ROLLING RADAR CONCEPT



Rolling Radar Concept

Preliminary Design Report

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Senior Design Team 05426

Brian McManus

Aaron Halterman

Caleb Herry

Gabe Ferencz

Gabe Chan

Department of Mechanical Engineering

Kate Gleason College of Engineering

Rochester Institute of Technology

76 Lomb Memorial Drive

Rochester, NY 14623-5604

Executive Summary

This report summarizes the progress made by the Rolling Radar Concept Senior Design Team. The goal of this project is to assess the feasibility of Lockheed Martin’s Rolling Radar Concept. This radar concept consists of a large, self-supporting array that rolls along a circular electrified rail. This array is attached to an axle that is supported by a smaller wheel at the other end of the axle. The array is propelled by a gravitational drive that rotates along an inner magnetic track that creates a moment enabling the array to overcome its inertia. The gravitational drive is magnetized and rotates by the electromagnetic force provided by the inner electromagnetic track.

The main focus of our project concerns the feasibility and reliability of the current design. This feasibility will be determined based on our analysis. Our project does not fit the typical mold of most senior design projects in that we are not building the conceptconstructing a prototype. Our emphasis for Senior Design 1 was primarily on the analysis of the control system, the weight of the gravity drive, and the magnetism of the EM track to control the gravity drive. Our concept development work therefore mostly entails the selection of an accurate controller to model the system, research to optimize the EM track system, and a practical selection of parametric graphs for gravity drive weight and other parameters in Microsoft Excel.

Much analysis was done for Senior Design 1 concerning the kinematics of the control system and the analysis for weight of the gravity drive. At this point neither the size nor the weight of the array is known; parametric studies need to be completed to evaluate the effect different parameters have on the capabilities of the radar. Optimizing these parameters was a main goal of Senior Design 1.

The purpose of this document is to provide the current research, analysis, and feasibility assessments, as well as plans for Senior Design 2. The research completed is provided in the Concept Development section. Various controllers, for example, are evaluated in this section for the control system to portray the method of selection for this aspect. The Feasibility section outlines which concept was chosen that will best suit the radar. This section also discusses the feasibility assessments that have been completed to date. Once our parametrics allow us to optimize parameters, specific performance specifications will be provided along along with an overall feasibility assessment of the aspects our analysis does not allow us to assess at this point in time. The analysis will be discussed in depth in the Analysis and Synthesis of Design section. Plans for further work in Senior Design 2 will be provided in the Future Work section.

1 Table of Contents

Executive Summary 2

1 Table of Contents 4

2 List of Figures 6

3 List of Equations 7

4 Recognize and Quantify the Need 8

5 Statement of Work 10

6 Concept Development 11

6.1 Control System 11

6.1.1 On/Off Control 12

6.1.2 Continuous Control 12

6.1.3. Proportional Control (P) 13

6.1.4 Proportional Integral Control (PI) 14

6.1.4 Proportional Integral Derivative Control (PID) 14

6.1.5 Tuning of Controller 15

6.3 Axle Position Sensing System 16

6.3.1 Optical Barcode Sensing System 16

6.3.2 Hall Effect Sensor System 18

6.3.3 Analyzing Position Sensing Systems 19

6.4 Carriage Position Sensing System 1920

6.5 Types of Magnets 20

6.5.1 Electromagnetic Track, Electromagnetic Carriage 21

6.5.2 Permanent Magnet Carriage, Electromagnetic Track 21

6.5.3 Electromagnetic Carriage, Permanent Magnet Track 22

6.5.4 Permanent Magnet Carriage, Permanent Magnet Track 23

6.5.5 Analyzing Magnet Configurations 24

6.6 Mathematical Model of Magnetic Track 26

7 Feasibility Assessment 26

7.1 Gravitational Drive Weight Analysis Feasibility 26

7.2 Axle Position Sensing Systems Feasibility 27

7.3 Types of Magnets 2728

8 Performance Objectives and Specifications 28

8.1 Design Objectives 29

8.1.1 Magnetic Propulsion System Design Objectives 29

9 Analysis and Synthesis of Design 30

9.1 System Model and Control 30

9.1.1 System Model Assuming Axle Twist is Negligible 30

9.1.2 System Model with Axle Twist 34

9.2 Array Size and Weight 38

9.2.1 Assumptions 39

9.2.2 Global Parameters 40

9.2.4 Parametric Analysis Method 41

9.3 Magnetic Propulsion System 4544

10 Future Plans 4645

10.1 Control System 4645

10.2 Reliability 4746

10.3 Parameterizing Gravitational Drive 4746

10.4 Derivation of a Mathematical Model of the System 4847

10.5 Electromagnet Power Requirements 4948

10.6 Control System 4948

10.7 Schedule 4948

11 References 5150

12 Appendix A - Schedule 5352

13 Appendix B - Excel 5453

2 List of Figures

Figure 1: Pugh's Method Comparison for Axle Position Sensing Systems 19

Figure 2: Pugh's Method Comparison for Electromagnets and Permanent Magnets 24

Figure 3: Specifications 29

Figure 4: FBD of Rolling Radar 31

Figure 5: Unity Feedback No Twist 32

Figure 6: Unity Feedback Position and Angular Velocity vs. Time 32

Figure 7: PID Controller with no Twist 33

Figure 8: Position and Angular Velocity vs. Time 33

Figure 9: FBD of rolling radar 34

Figure 10: Individual Components FBD 35

Figure 11: Unity Feedback with Axle Twist 36

Figure 12: Unity Feedback Position and Angular Velocity vs. Time 37

Figure 13: PID Control with Axle Twist 38

Figure 14: Position and Angular Velocity vs. Time 38

Figure 15: Parameter Plots 4443

Figure 16: Gravity Drive Mass with Start-up Time and Tilt Angle Variance 4544

3 List of Equations

Equation 1: Moment Equilibrium 31

Equation 2: Sum of Moments 31

Equation 3: Transfer Function 31

Equation 4: Main Array Moment Equation 35

Equation 5: Axle Moment Equation 35

Equation 6: Support Wheel Moment Equation 35

Equation 7: System Model Transfer Function with Twist 35

Equation 8: Shear Singularity Function 42

Equation 9: Moment Singularity Function 42

Recognize and Quantify the Need

The Rolling Radar Concept has many aspects that Lockheed Martin needs to assess. Due to time constraints and other factors, only a few of these aspects would fit the scope of our Senior Design project. As such, selection was chosen by the team based on time constraints and team skills. Another factor in the selection of aspects dealt with the inter-workings of the radar and the dependencies certain aspects have on one another. For example, it is necessary to analyze the weight of the radar in order to model an accurate control system, discussed in further detail below.

The weight of the gravitational drive is one of the main criteria for the feasibility of the design. If the gravity drive is determined to be too large, recommendations for alternate designs will need to be given to address the problem. The size of the radar array needs to be variable, as the final size will eventually be optimized by other parameters of the radar. Parametric graphs will therefore need to be generated.

A control system that uses the kinematics of motion of the radar needs to be addressed in order to analyze the stability and functionality of the radar. The weight of the gravity drive, discussed above, must be analyzed in order to have an accurate model of the radar. An accurate control system that is applicable to this design needs to be researched and developed.

The electromagnetic track (EM) is another important aspect of the radar that needs to be assessed. The EM track controls the gravity drive location, which ultimately controls the location and speed of the radar. The EM track also requires the weight of the gravity drive. The mechanics of this EM track as well as the selection of the magnets on the gravity drive and the EM track itself needs to be analyzed.

The current requirements are expressed in outline form below.

1. Gravity Drive Size

1. Determine Torque

1. mg (mass of gravity drive)

2. θ (tilt angle)

3. β (degree of gravity drive rotation)

4. r (radius of array)

2. Resisting forces on torque

1. B (rolling resistance)

2. Br (Kulumb resistance)

3. Acceleration Capabilities

1. m (see 1.1.1)

2. θ (see 1.1.2)

3. β (see1.1.3)

4. r (see 1.1.4)

5. mtot (total inertia)

1. ma (mass of array)

2. msw (mass of support wheel)

3. mr (mass of axle)

6. t (time)

7. ω1 (rotation speed of array)

2. Reliability

1. Forces/Stresses

1. Structural Support

1. Ground Reaction Forces

2. Component Analysis

1. Main (Array) Wheel

1. Material

2. Internal Forces / Moments

3. Fatigue life

2. Support Axle

1. Material

2. Internal Forces / Moments / Torsions

3. Fatigue life

3. Support Wheel

1. Material

2. Internal Forces / Moments

3. Fatigue life

3. Control System

1. Equations of Motion

1. J1, J2

2. B1, B2 (resistances)

3. ω1, ω2 (rotation speeds, see1.3.7)

4. k (axle spring constant)

1. Axle material

5. Tk (torque)

2. Simulink Diagrams

1. Inputs

1. Τk (see 3.1.5)

2. Gc(s): Gc = Gcontroller * Gactuator

1. Gcontroller

1. PID Controller

1. Integrator and differentiator blocks

2. D(s): Disturbances

1. Wind

1. Dryden wind plots

2. Gactuator

1. Mechanics of motion (see 3.1)

3. H(s): Bar Code Reader

4. Electromagnetic Propulsion System

1. Components of System

1. Types of Magnets

1. Electromagnets around array

2. Drive Carriage Magnetism

2. Orientation of Magnets

2. Mathematical Model of System Orientation

1. Orientation of drive carriage relative to platform

2. Amount of force produced by different configurations

1. Effect of configurations on speed of array

3. Materials for Magnets

1. Durability of Magnets

2. Feasibility

5 Statement of Work

A statement of work is necessary to quantify the amount of work needed in the time given. A tentative work breakdown was generated in the first week of SD1. This breakdown is shown in Appendix A with the schedule.

6 Concept Development

6.1 Control System

One of the requirements of was to have a servo controller system designed and analyzed for the gravitational drive. Many servo controllers are being used in the industrial world. Most are designed to control the rotational motion of different motors. The system that we need to control is different in that we need to control the translation of a gravity drive along an arc to create a moment, which will then create the rotational motion. To choose a control system we first needed to analyze how different controllers work to meet the requirements of our system.

A system controller, in simple terms, is a device that measures an input, usually some type of error, and then tries to minimize the error by maintaining a desired value by adjusting an output device. Controllers change the value of the system variable by adjusting the control output. An industrial system controller typically uses a control output to drive a control valve or actuator to control a system variable like fluid flow, pressure, velocity, or position to a desired setpoint. Our application has proved to be atypical as will be discussed later. Most system controllers do not work directly with the system variable and setpoint, but rather work with an error signal, as mentioned earlier. This is calculated by determining the difference between the actual value and the required value, i.e. the setpoint. The error represents the deviation of the system variable from the setpoint. Being that the actual value is required to determine the error, some type of sensor or measurement device is usually. Generally there will be the need for some type of conversion gain to make sure that the sensor and the system variable are speaking the same language, so to speak.

When evaluating the error, positive error indicates that the system variable is above the setpoint, and a negative error indicates that it is below the setpoint. For example, the angular velocity is greater or less than the desired speed. Because the system variable information is fed back from the system being controlled, this type of controller is sometimes called an error feedback controller. The controller uses the value of the error to determine the control output necessary to maintain the system variable at the setpoint. If the error is negative for example the controller will tell the actuator to speed up or boost its effect.

6.1.1 On/Off Control

The simplest types of controllers are called ON/OFF controllers, because they simply turn an output device ON or OFF depending on the value of the error. To keep the output from cycling rapidly ON and OFF, most ON/OFF controllers incorporate a deadband. A deadband is a range that encloses the desired output value. The controller output remains in the current state until the error moves out of the deadband. Because of deadband, the system variable controlled by an ON/OFF controller is always cycling back and forth around the setpoint. This means that there is generally not a steady state value. ON/OFF control is often called "bang-bang" control because the control output is cycled between two extremes.

2 Continuous Control

Most industrial processes use continuous controllers, in which the control output is an analog value that is continuously adjusted. This has the obvious advantage of eliminating all of the ups and downs and steady state oscillations in the system variable that are experienced with ON/OFF control. Most continuous controllers used in industry today use proportional, integral, and derivative action, and are thus called PID (proportional-integral-derivative) controllers. Being that this type of controller is the most common it was our first choice to control the gravity drive. However in choosing controller we needed to first look at the individual costs and benefits the various types of control. Each of these controller actions is explained in detail in the following sections.

6.1.3. Proportional Control (P)

The simplest continuous controller uses proportional control. These controllers get their name from the fact that the control output is proportional to the error signal. This type of control is simply a gain on the error signal. A large error generates a large control output, and a small error generates a small control output. .

An offset value determines what control output will be generated when the error is zero. This is generally set to 50% so that the control device will be 50% open with zero error. A proportional gain determines the amount of control action that will be generated by a given error signal: A small gain value will result in little control output change for a given change in the error signal, while a large gain value will result in a large change in the control output for the same change in the error signal. The primary problem with proportional control is that some non-zero error signal is usually required to generate the control output necessary to stabilize the system at the setpoint, so the process cannot be controlled precisely. The control output required to achieve the setpoint would have to be exactly equal to the offset value (50% in the above example) for the control to be accurate at the setpoint. In any other situation, there would be a non-zero error signal required to generate the appropriate control output, and this would result in a system that was always off of the setpoint, meaning unacceptable steady state error. For this reason proportional control was not chosen for our application.

6.1.4 Proportional Integral Control (PI)

The next type of control that was considered was proportional-integral (PI) control. Integral action can be added to proportional controllers primarily to solve the problem of steady-state error. Integral action eliminates the need for an offset value as well as dealing with the unacceptable steady-state error. Since the effect of the integral is to continuously add up the error over time, the output of a controller with the additional integral action will continue to change as long as the error is non-zero, and will cease to change only with zero error. If the system being controlled is stable, integral action will guarantee that the steady-state error eventually becomes zero. However in the system that we are analyzing with two rotating masses there was an integral control phenomenon that was inherent to our system model. This can bee seen by factoring out a 1/s from our plant model. We also analyzed the system with the assumption that there is minimal twist between the two masses and there fore the system can be looked at as one rotating mass. With this assumption the system model becomes simpler and of lower order.

6.1.5 Proportional Integral Derivative Control (PID)

We then needed to analyze the effects of proportional-integral-derivative (PID) controllers. Derivative action was added to proportional-integral continuous controllers to help them deal with sluggish processes. Systems with a great deal of mass that must be accelerated or decelerated tend to require controllers with derivative action. Obviously our system requires this type of control. Derivative action reacts to the rate of change of the error over time. This has the effect of reducing the output to minimize overshoot, anticipating that the system will soon reach the required value.

6.1.6 Tuning of Controller

The process of determining the gains in a controller that will best control a given system is called controller tuning. Gains that are too high will result in erratic swings in the output and unstable process variable behavior, while gains that are too low will result in sluggish output response and poor control. When the gains are ideally adjusted, i.e. the controller is correctly tuned, the system being controlled will respond smoothly and rapidly to changes in setpoint and recover quickly from disturbances to the system. For example, the system develops a desired velocity quickly with little or no overshoot and will also react well to disturbance. Changing all of the gains in a similar manner is not an effective means of controller tuning, however. The way in which proportional, integral, and derivative action relate to the system and each other must be considered, and this is dependent on the characteristics of the process being controlled, mainly the system model.

High proportional action is best for systems that react predictably to control output changes. Systems that react in an unreliable manner or contain noise in the measurement of the system output, will not behave well when controlled with high proportional gain.

Integral action behaves in almost the opposite manner of proportional action. Because integral action adds up the error over time, it is fairly immune to noise in the system output. The additive action also means that integral control does not react immediately to changes in the process, but reacts more slowly. These attributes make integral action best suited for fast responding, somewhat noisy systems or processes. Our preliminary analyses show that this is not the type of system that we need to control.

Derivative action behaves somewhat differently and some caution must be used in the application in practice. First, derivative gains should be adjusted carefully as the effect can be significant. Second, derivative action should be avoided in systems in which the system variable contains noise. Noise in the system output measurement will cause the error to bounce up and down very quickly, resulting in rapidly changing positive and negative slope values. These changes will be magnified by the derivative action, which will almost always result in an unstable control system in the presence of significant system output noise. Derivative action is indicative to systems that are slow reacting and one in which the system output measurement is dependable and noise-free.

6.3 Axle Position Sensing System

6.3.1 Optical Barcode Sensing System

One of the original electrical engineering focuses of the Rolling Radar project was the axle position sensing system. The radar array is attached at the end of the rotating axle. Therefore, determining the position and orientation of the axle is necessary in order to establish the azimuth position of the array. Since this is a critical aspect of radar analysis, this position needs to be very precise due to the hundreds of miles over which the radar may potentially be scanning. A small error in position readings will be amplified as a function of the distance from the array to the target, which would add up quite quickly. Assuming that the angular velocity of the rotating array is known, the position of the axle can be calculated externally by a microprocessor. Because determining the position and orientation of the axle is such an important factor in the functionality of the rolling radar design and has such stringent requirements in terms of accuracy, an external scanner should be implemented in order to serve as a redundant precaution in comparing the calculated position versus the actual position of the array.

One type of position sensor proposed is a barcode reader. Research was performed and questions arose concerning the implementation of the scanner. Barcode scanners used for positioning systems are currently available for linear applications. This type of system could easily be implemented for a circular track, especially if the track has a large circumference. Serious concerns were raised with the realization that it would be necessary to scan 360 degrees. Since the scanner would be mounted on or within the axle, it would rotate along with it. In order to effectively cover all points lying along the circumference of the array’s path of travel, a few solutions were presented. The use of fiber optic sensors for redirecting the light reflected off the barcode, the implementation of multiple barcode scanners, and the use of a barcode scanner that would remain stationary (i.e. directed towards the barcode at all times) within the axle were considered. A multiple barcode scanner system could easily determine the orientation of the array as only one scanner would be reading at a time based on a control algorithm. Any overlap in data between scanners could then be filtered out to determine the correct position. The accuracy in orientation calculations would then be a function of the number of barcode scanners used and the angles at which they scan relative to the platform’s horizontal plane.

6.3.2 Hall Effect Sensor System

A second position sensing system that was considered was one that implements Hall sensors. This type of sensor works by producing a voltage in the presence of a magnetic field generated by a magnet passing by it. The output voltage of the sensors is proportional to the strength of the magnetic field generated by the magnet passing by it, with the strongest voltage being produced when the magnet is directly in front of it. For the Rolling Radar project, magnets would be placed on the back of the radar array (facing the inside of the platform) while Hall effect sensors would be placed on the platform on an interval that exactly matches the interval of magnets placed on the array. Ideally, whenever a magnet reaches the bottom of the array on a rotation, a Hall effectEffect sensor will be directly adjacent to it. Each sensor will be indicative of the position that the array is directed towards. Therefore, the Hall effectEffect sensor with the highest output voltage would provide the current position of the array. Such a system was considered for this application because the reliability of a Hall sensor appeared to be greater than that of a barcode scanner. Due to the fact that the radar system may be deployed in the field, open to the elements, an optical barcode may be obscured from dust and dirt, thus hindering the performance and accuracy of a barcode scanner.

Although not hindered by small foreign objects, such as dirt, Hall effectEffect sensors are susceptible to poor temperature conditions, giving inaccurate readings when they fall out of their optimal operating ranges. Also, typical applications of these sensors require a close distance between the sensor and the magnet. Given the potentially large size of the rolling radar system, this would require the use of many sensors and magnets on the radar array in order to be effective. The cost of a Hall effectEffect sensor is cheaper than a barcode scanner but when multiple sensors need to be implemented, which will be dependent on the intended size of specific applications, the overall cost of a Hall effectEffect sensor system can easily eclipse that of an optical barcode scanner system. Also, with more components functioning as part of a system, the potential cost of maintenance and repair may be much greater than that of a system employing fewer components. With these considerations in mind, this type of system was deemed unfeasible for the axle position sensing system.

6.3.3 Analyzing Position Sensing Systems

Using a simple Pugh’s Method analysis comparing and weighing the benefits and disadvantages between both systems, as seen in Figure 1 below, the barcode scanner system was clearly more suitable for the Rolling Radar project than another. Because of its overall reliability, robustness, and accuracy, it is the most feasible when considering the different sizes that typical applications may be.

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Figure 1: Pugh's Method Comparison for Axle Position Sensing Systems

3 Carriage Position Sensing System

The method being used for rotating the radar array is a gravity drive system. The position of the gravity drive carriage along the circumference of the radar array with respect to the ground needs to be known. In order to conserve energy, it is necessary to turn on only sections of the electromagnetic track that lie immediately below and adjacent to the carriage. Therefore, the position of the carriage must be known with a reasonable accuracy. The precision requirements, however, are not nearly as demanding as those of the axle position due to the size of the magnetic segments. Methods for determining the position of the carriage are still being researched.

4 Types of Magnets

The use of an electromagnetic track to propel the radar array is similar in concept to the systems used in magnetic levitation trains and rail guns. Electromagnets consist of a magnetic core with a coil of insulated wire wound around it. When current flows through the coil windings, the core is magnetized. The core remains magnetized only if current is applied, thus giving electromagnets an on/off ability. A magnetic field is induced by the current flow and a force is created due to the magnetic flux. The direction of the force is dependent on the direction of the current flow, following the right hand rule. On the other hand, permanent magnets retain their magnetism even after it is removed from a magnetic field. Once it is magnetized, it does not require any power to function since it is naturally magnetic. For the rolling radar project, the electromagnetic system can be implemented through different configurations. The advantages and disadvantages of using permanent magnets and/or electromagnets on the gravity drive carriage and the radar array had to be determined.

6.5.1 Electromagnetic Track, Electromagnetic Carriage

One possible configuration of implementing the magnetic propulsion system is implementing electromagnets for both the track and the gravity drive carriage. This configuration would grant the greatest flexibility in controlling the interaction between the track and the gravity drive carriage. By varying the current applied to both the track and the gravity drive carriage, the amount of repulsive force between the track and carriage can be precisely regulated. This method would completely eliminate the need for permanent magnets, making it relatively simple to implement and possibly cheaper material-wise.

The largest drawback of this configuration is the difficulty of delivering power to the moveable gravity drive carriage. A method of regulating the current supplied to the carriage must also be devised, possibly increasing the cost of implementation. In addition to this, since power needs to be applied to both the track and the drive carriage, the power consumption of this configuration would be the highest of any other configuration. Also, due to the added complexity of this configuration, it could potentially have the highest maintenance cost as well.

6.5.2 Permanent Magnet Carriage, Electromagnetic Track

In this configuration, the gravity drive carriage will contain permanent magnets while the track will consist of electromagnets. The potential design concern of delivering power to the gravity drive carriage is eliminated with this configuration. Power only needs to be supplied to the electromagnetic track. Therefore, control of the system is also simpler than that of the previous configuration. The position of the gravity drive carriage is controlled solely by the current applied to the track, which produces a variable force repelling the static force of the carriage’s permanent magnets. Power consumption would be average and dependent on the size of the radar array, since the track would be constructed on the outer circumference of the array. Since the majority of this system would consist of electromagnets, with only a relatively small amount of permanent magnets in the gravity drive carriage, the cost of materials for this configuration would be lower than the designs involving heavy use of permanent magnets.

The drawbacks of this system would eventually be in the area of cost. Because power needs to be supplied to the electromagnetic track, the largest part of this system, maintenance costs may be a bit high. Also, the power used to operate the electromagnetic track may increase operation costs. However, these factors are minor compared to the overall benefits that this configuration can afford.

6.5.3 Electromagnetic Carriage, Permanent Magnet Track

Another configuration is the use of electromagnets in the gravity drive carriage and permanent magnets for the track. This design is the most similar to systems already in place in other applications, such as maglev trains and rail guns, where an electromagnet (or sets of “pancake” coils) flank a permanent magnet. The controllability of this configuration would be a little more difficult to achieve based on the fact that the electromagnets on the gravity drive carriage may maintain a residual magnetic field induced by the permanent magnets, even if power is not supplied to the carriage. However, this may only affect the amount of time it takes for the radar array to decrease its angular velocity and come to a stop, something that can be compensated for through the control system to be implemented.

As in other configurations that employ electromagnets in the gravity drive carriage, there exists the concern of supplying power to the carriage. On the other hand, since power is only being supplied to the gravity drive carriage, which is a small component compared to the overall size of the system, maintenance costs can generally be expected to be lower. However, the cost of obtaining and implementing large permanent magnets for use on the track may also be of concern.

6.5.4 Permanent Magnet Carriage, Permanent Magnet Track

The final configuration considered was the use of permanent magnets for both the gravity drive carriage and the track. The biggest advantage of such a system would be the fact that no power needs to be supplied to either thethe track or the gravity drive carriage, causing maintenance and operation costs to be relatively low with respect to the other possible configurations.

Because there is no way to vary the intensity of the magnetic field produced by the permanent magnets, this configuration is not very controllable. In order to decelerate and stop the radar array, some sort of physical braking system would need to be applied. Based on the design goals of this project, namely reliability, this configuration may not be feasible do to the friction created by a braking system. Also, the maximum angular velocity of the radar array would be dependent only on the strength of the permanent magnets used, thereby losing some versatility. The cost of implementing large permanent magnets capable of generating enough force to rotate the radar array for the given specifications of 5 to 12 RPM may be considerable high as well.

6.5.5 Analyzing Magnet Configurations

Using Pugh’s Method, each configuration was weighed in order to determine the arrangement that will be of the most benefit to the rolling radar system. The results are mainly drawn from the general rules of electricity and magnetism because the system parameters and its operation are unknown at this time. A simple Pugh’s Method comparison between permanent magnet and electromagnet configurations can be seen Figure 2 below. This comparison method is sufficient to eliminate the two configurations employing permanent magnets for use on the track on the radar array. Further analysis is required in order to determine the benefits of using electromagnets or permanent magnets for the gravity drive carriage.

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Figure 2: Pugh's Method Comparison for Electromagnets and Permanent Magnets

Based on this simple analysis, using permanent magnets on the gravity drive carriage and electromagnets for the track appears to be the best choice. The system can be easily controlled simply by varying the power being supplied to the electromagnetic track. Depending on the application, there is the possibility that the track will be large. Therefore, the power usage of such a system is average, since power will have to be supplied to a track with a size proportional to the circumference of the radar array. Because it is generally cheaper to implement electromagnets than permanent magnets, especially when considering the potential size of the system, this system has a potential cost benefit when compared to the other configurations. Since this configuration involves using permanent magnets in the gravity drive carriage, it would not have to be powered, thus simplifying implementation and eliminating the concern of delivering power to the moving carriage. The potential maintenance costs of this configuration are average due to the potential size of the track. Since power is being supplied to the track to create the magnetic field, there is a greater possibility that portions of the track may malfunction as opposed to a naturally magnetized track. If the provided requirements were more specific, a more detailed analytic approach could be taken. However, given the wide range of intended applications of the rolling radar system, the analysis was kept as general as possible. Therefore, the design would be able to work regardless of the intended size of the different applications.

Initially, a primary design concern was delivering power to the gravity drive carriage in order to power the electromagnet. However, upon further research into methods of powering the carriage, the concepts of using linear induction for this purpose were realized, which can be used on the electromagnetic track. Since the proposed system will employ permanent magnets in the gravity drive carriage, delivering power to that moving member is no longer a concern. In order to develop a mathematical model of such a system, the student version of the Ansoft’s Maxwell 3D simulation program is currently being used to determine if it will be able to simulate the electromagnetic fields and forces produced by the proposed magnet configurations.

5 Mathematical Model of Magnetic Track

The first step in developing the mathematical model of a magnetic track is deciding which type of system is going to be implemented. As there are still a few viable designs of such a system, this stage is still currently in development. Some of the more feasible options for implementing the electromagnetic portion of this system are linear induction motors, linear synchronous motors, and three phase motors. The analysis of these systems is currently underway. The mathematical model of the magnetic track system will be developed once the performance and feasibility of each type of system is evaluated.

7 Feasibility Assessment

7.1 Gravitational Drive Weight Analysis Feasibility

Calculation of the weight of the main array wheel assembly requires an initial estimate that will be used to determine parameter values of dependent components in the system. Once these dependent parameters are known they can be used in conjunction with controlling (global) parameters to optimize array weight for a given radius and tilt angle.

Since the weight of the gravitational drive depends on two global parameters (array radius and tilt angle), proportionality relations, and optimizations. The gravitational drive’s weight is evaluated with the following procedure.

1: Volume is evaluated for each component.

• Global parameters used in volume evaluation are array radius and optimum proportionality relations.

2: Mass is calculated based on the specified material’s density.

• Material property information is required.

The gravity drive mass equation is used to evaluate the necessary mass.

7.2 Axle Position Sensing Systems Feasibility

Because the array position sensing system is a secondary concern compared to other aspects of the project, such as making the radar array rotate, it is temporarily set aside so that the primary aspects of the design can be completed. The only aspect of the project that depends on the array position sensing system would be the control of the array’s movement. However, when modeling the control system, it can be assumed that the position of the array is already known from a hypothetical position sensor. It is necessary for the axle position to be known accurately, but the specific tolerances for the position accuracy were not provided with the specifications of the project. Therefore a position sensing system would not be feasible design concern at this point until more parameters are known. The higher-level design considerations will have to be determined in order to properly design a position determining system.

7.3 Types of Magnets

In order to choose the type of magnet and configuration to use, the whole system must be analyzed. After each type of magnet is investigated and the appropriate one is chosen, the magnet configuration can then be considered. Arriving at specific conclusions regarding the size and composition of the magnets will not be feasible since they will be largely dependent on the mass of the radar array being moved and its speed characteristics. Because the design being proposed should be applicable regardless of the actual size of the rolling radar system, the specifics of the size of the magnets will be left in a variable form, where it will be a function of the mass being moved. It would be more efficient to move a large object with a few large magnets than it is to do so with several smaller magnets. Given this conjecture, the larger the size of the array, the larger the size of the magnets to be implemented.

Calculations regarding the requirements of the magnetic field and the force the magnets need to exert on each other for the movement of the array will also remain in variable form. Similar to the relationships involving the size of the magnets, the larger the size of the array, the larger the amount force the magnets need to exert in order to move it. Because the strength of the magnetic field depends on the material through which the field must pass through, the composition of the magnets also depends on the size of the radar array being moved. Exact parameters can easily be chosen at a later time depending on the requirements for specific applications.

8 Performance Objectives and Specifications

The Rolling Radar concept is very open-ended at this stage in its development. Specifications are also open-ended and will most likely be quantified by our team. One of the basic objectives of the radar is to start and stop in a desired time range and be capable of stopping at a predetermined location. The start and stop times will be optimized once the weight and size of the radar aresize of the radar is determined. The longer the radar takes to achieve a desired velocity, the smaller the gravity drive needs to be. The desired velocity will be on the order of three to six revolutions per minute. A figure of current known specifications is shown in Figure 3. A specification of TBD corresponds to a spec the team will need to assess by optimization or analysis.

|Parameter |Specification |Unit |

|Start-up Time |TBD |sec |

|Stop Time |TBD |sec |

|Operating Velocity |3-6 |rev/min |

|Array Diameter |TBD |m |

|Array Weight |TBD |kg |

|Tilt Angle |10-45 |deg |

|Degree of Grav Drive |45-60 |deg |

|Rotation (Operating) | | |

|Force of EM |TBD |N |

|Reliability |TBD |TBD |

Figure 3: Specifications

8.1 Design Objectives

8.1.1 Magnetic Propulsion System Design Objectives

The magnetic propulsion system, consisting of an electromagnetic track along the circumference of the radar array and a permanent magnet-driven gravity drive carriage, should provide sufficient force to rotate a circular radar array of any given size and weight. By utilizing such a technique, the overall reliability of the system should be greater than that of any similar systems employing different modes of propulsion since the number of moving mechanical parts is minimized.

The mathematical model of the magnetic propulsion system should form the basis through which future application-specific calculations can be made. The model will provide a general formula from which the designer of a rolling radar system can calculate the strength of the electric field required to move a radar array of a particular size and weight. Other design specifications involving the size of the magnets as well as their composition will also come from the mathematical models. Since these change with the size of the radar array being implemented, the models will be functions of the array’s size and weight.

9 Analysis and Synthesis of Design

9.1 System Model and Control

To meet the requirement of an analysis of servo controller system we needed to first create a system model. The model would consist of an input torque created by the gravitational drive and outputs of velocity and position. Two concepts were considered to model the system.

9.1.1 System Model Assuming Axle Twist is Negligible

The first and most simple method is to make the assumption that the twist in the shaft connecting the array and the support wheel is minimal and can be neglected. With this assumption the system is a large rigid mass with torque from the gravitational drive generating angular velocity. The only forces opposing that motion are the rotational inertia and the friction that is proportional to the velocity. This results in the system model transfer function shown in Equation 3.

[pic]

Figure 4: FBD of Rolling Radar

|[pic] |Equation 1: Moment Equilibrium |

|[pic] |Equation 2: Sum of Moments |

|[pic] |Equation 3: Transfer Function |

We then needed to develop and actuator model that could induce the torque. For the preliminary design and analysis we decided to choose a general first-order actuator model. Further collaboration with the electrical engineers will be needed to more accurately model the actuation of the gravitational drive.

9.1.1.1 Unity Feedback Control

Shown in Figure 5 is a system with a simple unity feedback closed-loop control and the system response to a unit step input.

[pic]

Figure 5: Unity Feedback No Twist

[pic]

Figure 6: Unity Feedback Position and Angular Velocity vs. Time

9.1.1.2 System Control Using a PID Controller

Shown in Figure 8 is the same system with a PID controller and the system response. The effect of the controller can be seen in Figure 8 and it is fairly obvious to see it reduces oscillations and provides a faster response compared to the Unity Feedback shown in Figure 6. Optimal tuning will be analyzed and performed in the subsequent class as variables are still unknown

[pic]

Figure 7: PID Controller with no Twist

[pic]

Figure 8: Position and Angular Velocity vs. Time

9.1.2 System Model with Axle Twist

We have yet to determine whether the assumption of minimal twist is valid. A second method was therefore used to analyze the system. This method made the opposite assumption in that there will be significant twist in the array shaft. This resulted in three equations of motion, one for each main element shown in Figure 10.

[pic]

Figure 9: FBD of rolling radar

[pic]

Figure 10: Individual Components FBD

|[pic] |Equation 4: Main Array Moment Equation |

|[pic] |Equation 5: Axle Moment Equation |

|[pic] |Equation 6: Support Wheel Moment Equation |

After substituting out intermediate variables the system is modeled with a fourth order characteristic equation shown in Equation 7 that has oscillations that are much more complicated and difficult to control.

|[pic] |Equation 7: System Model Transfer Function with Twist |

Where

[pic] [pic] [pic] [pic]

In the initial analysis in Matlab, many assumptions were required that will need to be determined in the sequential class of senior design. The rotational inertia was calculated for both masses and the spring constant is dependant on the material selection for the array axel. The frictional resistance still needs to be determined. Because required values are still needed, the values in the plant model were assumed to be equal to 1.0.

9.1.2.1 Unity Feedback Control

Shown in Figure 11 is the system with a simple unity feed back closed loop control and the system response to a unit step input. The effects of a fourth order characteristic equation and a second order equation in the numerator can clearly be seen in Figure 12.

[pic]

Figure 11: Unity Feedback with Axle Twist

[pic]

Figure 12: Unity Feedback Position and Angular Velocity vs. Time

9.1.2.2 System Control using a PID Controller

The system shown in Figure 13 is not stable. We implemented a PID controller to attempt to control the general system’s behavior. We were moderately successful although the required tuning for the actual system will need to be done after all variables are determined and with further collaboration with the electrical engineers. The initial analysis and control system is shown below.

[pic]

Figure 13: PID Control with Axle Twist

[pic]

Figure 14: Position and Angular Velocity vs. Time

9.2 Array Size and Weight

Parametric studies are a great way to analyze a system for which little or nothing is known. This is why parametric evaluation of this system was chosen as the method for the analysis.

9.2.1 Assumptions

The parametric analysis of the sizes, weights, and other properties of the radar’s components proved to be problematic due to the large amount of variables and parameters involved. Therefore, some assumptions were needed to simplify the problem.

9.2.1.1 Proportionality Assumptions

The vast majority of our the assumptions made are proportionality assumptions. These proportionality relationships are invaluable for breaking down the complex system by describing dependent parameters and variables in terms of independent or global system parameters. As a result, these relationships need to be independent of one or more global system parameters (array radius, tilt angle, size, etc) in order to be useful.

An example of a proportionality relationship is[pic]. This relationship is used to eliminate the support wheel radius, axle length, and wheel separation distance from the analysis. These parameters become redundant once the support wheel parameters are described in terms of assumed conditions for optimum weight distribution. This relationship allows all support wheel parameters to be implicitly calculated instead of being global parameters, which need to be explicitly specified.

Other proportion assumptions include the ratios of the array wheel radius to each of the following parameters which are all independent of size.

• Array Thickness

• Support wheel radius

• Support wheel Thickness

• Axle radius

• EM Track Thickness

9.2.1.2 Component Assumptions

Just as was done for the whole array system, assumptions were made for each component in the analysis as well. Assumptions made for analysis of the main array wheel were mostly needed for calculating the mass and inertia moments. For example, the main array wheel can be treated as a solid copper ring when calculating the mass, volume, and inertial moments. The solid ring assumption was based on a few different factors. The weight of both the electromagnetic track (mostly copper) and the stainless-steel internal support structure are primarily located around the outside of the array wheel. Additionally, the copper EM track and steel frame are much heavier than the radar’s functional electronics. Lastly, objects closer to the axis of rotation have lesser effects on the inertial moment than objects farther from it.

Below is a list of all these assumptions, both global and component specific:

• No Friction

• Axle - Rigid Body

• Axle - Constant Cross-section

• Axle – Linear Radius Variance

• Array - Solid Copper Ring

• Array – Linear Thickness Variance

• Support – Solid Steel Disk

• Support – Linear Thickness Variance

9.2.2 Global Parameters

Global parameters are parameters that can be used to quantify the optimum value of dependent parameters. Initially, a list of global parameters was created. Parameters are removed from the list by finding ways to write them in terms of the others. The end goal is to reduce the global parameter list as much as possible by deriving relationships and defining optimal conditions.

Currently the radar’s only global parameters are the array radius and tilt angle. These two parameters need to be explicitly specified before anything else. Additionally, all the values that have been made for materials, material properties, and property proportions can be modified and everything recalculated through the interface.

The array radius is a global parameter currently used in property calculations for the gravity drive, supporting platform, axle and support wheel. Furthermore, applied component shear and moments are calculated and will be used for material selection, feasibility, reliability, and life cycle analysis.

OSince one of Lockheed’s primary interests in this project is the results of parametric studies, sotherefore, there is a massive amount of data and calculations to manage and perform. To facilitate calculation and management of all system property values for varying parameters, a combination of excel and VB functions such will be needed as these functions will be manifested in the form of worksheets, macros, user-forms, and custom VB-Modules are implemented. One of the most important functions of this excel-based parametric study is reliability. The first task in any comprehensive reliability study is calculating the internal and external forces applied to each component.

9.2.4 Parametric Analysis Method

The rolling radar has been split into three sections for analysis. These are the main array wheel, the support wheel, and the axle. The singularity functions for the axle will depend on the axle’s overall length and weight, the shear force and moment applied by the array wheel, and the shear force and moment applied by the support wheel. The applied shear forces from the array wheel and support wheel both depend on each wheel’s reaction forces, which are dependent on the tilt angle and the weights and sizes of the array wheel, support wheel, and axle.

9.2.4.1 Singularity Functions

Singularity functions are powerful functions allowing values for shear and moment in the axle to be calculated in terms of the distance from the array wheel only. The applied shear forces and moments on the axle can be described with these singularity functions which are dependant on the distance from the array end of the axle. The shear singularity function calculates the shear force as a function of X, where X is the distance from the end of the axle attached to the array wheel. The singularity function for shear from [pic] to [pic] is shown in

Equation 8 Equation 8.

[pic]

Equation 8: Shear Singularity Function

Where [pic]are the normal (shear) force applied to the axle by the main array wheel and support wheel, respectively. [pic] is the normal component of the axle’s weight per unit length, and [pic] and [pic] correspond to the distance between wheels and the overall length of the axle.

Since[pic], the bending moment singularity function is shown in

Equation 9

Equation 9.

[pic]

Equation 9: Moment Singularity Function

Where [pic] and [pic] are the applied moments from the array and support wheel, respectively.

9.2.4.1.1 Excel

The aforementioned These singularity functions have been coded into Excel using VB and can be used to generate the axle’s shear and bending moment diagrams of all radar configurations, for any parameter values. Once shear and moment are known, calculations can be made for material stresses, strains, fatigue, and life cycles. Additionally, we can begin to find optimum values for dependent parameters in terms of other their governing parameters. For example, the requirements and environment conditions given yield the parametric graphs and loading plots shown in

Figure 15 Figure 15.

[pic]

Figure 15: Parameter Plots

The Excel workbook is also used to create parametric graphs that do not depend on initial global parameters. Two examples are shown below in Figure 16.

Figure 16: Gravity Drive Mass with Start-up Time and Tilt Angle Variance

9.3 Magnetic Propulsion System

The electromagnetic propulsion system is one of the top priorities of the rolling radar project. Because the system proposes the movement of a potentially large object through unconventional means (such as the use of motors and gears), it is crucial to determine the fundamentals of its operation before other, more conventional, aspects of the rolling radar concept are examined. Some other aspects of the design, such as the axle position sensing system, are secondary in the sense that they depend on the movement of the array. For the time being, they are assumed to be functional and integrated into the system as a whole, without considering how they will be designed. Once the method of moving the array is designed, the systems used to control its movement, such as the axle position sensing system and the controllers, will be more useful and can be proposed and evaluated.

10 Future Plans

10.1 Control System

A major priority for the future design that has been previously stated is the calculation of the various constants that have not been quantified. These constants however, depend greatly on other system variables such as the size and weight of the array and gravity drive, as well as the magnitude of the velocity required and the amount of time to achieve the velocity or desired position. Being that our system will need to stop at a certain position as well as maintain a constant velocity, the control will probably require dual feed back to the controller.

The servo control and actuator system will need to be more accurately represented, which will require collaboration between the mechanical and electrical engineers. Research has already begun but needs to be furthered. Bode plots of the servo control system will also need to be generated.

The system will also need to compensate for several features of disturbance including wheel slip and wind gusts. Research for the wheel slip phenomena comes almost exclusively from previous studies on slip control for railway vehicle. Wind gusts disturbances will be treated as are normal disturbance to dynamic systems.

10.2 Reliability

The axle has two major functions: it is the system’s main stress-bearing component and allows coolant to flow into and out of the array. During operation the axle sustains fully reversed bending, rotational shear, and constant axial compression. Therefore, it is our primary concern for failure analysis. Shear stress and moment calculations for this component are determined parametrically based on optimization, proportionality relations, and two global parameters: array radius and tilt angle. In order to design and create an analysis system that can accurately determine reliability and with the level of autonomy required for reliability of a parametric study, further development should be done of the systems model and the current method for its analysis.

10.3 Parameterizing Gravitational Drive

The parametric analysis will be augmented with a more comprehensive method for determining system parameter values. Logic loops will be implemented to accurately determine system properties in such instances where optimization is dependent on more than two factors. The gravity drive weight requirements for example will implement a recursive loop which uses the current analysis method to estimate both the array mass and the gravity drive weight, calculates the electromagnetic track parameters from the estimated gravity drive weight, and then recalculates the array mass and gravity drive weight from the new electromagnetic track parameters. This logic loop will repeat until a solution is reached for a specified array radius and tilt angle.

A parallel development is to use applied component shear and moments to determine stresses necessary for material selection and future analysis sections on feasibility, reliability, and life cycle.

Plans for the interface include adding control over governing equations and global parameters, and creating options regarding optimization of radar sub systems. Ideally, the optimization analysis will use results from fatigue, life cycle and reliability sub analyses in logic loops to make design recommendations.

Lastly, since extended computation times are likely, an effort to reduce evaluation time will be made. Time savings will be accomplished by having the evaluation rely more heavily on visual basic, and less on excel worksheets, and to minimize data-passing between the two.

10.4 Derivation of a Mathematical Model of the System

The mathematical model of the electromagnetic track will be able to be completed by the end of the Senior Design II. The model will have to be left in variable form as per the requirements of the sponsor that the design can be implemented on any size with little to know modifications. Therefore, the model will be all-encompassing but pertinent numbers will not be provided. However, a variety of assumed device parameters will be used to demonstrate the validity of the mathematical model. These numbers will be system-dependent, so they will not carry over to systems with different parameters.

10.5 Electromagnet Power Requirements

The proposed system for moving the radar array consists of an electromagnetic track located along the circumference of the radar array and a gravity drive that moves along its edge with a permanent magnet. The strength of interaction between both components will depend on the magnetic field generated by both types of magnets. In order to vary this field, the power being delivered to the electromagnet track must be controlled. The amount of power required is dependent on the force needed to displace the gravity drive which, in turn, is dependent on the desired angular velocity of the radar array. Since one of the main design concerns of the Rolling Radar project is efficiency, the power needed by the electromagnets will be determined. Since this design must be generic so that applications of various sizes can be implemented, the model for the power requirements of the electromagnetic track will be left in variable form as a function of the desired angular velocity and force required.

10.6 Control System

Once the system for moving the radar array is designed, a control system must be developed in order to regulate its movement. The design of the controls will tie together many of the established and assumed components of the radar system as a whole. When finished, the control system should provide insight on how the radar array will be accelerated, stopped, and how it will compensate for disturbances. However, just as many of the other design aspects are left in variable form, the control system must allow for different applications as well. Also, because no specific model was given, the proposed control system cannot cater specifically to any one design.

10.7 Schedule

A tentative schedule can be seen in Appendix A. Additional and alternate direction may be given based on comments and recommendations from our sponsor after PDR. The first week of Senior Design 2 will be dedicated to taking any further direction that may be given and altering out schedule if necessary.

11 References

[1] Chick, Stephen E., and Mendel, Max B., An Engineering Basis for Statistical Lifetime Models with an Application to Tribology, IEEE Transactions on Reliability, Vol. 45, No. 2, June, 1996.

[2] R. Muniz, L. Junco and A. Otero, “A robust software barcode reader using the Hough transform”, in Proceedings of Information Intelligence and Systems, Oct. 1999, pp. 313-319.

[3] D.E. Gilsinn, G.S. Cheok, D.P. O'Leary, “Reconstructing images of barcodes for construction site object recognition”, Automation in Construction, Vol. 13, Issue 1, Jan. 2004, pp. 21-35.

[4] S.J. Shellhammer, D.P. Goren, and T. Pavlidis “Novel Signal-Processing Techniques in Barcode Scanning”, IEEE Robotics and Automation Magazine, March 1999, pp. 57-65.

[5] Z. Yaqoob and N.A. Riza, “Passive Optics No-Moving-Parts Barcode Scanners”, IEEE Photonics Technology Letters, Vol. 16, No. 3, March 2004, pp. 954-956.

[6] M.S. Kwak, S.K. Sul , "A New Method of Partial Excitation for Dual Moving Magnet Linear Synchronous Motor", IEEE Transactions on Industry Applications, March 2004, pp.499-505.

[7] G.W. McLean, "Review of Recent Progress in Linear Motors", IEEE Proceedings, Vol. 35, Part B, No. 6, Nov. 1988, pp. 380-416.

[8] O.V. Tozoni, “Amlev-a self-regulating version of Maglev”, IEEE Transactions on Magnetics, Vol. 37, No. 6, Nov 2001, pp. 3925-3933.

[9] C. Jiefan, W. Chengyuan, Y. Junyou, L. Lifeng, “Analysis of Direct Thrust Force Control for Permanent Magnet Linear Synchronous Motor”, Proceedings of the 5th World Congress on Intelligent Control and Automation, June, 2004, pp. 4418-4421.

[10] Y. Ikeda, R. Sakai, S. Mizumura, M. Kubo, "Basic Considerations on the Linear Motor Drive by Permanent Magnet Poles Mounted on Vehicles", Power Electronics Specialists Conference, June 1994, pp. 992-997.

[11] P. Zheng, S. Cheng, Y. Wang, “Research on the relation between the propulsive force and magnetic system of the coil launcher Based on the mechanism of hybrid switched reluctance motor”, IEEE Transactions on Magnetics, Vol. 39, No. 1, Jan. 2003, pp. 116-119.

[12] V. Pulatov, “Magnetic Propulsion Systems”, Progress in Aerospace Sciences, Vol. 37, Issue 3, 2001, pp. 245-261.

[13] R. C. Dorf, R. H. Bishop, “Modern Control Systems” 10th edition, 2005

[14] D. Frylmark, S. Johnsson, “Automatic Slip Control for Railway Vehicles” Feb. 2003

[15] D. Kaiser, “Fundamentals of Servo Motion Control” May 2002

[16] A. Bradshaw, J. M. Counsell, “A Knowledge Based Mechatronics Approach to Controller Design”

12 Appendix A - Schedule

13 Appendix B - Excel

-----------------------

Ф

Jtotal

Btotal

Support Wheel

Axle

Main Array

J1ώ1

B2 ω 2

TK

Τ

TK

B1 ω 1

Ф1

J1ώ1

TK

Ф2

Ф1

K

Ф2

B1

B2

K

J1

J2

Ф2

Ф1

Materials:

• Array:

Copper

• Axle:

Aluminum

• Support Wheel:

Stainless Steel

[pic]

Platform Diameter = 20m

Array Diameter = 10m

Support Wheel Diameter = 3.3m

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