# Time-Domain Dynamic Modeling and Analysis of Complex Heavy-Duty Gearbox Considering Floating Effect
###### Abstract  
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. h 2021 24 July 20  
quite unique and rigorous. The service life of a wind turbine is usually designed to last more than 20 years [5]. However, internal WTGs have the highest failure rate of all wind turbine components [6; 7], and the main cause of wind turbine standstill is the vibration issue [8]. Hence, the dynamic behavior and working performance of gearboxes have a significant impact on the whole machine, and research on the vibration characteristics is critical to the design and redesign of gearboxes. Considerable efforts have been made to give comprehensive insights into the dynamic behavior and vibration issues of gearboxes, especially of planetary gear sets [9; 10]. [PERSON] et al. [11] derived a time-varying dynamic model of a planetary transmission including the manufacturing error, assembly variation and time-varying stiffness. [PERSON] and [PERSON] et al. [12] developed an analytical lumped-parameter model of a planetary gear set and used it to investigate the natural frequencies and vibration modes. [PERSON] et al. [13; 14] investigated the vibration behavior of a planetary gear set with an elastic ring gear and an elastic planet carrier. [PERSON] and [PERSON] [15] derived a mesh stiffness model of an internal gear pair with a tooth root crack in the ring gear based on the potential energy principle. [PERSON] et al. [16] proposed a finite element formulation for the dynamic response of gear pairs. [PERSON] et al. [17] analyzed the main influencing factors on the meshing stiffness, as changes in the stiffness are a significant source of noise and vibration. She also designed a non-circular gear transmission system with continuously changing gear ratio and studied its kinematical characteristics [18]. [PERSON] et al. [19] studied the dynamic response of a WTG by enhancing the capability of FAST (a wind turbine CAE tool) [20] through the integration of a gearbox model built using Simscape, which took into account excitations from both the wind field and the generator. [PERSON] et al. [21; 22] used the lumped parameter method to study the dynamic behavior of a WTG with flexible pins and proved that the flexible pins can improve the load sharing ability. [PERSON] et al. [23] investigated the influence of non-torque loads on the dynamic behavior of planetary gears, including the loading distribution and loading sharing, and concluded that considering the non-torque load during the design stage is quite important to accurately determine the design load that will guarantee the service life of a WTG.