# Minimum Mass of Flywheel to Stabilize Angular Velocity

# Minimum Mass of Flywheel to Stabilize Angular Velocity

The minimum mass of the flywheel needed to stabilize the angular velocity of the rotating system is to be determined. The mass should ideally be as low as possible to allow for a lighter engine, while being large enough to perform its required task. The target value for the mass was set at 1 lb. The user requirements affected include long-lasting product, easily started engine, and a lightweight design.

## Strategy for Analyzing Engineering Specification

In order to correctly analyze this specification, necessary engine components need to be modeled and then the engine cycle can be simulated on MSC.ADAMS. The goal of this analysis is to find out how the density of the flywheel affects the stability of the engine and at what value of material density does it become too unstable to function. The key parameters are the torques applied by the piston, the grass against the blade, and the resistance from the inertial forces of the blade, crankshaft, and flywheel. Consequently, these three parts will be used for the dynamic simulation of the engine cycle. The densities of the materials that make up the parts need to be found in order for ADAMS to calculate the mass moments of inertia. The materials of the different parts as well as the power rating of the engine will most likely be determined by asking the manufacturer. Normal loading on the crankshaft will be simulated using half of the rated horse power since the engine does not regularly run at its peak power. This power is directly related to the torque created by the piston and will be modeled as an intermittent function of time to simulate a four stroke combustion cycle. The other forces applied will be to the end of the blades. These will act as a resistive torque applied by grass. The angular velocity of the system as a function of time will then be analyzed for different densities of the flywheel.

## Design Decisions/Parameters Affected

The concentrations of mass with regards to the shape of the flywheel can greatly affect the efficiency of the flywheel. The mass moment of inertia can change greatly depending on the shape, size, and density of the flywheel which is the key parameter that dictates how the flywheel functions.

## Key Geometric, Inertia, and Material Properties

The density and consequently the choice of material for the flywheel are greatly affected. The material of the flywheel and crankshaft was aluminum and the associated density was 9.898 x 10^-2 lbm/in^3. The material of the blade was stainless steel and the associated density was .279986 lbm/in^3. The size and shape of the flywheel are also affected, as they influence the overall inertias on the rotating system.

## Type of Analysis for Obtaining Results

The blade, crankshaft, and flywheel were assembled in ADAMS. To simplify the analysis, the system was given an initial angular velocity of 3600 rpm which was provided by Briggs and Stratton. The intermittent firings of the piston were simulated by applying a torque as a function of time to the system. In order to relate this to the output torque of the engine, a resistive torque was applied to the ends of the blades in the form of two forces. These forces also help simulate the resistance of the grass on the blade. The force was calculated by taking half of the power rating of the engine (3.0 hp) and its normal rpm and solving for the torque. The forces were then found with this torque and the radius of the blade. The equations used for this calculation can be seen below.

Power = Torque * Angular Velocity Torque = Force * Radius

With this resistive force, the function of time that defined the torque of the piston was then adjusted accordingly in order to simulate a stable system with a nearly constant angular velocity.

Now with the system correctly set up, the density of the flywheel was changed numerous times and simulated with the system in order to see how the stability of the system changed by observing the oscillating angular velocity. An increase in the range of the oscillations or a dramatic change in the slope overtime of the angular velocity will indicate that the system is no longer stable. A horizontal plot of small oscillations will indicate a steady system.

## Boundary Conditions and Loading

## Quantitative Results

Below is the resulting plot of the angular velocity of the system in two states. The red plot represents the system with an aluminum flywheel and the black plot represents the system with the flywheel having a negligible density.

Although the system appears to be oscillating, those variations in angular velocity are negligible with a range of around 4 degrees/second. Surprisingly, according to the calculations done by ADAMS, the presence of the flywheel showed to make very little difference in how steady the system performed. Changing the density of the flywheel to a miniscule value only increased the oscillation range by about .25 deg/sec. This result lead to further this analysis by individually changing the densities of the other components and simulating the system to see how they affected the engines stability. Below is a plot of the angular velocity before and after changing the density of the crankshaft. The second plot is the resulting angular velocity before and after changing the density of the blade.

It can be seen that the overall mass of the crankshaft and blade were much more significant in keeping the system stable. The amplitude of the oscillations when the density of the crankshaft was made negligible increased significantly more than that of the flywheel. The system was oscillating between 21600 deg/sec and 21610 deg/sec.

Changing the density of the blade created the most dramatic change in the angular velocity of the system. Over the span of two seconds, the average angular velocity changed from 21602 to 21595. Although this decrease is gradual, these results are indicating that without the blade attached to the engine that it would no longer remain stable and most likely eventually stall out.

After completing this analysis, these results seem to be skewed due to a number of simplifications. There were numerous components of the system that were not included in the model which could have changed the overall performance. Their affect was assumed to be negligible but may have had a larger effect than expected.

The resulting data is counter-intuitive to what one should expect. Conclusions drawn from this data indicate that the flywheel has no significant effect on stabilizing the system which contradicts its primary purpose. Moreover, the results also show that the system could not function properly at all without the blade which is a removable accessory. Ideally the stability of the system should not be dependent on a component that is often ephemeral.

## Suggested Changes to Improve the Quality of this Design

Since the flywheel had little significance on the system stability according to the model, there are little changes that can be suggested in terms of the density of the material used. An area that was not looked into was changing the shape and mass concentrations of the flywheel. This analysis would have introduced too many different variables and was not concentrated on due to the amount of time allotted for this project. Generally speaking though, there were some thin sections of mass towards the center of the flywheel that were doing little in terms of increasing the engine stability. These sections could be removed and relocated along its outer perimeter. This consequently would affect the stability of the flywheel itself as a part, but would increase its mass moment of inertia without an increase in the mass of the part. Such a change would make the engine’s performance more stable but may change the overall dimensions of the part.

Another suggested design change could be to slightly increase the thickness of the fins. Their primary purpose is to create airflow over the governor, but such a slight increase would do little in changing this function. The benefit of this change is that it would increase the moment of inertia of the flywheel and therefore increase engine stability. It would do so by not making any overall dimension changes. This change would also increase the mass of the flywheel which is trying to be minimized.

**Return to Lawn Mower Internal Combustion Engine**