Structure Sensitivity Analysis and Dynamic Performance Optimization of Marine Gearbox

The aim of this paper is to investigate the influence of structure parameters on the vibration characteristics and improve the dynamic performance of marine gearbox. A finite element model was established to solve the dynamic response by using modal superposition method. Based on the theory of multi-objective optimization design, the structure sensitivity analysis model of marine gearbox was established, which takes the structure parameters of the housing as design variables. The modal and response sensitivity was obtained by using the optimal gradient method. According to the results of sensitivity analysis, a modal and response optimization model of marine gearbox was established. The objective was to avoid natural frequencies from the excitation frequencies and minimize the root mean square of vibration acceleration of the evaluating points on the surface of housing. Then the modal optimization and response optimization of gearbox were carried out by using zero-order and first-order optimization method. The results indicate that the dynamic optimization of the gearbox can be achieved. After optimization, the amplitude of vibration acceleration of the evaluating points on the housing surface has been reduced and the resonance of marine gearbox can be avoided.

Research on a Generating Method of Spiral Flutes of Hourglass Worm Gear Hob

All of the cutting edges on an hourglass worm gear hob have different shapes and spiral angles. If the spiral angles are small, straight flutes are usually adopted. But for the hob with multiple threads, the absolute values of the negative rake angles at one side of the cutting teeth will greatly affect the cutting performance of the hob if straight flutes are still used. Therefore, spiral flutes are usually adopted to solve the problem. However, no method of determination of the spiral flute of the hourglass worm gear hob has been put forward till now. Based on the curved surface generating theory and the hourglass worm forming principle, a generating method for the spiral flute of the planar double enveloping worm gear hob is put forward in this paper. A mathematical model is built to generate the spiral flute. The rake angles of all cutting teeth of the hob are calculated. The laws of the rake angles of the cutting teeth of four hobs with different threads from one to four threads are analyzed when straight flutes and spiral flutes are adopted respectively. The laws between the value of the negative rake angles of the hob with four threads and the milling transmission ratio are studied. The most appropriate milling transmission ratio for generating the spiral flute is obtained. The machining of the spiral flutes is simulated by a virtual manufacturing system and the results verify the correctness of the method.

Dynamic Transmission Error Measurements From Spur Gear Pairs Having Tooth Indexing Errors

This paper complements recent investigations [Handschuh et al (2014), Talbot et al (2016)] of the influences of tooth indexing errors on dynamic factors of spur gears by presenting data on changes to the dynamic transmission error. An experimental study is performed using an accelerometer-based dynamic transmission error measurement system incorporated into a high-speed gear tester to establish baseline dynamic behavior of gears having negligible indexing errors, and to characterize changes to this baseline due to application of tightly-controlled intentional indexing errors. Spur test gears having different forms of indexing errors are paired with a gear having negligible indexing error. Dynamic transmission error of gear pairs under these error conditions is measured and examined in both time and frequency domains to quantify the transient effects induced by these indexing errors. Both measurements indicate clearly that the baseline dynamic response, dominated by well-defined resonance peaks and mesh harmonics, are complemented by non-mesh orders of transmission error due the transient behavior induced by indexing errors.

A 3D Multi-Body Dynamics Model for Chain-Type Continuously Variable Unit

This paper presents a new 3-dimensional multi-body dynamic model of a chain-type continuously variable unit (CVU). The modeling requirements and assumptions are presented first. Then, the paper discusses the approaches developed to mathematically represent the chain, pulleys, and their interactions in terms of contact and friction. Three dimensional representation of the chain is given. Actual geometries of the pins and pulleys are captured, including crowning on either member. The model is then used to investigate the effects of different operating conditions, including speed ratio and torque, on the quasi-static performance of a CVU. Several metrics are discussed to characterize the behavior of an example CVU under practical operating conditions; these include torque capacity and the ratio of clamping forces. The predictions presented show the sensitivity of the model to these operating conditions. Finally, trends that describe the CVU quasi-static behavior are explained in context of the parameters studied.

Baseline Experimental Results on the Effect of Oil Temperature on Shrouded Meshed Spur Gear Windage Power Loss

Rotorcraft gearbox efficiencies are reduced at increased surface speeds due to viscous and impingement drag on the gear teeth. This windage power loss can affect overall mission range, payload, and frequency of transmission maintenance. Experimental and analytical studies on shrouding for single gears have shown it to be potentially effective in mitigating windage power loss. Efficiency studies on unshrouded meshed gears have shown the effect of speed, oil viscosity, temperature, load, lubrication scheme, etc. on gear windage power loss. The open literature does not contain experimental test data on shrouded meshed spur gears. Gear windage power loss test results are presented on shrouded meshed spur gears at elevated oil inlet temperatures and constant oil pressure both with and without shrouding. Shroud effectiveness is compared at four oil inlet temperatures. The results are compared to the available literature and follow-up work is outlined.

Copula-Based Time-Frequency Distribution Analysis for Planetary Gearbox Fault Detection

Linear and bilinear time-frequency distributions (TFDs) have been employed in planetary gearbox fault diagnosis. For linear TFDs, there is a trade-off between the time localization and frequency resolution and the spectrogram may not have correct energy marginals. For bilinear TFDs, they cannot be interpreted as an energy distribution because of the existence of possible negative values even though they are designed for energy density representation. To overcome these shortcomings, TFDs based on copula theory have been reported in the literature. In this paper, we analyze two simulated data sets using linear TFD and copula-based TFD. The results show that the constructed copula-based TFD has desirable properties of being positive, free from cross-term interference, having high time-frequency resolution and matching well with true marginals. The copula-based TFD is also able to locate fault-induced impulses by vertical lines over a certain frequency range in the time-frequency domain. Consequently, this study confirms the advantages of the copula-based TFD as an energy distribution and its capability in fault detection for planetary gearboxes.

The Effect of Spur Gear Tribo-Dynamic Response on Pitting Crack Nucleation

This study investigates the role of the tribo-dynamic behavior in the contact fatigue crack nucleation for spur gears. To describe this fatigue phenomenon, a six-degree-of-freedom (DOF) lumped parameter dynamics formulation is coupled with a set of mixed elastohydrodynamic lubrication (EHL) governing equations. The former provides the dynamic tooth force to the EHL analysis, and the latter yields the gear mesh damping as well as the friction excitations that are required in the gear dynamics simulation. The converged tribo-dynamic surface normal pressure and tangential shear are then used to determine the multi-axial stress fields using the potential theory based closed-form stress formulation for half space. Lastly, the stress means and amplitudes are implemented in a multi-axial fatigue criterion to assess the fatigue damage.

Planar Tooth Profile Synthesis for Relative Curvature

This paper is the first that uses the new conjugation curvature theory [1] to directly synthesize conjugate tooth profiles with the given relative curvature that determines the Hertzian contact stress. Conjugation curvature theory offers a systematic methodology to synthesize the relative curvature for a tooth pair. For any given relative curvature between the contact tooth profiles, a generating point can be located on an auxiliary body. Under the rolling motion among the pinion pitch, the gear pitch and the pitch on the auxiliary body, the generating point will trace fully conjugate profiles on the pinion and gear bodies with the given relative curvature at the instant of the contact. Full conjugation throughout the contact of the profiles is guaranteed with the three instant centers remaining coincident [1]. The methodology is demonstrated with a planar tooth profile synthesis with given relative curvature. One may find that the Wildhaber-Novikov tooth profile, which is known to have low relative curvature and Hertzian contact stress, and its variations become special cases under such methodology.

Application of Audible Sound Signals for Tool Wear Monitoring and Workpiece Hardness Identification in Gear Milling Using Machine Learning Techniques

The machining process monitoring, especially the tool wear monitoring, is very critical in modern automated gear machining environment which needs instant detection of cutting tool state and/or process conditions, quick final diagnosis and appropriate actions. It has been realized that the non-uniform hardness of the workpiece material due to the improper heat treatment can cause expedited tool wear and unexpected tool breakage, which greatly increases difficulties and complexities in monitoring the tool conditions in gear cutting. This paper provides a solution to detect the wear conditions of the gear milling cutter in the cutting of workpiece materials with hardness variations using the audible sound signals. In this study, cutting tools and workpieces are prepared to have different flank wear classes and hardness variations respectively. A series of gear milling experiments are operated with a broad range of cutting conditions to collect sound signals. A machine learning algorithm that incorporates support vector machine (SVM) approach coupled with the application of time and frequency domain analysis is developed to correlate observed sound signals’ signatures to specified tool wear classes and workpiece hardness levels. The performance evaluation results of the proposed monitoring system have shown accurate predictions in detecting tool wear conditions and workpiece hardness variations from the sound signals in gear milling.

Effect of Track Geometric Irregularity on Dynamic Characteristics of Gear Transmission in a Locomotive

Gear transmission is a key component in locomotive where it delivers the traction or braking forces between the motor and the wheelset. Its working performance has a direct effect on the operating reliability and safety. Therefore, investigation on the dynamic characteristics of the gear transmission in locomotives is very meaningful. In this study, a gear transmission-locomotive-track spatial coupled dynamic model is established based on the classical locomotive-track coupled dynamics and the gear dynamics theory. Based on this model, the dynamic responses of the gear transmission can be analysed under excitations from different track geometrical irregularity, and the dynamic performance of the gear transmission can be obtained. This paper also studies the effect law of the track irregularity on the vibration of the gear transmission by using statistical indicators RMS (Root Mean Square) and PtP (Peak-to-Peak). The results indicate that the track geometrical irregularity has an obvious impact to the dynamic performance of gear transmission. The dynamic response of the gear transmission will increase violently when the locomotive runs on the track in a worse condition. The results are expected to be capable of providing some references for fatigue life prediction and reliability analysis of the gear transmissions in locomotive.