Abstract
Summary
This work uses a mathematical method to correlate the forces calculated to push-on and pull off a femoral head from a stem and correlate the results of in vitro testing.
Introduction
This work aimed to mathematically model the force needed to disassemble the THR unit for a given assembly load. This work then compared these results with the results of an in vitro experiment. The research presented aimed to determine the assembly forces necessary to prevent movement of the head on the stem through friction. By assessing the forces necessary to push the head onto the stem securely enough to prevent any movement of the head through friction, it is likely that the fretting and corrosion of the head taper interface will be reduced.
Methods
Mathematical equations were used to define the relationship between the push-on force and the taper specification in terms of friction, contact area and taper angle. Similar relationships were determined for the pull-off force and torque-off force. Push-on loads of 1–4 kN were used to calculate the normal force and then the pull-off force and torque-off force for the combinations. Stems were chosen to represent the trunnion interface available at Corin Ltd. The stems used had a 12/14 taper. Stems were paired with a size 32 mm diameter metal modular head. For this analysis it was assumed that µ1 was equal to µ2 on the basis of no change in material or surface finish. In vitro testing was conducted according to ISO7206-10, with variable assembly loads. The stems were held inverted vertically above the head. Each stem was pre-assembled to 1, 2, 3and 4 kN and the pull-off force was measured at each load (n=3). The roughness of the male and female trunnions was measured before and after testing. The results determined mathematically were compared with those found experimentally.
Results
Mathematical analysis showed that for an increasing push-on force the pull-off force also increases. Similarly, the same trend was seen for the torque-off force. Linear regression analysis provided a relationship between the push-on force and the pull-off force, pull off force equates to 0.508 multiplied by push-on force, the R2 value was calculated as 0.986. The roughness of the trunnion and female taper were not significantly different before and after experimentation. The coefficient of frictional between the two surfaces, calculated based on the experimental pull-off forces, varied from 0.2 to 0.35.
Discussion
Correlation has been shown between the results generated mathematically and those generated experimentally; pull-off force increases linearly with increasing push-on force. Further work is required to correlate the torque-off force determined experimentally with that calculated mathematically.
ISO testing uses a push-on force of 2 kN to assemble heads onto a stems, this allows comparison between stems, however, does not correlate with the clinical scenario. The optimum force of assembly is not known and there is no correlation between the assembly load used during in vitro testing and the impact load applied during operation. The force with which a THR is assembled is related to the possibility of fretting and corrosion which may occur over the life of the joint. Further work is required to ensure optimum fit between modular heads and stems.
