In metal working practice, some meaningful numbers specifying the state of friction are needed for estimating the required forming load and for evaluating and selecting the lubricants. The meaningful numbers have not lent themselves to experimental determination. It is usually assumed that the theory is correct and these values are derived as the adjustable parameters to give agreement between theory and experiment. Simulating tests are used to derive these values. One of these tests particularly related to forging operations is the ring compression test. Many investigators have analyzed the ring compression, generally based on the assumption of no bulging, of constant interface friction factor, and of non hardening. So, a correlation between the results derived from the test and theoretical analysis must be established for the test to be useful.
In this study, bulging, folding and strain hardening effect were considered in ring compression analysis by matrix method. With this method, the theoretical analysis for ring compression was carried out with non-hardening material specimen of which original outside diameter: inside diameter: height is 6:3:2, under the conditions of m=0.1, m=0.2, m=0.3, and m=0.5. The results were compared with those of the approximate theoretical analysis. Also, the theoretical analysis for strain hardening model of SAE 1045 was carried out under the condition of m=0.3, and the results were compared with those of nonhardening material. Experimental results were plotted on the calibration curves and load-height reduction curve to determine the friction factor for dry friction condition and for phosphate coating lubrication. Comparing the results, the analysis by using matrix method was observed to be superior to the approximate analysis, and the experimental results of SAE 1045 were more agreeable to the analysis of SAE 1045 than to that of non hardening material. But there was not much difference in calibration curves between two cases of analysis. Friction factors were determined to be about 0.3 for dry condition and about 0.05 - 0.1 for phosphate coating lubrication.
마찰측정을 위한 보정곡선을 얻기 위해서 matrix method를 사용하여 다음과 같은 가정하에서 링 압축을 해석하였다. 재료는 Mises의 항복조건과 소성유동법칙에 따라 물체 전역에서 소성변형을 하는 강소성재료로서 물체내에는 체적힘이 존재하지 않는다. 이와같은 가정하에서 링단면의 $\frac{1}{4}$을 여러 요소로 분할하고 이 유한 요소모형에 극한원리를 적용하여 전개하면 비선형 강성방정식이 나온다. 이 비선형 강성방정식을 선형화시켜서 풀면 비선형 강성방정식을 직접 푸는것보다 간단하고 콤퓨터 사용시간이 적어지므로 이 비선형 강성방정식을 Taylor series로 전개하여 그 일차항까지만 취하여 선형 강성방정식을 얻는다. 이와같이 나오는 선형 강성방정식을 사용하여 링의 축대칭변형을 단계적으로 해석하였다.
먼저 가공경화가 없는 재료에 대해서 m = 0.1, m = 0.2, m = 0.3 m = 0.5의 네가지 마찰상태에서 해석하여 기존해석에서 얻어지는 결과와 비교하였다. 이때 마찰전단응력은 $J = \frac{mY_0}{\sqrt{3}}$로 접촉면 전역에서 균일하게 작용한다고 가정하였다. 다음에 SAE 1045의 응력-변형률 곡선을 구하여 가공경화의 효과를 고려한 해석을 m = 0.3에서 행하여 이때 나오는 결과를 가공경화가 없을때와 비교하였다.
실험에는 Al 1100과 SAE 1045의 시편을 사용하였고 보정곡선과 비교한 결과 건조마찰상태는 m값이 0.3보다 약간 크고 인산 염피막윤활은 m값이 대략 0.05∼0.1에 해당되었다.
