3次元弾性論を応用した人工股関節の弾性流体潤滑性能の解析

Abstract

The authors consider that the pressure yielded in the fluid film is high enough to support the load on the femoral head of total hip prostheses. Because the congruity of hip prostheses is high, one of their frictional surfaces are soft, for example high density polyethylene (HDP). Squeeze film formation can be assisted by the deformation of the frictional surface. In this study the authors estimated the thickness of a fluid film formed between the acetabulum cup and femoral head of total hip prostheses through a numerical analysis based on the theory of elastohydrodynamic lubrication and on the theory of three-dimensional elasticity. This estimation required numerical conditions assigned to the area surrounding the human hip. The authors established one set of standard conditions as follows. The body motion is walking. The maximum load on the femoral head is 2400 N. The period is 1.5s. The viscosity of lubricant is 0.015 Pa.s. This value is high like that of synovial fluid in osteoarthritic human joints and rather lower than that in healthy joints. The authors assumed the model similar to the Maezawa total hip prosthesis. The radius of the femoral head is 2.0cm. The radial clearance between acetabulum cup and femoral head is 0.015cm. The material of the femoral head is HDP, for which Young's modulus is 1.8×10^8 N/m^2 and Poisson's ratio is 0.3. The minimum film thickness (hm) estimated here was 3.8μm under standard conditions. This value is rather high for fluid film lubrication, and is stable for the variation of maximum load. For example, a load of 3000N cannot change this value. But decreasing the viscosity of lubricant or increasing the loading period affected the fluid film formation. The authors tried through further estimation to search for more favorable designs of total hip prostheses. The results obtained were as follows. A larger radius of the femoral head introduces a higher value of hm. Smaller radial clearance (c) between acetabulum cup and femoral head, or Young's modulus (E), introduces a higher hm. But if c or E becomes smaller than critical conditions, the fluid film will fracture partially. These results may be also applied to prostheses that have HDP acetabulum cups, unless the cup is too thin.