**2.1 Helicopter gearbox for laboratory testing**

The gear transmission described below was used to perform numerous tests on the operation of split-torque transmissions (Krantz et al., 1992; Krantz, 1994, 1996; Krantz & Delgado, 1996), which can be considered a standard for aeronautical applications. The full assembly is depicted in Fig. 2.

Fig. 2. Helicopter transmission for laboratory testing

Split Torque Gearboxes: Requirements, Performance and Applications 59

Total transmission reduction is achieved by three gearing stages, clearly depicted in Fig. 3

 Engine input. Engine torque is accepted by an overrun clutch, mounted with a bevel pinion. This bevel gear, with a between-teeth ratio of 34/84, produces a transmission

 Intermediate stage. Dual offset spur gears are driven by a single pinion. The betweenteeth ratio of 41/108 produces a transmission ratio of 2.634:1, resulting in an output shaft speed of 3530 rpm. This meshing results in the first split in torque between the

 High-torque output stage. A double-helical gear is driven by a pinion coaxial with each intermediate stage gear. In this stage, the torque is split again between the two helical pinions, with the result that the output shaft simultaneously receives torque from four pinions for each bevel gear. In this transmission it is very convenient to combine torque

The between-teeth gear ratio is 23/232, so the transmission ratio is 10.087:1, resulting in an

This configuration uses double-helical gearing at the output stage to drive the output shaft. The helical pinions have opposing angles, which ensures equilibrium between the axial forces. When a double gear operates on the output shaft, the area of support is twice that of a simple gear. This causes a reduction in contact force, which in turn results in a reduction ratio that is twice that of the simple case, with the corresponding reduction in weight and mechanical load. Overall, this constitutes a transmission ratio of 65.64:1, with the total torque in the output shaft exercised by each engine of 28818Nm, split between the four pinions that engage the output shaft crown. This calculation is based on estimating overall losses, with each input

One of the main problems in split torque transmission is ensuring equal torque split between the paths. To ensure correct torque split, a long, torsionally flexible shaft is used between the intermediate-stage spur gear and the output-stage helical pinions. Section 4 describes the methods most frequently used to ensure correct torque split between paths.

To ensure simultaneous meshing of four gears (Fig. 1), configuration must comply with certain geometric constraints. A number of studies describe the complexity of simultaneous gearing in split torque gearboxes (Kish, 1993a) and in planetary gear systems (Henriot, 1979, Parker & Lin, 2004); other studies approach the problem generically (Vilán-Vilán et al., 2010), describing possible solutions that ensure the simultaneous meshing of four gears.

For four gears to mesh perfectly, the teeth need to mesh simultaneously at the contact points. The curvilinear quadrilateral and the pitch difference are defined below in order to express the meshing condition. From now on we will use this nomenclature of our own devising -that is, curvilinear quadrilateral - to indicate the zone defined by portions of pitch circles in the meshing area (Fig. 5). The pitch difference is the sum of pitches in the input and output gears minus the sum of pitches in the idler gears at the curvilinear quadrilateral. For perfect engagement between the four gears, the pitch difference must coincide with a

ratio of 2.470:1. In this stage, the output velocity is 9299 rpm.

split with reduction, as greater torque is transmitted in each stage.

and Fig. 4:

two intermediate gears.

output shaft speed of 350 rpm.

engine operating independently, of 12%.

**3. Feasible geometric configurations** 

whole number of pitches.

The transmission is sized for input of 373 kW at a speed of 8780 rpm. As can be observed in Fig. 2, the transmission has two stages:


This configuration results in torque of 9017.56 Nm. being transmitted through two paths.
