This study develops an optimization technique for a sinusoidal interlock design of a hybrid spur gear consisting of a metallic outer ring to support high contact stress bonded to a composite inner web for weight reduction. Two objectives (mass and shear traction on the metal-composite interface under static loading conditions) were minimized for four design variables subject to two constraints. Borg MOEA, a multi-objective evolutionary algorithm developed at The Pennsylvania State University, and an in-house finite element solver were used to generate Pareto-optimal solutions to this design problem. Two of the designs were then analyzed in greater detail to determine stress distributions throughout the gear. In the future, this technique will be refined and applied to optimization of more representative rotorcraft gears, with the aim of reducing drive train weight and meeting performance requirements.
Composite materials have been increasingly considered for use in rotorcraft drive system components due to their high strength to weight ratio, providing a means for significant weight reductions while maintaining overall strength. This was originally considered for large components like housings (Ref. 1) and drive shafts (Ref. 2). More recently, this has been extended to gearing with the hybrid (steel-composite) gear, which replaces the steel in the gear web with a lightweight carbon fiber composite. Original studies (Refs. 3,4) were conducted on a 88.9 mm (3.50 in) pitch diameter spur gear that featured a design where a hexagonal void was machined out of the gear web leaving the metallic tooth ring and hub.
The void was replaced by the carbon fiber composite. These studies focused on vibration characterization and endurance testing of the hybrid gear. Later studies using this design focused on multi-scale modeling of the composite material (Ref. 5) and loss-of-lubrication performance of the gear (Ref. 6). The loss-of-lubrication tests showed failure of the composite material at stress concentrations that exist at the corners of the hexagonal web. These initial studies were conducted to determine the feasibility of the hybrid gear concept and a design optimization was not performed.
Gears are mechanical components used for transmitting motion and torque from one shaft to another. Ever since invention of rotating machines, gears existed. Early records states that around 2600 BC Chinese used gears to measure the speeds of chariots. In 250 B.C Archimedes used a screw to drive toothed wheels which were used in engines of war. In 4 century B.C., Aristotle used gears to simulate astronomical ratios. Greek and Roman literatures mention the extensive use of gears in clocks of cathedrals and ecclesiastical buildings.
DESIGN & OPTIMIZATION
The proposed design of the spur gear features a sinusoidal interlock and an integral shaft. There are four separate components that make up the design: a web composite, two outer composite components and a metallic outer tooth ring. This design can be seen in Figure 1. Notice that the integral shaft is not shown in the figure. Instead during the optimization this diameter remained fixed and zero displacement boundary conditions were enforced at this surface.
The effects of loading on the gear teeth are not of interest here so the geometry for optimization was replaced by a gear blank with an outer diameter equal to the pitch diameter of the gear. This may change the magnitude of the stresses at the interface and may affect the magnitude of the mass, but the simplified gear blank provides a test article for developing the optimization technique. Future work will investigate the effect of gear teeth on the optimal solutions. Sinusoidal Interlock The sinusoidal interlock that defines the compositemetallic interface is defined analytically by Equation 1, where r is the radial coordinate, Rc is the radius of the centerline, A is the amplitude of the curve, Nc is the number of cycles in the sinusoid, θ is the angle and φ is a phase shift which will rotate the curve in-plane relative to the location of load application.
In this project an optimization technique was presented to perform a design optimization on a 88.9 mm (3.5 in) pitch diameter hybrid spur gear. The design features a sinusoidal interlock that separates a composite web from a metallic tooth ring. Two outer composites are included, overlapping this interface. The design also features an integral composite shaft for maximum weight savings. Four geometric design variables are varied as part of the optimization, subject to two constraints.
The objectives are to minimize the gear mass and the interfacial shear tractions. Borg MOEA was used to perform the optimization and determine the Pareto-optimal set of solutions. The optimization was run for 500,000 function evaluations and resulted in a set of six optimal designs. The optimization results show that changes can be made to the ranges of some of the design variables for future analyses.