为了了解不同成熟度苹果在不同曲率半径位置静压时的接触应力分布特性，本文采用Prescale感压胶片对苹果静压接触应力分布进行了测量分析和Hertz公式理论计算，并探讨了Hertz公式关于接触应力面积计算的精度以及修正方法。研究结果表明，苹果静压接触应力分布轮廓为近椭圆形，不同应力呈高低相间的不连续分布，低应力（≤0.2 MPa）主要在边缘分布，高应力（>0.5 MPa）只有零星分布，可忽略不计。当压力100 N以上时，两种成熟度苹果的应力面积有显著性差异。随着曲率半径增大，相同压力水平下苹果的应力面积因成熟度不同而表现出不同程度的增大趋势。接触应力面积的Hertz公式计算值与感压胶片测量值存在不同程度偏差，当引入λ=1.5780-0.0042F修正Hertz公式的等效弹性模量E*，可明显提高苹果静压接触应力面积的理论计算精度。

In this study, the pressure distribution of apple subjected to static loading was measured by the pressure sensitive film technique. The effects of apple maturity and curvature radius at contact location of fruit on pressure area were focused on. The results were calculated by Hertz equation; meanwhile, the calculation accuracy of the equation on contact pressure area was analyzed. The result showed that the contour of pressure distribution was near elliptical, and the discontinuous distributed pressures had the variation feature of rising and falling. The pessure less than 0.2 MPa occupied at the edge of the contact region, while the area of pressure over 0.5 MPa distributed at tiny spots. When the apple was loaded over 100 N, the pressure areas of two different maturity apples showed significant difference. With the increase of curvature radius, the pressure areas of apple at same load increased to varied extent due to maturity difference. Compared with film measurements of apple pressure area, the calculations with Hertz equation showed larger deviation. Hence, a correction coefficient (λ=1.5780 -0.0042F) was introduced to modify the equivalent elastic modulus in the Hertz equation. As a result, there was a good agreement between the measured contact areas and the predications using the modified Hertz equation. This indicated that the modified Hertz equation could precisely estimate pressure area of apple under static load.

国家自然科学基金资助项目（31160335）