﻿ 厚层铅芯橡胶支座力学性能
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (9): 1189-1194, 1233.  DOI: 10.11908/j.issn.0253-374x.2018.09.005 0

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ZHU Yuhua, AI Fangliang, REN Xiangxiang, LU Wensheng. Mechanical Properties of Thick Lead-Rubber Bearings[J]. Journal of Tongji University (Natural Science), 2018, 46(9): 1189-1194, 1233. DOI: 10.11908/j.issn.0253-374x.2018.09.005

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Mechanical Properties of Thick Lead-Rubber Bearings
ZHU Yuhua , AI Fangliang , REN Xiangxiang , LU Wensheng
College of Civil Engineering, Tongji University, Shanghai 200092, China
Abstract: Three kinds of thick lead-rubber bearings(TLRB) with different thicknesses of rubbers were designed in this paper. The basic mechanical properties of the TLRB were studied through mechanical properties test, such as vertical stiffness, equivalent horizontal stiffness, post-yield stiffness, yield shear force, and equivalent damping ratio. The effects of pressure stress and shear strain on mechanical properties of TLRB were studied. The comparison of mechanical properties between test and formula were analyzed. It is concluded that the difference of vertical stiffness of TLRB between test and formula is apparent and the difference is increasing as the thickness of rubber increases. The fitting formula of vertical stiffness about test was given, and the effect of fitting was satisfying. Because of the limit of samples, the applicability of the fitting formula should be checked in future work. The test value of horizontal properties of TLRB are similar to the formula value.
Key words: thick lead-rubber bearings    mechanical properties    vertical stiffness    horizontal properties    fitting formula

1 试验装置及试件

 图 1 压剪试验装置 Fig.1 The test machine

2 试验方法

 ${K_{\rm{V}}} = ({P_2} - {P_1})/({Y_2} - {Y_1})$ (1)

 ${K_{\rm{h}}} = ({Q_1} - {Q_2})/({X_1} - {X_2})$ (2)
 ${K_{\rm{d}}} = [({Q_1}-{Q_{{\rm{d1}}}})/{X_1} + ({Q_2}-{Q_{{\rm{d2}}}})/{X_2}]/2$ (3)
 ${Q_{\rm{d}}} = ({Q_{{\rm{d1}}}} - {Q_{{\rm{d2}}}})/2$ (4)
 ${\xi _{{\rm{eq}}}} = 2\Delta W/[\pi {K_{\rm{h}}}{({X_1}-{X_2})^2}]$ (5)

3 试验结果 3.1 竖向刚度的压应力相关性

 图 2 TLRB -1支座竖向刚度试验结果 Fig.2 Test result of vertical stiffness of TLRB -1

TLRB-1、TLRB-2、TLRB-3在压应力分别为2、3、4、5、6 MPa时的竖向刚度KV的试验值见表 2.

3.2 水平性能的剪应变相关性

 图 3 TLRB -1支座的水平滞回曲线(σ0=4 MPa) Fig.3 Hysteresis loops of TLRB -1 (σ0=4 MPa)
 图 4 水平等效刚度随剪应变变化曲线(σ0=4 MPa) Fig.4 Equivalent horizontal stiffness versus shearing strain(σ0=4 MPa)
 图 5 屈服后刚度随剪应变变化曲线(σ0=4 MPa) Fig.5 Post-yield stiffness versus shearing strain (σ0=4 MPa)
 图 6 屈服剪力随剪应变变化曲线(σ0=4 MPa) Fig.6 Yield shear forces versus shearing strain (σ0=4 MPa)
 图 7 等效阻尼比随剪应变变化曲线(σ0=4 MPa) Fig.7 Equivalent damping ratios versus shearing strain (σ0=4 MPa)

3.3 水平性能的压应力相关性

 图 8 TLRB -1支座的水平滞回曲线(γ=100%) Fig.8 Hysteresis loops of TLRB -1(γ=100%)
 图 9 水平等效刚度随压应力变化曲线(γ=100%) Fig.9 Equivalent horizontal stiffness versus pressure stress(γ=100%)
 图 10 屈服后刚度随压应力变化曲线(γ=100%) Fig.10 Post-yield stiffness versus pressure stress (γ=100%)
 图 11 屈服剪力随压应力变化曲线(γ=100%) Fig.11 Yield shear forces versus pressure stress (γ=100%)
 图 12 等效阻尼比随压应力变化曲线(γ=100%) Fig.12 Equivalent damping ratios versus pressure stress(γ=100%)

4 试验结果与理论公式比较 4.1 竖向刚度的比较

 ${K_{\rm{V}}} = {E_{{\rm{cb}}}}A/n{\rm{ }}{t_{\rm{r}}}$ (6)
 ${E_{{\rm{cb}}}} = {E_{\rm{c}}}{E_{\rm{b}}}/({E_{\rm{c}}} + {E_{\rm{b}}})$ (7)
 ${E_{\rm{c}}} = {E_0}(1 + 2\kappa S_1^2)$ (8)

TLRB支座所使用的橡胶材料的剪切模量G=0.42 MPa，κ=0.862，Eb=1 960 MPa，可求得TLRB支座竖向刚度的理论值，其与试验值的对比见表 3.

 ${K_{\rm{V}}} = C{\rm{ }}{E_{{\rm{cb}}}}A/n{\rm{ }}{t_{\rm{r}}}$ (9)

 $C = 0.28({\sigma _0}/\sigma ) - 0.09{S_1} + 2.45$ (10)

 图 13 TLRB支座竖向刚度随压应力变化曲线 Fig.13 Vertical stiffness of TLRB versus test and fitting

4.2 水平性能的比较

 ${K_{\rm{h}}} = {K_{\rm{d}}} + {Q_{\rm{d}}}/\gamma {T_{\rm{r}}}$ (11)
 ${K_{\rm{d}}} = (G{A_{\rm{r}}} + \alpha {A_{\rm{p}}})/{T_{\rm{r}}}$ (12)
 ${Q_{\rm{d}}} = {\sigma _{{\rm{pb}}}}{A_{\rm{p}}}$ (13)

TLRB支座在压应力为4 MPa时，剪应变γ=100%时的水平等效刚度Kh、屈服后刚度Kd的试验值与公式计算值的对比见表 4.

5 结论

(1) TLRB支座在竖向压缩试验中产生较大的竖向位移，使得支座在竖向压力作用下具有一定的阻尼特性.

(2) TLRB支座的竖向刚度随压应力的增大呈减小的趋势，单层橡胶越厚，竖向刚度越小.采用现有竖向刚度计算公式计算TLRB支座的竖向刚度时，需进行修正，给出的竖向刚度拟合公式效果较好.

(3) TLRB支座的水平等效刚度、屈服后刚度、等效阻尼比均随剪应变的增大而减小；随压应力的增大，水平等效刚度、屈服后刚度随之减小，而等效阻尼比逐渐增大；TLRB支座的屈服力主要和铅芯直径相关，与剪应变和压应力的相关性不大.

(4) 现有普通铅芯橡胶支座水平性能的计算公式应用于厚层铅芯橡胶支座时存在一定的误差，其适用性有待进一步研究.在橡胶总厚度一定的情况下，单层橡胶厚度的变化对支座水平性能的影响较小.

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