為瞭解隔震支承之真實力學行為，需將其於動態試驗條件下進行分析探討。在試驗系統容量不足的條件下，常採用縮尺方式進行試驗，以便於針對尺寸較大之隔震支承進行性能探討。本研究針對摩擦單擺支承探討合適之縮尺試驗方法，以垂直軸壓及平均水平速率相依性規劃兩者所對應之縮尺試驗條件。
本研究採用雙軸向動態試驗系統，此系統可提供實尺及縮尺摩擦單擺支承於規劃之動態試驗條件下進行試驗。然經由過往研究得知，雙軸向動態試驗系統於進行動態試驗時，具有自身之系統慣性力及摩擦力，對於試驗結果有著不可忽視的影響。故為提升試驗結果之可信度且使其更為直觀，本 研究使用精進與容量提升後之直接量測系統，除了 可以對試體力學行為進行直接量測，有效排除試驗中因試驗系統產生之慣性力與摩擦力 外，更能以超越過往的試驗條件下進行試驗並 在最後 以有限元素分析檢核直接量測系統之容量，以及提出以試驗方法得到其與試體之側向勁度表現。
經由試驗與分析驗證可知，摩擦單擺支承之力學行為受摩擦係數影響甚鉅，其實尺試驗結果可能無法以傳統縮尺試驗結果加以表徵。
過往依據長度 (L)以及時間 (S)為基礎進行縮尺，並無法呈現無單位之摩擦係數之縮尺， 因此本研究參考並整合過往相關研究，提出一描述摩擦單擺支承摩 擦係數的改良分析模型 以對摩擦係數 進行探討，藉由與試驗結果擬合，以出力歷時判定係數與遲滯迴圈面積比為量化指標，識別分析模型之相關參數。將實尺及縮尺分析模型模擬之摩擦係數相除，即可得到摩擦係數之縮尺因子。除考慮垂直軸壓及平均水平速率相依性，亦考慮摩擦係數縮尺因子，針對實尺試驗結果進行調整，以能確切擬合縮尺試驗結果。目前研究結果顯示，若能提供完整描述摩能確切擬合縮尺試驗結果。目前研究結果顯示，若能提供完整描述摩擦單擺支承力學行為之可信分析模型，則仍可利用縮尺試驗結果推估擦單擺支承力學行為之可信分析模型，則仍可利用縮尺試驗結果推估實尺試驗結果，反之，則必須進行實尺試驗以足以表徵其真實力學行實尺試驗結果，反之，則必須進行實尺試驗以足以表徵其真實力學行為。

Donducting full-scale dynamic tests is the only and straight way to fully understand the actual mechanical behavior of isolation bearings. Due to insudfficient capacity of existing testing systems, scale-down dynamic test results are usually adopted correspondingly to assess the dynamic performance of full-scale isolation bearings. This study aims to probe two scale-down test schemes proposed based on similar vertical compressive stress and average horizontal rate assumptions for friction pedulumn bearings.
The dynamic biaxial testing system in National Center for Research on Earthquake Engineering (NCREE) Tainan laboratory is used to test full-scale and scale-down friction pedulumn bearings in this study. For dynamically testing a large-scale specimen, the system inertia force and friction are not negligible and will cause significant error in the force measurement of the specimen. To have a more reliable and intuitive test result, a modified and enhanced measurement system is used to directly capture the force response of the specimen during testing, i.e., to preclude the system inertia force and friction from the force measurement. Finite element analysis is performed to examine the capacity of the designed direct force measurement system. Besides, a methodology is proposed to experimentally obtain the lateral stiffnesses of the direct force measurement system and specimen.
It is analytically and experimentally demonstrated that the mechanical behavior of friction pedulumn bearings greatly depends on the designed friction coefficient. Therefore, it is not easy to characterize the performance of full-scale friction pedulumn bearings using scale-down test results. By refering to some relevant researches, a refined analytical model which can describe the dependency of friction coefficients on some critical parameters is proposed and further discussed. The values of coefficients of determination and energy dissipation ratios are used as quantitative indice to determine the coefficients of the proposed analytical model. Through taking the ratio of predictions by the analytical model identified using full-scale tests to that identified using scale-down tests into account, a scale factor for friction coefficients can be further obtained. With the similar vertical compressive stress and average horizontal rate assumptions as well as the known scale factor for friction coefficients, the calibrated full-scale test results can reproduce the scale-down ones. In summary, full-scale tests for friction pedulumn bearings are necessary and cannot be replaced by scale-down tests unless there is a reliable analytical mode for describing the corresponding friction behavior.

參考文獻
[1]熊思閔，基於直接量測試驗探討鉛心橡膠支承墊之尺寸與溫度效應。2022，國立台灣科技大學營建工程系
[2]Wang, C. L, et al. "Identification of System Parameters of A Large-scale Dynamic Multiaxial Testing Facility." Submited to EESD (https://onlinelibrary.wiley.com/journal/10969845).2023.
[3]林旺春，劉瓊琳，汪向榮，楊卓諺，游忠翰，林晉丞，盧煉元，黃震興，張國鎮，雙軸向動態試驗系統之基本參數研究與探討。(2022).
[4]Zayas, V. A., Low, S. S., & Mahin, S. A. (1990). "A simple pendulum technique for achieving seismic isolation. Earthquake spectra.", 6(2), 317-333.
[5]Hamidi, M., et al. (2003). "Seismic isolation of buildings with sliding concave foundation (SCF)." 32(1): 15-29.
[6]Lomiento, G., et al. (2013). "Friction model for sliding bearings under seismic excitation." 17(8): 1162-1191.
[7]Sextro, W. (2007). "Dynamical contact problems with friction, Springer."
[8]Jaeger, J. C. (1942). "Moving sources of heat and the temperature at sliding contacts. " Proc. Roy. Soc. New South Wales, 76, 203.
[9]Nakahara, T. (2005). "A model of seizure based on Burwell and Strang's concept of wear mode transition. " Tribology and interface engineering series, Elsevier. 48: 547-553.
[10]De Wit, C. C., et al. (1995). "A new model for control of systems with friction." 40(3): 419-425.
[11]Yanada, H. and Y. J. M. Sekikawa (2008). "Modeling of dynamic behaviors of friction." 18(7): 330-339.
[12]Dolce, M., et al. (2005). "Frictional behavior of steel-PTFE interfaces for seismic isolation." 3: 75-99.
[13]Yao, J., et al. (2015). "Adaptive control of hydraulic actuators with LuGre model-based friction compensation." 62(10): 6469-6477.
[14]Golchin, A., et al. (2012). "Break-away friction of PTFE materials in lubricated conditions." 48: 54-62.
[15]Mokha, A., et al. (1991). "Experimental study of friction-pendulum isolation system." 117(4): 1201-1217.
[16]Zhang, Z. Z., et al. (1998). "Friction and wear behaviors of several polymers under oil‐lubricated conditions." 68(13): 2175-2182.
[17]Stranton, J. F. and J. C. Taylor (2010). "Friction coefficients for stainless steel (PTFE) Teflon bearings.", Wisconsin Highway Research Program Madison, WI.
[18]Haessig Jr, D. A. and B. Friedland (1991). "On the modeling and simulation of friction."
[19]Castaldo, P., et al. (2016). "Optimal design of friction pendulum system properties for isolated structures considering different soil conditions." 90: 74-87.
[20]Berman, A. D., et al. (1996). "Origin and characterization of different stick− slip friction mechanisms." 12(19): 4559-4563.
[21]Madi, M. S., et al. (2004). "Parameter estimation for the LuGre friction model using interval analysis and set inversion." 2004 IEEE International Conference on Systems, Man and Cybernetics (IEEE Cat. No. 04CH37583), IEEE.
[22]Márton, L., et al. (2011). "A practical method for friction identification in hydraulic actuators." 21(1): 350-356.
[23]Johanastrom, K., & Canudas-De-Wit, C. (2008). "Revisiting the LuGre friction model. IEEE Control systems magazine.", 28(6), 101-114.
[24]Bhattacharjee, B., et al. (2020). "Selection of suitable lubricant for sliding contact bearing and the effect of different lubricants on bearing performance: a review and recommendations." 37(3− 4): 13–25-13–25.
[25]Mokha, A., et al. (1990). "Teflon bearings in base isolation I: Testing." 116(2): 438-454.
[26]Constantinou, M., et al. (1990). "Teflon bearings in base isolation II: Modeling." 116(2): 455-474.
[27]Dicleli, M. , et al. (2003). "Seismic retrofitting of highway bridges in Illinois using friction pendulum seismic isolation bearings and modeling procedures." 25(9): 1139-1156.