The torsional vibration of a back-to-back gearbox system has been investigated experimentally and analytically. Gearboxes are typically part of a larger system, or drivetrain, which commonly includes electric motors, shafts, couplings, ball mills, turbines and generators. The dynamics of the system has been shown significantly to influence the gearbox response and requires inclusion in gearbox modelling. Assumptions are commonly made, however, to reduce the degrees of freedom of the model, and system dynamics is subsequently neglected. Receptance methods were applied to model a back-to-back gearbox system and were shown to be an effective modelling technique for geared system analysis. A detailed experimental modal analysis was performed using the swept-sine technique with an a.c. servomotor torsional exciter. Torsional excitation allowed for the dynamic response to be measured up to 1600 Hz. A multi-degree-of-freedom, frequency domain torsional model of the gearbox system was developed using receptances. The model included a combination of lumped-mass elements, and continuous shafts with distributed inertia and hysteretic damping. The modelled torsional natural frequencies were matched to the measured frequencies by the adjustment of system model parameters to achieve a high level of agreement. Matching of system natural frequencies resulted in the accurate prediction of the first nine associated torsional deflected shapes up to 1548 Hz. This paper presents the detailed results of a full torsional, modal analysis of a gearbox system, demonstrating receptance system modelling and an effective method for torsional excitation on rotating machines.

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The torsional vibration of a back-to-back gearbox system has been simulated in the time domain, using time domain receptance theory. Receptance analysis in the time domain is an extension of the frequency domain method and allows the benefits of a systems approach for modelling complicated systems. Meshing spur gears represent a complicated dynamic system. The excitation from the variation in gear mesh stiffness has been considered in the present model. A gear mesh kinematic simulation was developed to simulate the contact pattern and mesh stiffness for a spur gear pair with a contact ratio of less than 2.0. The time domain receptance model was verified using a simulated white noise input to generate frequency response functions up to 1600 Hz. The simulated torsional natural frequencies were compared with the experimentally measured results in Part 1 [1]. After the adjustment of model parameters, the first eight torsional natural frequencies were accurately matched by the predictions of the time domain model. The simulated frequency response functions of the time domain model accurately matched the frequency response functions from the frequency domain receptance model presented in Part 1 [1].

The coupled torsional and transverse vibration of a back-to-back gearbox system has been investigated experimentally and analytically. Receptance methods were used to model the system, and were shown to be effective. A detailed experimental modal analysis was performed using the swept-sine technique with an a.c. servomotor torsional exciter. Torsional excitation allowed for the dynamic response to be measured up to 1600 Hz. The model included a combination of lumped mass elements and continuous shafts with distributed inertia and damping. The bearings were modelled as having both radial and tilt stiffness and damping elements. The model simulated the experimental results well and predicted each of the first 11 natural frequencies to within 8 per cent. Of the 11 natural frequencies, 9 simulated deflected shapes matched very well, validating the modelling approach taken for the project together with the assumptions made in the derivation of the model. This paper presents the detailed results of a full torsional/transverse model analysis of the gearbox system.

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