JP4251532B2 - Friction evaluation method of sliding bearing - Google Patents

Description

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滑り始めからの時刻ｔにおける荷重で、速度ｖ（ｔ）は、滑り支承面と平行方向の滑り始めからの時刻ｔにおける滑り速度である。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σ₀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＝σ₀）＝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、累積滑り変位量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の評価方法について］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]
BACKGROUND OF THE INVENTION
The present invention relates to a method for evaluating the friction of sliding bearings for seismic isolation devices used in structures such as buildings and bridges.
[0002]
[Prior art]
Sliding bearings used as a means of seismic isolation for structures such as buildings and bridges use the low friction coefficient of sliding materials to behave as if the bearing materials and sliding materials are separated. Play a role in insulating).
[0003]
Conventionally, as a method for evaluating the friction of the sliding bearing, a first evaluation method relating to load, speed, and repetition described below and a second evaluation method relating to static friction and dynamic friction are known.
[0004]
[First Evaluation Method]
As the sliding material, a material having characteristics such as low friction, low wear, and high strength and chemically stable is used. However, a high material such as PTFE (polytetrafluoroethylene) frequently used as the sliding material is used. In the case of molecular materials, it is known that the coefficient of friction tends to depend on the load and speed, and that the coefficient of friction changes with repetition of reciprocating motion, that is, has a dependency on repetition. Conventionally, the dependency on load, speed, and repetition has been generally evaluated independently, and the amount of change in the friction coefficient (friction force) corresponding to the fluctuation range of each influence factor is considered as variation. However, it is often used for design.
[0005]
[Second evaluation method]
When a sliding bearing transitions from a stopped state to a sliding state, a frictional force acting on the bearing momentarily increases, and a phenomenon that the frictional force gradually stabilizes after the sliding state is confirmed by a sliding bearing loading experiment. The former is considered to be a phenomenon equivalent to static friction and the latter to dynamic friction. 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, conventionally, a dynamic friction state is always assumed, or a static friction immediately after the start of sliding (t = 0) Generally, a dynamic friction state is assumed after the calculation time point (t = Δt).
[0006]
[Problems to be solved by the invention]
[About the first evaluation method]
In a sliding bearing that is in a sliding state at the time of an earthquake, the speed and load fluctuate unsteadyly and receive repeated reciprocating loadings unsteadily, so the change of the friction coefficient (friction force) becomes considerably complicated. Therefore, in order to accurately evaluate the momentary response of seismic isolation structures to which sliding bearings are applied by seismic response analysis, it is necessary to estimate the friction coefficient under sliding conditions from load, speed, and repeated state quantities. is there.
[0007]
[About the second evaluation method]
From the experimental results of the elastic sliding bearing, when looking at the transition process of the frictional force from the static friction state to the dynamic friction state, as shown in FIG. 6, there is a tendency to transition continuously and smoothly over a period of time. .
[0008]
On the other hand, if the predicted values of the static friction coefficient and the dynamic friction coefficient at the start of slip (t = 0) and after the start of slip (t ≧ Δt) are μ _s and μ _d , respectively,

Therefore, if the coefficient of friction at a certain time is one of μ _s and μ _d , the moment of transition from the stop state (t = 0) to the slip state (t = Δt), FIG. As shown in FIG. 5, the predicted value of the friction coefficient is instantaneously shifted from μ _s to μ _d , and the evaluated friction force changes suddenly. If both μ _s and μ _d depend on time t,
[Expression 2]

Therefore, the same problem arises.
[0009]
An object of the present invention is to provide a friction evaluation method for a sliding bearing that 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]
A friction evaluation method for a first sliding bearing according to the present invention is a method for evaluating the friction of a sliding bearing in a sliding state, wherein 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 this sliding bearing friction evaluation method, the predicted value of the friction coefficient or friction force at an arbitrary time of the sliding bearing in the sliding state is expressed as a function form of load, speed, and repetition index. The friction of the sliding bearing is evaluated based on this predicted value.
[0012]
In this sliding bearing friction evaluation method, the number of repetitions can be used as the repetition index for the sliding bearing in a steady sliding state. In addition, for sliding bearings in a steady sliding state and sliding bearings in an unsteady sliding state, the repetition index may be the surface temperature of a sliding material or sliding plate that is a member that has slipped with the counterpart member. Cumulative sliding displacement from the beginning may be used.
[0013]
A second sliding bearing friction evaluation method according to the present invention is a method for evaluating the friction of a sliding bearing that repeats stopping and sliding, and the coefficient of friction or the frictional force in the process of moving from the stopped state to the sliding state is expressed by the 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 the slip is expressed continuously.
[0014]
That is, in this friction bearing friction evaluation method, when evaluating the friction of a sliding bearing that repeats stopping and sliding, first, the friction coefficient or friction force in the process of moving from the stopped state to the sliding state is evaluated by the static friction coefficient and the dynamic friction coefficient. A weight function is applied to the equation to continuously express the time from the start of the slip. Thereafter, the friction of the sliding bearing is evaluated based on the friction coefficient or the friction force.
[0015]
The above-described friction evaluation method for sliding bearings according to the present invention can be used for various applications. One example is a mechanical model that accurately understands (calculates) the friction of a sliding bearing and expresses the dynamic characteristics of the seismic isolation device during a performance test of a sliding bearing type seismic isolation device applied to structures such as buildings and bridges. It is used for construction. Another example is to use the sliding support type seismic isolation device to accurately calculate the magnitude of the shaking when an earthquake or the like occurs in an existing structure to which the sliding bearing type seismic isolation device is actually applied. .
[0016]
DETAILED DESCRIPTION OF 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). This sliding bearing is composed of 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 condition is previously determined as the friction coefficient μ (t) of each bearing at the time t from the start of sliding, the load N (t), the speed v (t), and the repetition index R (t). The function form is expressed as follows.
[Equation 3]

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

It may be expressed as The expression (1) or (1) ′ can be obtained as an empirical expression by multiple regression analysis of actually measured data.
[0018]
(Use of repeat count as repeat index)
If the sliding displacement is limited to 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 expressed, the repetition index R (t) of the expressions (1) and (1) ′ is used. The number of repetition cycles n (t) can be used. That is,
[Equation 5]

[Formula 6]

(Use of temperature as a repeat indicator)
When the sliding state continues, the sliding material surface starts to rise in temperature due to clone friction. If the sliding material, the friction coefficient, the bearing and the surrounding heat transfer properties are equal, the sliding material surface temperature or the sliding plate surface temperature T (t) as the repetitive index R (t) of the equations (1) and (1) ′ Can be used. That is,
[Expression 7]

[Equation 8]

These equations (3) and (3) ′ can be applied to unsteady loads such as when earthquake motions act.
[0019]
(Use of cumulative slip displacement as a repeat index)
Actually, since it is difficult to accurately measure the temperature of the sliding material surface, it is difficult to obtain the equations (3) and (3) ′ from the regression analysis with respect to the temperature T (t). Further, the temperature rise rate 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 depends on the heat conductivity of the sliding portion, the temperature T (t) is set. It is also difficult to set as a given condition.
[0020]
However, if the sliding state continues, the total amount of frictional heat Q is proportional to the total amount of frictional work. That is,
[Equation 9]

Is established. Here, S (t) is the cumulative slip displacement from the start of slip to time t.
[0021]
Therefore, when the load, friction coefficient, and heat transferability of the sliding part can be regarded as equivalent, the friction coefficient μ (t) of each bearing at time t is expressed by the following formulas (3), (3) ′ and (4): 10]

[Expression 11]

Thus, the friction coefficient μ (t) can be expressed by a mechanically clear physical quantity 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 is evaluated by incorporating a repeated index with respect to the result of the reciprocating continuous loading test of the sliding bearing performed under a constant surface pressure.
[0023]
The formulas (2) ′, (3) ′, and (5) ′ are modified as follows using the standard surface pressure σ ₀ .
[Expression 12]

[Formula 13]

[Expression 14]

Here, α is an increase / decrease coefficient of the friction coefficient accompanying the change of the surface pressure, and α (σ = σ ₀ ) = 1. By assuming an appropriate function for h _n (or h _T , h _S ) and performing multiple regression analysis with n (t) (or T (t), S (t)) and v (t) as variables Thus, an approximate expression of the friction coefficient regarding the speed and the repetition index can be obtained.
[0024]
Below, the example which calculated | required the approximate expression corresponded to (6)-(8) Formula from the regression result of the friction coefficient by the loading test of a model support is shown. The test data is a reciprocating continuous loading test under a surface pressure of 9.8 N / mm ² (vertical load 173 kN) for a 150 mm diameter elastic sliding bearing material using a PTFE material on the sliding surface and a sliding plate (made of stainless steel). The friction coefficient (average value of the dynamic friction coefficient) for each repeated cycle was obtained. FIG. 1 shows the relationship of speed v−friction coefficient μ, FIG. 2 shows the relationship of the number of repeated cycles n−friction coefficient μ, FIG. 3 shows the relationship of slip material surface temperature T−friction coefficient μ, and FIG. 4 shows the cumulative slip displacement S−friction. It shows relationship coefficient μ, respectively. The regression curves shown in these figures are values according to the following approximate expression obtained by multiple regression analysis using n (or T, S) and v as variables.
[Expression 15]

[Expression 16]

[Expression 17]

The approximate expressions (9) to (11) of the friction coefficient μ at the surface pressure of 9.8 N / mm ² capture well the change of the friction coefficient with the fluctuation of the speed and the repetition index. From these approximate equations, the friction coefficient of the bearing can be obtained for an arbitrary speed, the number of repeated cycles, the sliding material temperature , and the cumulative sliding displacement .
[0025]
[Second Embodiment]
This embodiment is also applied to a sliding bearing disposed between a structure such as a building or a bridge and the ground (foundation). This sliding bearing is composed of a bearing material having a sliding surface such as PTFE and a sliding material made of stainless steel or the like. It is formed by a material or a sliding plate.
Corresponding reasons foregoing invention has been described in the for the second valuation method on the problem to be solved, it is continuously and smoothly express the transition to dynamic friction from static friction on the prediction equation and the actual behavior Is good. In order to solve this problem, a weighting function W (s) with the slip displacement amount s as a variable is introduced, and a corrected friction coefficient expressed by the following equation is defined (see FIG. 5).
[Formula 18]

Here, s is a slip distance (when it stops, it is reset to 0), and a is a static friction holding section distance. That is, the sliding displacement amount s is the amount of movement in the direction parallel to the sliding bearing surface.
[0026]
The weight function is an arbitrary function satisfying 0 ≦ W (s) ≦ 1 (0 ≦ s ≦ a), W (0) = 1, and W (a) = 0.
[0027]
【The invention's effect】
According to the present invention, it is possible to evaluate the friction of the sliding bearing close to the actual sliding state, and it is possible to improve the evaluation accuracy.
[Brief description of the drawings]
FIG. 1 is a diagram showing a relationship of speed v-friction coefficient μ according to a loading test result relating to a first embodiment of the present invention.
FIG. 2 is a diagram showing a relationship of the number of repeated cycles n-friction coefficient μ according to the same loading test result.
FIG. 3 is a diagram 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 of cumulative slip displacement S-friction coefficient μ according to the same loading test result.
FIG. 5 is a diagram showing an expression of frictional force related to the second embodiment of the present invention. FIG. 6 is a diagram showing a transition process from static frictional force to dynamic frictional force.
FIG. 7 is a diagram showing that the evaluation frictional force changes suddenly when an instantaneous transition is made from static friction to dynamic friction.

Claims (5)

A method for evaluating the friction the slip bearing a seismic isolation device used in the structure,
The friction coefficient μ (t) of the sliding bearing at time t from the start of sliding
Expressed as a function form of the load N (t), the speed v (t), and the repetition index R (t) and predicted at each time step ,
The slip friction evaluation method of the bearing Assess friction sliding bearings based on the estimated friction coefficient μ (t). In the friction evaluation method of the sliding bearing of Claim 1,
For a sliding bearing in a steady sliding state, the sliding bearing friction evaluation method is characterized in that a repetition cycle number n (t) is used as the repetition index R (t). In the friction evaluation method of the sliding bearing of Claim 1,
A sliding bearing friction evaluation method using a sliding material surface temperature or a sliding plate surface temperature T (t) as the repetition index R (t). In the friction evaluation method of the sliding bearing of Claim 1,
The sliding bearing friction evaluation method using cumulative sliding displacement S (t) from the beginning of sliding to time t as the repetition index. A method for evaluating the friction the slip bearing a seismic isolation device used in the structure,
Each of the static and dynamic coefficients of friction, a variable sliding displacement amount s to be reset when the stop, in the static friction holding period, the weighting function gradually decreases, the weight functions that are partial incremental polymerization in function is gradually reduced Apply
Predicting the friction coefficient of the process from the stop state to the slip state by continuously expressing the time from the start of the slip ,
The slip friction evaluation method of the bearing Assess friction sliding bearings based on the estimated friction coefficient μ (t).

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