Continuous-Thread Model of Load Distribution and Nut Wear in Grease-Lubricated Lead Screws

Even under constant operating conditions, greases lubricating lead screw assemblies, as well as materials comprising their nut and screw threads, must perform over a range of contact pressures that not only varies from thread to thread but also evolves with the sliding distance as most heavily loaded threads wear most rapidly. An example modeled here, consisting of a nut whose bulk body is rigid and an elastic screw body having continuous elastic meshed threads, reveals the broad distribution of load along the length of the nut threads in an unworn lead screw assembly, as well as the distribution of wear depth that must accompany an eventual steady-state of uniform rate of nut thread wear. Thread load redistributions brought on by changes in operating conditions such as applied load, or even temperature in the case of a nut/screw pair of dissimilar materials, are similarly modeled. Such load redistributions in worn lead screws may cause either the top or the bottom positions of the nut thread to become most heavily loaded, depending on whether an operating condition is increased or decreased. Most importantly, the extent of these redistributions using this continuous thread model can significantly exceed those predicted by an earlier preliminary model where threads were considered as discrete turns and contact pressures could only be described as an average value over each turn. The operating condition changes are shown capable of causing worn threads at either extreme of the nut to become momentarily unloaded and removed from the contact, and this continuous-thread model indicates that even smaller changes in the operating condition can initiate such unloading, as compared to predictions from the discrete-thread model.