D. Walton

Microcomputer optimisation of machine tool spindle stiffnesses

Abstract The work involved in optimising the stiffness of a spindle is complicated and time consuming and is impractical without the aid of a computer. An interactive computer program for optimising and designing spindles to various specifications is described. In the interests of small companies and personal convenience, the program runs on IBM compatible PC computers. Data on the design of the spindle, the configuration of the spindle, the type of loading, the support system, the diameters which are to be selected by the program and the constraints on the design are supplied interactively to the computer. The program then searches for an optimum design. The program, SODA, has been applied to the optimisation of an existing grinding machine spindle and the results are reported.

Lubrication Regimes in High-Performance Polymer Spur Gears

Little has been published on the behaviour of polymer gears operating under lubricated conditions. An experimental and analytical programme was undertaken to classify the regimes of EHL under which polymer spur gears operate. In doing so theoretical film thicknesses were calculated and then used to classify the regime according to Johnsons Map. The effects of lubrication on the operating efficiencies of high-performance polymer gears were interpreted and from these results coefficients of friction were derived. In addition to this the effect of tooth geometry was investigated and the beneficial influence of high-pressure angle tooth geometry is demonstrated. At loads typically associated with polymer gears the operating regime is shown to be mixed film lubrication. When high-pressure angle gears were tested at high loads the operating regime became full film lubrication and relatively little tooth flank damage occurred.

A kinematic analysis of meshing polymer gear teeth

This article describes an investigation into the contact behaviour of polymeric gear transmissions using numerical finite element (FE) and analytical techniques. A polymer gear pair was modelled and analysed using the ABAQUS software suite and the analytical results were calculated using the BS ISO 6336 rating standard. Before describing the results, the principles of the strategies and methods employed in the building of the FE model have been discussed. The FE model dynamically simulated a range of operating conditions. The simulations showed that the kinematic behaviour of polymeric gears is substantially different from those predicted by the classical metal gear theory. Extensions to the path of contact occur at the beginning and end of the meshing cycle. These are caused by large tooth deflections experienced by polymer gear teeth, as a result of much lower values of stiffness compared to metallic gears. The premature contact (occurring at the beginning of the meshing cycle) is hypothesized to be a factor in pitch line tooth fractures, whereas the extended contact is thought to be a factor in the extreme wear as seen in experiments. Furthermore, the increase in the path of contact also affects the induced bending and contact stresses. Simulated values are compared against those predicted by the international gear standard BS ISO 6336 and are shown to be substantially different. This is particularly for the case for bending stresses, where analytically derived values are independent of contact stiffness. The extreme tooth bending and the differences between analytical and numerical stresses observed in all the simulations suggest that any future polymeric gear-rating standard must account for the effects of load sharing (as a result of tooth deflection) and friction (particularly in dry-running applications).

The optimum design of KHV planetary gears with small tooth differences

Abstract This paper deals with the design of KHV planetary gears, looking particularly at applications which give high reduction ratios. Under these conditions the differences in tooth numbers between the annulus and planet gears are small and problems of interference become critical. In addition, the working pressure angle can be as much as three times the generated pressure angle, resulting in large bearing forces and low transmission efficiencies. A method of minimizing the working pressure angle while achieving interference-free gears for cases where the tooth differences may be as small as unity is described.

A computer design aid for internal spur and helical gears

Abstract This paper describes an interactive program to design internal gear pairs. From a specification, the program first performs a kinematic analysis to determine tooth numbers and to satisfy centre distance requirements, and then proceeds to calculate the facewidth. It is possible to call up any design standard in order to stress the gears; that used here is the British standard. Calculated facewidths are compared with design practice and, if outside accepted bounds, the program will after tooth numbers, or module or request a change in gear material. A complete design is provided, which includes all the necessary information for manufacture. Where the design specification places tight tolerances on centre distances and/or gear ratios, the program automatically makes the required centre distance and tooth profile corrections. On every occasion the program will find a satisfactory solution, or guide the user towards one. The program is flexible and allows the experienced designer maximum freedom to direct the design. The program contains many built-in databases, such as standard tooth cutters and material properties, and will draw the gear pair if required. The paper describes the design method and the structure of the program and a sample design is given and compared with a manual design to the same requirement.

The optimisation of internal gears

Abstract The design of a pair of internal spur on helical gears is treated with the objective of minimising the centre distance or gear volume for a given specification. The designs obtained satisfy all the necessary conditions for kinematic limits on contact ratio, interference and gear ratio tolerance and meet strength and wear criteria according to the design standard selected. A set of design variables are defined in terms of the number of pinion and annulus teeth and the module. The objective functions of minimum centre distance and volume are expressed. Some special search strategies named ‘belt zone search’ and ‘half section algorithm’ are presented in order to solve the problems of a discrete number of variables and to reduce the calculation time. The effects of tolerances placed on the design specification and the influence of acceptable facewidth limits on the optimum results are described.