Time-Domain Dynamic Modeling and Analysis of Complex Heavy-Duty Gearbox Considering Floating Effect

Expert insights into the time-domain dynamic behavior of heavy-duty gearboxes form the foundations of design evaluation and improvement. However, in the existing lateral–torsional coupling (LTC) modeling method for gearboxes that is normally used for frequency-domain dynamic behavior, the meshing forces are modeled as spring dampers with fixed acting points on the meshing gears to simulate only the transient LTC effect, and thus the steady state characteristic in the time domain cannot be obtained due to the unrealistic distortion of positions and orientations as the gear angles increase. In this paper, a novel and generally applicable LTC modeling method for heavy-duty gearboxes, mainly planetary gear sets with floating components, is proposed by using space-fixed spring dampers with floating acting points on the meshing gears to study the time-domain dynamic response and to support the dynamic design of heavy-duty gearboxes. Based on the proposed method, a LTC model of a 2 megawatt (MW) wind turbine gearbox with floating components considering the time-varying meshing stiffness, bearing stiffness, torsional stiffness, and floating effect was established. The simulated results of representative components were in accordance with experimental results on a test rig, and dynamic behavior was calculated.

Gear root bending strength: a comparison between Single Tooth Bending Fatigue Tests and meshing gears

Gear tooth breakage due to bending fatigue is one of the most dangerous failure modes of gears. Therefore, the precise definition of tooth bending strength is of utmost importance in gear design. Single Tooth Bending Fatigue (STBF) tests are usually used to study this failure mode, since they allow to test gears, realized and finished with the actual industrial processes. Nevertheless, STBF tests do not reproduce exactly the loading conditions of meshing gears. The load is applied in a pre-determined position, while in meshing gears it moves along the active flank; all the teeth can be tested and have the same importance, while the actual strength of a meshing gear, practically, is strongly influenced by the strength of the weakest tooth of the gear. These differences have to be (and obviously are) taken into account when using the results of STBF tests to design gear sets. The aim of this paper is to investigate in detail the first aspect, i.e. the role of the differences between two tooth root stress histories. In particular, this paper presents a methodology based on high-cycle multi-axial fatigue criteria in order to translate STBF test data to the real working condition; residual stresses are also taken into account

A study on prediction & validation of meshing gear pair backlash under various manufacturing and assembly errors

Backlash is a need for proper gear mesh but also a defect if not controlled closely. Few studies have focused on controlling backlash with some mechanical solutions that can be applied. Few other studies have shown interest in estimation of minimum / maximum variable backlash. The operating backlash of meshing gears is affected by many factors among which runouts, pitch errors and tooth thicknesses are the three most pronounced manufacturing errors. All these three parameters are the measurable ones once the gears are manufactured. Center distance and phasing of meshing gears are the examples of assembly errors which may affect the operating backlash. A software has been developed to predict likely maximum and minimum backlash of a gear pair selected arbitrarily and assembled together. For the validation of software predictions an experimental setup is needed for backlash measurements. Thus, a special test rig is designed and constructed for experimental measurements of the operating backlash under some manufacturing and assembly errors of a gear pair. Good agreements have been achieved between backlash predictions and measurements thus validating the in-house prepared software for backlash calculations.

Thermomechanical coupled contact analysis of alternating meshing gear teeth surfaces for marine power rear transmission system considering thermal expansion deformation

Marine power rear transmission system is a constant power system under specific working condition, which relies on alternating meshing gears to transfer the movement and torque. It is difficult to accurately determine the actual thermal stress and thermal deformation for time-varying distribution using the traditional methods. Elastic structural mechanics modeling and method details of thermal expansion deformation are presented and analyzed. Both the actual reflection thermoelastic contact condition for meshing gears and the coupling effect results of the practical loading process of marine power rear transmission system carried out on alternating meshing gear surfaces are also detailed. In this article, the changes in gear meshing angles of several key meshing positions are presented. The 16 meshing positions of contact stresses and loaded deformation approach are analytically evaluated in terms of the rotation range of driving spur gear (35°) and driving helical gear (36°). The purpose of this study is to confirm the significant stress concentration areas of gear meshing in and meshing out and to obtain that the deformation amounts of gear meshing impact positions within selected zones. The aim of this article is to reach gear deformation on the basis of theoretical conception.

Modeling of the kinematic geometry of spur gears using matlab

The analytical method of gear design is calculation-intensive and it is usually difficult to achieve optimum backlash and interference-free involute profile that are required to generate geometrical compatibility in a pair of meshing gears when design procedure is entirely based on this method. Some amount of backlash is often required in the assembly of gears but excess backlash can lead to increase vibration and wear of the gear assembly. Also, interference-risk profile can result in undercutting of gear tooth. This paper optimized a spur external involute-profile gear by developing an application for the modeling of its geometrical compatibility using Matlab®. The application uses existing models to test for interference and a proposed model to determine effective backlash in a gear. The backlash values resulting from the application are more confined and the model is applicable to a wider range of modules suggested by American Gear Manufacturers Association. Simulation of the gear-set in Solidworks® for kinematic geometry presents an interference-free tooth contour and an effective backlash.

Base curves of involute cylindrical gears via Aronhold’s first theorem

The subject of this paper is the synthesis of the base curves of involute cylindrical gears, for uniform and non-uniform transmission ratio, by means of Aronhold’s first theorem and the return circle. The base curves can be generated in several ways, as reported in the literature, but this approach comes from the kinematics fundamentals; it is, thus, more straightforward than the alternatives for the case of non-uniform transmission ratio, which leads to non-circular gears. The base curves of circular and non-circular gears are obtained by intersecting, at each pitch point, the corresponding return circle with the line of action for a given pressure angle. This is possible for involute cylindrical gears since the tooth profile of the rack is represented by a line, and the conjugate profiles of the two meshing gears can be generated by its envelope.