A key design feature was the elimination of the bearing interface that existed in the generic planetary gear set layout. The new planetary gears were simulated using FEA and MBD to assess the viability of the concept.

## Introduction

*General**Problem statement and hypothesis**Objective of the thesis**Scope of work*

The proposed model of the gearbox system will be analyzed using FEA to estimate loads and deformations. In the bearingless floating compound planetary gearbox, the dynamics and load-carrying characteristics of the new design will be evaluated using FEA and MBD software.

## Misalignment-insensitive gearing using kinematic Rzeppa joint and various compliant

### Literature review

In addition to reducing the contact area, improper alignment degrades the mechanical properties of the gear transmission. 1 Thin spur gears with beveled mesh rims on the left, center and right sides of the tooth (Li, 2012).

### Numerical modeling

This article considers an in-plane angular deviation scenario, which is known to normally cause problems. To simulate the misalignment scenario, a parametric study was created in the SolidWorks 3D modeling platform so that any misalignment scenario could be realized (Figure 2.6). Simulations were performed for different misalignment values for the benchmark, flank modified and proposed designs (models A-E), for misalignment values of 0° (no misalignment), 0.1°, and up to 0.2° (in-plane). a) b).

The benchmark model (Model A), a crowning model (Model B), and a web-modified model (Model D, E) were assigned the same boundary conditions, consistent with the actual operation of the gears. In both cases, the gear rotates around the cylindrical support under an external torque, corresponding to 20% of the critical load (calculated on KissSoft), while the pinion was fixed to counteract the rotational movement of the gear. A relatively low torque size was chosen compared to the allowed margin by taking into account a further increase in loads in misaligned scenarios.

For the proposed design (model C), boundary conditions are more complicated compared to the benchmark model due to the presence of different contacts that must be properly defined. First, the contact between the balls and the outer ring grooves is defined as frictionless to compensate for the inability of the balls to rotate in the simplified model. As with models A and B, the pinion is fixed while the inner ring was free to rotate about its cylindrical support under an external 100 Nm torque (Figure 2.9).

### Meshing

Meanwhile, the reference point coordinates for the ball groove interference are x=36.7mm, y=4.3mm, z=0mm (point Y), and point Z with coordinates of (68mm, 8.5mm, 10mm), which matches the flank modified design. In addition, for the conformal web design, the reference point T was selected for mesh sensitivity analysis (64.2 mm, 1.1 mm, 13 mm) (Figure 2.10). The nominal element size at the primary contact interfaces was gradually reduced in subsequent iterations until the acceptable error in the reference points was obtained and convergence occurred.

From the mesh sensitivity analysis graph of Figure 2.15, for points X, Y, Z and T, it is clear that as mesh density/element number increases, the reference stress values begin to approach its asymptotic margin, meaning that the reference stress values appear to converge with decreasing errors in subsequent iterations. The model with crowning modification required more refined interlocking in contact areas compared to other designs, due to the complex flank modification that must be accurately defined.

Transmission error (TE) calculation

### Results and discussion

*Benchmark model (Model A)**Crowned gears (Model B)**Proposed design (Model C)**Gear with compliant web (Model D and Model E)*

However, due to a rapid decrease in the contact area, the maximum stress also increased, but it did not exceed strain values obtained in the case of the misaligned benchmark system. Numerical simulations on the new gears with integrated Rzeppa joint revealed the ability of the proposed design to adapt to the angular displacement of the gear and automatically adjust to any misaligned position (Figure 2.22). In addition, in the case of the proposed model, the maximum stress shifted to the ball-groove interface. a) b) c) Figure 2.

23 Vector displacement field, showing the automatic realignment action of the proposed design (Model C gear adjusts its orientation to the fixed gear). On the other hand, the average TE magnitude of the model with the mechanical connection was 9 times higher, but no significant oscillations were observed on the graph. Therefore, their correlation indicates almost the total insensitivity of the kinematic joint design to misalignment, unlike conventional gears.

28 Static TE for the standard (left) and proposed (right) models over one mesh cycle as a function of gear position θ1. Computational results prove that the proposed universal joint gear transmission model can eliminate the harmful effects of gear distortion automatically. While the contact stresses at the gear tooth interface remain unaffected, the compensation is a somewhat increased stress on the contact surfaces between the balls and the Rzeppa coupling groove.

## Bearingless floating-carrier compound planetary gearbox

### Literature review

For example, Lin and Parker (2002) developed a mathematical model of single-stage planetary gear transmission and discovered three modes, such as rotational, translational and planetary modes. The occurrence of defects within a planetary gear system due to premature failure of components significantly affects the dynamic behavior. For example, Chen and Shao (2013) investigated a case of wind turbine planetary gears with a tooth root crack.

They found that cracks in the teeth of a sun gear have a more serious impact on the dynamics of planetary gears than the failure of the teeth of a planet gear. In addition, Chen, Zhu, and Shao (2015) developed a method to detect planetary gear failure based on the time-varying mesh stiffness graph and dynamic response. Mundo (2006) proposed a new topology of planetary gear set with non-circular gears, which adopts the advantages of epicyclic gears.

Misalignment of the gears in planetary gears leads to time-varying mesh stiffness, increased loads in gears and bearings. Another paper dedicated to the reliability of planetary gears was Nejad, Gao and Moan (2014), who developed a mathematical model to estimate the long-term fatigue effect. Furthermore, the authors claimed that in typical planetary gear sets, due to the higher number of cycles and low number of teeth, the sun gears show the greatest signs of fatigue and tend to fail prematurely.

### Numerical modeling

Boundary conditions for the quasi-static FEM analysis of the new planetary gear are as follows: the input shaft was given a torque with a magnitude of 100 Nm and the free rotational motion was given around its axis by means of cylindrical support. In addition, the ring gear was fixed as well as the output shaft to resist rotation. As with any FEA, discretization or meshing is vital to the analysis and has a significant impact on the accuracy of the simulation.

Given these facts, the main focus was on the gearing interfaces between individual spur gears in the planetary gearbox. Furthermore, due to the limited capacity of the workstation in terms of computing power and memory, it was impossible to discretize whole bodies. Dynamic and kinematic simulations of the proposed design and benchmark system took place in multi-body dynamics (MBD) software called RecurDyn.

The main purpose of the dynamic simulation is to observe the behavior of the new system in real life and verify the initial hypothesis. In addition, the input shaft was given a rotational speed of 100 rads/sec, while the output shaft was given a torque of 10 Nm to resist the rotation. The full setup of the MBD assay, including the synaptic network, is shown in Figure 3.7. a) b).

### Results and discussion

Furthermore, this unfavorable condition of the gearbox was evident from the strain graph (Figure 3.9). Under the applied loads, one end of the primary planet gear moves sideways, resulting in an extremely deformed condition, which in turn, despite the maximum deformation magnitude of only about 77 µm, leads to an abnormal contact path where the load is concentrated at the edge. In addition, according to the previous part of the misalignment, these misaligned gears will create noise and vibration, which obviously leads to complete destruction of the transmission.

Unfortunately, the current design topology was not sufficient to solve the problem to meet the criteria of a robust, reliable and compact powertrain. The main purpose of the MBD simulation was to demonstrate the feasibility and viability of the concept. The main reduction ratio of the model is estimated based on the input and output rotational speeds.

From the velocity graph it is clear that this particular design of the planetary gearbox has a reduction ratio of about 1:3. These fluctuations can be caused by improper alignment of the planets, which was observed in the FEA results, where load distribution is not equal along the tooth contact lines. Thus, MBD simulation shows another adverse consequence of the misalignment of the planet such as non-uniform output velocity, which leads to another problem of torque ripple.

## Conclusion

Quasi-static and kinematic simulations showed that the planetary gear with the proposed layout continues to face the same problems as the conventional gear. Therefore, the theme of the bearingless planetary gear with a floating carrier will find its continuation as an independent research task. Dynamic characteristics of a planetary gear system with a tooth gap under different pitch sizes and angles.

Analysis of fault characteristics of a planetary gear system with tooth root crack and flexible ring gear. Efficiency of the Planetary Gear Hybrid drivetrain.” Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering. Design of a single-stage planetary gear train with improved load distribution conditions and reduced transmission errors.

Theoretical and experimental efficiency analysis of multi-degree-of-freedom epicyclic gear trains.” Multibody system dynamics. A survey of formulas for the mechanical efficiency analysis of epicyclic gear trains with two degrees of freedom. Journal of Mechanical Design. An automated method for the analysis of loaded tooth contact of high contact ratio gears, with or without flank modification, taking into account point angle contact and shaft misalignment.