present invention is a method for evaluating the friction of a sliding bearing in a sliding state, in which a predicted value of a friction coefficient or a frictional force at an arbitrary time is repeated with a load and a speed. It is characterized by being expressed as a function form with an index.
[0011]
That is, in the friction evaluation method of the sliding bearing, the predicted value of the friction coefficient or the frictional force at any time of the sliding bearing in the sliding state is expressed as a function form of the load, the speed, and the repetition index. The friction of the sliding bearing is evaluated based on the predicted value.
[0012]
In this method for evaluating the friction of a sliding bearing, the number of repetitions can be used as the repetition index for the sliding bearing in a steady sliding state. In addition, for a sliding bearing in a steady sliding state and a sliding bearing in an unsteady sliding state, the repetition index may be a surface temperature of a sliding material or a sliding plate that is a member that is slipping with a partner member, The cumulative slip displacement from the beginning may be used.
[0013]
A second method for evaluating the friction of a sliding bearing according to the present invention is a method for evaluating the friction of a sliding bearing that repeatedly stops and slides, and calculates a friction coefficient or a frictional force in a process of shifting from a stopped state to a sliding state by using a static friction coefficient. In addition, a weighting function is applied to the evaluation formula of the dynamic friction coefficient, and the time from the start of slipping is continuously expressed.
[0014]
That is, in this method of evaluating the friction of a sliding bearing, in evaluating the friction of a sliding bearing that repeatedly stops and slides, first, a friction coefficient or a frictional force in a process of shifting from a stopped state to a sliding state is evaluated by a static friction coefficient and a dynamic friction coefficient. A weighting function is applied to the expression to continuously express the time from the start of slipping. Thereafter, the friction of the sliding bearing is evaluated based on the friction coefficient or the frictional force.
[0015]
The above-described method for evaluating friction of a sliding bearing according to the present invention can be used for various applications. One example is a dynamic model that accurately grasps (calculates) the friction of a sliding bearing and expresses the dynamic characteristics of the seismic isolating device during the performance test of the sliding bearing type seismic isolation device applied to structures such as buildings and bridges. It is used for construction. Another example is to use a slip-bearing type seismic isolation device to accurately calculate the magnitude of the shaking when the shaking due to an earthquake or the like occurs in an existing structure actually applied. .
[0016]
BEST MODE FOR CARRYING OUT THE INVENTION
[First Embodiment]
This embodiment is applied to a sliding bearing disposed between a structure such as a building or a bridge and the ground (foundation). The sliding bearing includes a bearing material having a sliding surface such as PTFE and a sliding material such as stainless steel. It is formed by a material or a sliding plate.
[0017]
In this embodiment, the friction coefficient under the sliding state is determined in advance, and the friction coefficient μ (t) of each bearing at the time t from the start of sliding is determined by the load N (t), the speed v (t), and the repetition index R (t). Is expressed as the following equation.
[Equation 3]

R (t) is an index that quantifies the degree of progress of repetition. The load N (t) is a load acting at right angles to the sliding bearing surface, and the speed v (t) is a sliding speed in a direction parallel to the sliding bearing surface. The coefficient of friction can be predicted at each time step by the equation (1). Further, by multiplying both sides of the equation (1) by the load N (t), a formula of the frictional force is obtained. Equation (1) also uses the apparent surface pressure σ (t) obtained by dividing the load N (t) by the apparent area A of the bearing.

It may be expressed as follows. Equation (1) or (1) ′ can be obtained as an empirical equation by multiple regression analysis of the measured data.
[0018]
(Use of repetition count as repetition index)
If it is limited to the case where the slip displacement is a stationary wave having a constant amplitude (for example, a sine wave or a triangular wave), when the friction coefficient under the same condition is represented, the repetition index R (t) of the equations (1) and (1) ′ is used. The number of repetition cycles n (t) can be used. That is,
(Equation 5)

(Equation 6)

(Use of temperature as repetition index)
If the sliding condition continues, the surface of the sliding material starts to increase in temperature due to the clonal friction. Assuming that the sliding material, the coefficient of friction, the bearing and the heat transfer around it are equal, the repetition index R (t) of the formulas (1) and (1) ′ is the sliding material surface temperature or the sliding plate surface temperature T (t). Can be used. That is,
(Equation 7)

(Equation 8)

These equations (3) and (3) ′ can be applied to an unsteady load such as when a seismic motion is applied.
[0019]
(Use of cumulative slip displacement as a repetition index)
In practice, it is difficult to accurately measure the temperature of the surface of the sliding material, so that it is difficult to obtain the equations (3) and (3) ′ from the regression analysis on the temperature T (t). The rate of temperature rise of the sliding material due to frictional heat is proportional to the product of the load N, the speed v, and the friction coefficient μ. However, since the actual temperature rise also depends on the heat conductivity of the sliding portion, the temperature T (t) is reduced. It is also difficult to determine the conditions.
[0020]
However, when the sliding state continues, the total amount of frictional heat Q is proportional to the total amount of frictional work. That is,
(Equation 9)

Holds. Here, S (t) is the cumulative slip displacement from the start of slip to time t.
[0021]
Therefore, when the load, the coefficient of friction, and the heat conductivity of the sliding portion can be considered to be equivalent, the friction coefficient μ (t) of each bearing at time t is expressed by the following equation from the equations (3), (3) ′ and (4). 10)

[Equation 11]

Thus, the friction coefficient μ (t) can be expressed by mechanically clear physical quantities such as load (or apparent surface pressure), speed, and cumulative slip displacement.
[0022]
(Example)
The following shows an example in which the friction of the sliding bearing was evaluated by incorporating a repetition index with respect to the reciprocating continuous loading test result of the sliding bearing performed under a constant surface pressure.
[0023]
Equations (2) ′, (3) ′, and (5) ′ are modified as follows using the standard surface pressure σ ₀ .
(Equation 12)

(Equation 13)

[Equation 14]

Here, α is an increase / decrease coefficient of the friction coefficient due to a change in the surface pressure, and α (σ = σ ₀ ) = 1. h _n (or _{_h} T, _h _S) assumes an appropriate function for, n (t) by performing a multiple regression analysis that a variable (or T (t), S (t )) and v (t) , An approximate expression of the coefficient of friction with respect to speed and repetition index can be obtained.
[0024]
The following shows an example in which an approximate expression corresponding to the expressions (6) to (8) is obtained from the regression result of the friction coefficient by the loading test of the model bearing. The test data shows a continuous reciprocating loading test of a 150 mm diameter elastic sliding support and a sliding plate (made of stainless steel) using PTFE material on the sliding surface under a surface pressure of 9.8 N / mm ² (vertical load 173 kN). The coefficient of friction (average value of the coefficient of dynamic friction) for each repetition cycle was obtained. FIG. 1 shows the relationship between the speed v and the friction coefficient μ, FIG. 2 shows the relationship between the number of repetition cycles n and the friction coefficient μ, FIG. 3 shows the relationship between the sliding material surface temperature T and the friction coefficient μ, and FIG. The relationship between the coefficients μ is shown. The regression curves shown in these figures are values obtained by the following approximate expression obtained by multiple regression analysis using n (or T, S) and v as variables.
[Equation 15]

(Equation 16)

[Equation 17]

The approximate expressions (9) to (11) of the friction coefficient μ at the surface pressure of 9.8 N / mm ² well capture the change in the friction coefficient due to the change in the speed and the repetition index. From these approximate expressions, the friction coefficient of the bearing can be determined for any speed, number of repetition cycles, and slip material temperature.
[0025]
[Second embodiment]
This embodiment is also applied to a sliding bearing arranged between a structure such as a building or a bridge and the ground (foundation), and the sliding bearing includes a bearing material having a sliding surface made of PTFE or the like and a sliding material made of stainless steel or the like. It is formed by a material or a sliding plate.
For the reason described in [Second Evaluation Direction] of the problem to be solved by the above-described invention, it is better to express the transition from static friction to dynamic friction continuously and smoothly in the prediction formula in correspondence with the actual phenomenon. good. Therefore, in order to solve this, a weighting function W (s) having the slip displacement s as a variable is introduced, and a modified friction coefficient represented by the following equation is defined (see FIG. 5).
(Equation 18)

Here, s is a sliding distance (if stopped once, it is reset to 0), and a is a static friction holding section distance. That is, the sliding displacement s is a moving amount in a direction parallel to the sliding bearing surface.
[0026]
The weight function is an arbitrary function that satisfies 0 ≦ W (s) ≦ 1 (0 ≦ s ≦ a), W (0) = 1, and W (a) = 0.
[0027]
【The invention's effect】
ADVANTAGE OF THE INVENTION According to this invention, the frictional friction of a sliding bearing can be evaluated by approaching an actual sliding state, and the effect that the evaluation precision can be improved can be obtained.
[Brief description of the drawings]
FIG. 1 is a diagram showing a relationship between a speed v and a friction coefficient μ according to a load test result according to the first embodiment of the present invention.
FIG. 2 is a diagram showing the relationship between the number of repetition cycles n and the friction coefficient μ according to the results of the loading test.
FIG. 3 is a view showing a relationship between a sliding material surface temperature T and a friction coefficient μ according to the loading test result.
FIG. 4 is a diagram showing a relationship between the cumulative slip displacement S and the friction coefficient μ according to the loading test result.
FIG. 5 is a diagram showing a representation of a frictional force according to a second embodiment of the present invention. FIG. 6 is a diagram showing a transition process from a static frictional force to a dynamic frictional force.
FIG. 7 is a diagram showing that the evaluation frictional force changes suddenly when the state is instantaneously shifted from static friction to dynamic friction.

Claims

A method for evaluating the friction of a sliding bearing, wherein a predicted value of a friction coefficient or a frictional force at an arbitrary time is expressed as a function form of a load, a speed, and a repetition index. .

2. The friction evaluation method for a sliding bearing according to claim 1, wherein the number of repetitions is used as the repetition index for the sliding bearing in a steady sliding state.

The friction evaluation method for a sliding bearing according to claim 1, wherein a surface temperature of a sliding material or a sliding plate is used as the repetition index.

2. The friction evaluation method for a sliding bearing according to claim 1, wherein a cumulative sliding displacement from the start of sliding is used as the repetition index.

A method of evaluating the friction of a sliding bearing, in which a weighting function is applied to a frictional coefficient or a frictional force in a process of shifting from a stopped state to a sliding state to a static friction coefficient and a dynamic friction coefficient evaluation formula, and the time from the start of sliding is calculated. A friction evaluation method for a sliding bearing characterized by being continuously expressed.