We would also like to thank the organizer of the Capstone project course, Professor Konstantinos Kostas, for his encouragement and skillful management of the overall process. Namely, when loaded TCR is slightly less than integer, it is possible to achieve desired constant mesh stiffness, while exact integer causes spikes in the curve. Second, applying tip relief to spur gears changes the ratio between theoretical and loaded TCR: in the case of gears with tip relief, loaded TCR is less than theoretical one, while for regular gears loaded TCR is always higher than theoretical.

Third, when helical gears have a high (more than 2) integer overlapped contact ratio (OCR), the effect of TCR is almost negligible. To find a solution for gear misalignment, 4 different gear web designs were studied: plain, spoke, split gear (spoke pinion modification), and multicomponent topologies.

## Introduction

*Problem statement**Load-insensitive gearing**Misalignment insensitive gearing**Design integration**Contributions*

It will be shown that the last three parameters can be reduced to the contact ratio, which is commonly used in gear analysis and especially in the investigation of the vibration issue. Khurmi et.al., 2005) The goal of the project is to find the best load configuration, contact ratio and tip relief for constant mesh stiffness, then integrate this design into the system along with the self-locking mechanism. real-time loading and split torque. topology. In order to find a suitable solution, four different gear network designs will be studied: common, spline, split-pinion (spinion modification) and multi-component topologies.

After developing two different designs that provide load insensitivity and misalignment insensitivity to gears, the final task becomes combining these two properties into a single one. If successful, there will be a design that will withstand deviations in load and orientation with equal ease.

## Literature review & Background material

### Dynamic loads

The cross or overlapped contact ratio being integer led to the minimum fluctuation of web stiffness, while the total contact ratio being integer showed its maximum fluctuation. Second, the investigation of the load variations on the contact lines showed that the length of the contact lines fluctuates only when the total contact ratio is an integer. Third, the amplitude of the fluctuation of the total length of the contact lines has shown that it corresponds to the amplitude of the change of the stiffness of the grid, therefore, a rough approximation of the fluctuation of the stiffness of the grid can be obtained by observing the total length of the contact lines.

The exact amount of tooth tip relief is specified in British Standard (BS 1970) and (ISO/DIS 1983) and the effect of different sizes of the amount and allowable length of tip relief on tooth stress concentrations has been investigated ( Shanmugasundaram et al., 2014). Therefore, the introduction of the preload mechanism helps to adjust the positive effect of the profile modifications for a wide range of loads, while the implementation of two parallel gears will significantly reduce the overall excitations by dividing the load between two pairs of gears.

### Misalignment

The problem that has not been sufficiently investigated is that profile modifications are only adapted for only one type of load and not for a wide range of loads, which is common in aeronautical applications. Consequently, the introduction of preload mechanism helps to adjust the positive effect of profile modifications for a wide range of loads, while the implementation of two parallel gears will significantly reduce overall excitations by dividing the load between two gear pairs. particular scope based on results of parametric study. Much more convenient solution would be to have such a gear pair where both components can adjust their relative position by themselves to increase contact area as much as possible.

This will be very beneficial because in this case the system will show a good behavior even for varying misalignment. This will partially improve the contact area between two gears and reduce the need for tooth profile modification as much as possible.

## Methods, tools and results description

### Load-insensitivity

*Milestones**Methodology**Mesh stiffness results for 1 st semester**Final mesh stiffness results**Transmission error results for entire system*

The investigation of mesh stiffness started from the creation of 3D geometry shown on Figure 3.1 in Kisssoft software. The model shown is taken from case study done by Shanmugasundaram as a preliminary model for estimating effects of tip relief and crowning on mesh stiffness variation. However, the mesh stiffness curve flattens slightly in the case of overlap contact ratio with tip relief that is more than 2.

Next, our study continues to examine the relationship between load variation and overlap web stiffness, with transverse and total 2 with/without tip relief (Table 3.3). Therefore, these results lead to the conclusion that the use of tip relief helps to reduce the fluctuations in web stiffness with increasing load. The next step was to observe the sensitivity of the mesh stiffness with the transverse contact ratio varying from 1.58 to 2.

In general, from inspection of this figure it can be concluded that increasing the helix angle has a positive effect on reducing the lattice stiffness fluctuations up to a certain degree. Therefore, this leads to the conclusion that the overlap contact ratio is more important than the transverse one for reducing the web stiffness fluctuations when it is close to or greater than 2. Although the transverse contact ratio increases up to 1.8 with the overlap 1.2, it produces the mesh stiffness curve with more fluctuation than the curve with transverse contact ratio 1 and overlap 2 (light blue curve).

An important finding along with using the latest version of KISSsoft was the importance of the transverse contact ratio under load for the mesh stiffness curve. As can be seen from Figure 3.7, the stiffness of the spur gear mesh is highly dependent on the load and is more specific on the loaded transverse contact ratio (TCR). Therefore, these results lead to the conclusion that tip relief does not change the theoretical TCR, however, it changes the loaded TCR and as a result the smoother web stiffness curve can be achieved at higher loads.

Each of them has its own effect on the mesh stiffness results, so each is studied separately. Therefore, using integer overlap contact ratio together with slightly less than integer transverse contact ratio under load yields nearly constant web stiffness curve while implementing torque topology with preload mechanism.

### Misalignment insensitivity

*Milestones**Justification for use of static structural studies**Parameters**Model creation for finite element analysis**Milestone 1: parametric study of ordinary gears**Milestone 2: multicomponent pinion**Milestone 3: spoked pinion**Milestone 3: fragmented pinion*

Since preload mechanism allows correction of actual load on teeth, it will allow to keep transmitted load constant and vary actual load by setting up angular displacement using actuator (Figure 3.12). For the part of the project related to gear misalignment, static structural studies were used to obtain the stress distribution patterns. This means that before any oscillation affects the performance of the gears in any way, stress is completely distributed.

As it turned out during the studies, two pairs of teeth in contact when gears interact with each other cause additional problems, because solving the fine mesh model generated in both pairs of teeth requires more resources in terms of RAM and productivity of the hardware. After that, contact surfaces of the engagement teeth were subjected to 3rd level mesh refinement, which made the mesh in that area finer. In the case of the sprockets with the spokes, additional mesh sizes of 15 mm were applied to the spokes closest to the contact tooth.

As the model was relieved of extra teeth, the orientation of the gears was fixed and the mesh was improved, a parametric study was carried out for regular gears. As can be seen, a noticeable difference in the stress distribution still exists, but it is far less dramatic than for misalignment of the same magnitude around the X-axis. The second milestone in the project was to create multi-component web for the gear and study its behavior.

An important moment is that they must be inclined to the radial lines connecting the center of the pinion with the center plane of each tooth, otherwise their resistance will be low. To study the performance of the spoke pinion, two parameters were chosen: the width of the spoke, W, and the thickness of the spoke, T. One of the observations that can be made from these results is that even the highest peak voltage is lower than with normal gears. with the same misalignment (519.7 MPa vs. 560.32 MPa).

There are several measures that can be taken to improve this situation: increasing the width and thickness of the spokes (which probably won't be effective) and adding some malleable material between the teeth (which may help). Before these measures are taken and proven to improve equipment performance, this design should be considered inappropriate.

## Implementation and Integration

This design shows low uniformly distributed stress on the engaging surfaces, but still cannot be considered successful due to extremely high stress on the spokes (over 1200 MPa). At the same time, when large gears carrying extremely high loads and rotating at low speeds, as in naval applications, are involved, misalignment is the major problem, inducing high stresses on the teeth. However, there are still some applications, such as Automotive, where load and displacement insensitivity is equally desired, so a combined solution can be used there.

Therefore, an additional challenge for future work is to create a torque-splitting topology, which will be compatible with gears with modified webs and point-relieved teeth, so that it will be insensitive to both load and misalignment.

## Conclusion

For the distortion study, four different web configurations were analyzed: regular, multi-component, slotted, and fragmented pinion configurations. The multi-component mesh was successful in terms of uniform stress distribution, but its complexity may cause additional manufacturing difficulties. The spline pinion topology showed complex behavior but was still effective in terms of stress redistribution.

The split pinion helped achieve better stress distribution, but there is one major limitation: incredibly high stress on the spokes, which makes this configuration unusable. It is still possible, however, that some special measures, such as inserting a soft material into the slots of the chipped gear, will solve this problem and make a valid solution out of this design. Evaluation of the Effect of Misalignment and Profile Modification in a Spur Gear Drive by Finite Element Mesh Simulation.” Journal of Mechanical Design.

Design for straight inclined devices based on low sensitivity of installation errors and experiment tests. Journal of Aerospace Power. Hoshima Reddy, 2016 "Investigation on the Effects of Tooth Profile Modifications and Transmitted Torque on the Tooth Connections of a Helical Gear Pair", International Journal of Applied Engineering Research, Vol. Liu, Lan, Yunfei Ding, Liyan Wu, and Geng Liu, 2015, "Effect of Contact Ratios on Mesh Stiffness of Helical Gears for Low Noise Design," Power Transmission Engineering.

Palmer, David and Michael Fish, 2012, "Evaluation of methods for calculating the effects of tip relief on transmission error, noise and stress in loaded spur gears", Gear Technology. Shanmugasundaram, Sankar, Manivarma Kumaresan and Nataraj Muthusamy, 2014, "Effects of Pressure Angle and Tip Relief on the Life of a Speed Up Gearbox: A Case Study", Springer Plus, 3:746. Welbourn, D.B Fundamental Knowledge of Gear Noise- A Survey", Engine and Gearbox Noise and Vibration Conference, Cranfield Institute of Technology, Paper C177/79, p.