Embed Size (px)
Citation preview
Balancing Omni-directional, Multi Surface Skateboard
(BOMSS)
Final Design Report
December 10, 2009
Casey Christensen
Harrison Cobb
Misael Marriaga
2
Table of Contents
Requirements Specification ……………………………………………………………………………………….……………….. 4
Final Design …………………………………………………………………………………………………………………………….…… 8
Block Diagram .................................................................................................................................... 9
Functional Decomposition of Blocks …………………………………………………………………………..……………… 10
Alterations to Original Design ………………….…………………………………………………………………………………… 12
High Level Flow Chart Description…………………………………..………………………………………………………….…… 14
High Level Flow Chart …………………………………………………………………………………………………………………… 15
Microprocessor Flow Chart Description …………………………………………………………………………………………… 16
Microprocessor Flow Chart …………………………………………………………………………………………………….... 17
Power Supply Circuit and Description …………………………………………………………………………………………… 18
Voltage Indicator Circuit and Description …………………………………………………………………………… 20
Power Budget …………………………………………………………………………………………………………………………..22
Torque Deliverability ………………………………………………………………………………………………………………..…. 24
Chain Length ……………………………………………………………………………………………………………………………….. 27
Preliminary Controls System Design …………………………………………………………………………………………… 29
Physical Diagrams ………………………………………………………………………………………………………….……….. 35
Frame Analysis …………………………………………………………………………………………………………………………..…… 39
Fall 2009 Schedule …………………………………………………………………………………………………….…………….. 49
Analysis of Fall 2009 Schedule ………………………………………………………………………………………………….…… 50
Spring 2010 Schedule …………………………………………………………………………………………………………………… 51
Budget Analysis ………………………………………………………………………………………………………….……….. 52
Updated Budget ..................................................................................................................... 53
Design Consideration Analysis of Components ………….………………………………………………..……………..…. 54
Component Selection Breakdown ……………………………………………………………………………....…………. 56
Pictures ……………………………………………………………………………………………………….………………………. 63
Appendices ………………………………………………………………………………………………………………….……………. 67
Technical drawings ……………………...…………………………………………………………………………….. Appendix A
MatLab Code for Lagrange’s Equations ............................................................................... Appendix B
Shaft Data Sheets ……………………………………………………………………………………………..……… Appendix C
Battery Data Sheet ....………………………………………………..……..……………………………………….. Appendix D
3
DC-DC Converter Data Sheet …………………………………………………………………………………...…… Appendix E
Motor Controller Data Sheet ……………………………………………………………………………………….… Appendix F
Development Board Data Sheet …………………………………………………………………….……… Appendix G
Angular Rate Sensor Data Sheet ……………………………………………………………….…………… Appendix H
Accelerometer Data Sheet ……………………………………………………………...…………………….…… Appendix I
Modular Encoder Data Sheet …………………………………………………………………………………….…… Appendix J
4
Requirements Specification
Balancing Omni-directional, Multi Surface Skateboard (BOMSS) Harrison Cobb, Misael Marriaga, Casey Christensen
Overview
Riding a skateboard can be difficult and discouraging to learn. We will create a device that will allow beginners to quickly enjoy being able to ride a skateboard. It will also have a compact design that allows it to be easily maneuvered in an urban environment. The BOMSS will be a skateboard-style, self-balancing vehicle. Basic design consists of a platform for the rider to stand on, with two independently operated wheels fastened centrally to the underside. The BOMSS will be an enjoyable recreation vehicle for users of nearly any age that are looking for a unique and inventive new way to spend their time. Its maneuverability and ability to operate efficiently in many different environments will make it stand apart from other similar recreational and transportation vehicles.
Operational Description The design is a two wheeled, self balancing vehicle that provides a dynamic turning
radius, meaning that the turning radius is proportional to the velocity of the vehicle, with a near zero turning radius at no forward motion. If the vehicle, for example, is traveling at a rate of 4 m/s, the turning radius will be much greater and therefore more stable than if the vehicle were traveling at a rate of 0.5 m/s, where the radius would be significantly decreased. This will make the vehicle useful and easy to maneuver in an urban environment. The Balancing, Omni-directional, Multi Surface Skateboard (BOMSS) will utilize accelerometers and gyroscopes to sense the angular position of the skateboard with respect to the horizontal plane. This information will then be used as an input in its controls algorithm. The vehicle will be maneuverable in the forward and aft direction, as well as steering left and right.
Safety features will include a minimum rider weight and an anti-theft key. Before power is delivered to the system, the rider must insert a removable anti-theft key and then fully depress a mechanical weight sensor. Power is provided by a rechargeable, on-board battery.
5
Technical Requirements:
1. The BOMSS will achieve a maximum speed of no less than 4 m/s (13 ft/s) and no more than 10m/s (33 ft/s) for safety concerns.
2. The BOMSS will be powered for a runtime of no less than 60 minutes at an average of 30% maximum speed.
3. A turning radius of no greater than 1mx1m (3ftx3ft) at zero forward motion. 4. The BOMSS will have a low battery indicator light (cutoff voltage to be determined). 5. The BOMSS will be capable of carrying a 91kg (200lbs) adult over dense materials
such as pavement and concrete, on both a flat and inclined plane. 6. The BOMSS will weigh no more than 23kg (51 lbs).
Deliverables:
1. User’s manual 2. Self balancing skateboard with anti-theft key 3. CAD drawings, electronic schematics, 3D views and analyses 4. Code and flowcharts 5. Report of testing 6. Final report
Testing Plan:
To ensure proper operation, the following tests will be conducted:
Run Time Test: To test run time, the BOMSS will be required to maintain operation for a total
time of approximately sixty (60) minutes. The rider will weigh between 91 and 100 kg (200-220lbs) and will be required to maneuver a predetermined course (refer to Figure 1) around the Harding University campus containing level planes, inclines, and declines over a multitude of surfaces. Riding times can be discontinuous, but a total time of sixty (60) minutes must be summed at an average of 30% of the maximum speed before the battery is recharged.
6
Figure 1
Figure 1: The course the BOMSS will be required to navigate during the test period is indicated in red. The starting and ending place is the Pryor-England Science Center highlighted in yellow. The BOMSS will complete the course at least once to demonstrate its ability to operate on varying surfaces. Care was taken in determining the course as to not encounter any dangerous traffic or intersections that would place the tester in harm’s way.
Maximum Speed Test:
To test the maximum speed, the BOMSS will be mounted and proven to travel a measured distance in a given amount of time. A stopwatch will provide an adequate amount of accuracy. The distance will be forty (40) meters on a flat, asphalt or concrete surface. Time to travel this distance must be between four (4) and ten (10) seconds.
Turning Radius Test: To test turning radius, only a maximum turning radius will be required. The
skateboard will be placed inside a taped-off square of one (1) meter by one (1) meter, and then mounted. A satisfactory test will be if the skateboard can be maneuvered a full 360° without leaving the taped square.
7
Implementation Consideration The operational components will be contained in water and vibration resistant
compartments where they will be protected from collisions with foreign objects. These compartments and the components they contain will be easily accessible to the user, while remaining “hidden” within the structure as to not interfere with the user’s ability to effectively operate the vehicle.
8
Final Design
9
10
Functional Decomposition of Blocks
Physical Input Parameters: These parameters include the actual mass of the skateboard and its calculated rotational inertia, as well as average estimates of the rider’s mass, rotational inertia, and height.
Equations of Motion: Provided with physical input parameters, these equations will be integrated as part of the controls algorithm into the software that enables the board to maintain a level plane.
Balance and Turn Sensors: These sensors include an accelerometer and an angular rate sensor (gyroscope) for balance, and force sensors for turning. The accelerometers will provide the microcontroller with readings of the component of gravity perpendicular to the skateboard with the purpose of calculating the board’s angular position. The angular rate sensors will provide readings on the angular velocity of the skateboard to the microcontroller, which will calculate the direction in which the skateboard is tilting. These calculations will be used to determine the proper adjustments of the motors to keep the skateboard on a level plane. The accelerometer will require a supply of no less than 2.2 V and no more than 3.6 V. The output signal will be no less than 289.5 mV/g and no more than 326.5 mV/g. The accelerometer reads ±4 g. The angular rate sensors will require a supply of no less than -0.3 V and no more than 6.0 V. It will have a typical sensitivity of 2.0mV/°/s.
The turn sensors will be composed of four force pads strategically placed underneath the heel and toe positions of both foot platforms. Any change in force on the pads will cause a change in resistance and, therefore, voltage dropped over the sensor. This voltage will be measured and used to determine the desired turning radius.
Speed Sensors: These sensors include two rotary encoders, one place on each wheel shaft. The purpose of these two sensors is to independently measure the instantaneous speed of each wheel. These values will be used in determining the amount of change in motor voltage necessary to obtain the desired output, provided by the user.
Software/Memory: The software implements an electrical manifestation of the equations of motion. Using the derived equations along with the collected sensor values, the software will cooperate with the development boards imbedded memory to calculate the duty cycles necessary for the microprocessor to precisely control the motors in maintaining a level platform as well as maneuvering the skateboard.
11
Microprocessor: This unit will compile the sensor information and communicate with programmed software. Once the sensor information is collected, the derived equations of motion can be applied through software to calculate the necessary duty cycle, which controls each wheel’s motion independently. The microprocessor may require up to four (4) A/D (Analog to Digital) ports for sensor input, and will require multiple ports for output to the motor controller.
Voltage Regulator: The voltage regulator contains hardware to supply various voltages necessary to run the 1) balance and turn sensors, 2) microprocessor, 3) motor controller, and 4) possibly each motor. Voltages required include +3.1V, +5V, +12V, and +24V.
Power Source: The chosen power source will be a 24V rechargeable battery, with a capacity rating of at least 12 Ah. Options include SLA, NiMH, and NiCd.
Motor Controller: This unit will accept the signals from the microprocessor and control both the speed and direction of each independent motor.
Left and Right Motors: Motors selected are 350 watt motors. Each motor is independently controlled by the microprocessor via the programmed motor controller. Based on inputs from the accelerometers and angular rate sensors, the controller will drive the motors appropriately to maintain balance as well as produce motion.
Battery Level Display: The battery level display is an LED voltage display typically used in remote controlled aircraft. This will provide the user with instant information on the state of charge of the battery.
On/Off switches: There are two individual On/Off switches, both of which engage/disconnect power from the battery. Note that neither switch will provide any function to the BOMSS unless the aforementioned anti-theft key is securely in place. The first switch is a “main power” push button switch that, when engaged, will allow the BOMSS to be powered and ready for a rider. However, it does not allow for any unauthorized motion or balancing at this point, as the second switch also needs to be engaged for full operation. The second switch is a safety switch that is activated by a specified weight depressing the foot platforms. Without this second switch in place, if the main power button were engaged and the platform were inadvertently brought level without a user being onboard, the BOMSS would begin its balancing operations and could become unsafe. This safety concern required the addition of this second weight sensor switch.
12
Alterations to Original Design Turning
In the original design of the skateboard, the turning rate was designed to be controlled by the rider shifting his weight and tilting the skateboard in the direction that he desired to turn. As the structural design of the skateboard was being developed, it was determined that building a tilting base on which to mount the skateboard would be a challenge of high complexity. After much discussion and brainstorming, a new design arose. It consists of two force pads strategically placed underneath the heel and toe positions of each foot platform. Any change in force on the pads will cause a change in resistance and, therefore, voltage drop over the sensor. This voltage can be measured and mapped to a predefined reference table to determine the desired turning radius. In this manner, the necessary alteration in motor voltage will be calculated to achieve the rider’s desired turning rate.
Weight Sensing Method
The mechanical weight sensing device intended for use on the BOMSS is undergoing a redesign. The moving parts have the potential to fail over time rendering the device useless until replaced. This area is also an unsealed section of the skateboard and will allow water or other material into the frame, potentially causing malfunction of the circuitry. To eliminate this problem, we are integrating this system into the force sensors used for turning. These sensors will be compressed between the outer lexan covering and the metal sub-frame on the foot platforms. When this sensor is compressed with the weight of a rider, a voltage will be sent to the microcontroller, allowing the skateboard to be operational only if both sensors indicate proper weight has been applied. With this system, the skateboard will have less moving parts that have the potential to fail, and will also be more effectively sealed from water and other foreign contaminants. We are continuing research on these sensors to determine the specific components for our application.
13
High Level Flow Chart Description The following flowchart (figure 2) is a high level flow diagram of both the mechanical
and software system during normal useage of the skateboard. Both the main power supply button must be pressed and the anti-tamper device in place to supply power to the system. Once these two criteria are met, the microprocessor initializes itself and then the sensors. The microprocessor immediately begins sensing for appropriate weight in a latent waiting period as a safety measure; only adequate weight will allow the board to be ridden.
After the initialization procedure, if an adequate weight is supplied, the board will continue with the program. The skateboard remains responseless until it is rendered level for the first time. Upon reaching this state, the motors are engaged and the skateboard will respond as requested. Throughout this entire process, too little weight will cause the motors to disengage, and the system to return to a latent period, until weight is reapplied and the skateboard returned to a level platform.
Once the skateboard has reached an initial leveling, it will respond to any rider input by attempting to maintain a level plane. As the rider leans forward or backward, the accelerometer will create a voltage, which corresponds to an angle of position, that can be measured by the microprocessor. Any turning motion provided by the rider will manipulate the skateboard to maneuver with a dynamic turning radius (The method for turning was recently shown to be difficult and somewhat impractical to implement; we are discussing various methods and designing a decision matrix to help determine the most effective choice. For more information, see page 12. The microprocessor will provide the computing power to determine the appropriate response by the motors to maintain the aforementioned level plane. It will do so by computing differences in sensor values and algorithmically determined values, and then calculating the necessary alteration in the current state of the board. This difference will be manifested in the form of a pulse width modulate signal sent to the Sabertooth motorcontroller (motor driver), which supplies the motors with appropriate voltages and directional control. The response of the motors, along with any additional inputs by the rider, create a feedback loop that provides motion and rider control.
14
High Level Flow Chart
Figure 2: High Level Flow Diagram
15
Microprocessor Flow Chart Description The following figure (Figure 3) is a more detailed diagram of the microprocessor
processing of the information captured at the sensors. This diagram assumes sensor initialization and proper weight are already accomplished.
The process begins with sensor capture of both the accelerometer and angular acceleration sensor (gyroscope). The angular value is compared to an algorithm or database that will be designed by our group to provide smooth translation of angular input to forward motion. This algorithm will provide what is referred to as the desired velocity. A sensor capture from the rotary encoders provides the actual velocity of the skateboard. These two values will be subtracted to provide the error in velocity.
The control equations developed by Misael will then provide the necessary change in torque, and therefore the necessary change in motor voltage, to maintain a level plane. This will give a straight line calculation as well as the direction of change in motor torque.
At this point, a sensor capture from the turning sensor will provide information on the amount of turn desired by the rider. If there is no turn input, the microprocessor’s pulse width modulator (PWM) will output the required duty cycle for a straight line pathway to the motorcontroller. If a turn input is detected, however, there are two options: a tank turn, or a dynamically determined turning radius turn. The two will be selected based on a threshold value for forward velocity. If the actual velocity is below this threshold, a tank style turn will be commanded of the motorcontroller and motors. If the actual velocity exceeds the maximum determined value for executing a tank style turn, the desired amount of turn will be compared with the forward velocity and the resulting turn radius to produce an alteration of the duty cycle from straight line path. The desired amount of turn will be provided by an algorithm, again created by the group to provide a safe, smooth, and operable turning radius for the rider.
All of the duty cycles produced by the PWM in the above sequence can then be sent to the motorcontroller for translation into a mechanical manifestation of torque by the motors.
16
Microprocessor Flow Chart
Figure 3: Microprocessor Flow Diagram
17
Power Supply Circuit and Description
Figure 4: Power Supply Circuit
Circuit Description
The power supply circuit (figure 4) is used to supply power to all of the sensors and the microprocessor. The 12.8 volts is directly supplied by the DC-DC converter. This will be a stable signal, with 4% fluctuation in line current, and a maximum current of 2A. The decision to use voltage regulators was made because of the sensitivity and criticality of the components. Voltage regulators will provide a smooth supply voltage at the loss of a minimal amount of power in the form of heat; this is acceptable. Using equivalent resistances, each of the sensors are modeled to draw the average current designated by the datasheets (See appendices). A 12V regulator will provide 11.7 volts to the microprocessor (the difference is due to the voltage regulator requiring approximately 13V to operate at the specified output voltage) and a 5V regulator will provide for the left and right rotary encoders, accelerometer, and gyroscope. A 250 Ω equivalent resistor bank will be used to drop the supply to 3.1V for the accelerometer and gyroscope.
The equivalent resistance for the microprocessor is undeterminable until the component is received, but liberally estimated at 500mA, as the true current draw was unable to be found. The purpose of this circuit analysis was to determine proper voltage. All
18
capacitors in the circuit are used for dampening unexpected, high frequency fluctuations in voltage.
19
Voltage Indicator Circuit and Description
Figure 5: Voltage Indicator Circuit with LED’s
Circuit Description
The voltage indicator circuit (Figure 5) uses three colored LED’s to inform the rider of the charge state of the battery. The familiar colors of green, yellow, and red were chosen to lower the chance of misinterpretation. The LED’s change from green to yellow to red as the voltage provided by the battery decreases from full charge to approximately 22V. The battery voltages chosen for our purposes are shown below. This circuit’s purpose is to allow the rider to recharge the battery pack before any damage is caused by over draining the battery.
The circuit utilizes a quad comparator to compare the battery’s instantaneous voltage state to a stable, known voltage. The known voltage can be controlled by varying the
20
resistances in series with the 12.8V source to alter the voltage at which the LED’s are turned on and off. The 12.8V will be drawn from the DC-DC converter.
Upon simulations with Multisim, there has been a problem with the lights switching at various random voltages. Initial considerations are that the capacitors are inadequate for the given circuit, or that Multisim has a software anomaly. Key components for this circuit are arriving soon, after which a breadboarded model can be developed to determine the cause of this aberration. Voltages at which the different LED’s light up are approximated due to the inconsistency of Multisim and lack of a breadboarded circuit; however, more accurate numbers will be obtained upon actual construction of the circuit.
LED Turn on/off Voltages
Above 23.7V – Green LED lights up
22.1 V – 23.5V – Yellow LED lights up
Below 22.1V – Red LED lights up
21
Power Budget
Figure 6: Power Distribution Chart
Power Budget Description
The above diagram (Figure 6) is an expected power distribution chart. The battery is designed to produce just below 10.8A over the course of 60 minutes at 100% discharge. Assuming the microprocessor draws 0.5A, which is likely an overestimate, the entire system, with motors running at the designated 30% power, will draw only 8.9A for the duration of the hour. Using the 10.8A as the maximum current able to be drawn from the battery at 24V, a total 259.2W can be produced. Calculating the power drawn by the sensors at 3.1V results in 0.53W. Using an assumed 500mA and 12V source, the microprocessor will draw a maximum of 6.4W. This value will likely be lower. Additional losses of 2.56W and 0.433W are expected due to the non-ideal efficiency of the DC-DC converter and the voltage regulators, respectively. In displaying voltage LED’s, a negligible amount of .446W are diverted to the voltage indicator circuit.
The greatest power consumption occurs in the motors. Running at 30% of total power, both motors will draw a total of 180W over one hour. When necessary, the battery will be able to discharge at a higher current, using the reserve power of 68.83W for short bursts of speed as well as losses unaccounted for. A 100% discharge is assumed at this point, which is not ideal when using Sealed Lead Acid batteries. It is more practical to assume that the power needs can be met without encroaching upon the full discharge; this capability will lengthen the life of the battery.
22
For additional details about discharge current vs. dicharge time, nominal capacities, and shelf life, refer to Appendix D.
23
Torque Deliverability
Motors were selected based on the results of a crude torque requirement analysis. The analysis consisted in balancing forces and torques of the skateboard system assuming that the skateboard is moving at 3 m/s, carrying a person with a mass of 91 kg, and moving up an incline of 5 degrees. Figure 7 shows the free body diagram of a rough model of the skateboard-rider system.
Figure 7
Figure 7: Free body diagram of a rough model of the skateboard-rider system. The skateboard is traveling at constant velocity up an incline Ѳ degrees above the horizontal. The driving force, F, and the weight, mg, are represented with arrows, as well as the acceleration. Note, though, that the acceleration is zero because the skateboard is traveling at constant velocity in the same direction as the acceleration.
A description of the variables used in the diagram follows:
F=External force acting on the system that provides an acceleration in the desired direction. a= Acceleration of the system in the desired direction. Ѳ=Angle of the incline with respect to the horizontal. m= Total mass of the skateboard-rider system. g= Gravitational acceleration. It is assumed to be 9.81 m/s2.
Applying Newton’s Laws of motion in the direction tangent to the path of the system, we found the following relation,
� = � (� + ����Ѳ) (1)
24
Next, the free body diagram of a wheel representing both, left and right wheels, was drawn, figure 8.
Figure 8
Figure 8: Free body diagram of a wheel representing both wheels on the skateboard. It is assumed to be rolling without slipping.
The following variables were used: T=Torque applied by the motors on to the wheels. v=Velocity of the system, assuming that the center of mass of the wheels are at the center and the wheels are rolling without slipping. ω=Angular velocity of the wheels. R=Radius of the wheels. Since the wheels are assumed to be rolling without slipping, equations 2 and 3 hold true:
� = �� = � (� + ����Ѳ)R (2)
� = ��
(3)
The power that needs to be delivered to the motors, under the conditions described above, is given by
� = �� = � �� + ����Ѳ�� (4)
Known Values:
Set � = 114��, � = 9.81 ��� , Ѳ = 5°, � = 0 �
�� , ��� � = 3 ��
.
25
Solution:
� = �114����0��� + �9.81
����sin�5°��(3
��)
P=292.4 W
The motors were selected based on this rough estimate of power requirement. It was decided that two 300 W DC motors should suffice to provide the amount of torque to the wheels in order to get the skateboard to move in the desired direction. Namely, these motors are MY1016 DC motors from www.unitemotors.com (no data sheets are provided by the manufacture of the motors). Each of the motors has a pinion with eleven teeth attached to the shaft.
Furthermore, it is desired to decrease the load on the motors. Equation 5 shows the relation between the number of teeth and the torque on the sprocket and pinion.
�� = ����
�� (5)
Here �� and ��is the torque on the sprocket and pinion, respectively; and �� and �� are
the number of teeth on the sprocket and pinion, respectively. Therefore, by choosing a sprocket with significantly more teeth than the pinion, the torque delivered by the motor can be increased by a factor equal to the ratio of the number of teeth on the sprocket to the number of teeth on the pinion. A sprocket with sixty-five teeth was chosen based on research of prices and availability.
26
Chain Length To determine the correct overall chain length (L) needed, a simple series of calculations can be made. Figure 9 shows a simple diagram of two sprockets with a chain connecting them.
Figure 9
Figure 9: Two sprocket system connected by a chain. To determine the overall length of the chain (L), refer to equations 6 through 8.
To accurately determine the length of the chain required, the straight line distance between the sprockets and the curved portion of the sprockets that is contacted by the chain needs to be determined. A center distance (C) was set to be no less than 0.152 m(6 in.) in length, but no greater than 0.177 m(7 in.). The larger sprocket denoted by the diameter D has a known value of 0.133 m (5.25 in.) while the smaller sprocket, referred to as the pinion in some cases, is denoted by the diameter d and has a known value of 0.03 m (1 in.).
27
With the information provided, the exact chain length required can be easily determined using equations 6 through 8 below.
θd=π-2*sin-1(�����
) (6)
θD=π+2*sin-1(�����
) (7)
L = �4C� − (D − d)� + ��
(Dθ� + dθ�) (8)
Known Values:
Set C ≥ 0.152 m (6 in.), D = 0.133 m (5.25 in.), d = 0.03 m (1 in.)
Solution:
sin-1(�.�����.��
�(�.���)) = 0.0092 m (0.362 in.)
θd=π-2*0.0092 = 0.061 m (2.42 in.)
θD=π+2*0.0092 = 0.098 m (3.87 in.)
L ≥ �4(0.152)� − (0.133 − 0.03)� + ��
(0.133(0.098) + 0.03(0.061))
L ≥ 0.574 m (22.59 in.)
Our supplier, monsterscooterparts.com has many options for chain lengths. The chain nearest to the required length is a 94 link #25 chain. This chain has a length (L) of 0.60 m (23.5 in.). This chain will allow the center distance (C) to be approximately 0.165 m (6.5 in.). The design for mounting the motors allows them to be moved slightly and tightened in the required spot. The bolts will run through a mounting plate and be tightened down, allowing no flexing of the motor, which can cause the chain to bind or come off of the sprockets. Said plate will have slotted holes cut in it, allowing the motor to be loosened, moved, and then tightened back down. This method will be useful in that exact measurements do not need to be made initially on where to drill the holes, and as the chain stretches from use over time, the motor can be moved to account for this stretching, allowing proper chain tension.
28
Preliminary Controls System Design Figure 10 depicts a general representation of the preliminary design of the controls
system of the skateboard. Each block encompasses specialized controls algorithms of subsystems, such as the motors, or mathematical relations of the measured state variables. A description of each block follows.
Figure 10
Figure 10: General Design of the Controls System Block Diagram.
This block represents the desired steady state response of the system; referred to as the reference by most text books on control theory. A very important assumption made when modeling the system was that the board and the rider behave as one rigid body with the rider always standing
perpendicular to the board. Therefore, as the center of mass of the rider moves somewhere not directly above the axle of the wheels, the board tilts so that it continues to be perpendicular to the rider. In order to keep the skateboard at a level plane, the controls system is designed to keep the center of mass of the rider directly above the axle of the skateboard, that is, zero displacement of the center of mass with respect to a point O on the axle. Another design feature of the controls system is to maintain the rate of turning of the skateboard,ψ& , as a
function of the angle of rotation of the control foot-pad, allowing the rider to drive the skateboard to a desired turning ratio by turning the foot-pad.
The controller, which in this case is the microprocessor, will receive the steady state error signal so that it can control the voltage administered to
each of the left and right motors, namely LV and RV respectively.
29
This block contains a mathematical model of the motors in the form of transfer functions. The purpose of this block is to interpret the voltage input of the motors as the torques provided to the wheels, which ultimately become the desired forces that drive the
motion of the skateboard, namely LF and RF . Figure 11 shows a model of a DC motor typically
used in controls systems textbooks.
Figure 11
Figure 11: Schematic representation of a DC motor typically used in a control systems textbooks. This schematic can then be used to obtain the relationship between the input voltage and output angular displacement of a motor. The motor is given an input voltage V to develop a torque on the output shaft. The parameters R, L, Vemf, and b are the armature resistance, armature inductance, back emf, and viscous damping coefficient, respectively, which can be determined experimentally. θ and θ&are the angular position and velocity, respectively. J is the angular inertia of the load “seen” by the DC motor. The armature current ai is not shown.
Following common practice for modeling DC motors, the model in Figure 11 was assumed to be suitable for both DC motors driving the skateboard. Since both motors are identical, it is assumed that all values for the parameters are the same for both motors. For DC motors the back emf is proportional to the angular speed of the shaft, that is
emf bV K θ= &
(9)
where bK ( )Vs rad is a constant of proportionality called the back emf constant. The torque
developed by the motors is proportional to the armature current; thus
t aT K i= (10)
where tK ( )Nm A is a constant of proportionality, called the motor torque constant. Both
constants bK and tK can be determined experimentally. The transfer function of both DC
motors is ( )( )
( ) 1t
t b
K RJsV s K Ks s b
J R
θ=
+ +
(11)
The parameters in the transfer function will be determined experimentally. An ohmmeter will be used to measure the resistance between the two armature wires. The motor
T
30
torque constant will be measured by placing the motor on a lathe machine set to revolve at a specified angular velocity ω, and use an ammeter to measure the steady state current produced by the motor. Assuming no power loss for initial measurements, and recalling that the torque delivered by the motor is proportional to the current applied to the motor, it is stated that the input power is equal to the output power. Therefore
2
t a aK i i Rω = (12)
And thus
at
i RKω
= . (13)
In order to measure the back emf constant, the steady state voltage across the armature wires is measured with a voltmeter while the lathe machine is making the shaft of the motor rotate at angular velocity ω. Equation 9 above is used to solve for bK .
A mathematical model of the system is contained in this block. The input forces are related to the state-space variables to drive them to the desired steady-state response.
The mathematical model consists of a system of second order differential equations that describe the dynamics of the rider-skateboard system. These equations are of the form
( ) ( , ) ( ) ( )M q q C q q q K q Q i+ + =&& & & (14)
where ( )M q is the inertia matrix, ( , )C q q& is the damping matrix, ( )K q is the stiffness
vector, Q is the matrix of external torques applied by the motors, and
l
rqθθα
=
(15)
31
Figure 12
Figure 12: The diagram on the left is a top view of the skateboard with the turning angle ψ depicted. The directions of the wheels are shown with their respective velocities. The distance A is the distance between the centers of the wheels. COM is the center of mass of the skateboard/rider system. Rw, θl, θr correspond to the radius of the wheels and the turning angle of the left and right wheels respectively. The diagram on the right shows a perspective view of the tilted skateboard. The tilt angle α is shown. The distance “a” corresponds to the height of the COM directly above the center axle. M and I corresponds to mass and moment of inertia respectively. The subscripts “b, w, and m” stand for body, wheel, and motor respectively. η is the gear ratio.
The inertia matrix ( )M q is found to be
1 2 3
0 2 1 3
3 3 4
( )0
a a b
a a b
b b
m m m m m mM q m m m m m m m
m m m m m
− = + −
(16)
32
where
0 2
2 2 2 2 2 2 2 2 2 21
2 2 2 2 22
2 23
2 2 2 2 24
2 2
2
144 4 2 4 4
2 4
4
4 4 8
cos(2 )2cos( )
2
w w b w b w b w m w
b w b w b w
m
b b m
w ba
w bb
mA
m M A R I R a M R A M R A I A I
m M A R M a R I R
m A I
m A M a A I A I
a R MmA
aR Mm
ψ
ψ
ψ
η
η
η
α
α
=
= + + + + +
= − −
= −
= + +
=
=
(17)
The nonlinear damping matrix is
( ) ( )
2
2
0
2 2
2 2
2 2 2
sec( )1 14
sec( )( , ) 1 14
02 2
00
2
w
w
r l l r
b t b
b t b
b b b
AaR
AC q q caR
K KK K
K K K
α
α
θ θ θ θ
α αη µ η
η µ ηη η η
− −
= − − +
− −
+ − + − − −
&
& & & &
& &
(18)
where
2 2
0 2
sin(2 )w ba R McA
α α=
&
(19)
The terms labeled µ in equation 18 are friction coefficients, and the subscripts t under µ stands for tire. The friction coefficients will be determined experimentally and modified as required once the skateboard is assembled next semester. For purposes of simulations and initial design, these coefficients will be assumed to be negligible since the inertia forces and external torques are assumed to be larger than damping forces. Furthermore, the coefficients are assumed to be negligible because bearings for wheels and DC motors are manufactured to have negligible damping.
33
The nonlinear stiffness vector is
0( ) 0
sin( )b
K qgaM α
= −
where g is the gravitational acceleration. The matrix of torques applied by the motors is
1 0( ) 0 1
1 1
lt
r
iQ i K
iη
= − −
where tK is the torque constant of the motors, li and ri are the currents supplied to the left
and right motors, respectively.
The state-space variables of the system are measured with the sensors, which include an accelerometer, angular rate sensor, and rotary encoders. These
measurements are fed back to the controls system and compared with the desired steady-state response to obtain the steady-state error that is delivered to the controller.
34
Physical Diagrams
Figure 13
Figure 13: View of entire skateboard model. All components are included.
35
Physical Diagrams (Continued)
Figure 14
Figure 14: Top view of exploded skateboard. Motors, lexan, wheels, and sprockets are moved away from frame for ease of viewing.
Figure 15
Figure 15: Side view of assembled skateboard. Basic fit and scale of parts can be easily seen with respect to the frame size. Frame dimensions can be found in Appendix A.
36
Physical Diagrams (Continued)
Figure 16
Figure 16: Perspective view of assembled skateboard containing all components.
Figure 17
Figure 17: Front of assembled skateboard.
37
Physical Diagrams (Continued)
Figure 18
Figure 18: Bottom perspective view showing placement of battery, motors and frame design.
38
Frame Analysis General Construction:
The frame is constructed from 1” X 1” X 1/16” and 0.75” X 0.75” X 1/16” square metal tubing. Figure 19 shows the technical drawings where the 1” tubing is shown in black and the 0.75” tubing is shown in red. The larger tubing has an average weight of 0.95 kg/m (0.63 lb/ft) and the smaller tubing has an average weight of 0.62 kg/m (0.42 lb/ft).
Figure 19
Figure 19: Side, top, and bottom of metal frame. Black lines depict 1” square tubing while red lines depict 0.75” square tubing. Material:
Steel tubing was chosen for the frame construction for its superiority over other options. Some of the other possible building materials include solid steel bar, aluminum tubing or bar, and wood. A solid steel bar has significantly greater strength and resistance to bending
39
and fatigue, but its substantial weight made it an unreasonable option for our project. Aluminum is a very light material that would make meeting out weight restrictions very simple. However, to weld aluminum, bar or tubing, a specific aluminum welder is required. I personally do not have access to these types of welders and paying a professional to do the work for us is out of our budget range. Finally, a wooden structure was considered, but dismissed for a few reasons. First of all, we want the skateboard to be water resistant. Wood, although it can be sealed rather well, still has the possibilities of becoming wet and separating at the joints. Also, if the structure was to get hit somehow, it is possible that the wood may shatter or break, losing its entire structural integrity, needing to be replaced. And finally, attaching the axle to the wooden side would be difficult. There would be a high possibility that the axle would quickly become loose or break off of the side of the board causing a dangerous situation for the rider. Taking all of these considerations into account, steel tubing was decided to be the best building material for our frame.
Table 1
Frame Material Alternatives
Selection Criteria Weight Steel
Tubing Aluminum Tubing Wood
Strength to Weight Ratio 0.5 0.5 0.3 0.2 Availability 0.05 0.45 0.15 0.4 Weight 0.15 0.1 0.65 0.25 Workability 0.2 0.65 0.15 0.2 Cost 0.1 0.15 0.8 0.05 Score 1 0.43 0.37 0.3
Table 1: Decision Matrix. Finding a material that meets the strength and weight specifications stipulated.
Design Justification:
The frame was designed for structural integrity while remaining within the stipulated weight restriction. The smaller tubing, 0.75” square, is used in areas where bracing is needed and the 1” square tubing was unnecessary. The strength of both tubing sizes is virtually the same, so in these areas, using the smaller size does not weaken the frame structure, it only lightens the overall mass. The sides of the frame and the standing platforms are designed with 1” square tubing for superior strength and rigidity. All cross members and bracing were incorporated into the frame to help distribute the weight of the rider to the entire frame structure, not only the area where the weight is applied. This can specifically be seen in the side
40
view. The four 0.75” tubing sections, denoted in red, to the far right and far left of the frame were placed there to take the weight of the rider and allow that weight to be applied to the entire frame. If these members were not included, the top of the frame and standing platforms would take the entire mass of the rider and the stresses would be too great, causing immediate failure of the structure. The weight can now “flow” through the smaller cross members and bracing so the entire structure can remain structurally sound. This is visually demonstrated in figures 20 and 21 below.
Figure 20
Figure 20: If there are no bracing elements incorporated into the frame side, the frame would deflect as shown. When the rider stands on the foot platforms, all of their weight is located at two points, causing significant stress concentration and deflection. This analysis demonstrates the results of a weight in excess of 100 times greater than the 91 kg weight limit for visual representation.
Figure 21
Figure 21: With bracing in the frame design, the weight is distributed to the entire frame structure. The overall shape of the frame is maintained with only slight deformation. This analysis demonstrates the results of a weight in excess of 100 times greater than the 91 kg weight limit for visual representation.
41
Overall Weight:
With the current design of the frame, the overall weight is approximately 8.47 kg (18.6 lbs). This weight reflects the entire metal frame in its assembled condition. With the maximum overall, fully constructed weight of 23 kg (51 lbs), the frame needed to be as light as possible while being structurally sound. With all of the components that will be used, approximately 9.07 kg (20 lbs) was allocated for the frame weight to ensure the completed design remained within the constraints.
Calculations:
Using AutoCAD, the total length of the 0.75” tubing was determined to be 6.40 m (21 ft), and the total length of the 1” tubing was determined to be 4.75 m (15.6 ft)
6.40 m * 0.62 kg/m = 3.96 kg
4.75 m * 0.95 kg/m = 4.51 kg
Overall weight: 3.96 kg + 4.51 kg = 8.47 kg (18.6 lbs)
Side Covering:
For protection from the outside environment, the frame will be covered in 1/8” lexan sheeting, attached with screws directly to the metal frame. Each sheet will also have silicone applied to the joints to eliminate water or other liquid from entering the structure.
Stress Concentration:
Maximum stresses will occur where the rider will be standing, and on the axles for the main drive wheels. In these stress areas, it is important to determine if the device will support the load that will be applied to it. The skateboard is not designed to withstand any drops. It is designed to travel across mostly smooth surfaces. Therefore, the stress analysis was performed to reflect only the weight of the rider and the total weight of the skateboard. SolidWorks does these analyses accurately if the user properly assigns constraints and stresses. Figures 22 through 27 show the results of the stress analyses.
42
Figure 22
Figure 22: Stress plot. The figure shows a perspective of the frame and shaft assembly after stress analysis on SolidWorks. A load, represented by the arrows, was applied to frame on the foot platforms to simulate the weight of the rider. Furthermore, the applied load was larger than the maximum weight for the rider listed on the requirement specifications in order to account for dynamic disturbances such as vibrations and irregularities on the ground.
Figure 23
Figure 23: Close up view of the maximum stress concentration of one of the wheel shaft.
43
Figure 24
Figure 24: Close up view of the maximum stress concentration on the wheel shaft (right side). The maximum value on the entire shaft is located in the darkest red area on the shaft and has a value of approximately 90 N/mm2 (MPa) as seen in the summary table, highlighted in blue.
44
Figure 25
Figure 25: Close up view of the maximum stress concentration on the wheel shaft (left side). The maximum value on the entire shaft is located in the darkest red area on the shaft and has a value of approximately 92.5 N/mm2 (MPa) as seen in the summary table, highlighted in blue.
45
Figure 26
Figure 26: The maximum displacement of the assembly seen in the figure is 1.213 e-001 mm. However, the actual displacement of the fame will be less than this order of magnitude (10e-1 mm). The bonding function on Solidworks did not allow perfect bonding along the intersecting lines of the cross member and the foot platform to the frame in the aft section. There is a bond on all items of the frame, but in this section mentioned, only a point on the corner could be permanently bonded. If the program would allow bonding, the frame would deflect in a symmetrical manner, reducing the maximum overall deflection seen in the figure in red. We know this value will decrease because the forward section in the figure was mated completely and bonded at all points. This section shows clearly, with the color distribution that there is less stress and less deflection. When properly mated, the symmetrical frame will have the same deflection on both platforms. The forward section experiences an approximate 8e-2 mm deflection. The aft section would also carry this same value if the mates were complete on the frame. In general, no significant bending or permanent deflection occurs as the frame is currently assembled, telling us that when the frame is built and all bonds are welded permanently, the possibility of failure is almost zero. This displacement shown in figure 24 is very small, in the magnitude of 10-4, meters and can be considered negligible.
46
Figure 27
Figure 27: Front view of deflection plot with forces and restraints shown.
Mr. Wells and I performed linear as well as non-linear analyses of the system to determine if there was a significant difference in the displacement and stress results. The results were not significantly different, so a simple linear analysis can be performed on the system.
As seen in figures 22-27, the axle is the weakest point of the system. Having this weak point means failure may occur at some point. We needed to analyze the system at the failure point to determine if a new axle and wheel set was needed. To do this, Solidworks is able perform a stress analysis on the frame as it will be constructed next semester. The red regions on the frame denote the highest stress at a given point and the color blue represents a stress value of zero. As seen in figure 22, the highest stress value is 92.5 MPa for the entire frame and axle assembly. This maximum value is located on the axles as seen in figures 23,24 and 25. One axle has a maximum value of approximately 90 MPa (figure 24), while the other a maximum of 92.5 MPa (figure 25). The differing values can be explained by the complications involved in mating the frame together in a complete manner (refer to figure 26). Research was done on the AISI 1566 steel shaft we will use for the axles and the value for the yield strength was found to
47
be 190-210 GPa on efunda.com. With this value known, we can that the shafts are strong enough to support the weight we will impose on them. The axle will support approximately 2000 times more stress, making the shaft sufficiently strong to withstand the imposed weight previously set (91 kg).
Also, the applied loads used in the simulations were greater than the maximum value that the skateboard will actually experience from the rider’s weight. This was done in order to account for dynamic loads experienced, for instance, by irregularities on the ground.
Factors of Safety
Engineers must accommodate uncertainty. Uncertainty always accompanies change. Material properties, load variability, fabrication fidelity, and validity of mathematical models are among concerns to designers. A method used to address uncertainties establishes a factor of safety based on the absolute uncertainties of a loss-of-function parameter and a maximum allowable parameter. Here the parameters can be load, stress, deflection, etc. Thus, the design factor n is defined as
� =loss − of − function parameter
maximum allowable parameter
Since stress may not vary linearly with load, using load as the loss-of-function parameter may not be acceptable. It is more common to express the factor of safety in terms of a stress and a relevant strength of the same type as the stress. It is important to note that the strength of a material is an inherent property of a part, or mechanical element built into it because of the use of a particular material and process. The stress is a state property at a specific point within the body, which is a function of load, geometry, temperature, and manufacturing processing. The factors of safety of the frame and the shafts were calculated by finding the point of maximum stress on the stress plot obtained with the analysis done in SolidWorks. The stresses on the frame are not considered since the yield strengths of steels oscillates about 280 MPa and the maximum stresses shown in the simulation (figure 22) are approximately 20 MPa. The shafts experience the highest stress found in the simulation. This stress has a maximum value of 92.5 MPa on each shaft. This value is well below the yield strength of steel indicating that the shafts will withstand the weight of the frame and the maximum weight of the rider specified in the requirement specification. The factors of safety are 14 for the frame and 3 for the shafts indicating that the frame will withstand 14 times the load applied in the simulation and the shafts will withstand 3 times the load applied in the simulation.
48
Fall 2009 Schedule
49
Analysis of Fall 2009 Schedule According to the schedule developed earlier this semester, there are only four items of interest that need to be completed after the Thanksgiving break. In reviewing the chart, only one aspect is behind schedule. The stress analysis to be performed on Solidworks is not complete, but will be finished by the December 10th stage gate review. All other aspect of the project are on schedule, or ahead of schedule and were completed before the projected completion date. At this point, there are no jobs to be done that have not be worked on or completed.
There are a few areas of concern in the Spring semester. The equations of motion need to be implemented into the software so that the microcontroller can “understand” how the skateboard is behaving at any given time. Harrison and Misael will be working on this together. Also, the control system is currently being compiled and is scheduled to be complete before we return next semester. This information will then need to be implemented into the microcontroller and will simulate a PID controller. Finally, the frame construction is important to the overall completion of the project. It needs to be constructed accurately and completely as to not allow any undue stress and failure at any given point. If the structure is not welded properly, higher stresses will occur and failure may result from an improperly constructed frame (see the stress concentration section on page 41 for details).
50
Spring 2010 Schedule
51
Budget Analysis When the original budget was made, many aspects of the building process were not included, and the team did not realize everything that would be involved. Since then, many changes have been made and the final budget has been updated to include everything needed to complete the project. This finalized breakdown can be seen on page 52. Several items on the final budget were more expensive than estimated, but many items were able to be purchased at a lower rate than previously budgeted. The savings outweighed the extra costs involved, so the budget, although originally incomplete, now has more in its contingencies and miscellaneous fund.
Items Costing More Than Anticipated:
Lead acid battery (+ $13.00)
Gyro (+$11.49)
Attachment Hardware (+$10.00)
Motor Controller (+$82.49)
Wheels (+$16.72)
Total cost of underbudgeted items: $133.70
Items Costing Less Than Anticipated:
Motors (-$35.88)
Accelerometers (-$4.00)
Lexan (-$22.36)
Metal (-$111.52)
Modular Encoders (-$20.00)
Microprocessor (-$56.10)
DC-DC Converter (-$5.26)
65 Tooth Sprockets (-$4.12)
Total saved from overbudgeted items: $259.24
52
Updated Budget Item Cost Vendor Date Updated Ordered
300W motor (2) $37.06 each monsterscooterparts.com 11/4/2009 Y Lead acid battery $112.90 advancedbattery.com 11/4/2009 Y Accelerometers (2) Free Samples Ordered freescale.com 10/1/2009 Y Dual Axis Gyro $11.49 digikey.com 11/4/2009 Y Lexan Sheeting $62.72 estreetplastics.com 10/9/2009 Y Metal for Frame Construction Free Donations HU Metal Shop Y Modular Encoders Free Samples Ordered honestsensor.com 11/1/2009 Y Attachment Hardware ~ $35.00 Lowes 10/28/2009 N Wheel Shafts $19.05 mcmastercar.com 11/4/2009 Y Microprocessor $43.90 futurlec.com 11/14/2009 Y Motor Controller $82.49 dimensionengineering.com 11/14/2009 Y DC-DC Converter $26.45 powerstream.com 11/14/2009 Y #25 Chain With Master Link $11.86 each (2) monsterscooterparts.com 11/4/2009 Y 65 Tooth Sprocket For #25 Chain $16.06 each (2) monsterscooterparts.com 11/4/2009 Y Drive Wheels , front wheels $36.72 Bike City, Searcy AR 10/3/2009 Y Pro-Etched Circuit Board ~ $60.00 piclist.com 10/4/2009 N Contingencies & Misc. ~ $229.32
Total Cost $850.00
Budget Including Costs of Free Materials Items Costs Possible Vendor Date Updated
300W motor (2) $37.06 each monsterscooterparts.com 11/4/2009 Lead acid battery $112.90 advancedbattery.com 11/4/2009 Accelerometers (2) $4.00 freescale.com 10/1/2009 Dual Axis Gyro $11.49 digikey.com 11/4/2009 Lexan Sheeting $62.72 estreetplastics.com 10/9/2009 Metal for Frame Construction $111.52 Lowes 11/30/2009 Modular Encoders $20.00 honestsensor.com 11/1/2009 Attachment Hardware ~ $35.00 Lowes 10/28/2009 Wheel Shafts $19.05 mcmastercar.com 11/4/2009 Microprocessor $43.90 futurlec.com 11/14/2009 Motor Controller $82.49 dimensionengineering.com 11/14/2009 DC-DC Converter $26.45 powerstream.com 11/14/2009 #25 Chain With Master Link (2) $11.86 each monsterscooterparts.com 11/4/2009 65 Tooth Sprocket For #25 Chain (2) $16.06 each monsterscooterparts.com 11/4/2009 Drive Wheels (2), front wheels (2) $36.72 Bike City, Searcy AR 10/3/2009 Pro-Etched Circuit Board ~ $60.00 piclist.com 10/4/2009 Contingencies & Misc. ~ $93.80
Total Cost $850.00
53
Design Consideration Analysis of Components Item Desirable Features Undesirable Features
Motors
• High torque deliverability • Compact size • Water and dust resistant • Eleven tooth pinion included and permanently attached • Easily mounted and removed via included motor mount
• Heavy • 24V requirement • Costly
Battery • 20Ah power output • 500 cycle use
• Heavy • Large dimensions • Inconsistent power deliverance • Costly
Accelerometers
• Compact, multi- axis design • Free • Low current • High shock resistance • Temperature resilient
• Difficult to mount • Electrostatic discharge sensitive • Requires encapsulation
Gyro
• Compact, dual axis design • Low power consumption • Wide operating temperature range • Single supply operation • Integrated filtering and amplification
• Electrical and mechanical shock sensitive • Difficult to mount • Requires encapsulation
Lexan Covering
• 1/8" thick sheets can be drilled safely • impact and shatter resistant • lighter than equivalent plexi-glass alternatives • Easily cut and manipulated • High temperature resistance
• Increased costs over similar alternatives
Sub-frame Metal
• High strength • Many tubing sizes available • Thin walled tubing used for weight saving while maintaining strength • Readily available
• Heavy • Frame will be painted and covered to provide full protection from outside elements • Can rust rapidly if not treated or painted • Requires welding • Expensive
Modular Encoders
• Durable• Easily mounted on small shafts• Lightweight• Designed for DC motors• Most models allow various mounting capabilities without making alterations to the shaft• Inexpensive
• Tolerates limited (+/- .050”) axial motor shaft movement • Modular encoders are difficult to seal from water, dirt, and other foreign materials • Limited hub diameter options • Resolution may be insufficient
54
Design Consideration Analysis of Components (continued)
Item Desirable Features Undesirable Features
Lexan Attachment Hardware
• Inexpensive • Readily available in small quantities • Standardized – easily replaced
• Many pieces needed • Can come loose over time • Requires tapping of metal frame
Wheel Shafts
• Large mounting diameter • Easily integrated and attached to frame • Machineable • High stress resistance
• Requires machining for proper wheel mounting
Microprocessor
• High-frequency operation • Development board platform • ‘C’ programming language • Contains required I/O pins
• Requires 12v supply • Bulky • More costly than simple controller
Motor Controller
• Controls both brushed motors simultaneously • Reversible direction • Onboard 5v DC supply • Ease of implementation
• Costly
DC-DC Converter • Energy efficient • Steady 12v voltage regulation
• Bulky • More costly than voltage regulator
Chains
• Doesn’t require perfect tension or slack to operate effectively • Length can be altered easily • Limited stretching • Cheap • Availability
• Require precision alignment between both sprockets • Debris easily accumulated on chain
Sprockets
• Many size options available • Cheap • Various mounting options • Strong construction
• Difficult to mount • Potentially dangerous
Wheels (main) • Inexpensive • Lightweight and durable • Sealed bearings
• Plastic spokes with metal shaft • Difficult to mount sprocket to wheel
Wheels (Safety) • Free • Sealed ball bearings
Pro-Etched Boards
• Professional craftsmanship • Lessened workload
• Outsourcing required • Costly • Product acquirement wait time
55
Component Selection Breakdown 24V DC 300W Brushed Electric Motors
These motors were selected for the capability of maintaining an arbitrarily selected speed of approximately 3 m/s up an incline angle of 5°. Originally 350W motors were selected, but unavailability forced us to reconsider and downsize. The 24v requirement was selected to lower the current required to be drawn by the circuitry. Brushed motors are being used to lower the cost of each motor as well as of a motor controller. According to monsterscooterparts.com each motor selected is designed for powering an adolescent’s electric scooter individually, but the independent turning radius requires the use of two motors.
Table 2
Motors Alternatives
Selection Criteria Weight 300 W 350 W 400 W Torque Deliverability 0.3 0.2 0.33 0.47 Compact Size 0.2 0.33 0.33 0.33 Power Consumption 0.3 0.5 0.3 0.2 Low Weight 0.15 0.33 0.33 0.33 Inexpensive 0.05 0.44 0.39 0.17 Score 1 0.35 0.32 0.33
Table 2: Decision Matrix. All motors considered were of the same brand and distributor.
24V 20Ah Battery
The decision was made to use a 24 volt battery to lower the amount of current flowing through the circuitry. A large Amp-hour (Ah) rating is necessary to achieve the amount of usage time as specified in the Requirements Specifications report. The skateboard will require approximately 8.8A, including each motor as well as the microcontroller and sensors. At first examination, the 20Ah well exceeds the current requirements demanded to meet our requirements specification; however, upon further inspection, it was found that the battery will produce just under 10.8A over a period of 60 minutes. This power output is 22% greater than required, which will provide a margin of safety for any unaccounted for power loss in the motors and other circuitry devices. The decision to purchase a sealed lead acid (SLA) battery type was based largely on the runtime.
56
Table 3
Battery Alternatives
Selection Criteria Weight NiMH SLA Li-ion Run time 0.5 0.4 0.5 0.1 Life of Battery (# of cycles) 0.1 0.33 0.33 0.33 Weight 0.1 0.35 0.2 0.45 Sustained Power Delivery 0.2 0.15 0.25 0.6 Cost 0.1 0.85 0.1 0.05 Score 1 0.32 0.36 0.15
Table 3: Decision Matrix. The type of battery was the main topic of concern when selecting the correct one for our application.
Analog Devices ADXL335 Accelerometer
The design of this project requires accelerometer sensing in two dimensions. This accelerometer is capable of returning values of linear acceleration up to 3 g’s in three dimensions. The high resistance to mechanical shock, as well as the low power consumption, makes this accelerometer a desirable component in our project. An additional benefit to the selection of this accelerometer was the availability of obtaining free samples.
STMicroelectronics LPR5150AL Angular Rate Sensor (Gyroscope)
The design of this project requires two dimensional angular rate sensing. This gyroscope is capable of detecting angular acceleration in two perpendicular directions. The onboard features of amplification and low-pass signal filtering increase the simplicity for manipulation of the signal information. The LPR5150AL is highly resistant to electrical and mechanical shock. Also, this gyroscope is available for a low price when purchased in single quantities, which allows for easy replacement if necessary.
Lexan Covering
In determining a method to cover the metal frame of the skateboard, the lightest and cheapest method was being sought. Metal can be attached permanently and efficiently, but is very heavy and costly. Through much deliberation, lexan sheeting was chosen for many reasons. It is lightweight, can be drilled easily, and silicone can be added to the metal frame for a strong and water resistant bond. Lexan was chosen because it is the best material for our application.
57
Table 4
Side Covering Material Alternatives
Selection Criteria Weight Lexan Wood Metal Plexi Weight 0.4 0.4 0.2 0.05 0.35 Cost 0.1 0.3 0.4 0.05 0.25 Workability 0.5 0.65 0.07 0.25 0.03 Score 1 0.52 0.16 0.15 0.18
Table 4: Decision Matrix. The type of material was the main topic of concern in selecting the material.
Sub-frame
A high strength and lightweight material was needed to construct the frame. The frame needed to support the weight of not only the rider, but the components inside the frame as well. With a combined weight of 114 kg (250 lbs), the choice to construct the frame from metal was the best choice. However, with a significantly higher cost over other building materials (approximately $115.00), it would be too costly to use. The decision was made to try to acquire free materials before another building material was considered. Donations of enough material were made by the Harding University metal shop on campus. Stress analysis is being conducted to determine the strength of the frame as it is designed.
Table 5
Frame Material Alternatives
Selection Criteria Weight Steel
Tubing Aluminum Tubing Wood
Strength to Weight Ratio 0.5 0.5 0.3 0.2 Availability 0.05 0.45 0.15 0.4 Weight 0.15 0.1 0.65 0.25 Workability 0.2 0.65 0.15 0.2 Cost 0.1 0.15 0.8 0.05 Score 1 0.43 0.37 0.3
Table 5: Decision Matrix. Finding a material that meets the strength and weight specifications stipulated.
58
Honest Sensor HS30A Optical Encoders
Several options were given for rotary encoders, but the implementation of our stationary shaft required the use of an optical encoder. The encoder will be directly attached to the motor shaft, and will sense the actual rotational velocity of the wheel, which can be translated into forward velocity.
Table 6
Rotary Encoders Alternatives
Selection Criteria Weight Through Hole Shafted Mounting Method 0.75 0.9 0.1 Availability 0.25 0.05 0.95 Score 1 0.67 0.33
Table 6: Decision Matrix. Few encoders fit onto our motors or in our application.
Lexan Attachment Hardware
Using machine screws to attach the lexan sheeting to the metal frame will be the most secure method. The lexan will be cut to size, drilled, and then laid on the metal frame. The frame will be drilled and tapped for threads at the hole locations. Silicone will be used at the joints for water resistance and Lock-Tite will be applied to the threads to ensure they do not back out over time. Using this method of attachment is cheap and the hardware is standardized so any replacements can be easily made.
Wheel Shafts
Finding shafts that were the correct diameter for the wheels we have was not possible, so shafts were ordered in a larger diameter than required and will be milled down to the correct diameter. Steel shafts were chosen for their strength and weldability. The shafts may be a weak point of the system and are currently being analyzed in SolidWorks to determine if they are applicable to our application.
59
Table 7
Shaft Alternatives
Selection Criteria Weight Aluminum
Stock Steel Stock
Aluminum Machined Steel Machined
Strength 0.85 0.1 0.4 0.1 0.4 Attachment to Frame 0.1 0 0.5 0 0.5 Cost 0.05 0.4 0.1 0.4 0.1 Score 1 0.1 0.4 0.1 0.4
Table 7: Decision Matrix.The wheel chair wheels were not a standard diameter, so we needed to either buy a precisely machined bar or machine it ourselves.
PIC18F458 Development Board
A development board was decided upon to create ease of use and to lower the chances of accidental burnout and improper soldering. This specific processor operates at its maximum crystal speed, a frequency of 10MHz. Initially, a slower processor was chosen, but the increasing amount of input/output required caused us to select the development board with more processing power. Also, the large number of input/output and Analog/Digital channels is useful for the accelerometer, gyroscope, rotary encoders, and motor controller. This development board contains 32Kbytes of internal program flash memory and 256bytes of EEPROM. This should be more than adequate for our foreseeable needs, and can be easily modified if necessary.
Table 8
Microprocessor Alternatives
Selection Criteria Weight PIC18F458 PIC16F877 PIC18F4550 Processor Speed 0.4 0.5 0.2 0.3 Programmability 0.3 0.3 0.2 0.5 Power Consumption 0.1 0.3 0.3 0.4 Size 0.05 0.35 0.4 0.25 Cost 0.15 0.3 0.5 0.2 Score 1 0.38 0.27 0.35
Table 8: Decision Matrix.The wheel chair wheels were not a standard diameter, so we needed to either buy a precisely machined bar or machine it ourselves.
60
Sabertooth 2X10 Motor Driver
This motor driver was selected based upon our motor current and voltage requirements for operation. The Sabertooth 2X10 is designed to independently operate two brushed motors at 8A continuously, with a momentary peak of 15A, per channel. This exactly fits our design needs. More so, the Sabertooth 2X10 has simple implementation as well as a 5V, onboard power supply if needed. This motor driver also has built in over-current and thermal protection to prevent accidental burnout of the device. The Sabertooth 2X10 was the only motor driver that fit our requirements; therefore, there is no decision matrix.
PowerStream DC292 Adjustable DC/DC Converter
The Powerstream DC292 was selected as the source of lowering the 24V supplied by the battery to the 9V-12V input required at the microprocessor. The high output amperage of 2A allows for all of the sensors to also be powered by this converter. A steady supply of 12V is necessary because all of the critical components, including the microprocessor, gyroscope, accelerometer, and optical encoders, are going to be powered by this device. The DC292 provides 78% efficiency when running at 24V/12V conversion.
Table 9
DC-DC Converter Alternatives
Selection Criteria Weight PST-DC292 PST-DC-210 Implementation 0.4 0.7 0.3 Efficiency 0.3 0.45 0.55 Size 0.07 0.7 0.3 Weight 0.03 0.75 0.25 Cost 0.2 0.7 0.3 Score 1 0.63 0.37
Table 9: Decision Matrix. The DC-DC converters were initially narrowed down based on input/output voltages. From these options, the final selection was based mostly on ease of implementation and power efficiency.
Chain
The chain was selected based on the size of the sprockets, pinion, and center distance between them. Calculations were made and it was determined that a chain of length 0.574 m (22.59 in) was needed to couple a sprocket with a diameter of 0.133 m (5.25 in.) and a pinion with a diameter of 0.03 m (1 in.) having a center distance of no less than 0.152 m (6 in.) and no
61
greater than 0.177 m (7 in.). Among the products on Monster Scooter Part’s website, a 94 link #25 chains had dimensions nearest to the calculated value. Other important factors that were taken into considerations were the easy alterability of its length and its inexpensive cost.
Sprockets
The sprockets that will be attached to the wheels for torque transmission from the motors were selected based on the ratio of the number of teeth to number of teeth on the pinion. Limited options and cost were not significant factors in the decision. The 0.133 m (5.25 in.) diameter sprockets, having 65 teeth would increase the torque delivered by the motor by a factor of 5.9. This was considered to be reasonable in order to reduce the load on the motors, thus we decided to purchase these sprockets. Also, it is important to have a tight mesh between the gear teeth and the chain. Since the chain and sprocket are both #25 standardized, the mesh will be exact and there will be no interference.
Wheels
The main drive wheels have an 8 inch diameter. After researching many options, wheel chair wheels were the best choice due to them being readily available. They have a hard rubber outer rim to allow it to grip most surfaces and a metal hub with bearings for mounting. The bearings will significantly reduce wear on the shafts they will be mounted on. The sprocket will be directly bolted to the wheel itself and driven by a chain attached to the sprocket on the motor.
The safety wheels are skateboard wheels and will be free rolling, attached to the front and rear of the skateboard. Skateboard wheels were chosen because they are resistant to wear, cheap, and have bearings to allow a smooth rolling action.
Table 7
Wheels Alternatives
Selection Criteria Weight Wheel Chair Inflatable Durability 0.75 0.85 0.15 Attachment to Frame 0.2 0.5 0.5 Cost 0.05 0.65 0.35 Score 1 0.77 0.14
Table 7: Decision Matrice. Finding a wheel that meets the strength and durability requirements.
62
Pro-etched Boards
The requirements for this project include the purchase and use of a professionally etched circuit board; though this is a hindrance financially, it will lessen workload and provide highly professional craftsmanship. The specific provider and circuit to be etched are not currently selected. We are currently in the process of designing circuit boards, so pricing information is unavailable. Company options include PCB Artist, Suntron Corporation, and TELCO Intercontinental Corp.
63
Pictures
Figure 28: 65-tooth sprockets
Figure: 29: 94-link chains
64
Pictures
Figure 30: 300W motors
Figure 31: Close up of motor
65
Pictures
Figure 32: 24V 20Ah battery
Figure 33: Drive wheels from wheelchair
66
Pictures
Figure 34: Safety wheels from skateboard
67
Appendices
