The model that the team will create needs to mimic the behavior of the bacteria that it is trying to replicate. To do this, several specifications will need to be created in order facilitate the design of the robot. Through research and calculations, the team gathered several data points that will be used later in the design and analysis of the propulsion mechanisms. The data that was gathered is summarized in the following table.
Design Specification | Value |
Length | 2 µm |
Typical Speed | 30 µm/sec |
Density of Water | 998 kg/m3 |
Dynamic Viscosity | 1.003 x 10-3 N*s/m2 |
Reynolds Number | 5.97 x 10-5 |
Required Force | 1.81 x 10-15 N |
Table: Summary of Model Benchmarks
Calculation of Reynolds Number:
The Reynolds number will be the basis for all of the scaling operations that will be performed as well as selecting an appropriate fluid to test the scale model in. From the calculated results, we can confirm our assumption that the robot will operate in a highly viscous environment.
Preliminary Calculation of Required Force:
The force required to move the robot will be equal to the drag that is induced on it by the environment. To begin the calculations, the team had to first calculate the drag coefficient for the model at its micro-scale conditions. To do this the team used Stokes’s theorem because it defines a linear relationship between drag coefficient and Reynolds number for an object with a spherical frontal area. After calculating the drag coefficient the team used the drag formula to find the drag force the model would have to overcome to achieve the desired speed at micro-scale conditions.
Preliminary Design and Prototype Benchmarks
Now that the layout for the prototype has been selected, it needs to be dimensioned in accordance with the principle of dimensionless homogeneity. The most important factor in the sizing of the robot and its components is to remember to keep the Reynolds number constant throughout the calculations. This ensures the prototype will experience the same ratio of inertial forces to viscous forces that the model will experience. To begin the sizing analysis, the team first had to pick a scaling factor to be used in the calculation of the prototype dimensions. The team chose its scaling factor based on the characteristic length of the robot. The team chose a prototype length of (3) centimeters, as this will allow us to use pre-fabricated piezoelectric actuators to generate the motion. In addition to picking the prototypes length, the team had to pick a fluid to test the robot in so that it would experience the same ratio of inertial forces to viscous forces that the micro-robot would. To achieve this, the team chose to use silicone oil because it can be ordered from chemical companies in a wide range of viscosities.
The first step of the final design is to use the Reynolds that was calculated earlier to find the new velocity the robot will have to achieve at a prototype scale. The calculations for this procedure are outlined below and the results summarized in a table at the end.
Based on the Reynolds number for the bacterium, we can calculate the new velocity that the prototype will need to achieve in order to properly re-create the conditions that the robot will experience. Next, the new force output required by the robot to move is determined using the scaling laws of Pi's Theorem.
The required applied force for the prototype is within reason, as we stated before, the robot will experience a high viscosity environment at the microscopic level.
Specification | Model Value | Prototype Value |
Length | 2 µm | 6 cm |
Typical Speed | 30 µm/sec | 4.98 mm/sec |
Density of Working Fluid | 998 kg/m3 | 973 kg/m3 |
Dynamic Viscosity | 1.003 x 10-3 N*s/m2 | 486.5 N*s/m2 |
Reynolds Number | 5.97 x 10-5 | 5.97 x 10-5 |
Required Force | 1.007 x 10-9 N | 1.1 x 10-4 N |
Table: Summary of Model and Prototype Design Values for Proposed Robot
Detailed Theoretical Force Calculation
To begin the analysis of the theoretical force outputs and design of the timing graph, the team used the maximum force achievable by the actuators to calculate the maximum move time of the actuators from rest to desired displacement. The tail was modeled to behave in a 2-D fashion to facilitate the calculations. Below is the free body diagram that was used in conjunction with the formulas to perform the calculations.
The team used the drag force equation to calculate the velocity with which the tail can move from rest to its desired displacement of 2 mm. With this velocity and know move distance we can find the maximum move time, the calculations are illustrated below.
From the calculations we can see that the maximum move time for the tail section is approximately (9) microseconds. However from research done on piezoelectric actuators in practical applications we know that an actuator cannot perform at these conditions for too long as it will break down the actuator and degraded its performance. In addition, the robot does not require a 67 Newton force output; in reality it requires a much smaller force output which allows us to increase the move time of the actuators, which is directly related to force output.
Power Stroke:
The power stroke is the most important of the tail’s move profile as it will be responsible for propelling the robot forward through the water. In order for the robot to have a long lifespan, the move times will need to be significantly less than the maximum move time to preserve the actuators from degradation. To this end, the team chose to use a rise time a factor of 100 lower than the max rise time. From this assumption, the team calculated the theoretical x-component of the force output from the tail and found it to be greater than the required force to move the robot, which is the primary constrain of this section.
Set-Up Stroke:
The set up stroke is the first force the robot will experience when it is turned on. This stroke moves the tail into position to begin the power stroke. The reason that there are two different forces is due to the high viscosity nature of the working fluid. When the tail moves up it creates a force which acts against the desired direction of travel, therefore, it was necessary to reduce this force while maintaining a high output from the power stroke. To achieve this, the team raised the move time of the set up stroke by a factor of 10. From the calculations it can be seen that by increasing the time it takes the tail to move into position, the force it generates is substantially reduced and leaves us with an unbalanced force capable of propelling the robot.
