**6. References**

50 Mechanical Engineering

knowledge compliments the design and development efforts in vibration signal analysis based machine condition monitoring technologies. In the near future, accurately simulated signals of a faulty gearbox can aid the machine learning process of fault diagnosis algorithms based on neural networks. Performing this task in experiments are time consuming and costly exercise; simulation model based approach appears much more

The authors hope that the work presented in this chapter will stir the thoughts and the new ideas in readers that will contribute to the advancement of the gear engineering and the technologies in detecting and diagnosing the incipient faults in geared transmission

Unless otherwise stated the following tables defines the symbols and the acronyms used in

desirable.

systems.

this chapter.

 *xi, yi,* 

*K, Kmb*

*T* Torque

**5. Nomenclature** 

Ø Pressure Angle LoA Line of Action PoA Plane of Action LoC Line of Centres

Pb Base pitch CR Contact Ratio

*N* Number of teeth on a gear

gearmesh

GTE Geometrical Transmission Error STE Static Transmission Error LTC Long Term Composite of TE STC Short Term Composite of TE

*A A*<sup>1</sup> <sup>2</sup> A vector connecting points *A1* and *A2*

Rb,, rb Gear Base Radius and Pinion Base Radius Rgear, rpinion Gear Pitch Radius and Pinion Pitch Radius Ro and ro Gear Outer Radius Pinion Outer Radius

TE Transmission Error (Measured experimentally)

ME Motion Error (Numerically calculated TE) *xi, yi, zi* Translation at *ith* Degrees of Freedom

and misalignment of the gear pair.

*zi* Rotation about a translational axis at *ith* Degrees of Freedom

*C, Cmb* Damping matrices. The subscript '*mb*' refers to damping at the gearmesh. *H* An 'on/off' switch governing the contact state of the meshing gear teeth. *te* A vector representing the combined effect of tooth topography deviations

Linear stiffness elements. The subscript '*mb*' refers to stiffness at the


Gearbox Simulation Models with Gears and Bearings Faults 53

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**3** 

*University of Vigo,* 

*Spain* 

**Split Torque Gearboxes: Requirements,** 

Although the simplest gear systems are those with just one gear engagement area between a pair of gears, alternatives are available for applications where it is necessary to transmit a very high torque in a very small space. One option to increase power density is to use the split torque systems that were mainly developed for the aviation industry. These gear systems are based on a very simple idea: division of the transmission of force between several contact areas, thereby increasing the contact ratio. This gives rise, however, to the

(a) (b)

Split torque gearboxes are configurations where a driving pinion (1) meshes with two intermediate idler pinions (2, 3), which simultaneously act on another gear (4). From now on, this assembly will be called four-gear meshing. In this case, the torque split is from gear (1) to gears (2) and (3) which engage gear (4). This gear assembly results in the reduction in gear speed causing an increase in available torque; hence, the split torque transmission

Fig. 1. (a) Standard gearbox assembly; (b) Split torque gearbox assembly

**1. Introduction** 

problem of meshing four gears (Fig. 1).

means we can use smaller gears.

**Performance and Applications** 

Abraham Segade-Robleda, José-Antonio Vilán-Vilán, Marcos López-Lago and Enrique Casarejos-Ruiz

