Flexible Planet Research Articles

SimAb: A simple, fast, and flexible model to assess the effects of planet formation on the atmospheric composition of gas giants

Context. The composition of exoplanet atmospheres provides us with vital insight into their formation scenario. Conversely, planet formation processes shape the composition of atmospheres and imprint their specific signatures. In this context, models of planet formation containing key formation processes help supply clues to how planets form. This includes constraints on the metallicity and carbon-to-oxygen ratio (C/O ratio) of the planetary atmospheres. Gas giants in particular are of great interest due to the amount of information we can obtain about their atmospheric composition from their spectra, and also due to their relative ease of observation. Aims. We present a basic, fast, and flexible planet formation model, called Simulating Abundances (SimAb), that forms giant planets and allows us to study their primary atmospheric composition soon after their formation. Methods. In SimAb we introduce parameters to simplify the assumptions about the complex physics involved in the formation of a planet. This approach allows us to trace and understand the influence of complex physical processes on the formed planets. In this study we focus on four different parameters and how they influence the composition of the planetary atmospheres: initial protoplanet mass, initial orbital distance of the protoplanet, planetesimal ratio in the disk, and dust grain fraction in the disk. Results. We focus on the C/O ratio and the metallicity of the planetary atmosphere as an indicator of their composition. We show that the initial protoplanet core mass does not influence the final composition of the planetary atmosphere in the context of our model. The initial orbital distance affects the C/O ratio due to the different C/O ratios in the gas phase and the solid phase at different orbital distances. Additionally, the initial orbital distance together with the amount of accreted planetesimals cause the planet to have subsolar or supersolar metallicity. Furthermore, the C/O ratio is affected by the dust grain fraction and the planetesimal ratio. Planets that accrete most of their heavy elements through dust grains will have a C/O ratio close to the solar C/O ratio, while planets that accrete most of their heavy elements from the planetesimals in the disk will end up with a C/O ratio closer to the C/O ratio in the solid phase of the disk. Conclusions. By using the C/O ratio and metallicity together we can put a lower and upper boundary on the initial orbital distance where supersolar metallicity planets are formed. We show that planetesimals are the main source for reaching supersolar metallicity planets. On the other hand, planets that mainly accrete dust grains will show a more solar composition. Supersolar metallicity planets that initiate their formation farther than the CO ice line have a C/O ratio closer to the solar value.

A coupling dynamics analysis method for a multistage planetary gear system

The lumped parameter and finite element methods (FEM) are two relatively common modeling approaches for the coupling vibration analysis of the planetary gear system. In order to overcome the lack of fidelity of the lumped parameter models and the high computational cost of finite element models, and in order to obtain accurate vibration response predictions to understand the coupling vibration mechanism in the planetary gear system, a comprehensive, fully coupled, dynamic modeling method is proposed by applying a virtual equivalent shaft element. The continuous planetary gear transmission system is divided into numerous shafting elements. The dynamic model of the planetary gear system is constructed applying these shafting elements, including the shaft segments and flexible ring gear, and as well as the flexible planet carrier. The proposed method is implemented on a two-stage planetary gear system, and it is verified by comparing the results to the calculations using existing lumped parameter and FEM. The quasi-static and dynamic modeling results are presented to study the dynamic behavior and coupling characteristics in-depth. The proposed method can be used to guide the design of high reliability and low vibration planetary gear systems.

M-DOF dynamic model for load sharing behavior analysis of PGT

A Multi-degree-of-freedom (M-DOF) nonlinear dynamic model for n-pinion Planetary gear train (PGT) is presented in this paper to investigate load sharing behavior of planet gears. In this dynamic model, manufacturing and assembly errors, elastic deformation and time-varying mesh stiffness are considered. Two sets of elastic compatibility equations are proposed to describe compatibility relationship between displacements, errors and elastic deformations. By means of Ishikawa formula, time-varying mesh stiffness of the gear pair is determined. The dynamic motion equations are solved with Runge-Kutta numerical integral method, which yields the displacements and deformations of each component. With the model, dynamic load sharing behavior of planet gears is evaluated. An example of 3-pinion PGT dynamic modeling is included, for which the influence of floating sun gear and adding flexible planet pin on the load sharing characteristics is analyzed.

Modal Prediction and Sensitivity Analysis of Wind-Turbine Planetary Gear System with Flexible Planet Pin

Modal Prediction and Sensitivity Analysis of Wind-Turbine Planetary Gear System with Flexible Planet Pin

Influence of Planet Pin Stiffness on Load Sharing in Planetary Gear Drives

Others have done significant work on the subject of load sharing among the planets of planetary gear drives; a brief review of that work is presented. Little work has been done, however, to evaluate the utility of the Hicks type flexible planet pins in improvement of load sharing in a planetary gear stage. This work shows the potential value of the three variations of the Hicks type flexible planet pin used on cantilever carriers, and a new design of a low spring constant planet pin that can be used on straddle type carriers. This is done by the calculation of the spring constants of gear meshes, bearings, and various designs of planet pins using the finite element method for a specific design of a planetary gear stage with spur gears and eight planets. The result showed significant differences. Low spring constant flexible pins are shown to have significantly superior load sharing characteristics.

A Numerical Approach to Calculation of Load Sharing in Planetary Gear Drives

In AGMA 6123-B06 [2006, “Design Manual for Enclosed Epicyclic Gear Drives,” ANSI/AGMA Paper No. 6123-B06], a specific table is given for estimation of the planet load share factor Kγ, as it is termed in that publication; that table is vague as to the exact relationship of tolerance and load to the value of Kγ. Others have done significant works on the subject of load sharing among planets; a brief review of that work is presented. This work calculates a useful value of Kγ directly from design tolerance values and the torque applied to the carrier, and other factors showing how this can be done. This formulation is designed explicitly for nonfloating systems, but may be adaptable to floating systems. The use of flexible planet pins to improve load sharing is discussed. In addition, treating Kγ as a constant with respect to torque for a given planetary design is shown to be inaccurate.

Epicyclic gear dynamics

A summary of a computer program and sample results are presented that predict the dynamic gear tooth load response for single-stage epicyclic gearing systems. The model used is an extension of the Richardson model developed in 1958 and the high-contact-ratio enhancements made by Cornell and Westervelt in 1978. The program has a preprocessor that will generate all the necessary geometric data for solving the system dynamics with a minimum of user input data. The program has the capability of modeling symmetric and buttressed, external and internal spur gear teeth, as well as the helical tooth form. Tooth profile modifications, planet gear phasing, gear tooth runout, and spacing errors can be modeled and evaluated. Summary tables are generated along with plotted data for dynamic tooth loads, flash temperatures, tooth bending stresses, hertz stresses, etc. The program also includes options for evaluating a floating input pinion, a flexible planet carrier, or a flexible ring gear, and the system natural frequencies. A speed survey option is also available to find peak dynamic loads.