Effective gear designs balance strength, durability, reliability, size, weight, and cost. Even effective designs, however, can have the possibility of gear cracks due to fatigue. In addition, truly robust designs consider not only crack initiation, but also crack propagation trajectories. As an example, crack trajectories that propagate through the gear tooth are the preferred mode of failure compared to propagation through the gear rim. Rim failure will lead to catastrophic events and should be avoided. Analysis tools that predict crack propagation paths can be a valuable aid to the designer to prevent such catastrophic failures.
Traditionally, high-quality gears are cut to shape from forged blanks. Great accuracy can be obtained through shaving and grinding of tooth forms, enhancing the power capacity, life and quietness of geared power transmissions. In the 1950s, a process was developed for forging gears with teeth that requires little or no metal to be removed to achieve final geometry. The initial process development was undertaken in Germany for the manufacture of bevel gears for automobile differentials and was stimulated by the lack of available gear cutting equipment at that time. Later attention has turned to the forging of spur and helical gears, which are more difficult to form due to the radial disposition of their teeth compared with bevel gears. The main driver of these developments, in common with most component manufacturing, is cost. Forming gears rather than cutting them results in increased yield from raw material and also can increase productivity. Forging gears is therefore of greater advantage for large batch quantities, such as required by the automotive industry.
Early in the practice of involute gearing, virtually all gears were made with the teeth in a standard relationship to the reference pitch circle. This has the advantages that any two gears of the same pitch, helix angle and pressure angle can operate together, and that geometry calculations are relatively simple. It was soon realized, though, that there are greater advantages to be gained by modifying the relationship of the teeth to the reference pitch circle. The modifications are called profile shift.
In recent years, the demands for load capacity and fatigue life of gears constantly increased while weight and volume had to be reduced. To achieve those aims, most of today's gear wheels are heat treated so tooth surfaces will have high wear resistance. As a consequence of heat treatment, distortion unavoidably occurs. With the high geometrical accuracy and quality required for gears, a hard machining process is needed that generates favorable properties on the tooth surfaces and the near-surface material with high reliability.
Economic production is one of the main concerns of any manufacturing facility. In recent years, cost increases and tougher statutory requirements have increasingly made cutting fluids a problematic manufacturing and cost factor in metalworking. Depending on the cutting fluid, production process and supply unit, cutting-fluid costs may account for up to 16% of workpiece cost. In some cases, they exceed tool cost by many times (Ref. 1). The response by manufacturers is to demand techniques for dry machining (Ref. 2).
Mineral-oil-base lubricants show a significant decrease of kinematic viscosity with rising temperature, as exemplified in Figure 1 by lubricants for vehicle gears. An important attribute of lubricants is their viscosity index (VI), according to DIN/ISO 2909 (Ref. 4). Viscosity index is a calculated coefficient, which characterizes the change of viscosity of lubricants as a function of temperature. A high viscosity index represents a low variation of viscosity due to temperature and vice versa. A low viscosity-temperature-dependence is required for lubricants that are operated at significantly varying temperature conditions, such as vehicle engine and gear lubricants in summer and winter time. This way, the oils remain flowing and pumpable at low temperatures on the one hand; and on the other hand, sufficiently thick lubricant films can be formed at higher temperatures for a safe separation of the surfaces.
Crown gearings are not a new type of gear system. On the contrary, they have been in use since very early times for various tasks. Their earliest form is that of the driving sprocket, found in ancient Roman watermills or Dutch windmills. The first principles of gear geometry and simple methods of production (shaper cutting) were developed in the 1940s. In the 1950s, however, crown gears' importance declined. Their tasks were, for example, taken over by bevel gears, which were easier to manufacture and could transmit greater power. Current subject literature accordingly contains very little information on crown gears, directed mainly to pointing out their limitations (Ref. 1).
The configuration of flank corrections on bevel gears is subject to relatively narrow restrictions. As far as the gear set is concerned, the requirement is for the greatest possible contact zone to minimize flank compression. However, sufficient reserves in tooth depth and longitudinal direction for tooth contact displacement should be present. From the machine - and particularly from the tool - point of view, there are restrictions as to the type and magnitude of crowning that can be realized. Crowning is a circular correction. Different kinds of crowning are distinguished by their direction. Length crowning, for example, is a circular (or 2nd order) material removal, starting at a reference point and extending in tooth length or face width.
Base helix error - the resultant of lead and profile errors is the measured deviation from the theoretical line of contact (Fig. 1). It can be measured in the same way that lead error on a spur gear is measured, namely, by setting a height gage to height H based on the radial distance r to a specified line of contact (Fig. 2), rotating the gear so as to bring a tooth into contact with the indicator on the height gage, and then moving the height gage along two or more normals to the plane of action. The theoretical line of contact on helical gear must be parallel to the surface plate, which is attained by mounting the gear on a sine bar (Fig. 3).
Face-milled hypoid pinions produced by the three-cut, Fixed Setting system - where roughing is done on one machine and finishing for the concave-OB and convex-IB tooth flanks is done on separate machines with different setups - are still in widespread use today.