Drivetrain
A. Overview
Many important points were brought up about the drivetrain in the Concept Design Review. The important points that I will be further discussing in this system design review is:
· Bevel Gear concerns
· Cantilevered shaft off bearing issues
· Motor Curve / Efficiency
· Drivetrain Metrics
· Drivetrain Part Replacement Time
· Motor System Response Simulation
In addition to these points, other risks will be assessed and mitigated with the refined design of the drivetrain.
B. Concept Refinement
Miter/Bevel Gear and Cantilevered Axle Design:
A large concern, which was initially underestimated, is the transfer of power through the miter or bevel gears. On paper there is not a clear problem in this regard, but in actuality there were large problems in retaining gear meshing in the past robotic module projects.
One aspect of the problem is the miter/bevel gears will transfer force axially through the gears. If set screws are used to mount the gears, the gears will eventually slide away from each other due to the forces exerted by the gears. This will consequently lead to the miter/bevel gears slipping. It was suggested to use pins to stop the sliding of the gears by the RP10 team. The issue with using pins is that since our specified axle is ¼” the pin would need to be very small. Due to the torque transmitted from our motor the pin could easily be sheared. Also the axles will be jeopardized in bending and torque transmission if a hole were to be drilled through it.
The other contributing effect is the long cantilever axle design that was also implemented on past Robotic modules. The longer the axle is from the bearing the larger the bending moment will be from the miter/bevel gears. The deflection of the axle due to this bending moment will also aide in creating the opportunity for the gears to slip. The RP10 design team recommended using larger diameter axles as to aide in preventing bending moments in the cantilever design. This is a viable possibility, but since RP1 has to be smaller than the previous robotic module projects we will explore the possibility of a different solution.
Original Miter Gear Concept:
Refined Miter Gear Design:
The solution that was developed to deal with both of these issues is to use an aluminum L bracket that would constrain the two bevel gears together. The bracket would be 1/8” in thickness and have two thrust bearings mounted into it. See figure 1-2 for a detailed view. This bracket constraint would guarantee meshing of the gears while removing the need for pins and larger diameter axles. Initial calculations conclude that a 1/8” thick bracket would deflect very minimally at the max torque value of the motor. Also since it would be constrained by the motor axle plane and upper yoke axle plane, in theory, the bracket would not need to be mounted to the yoke. The bevel gear bracket does introduce two new negative points. The first one is simply the difficulty in assembly due to the new bracket. It seems reasonable that the drivetrain could still be assembled in relative ease since all the parts can be put together loose and then tightened. The last problem is the dimensions on the bracket would be critical, which is something we are trying to reduce.
Motor Curve / Efficiency:
Another very important point brought forth was what is the speed at which the motor will operate? It was highly stressed that the motor should operate at its most efficient speed. Following this requirement velocity of the robotic module was ranked the second most important consideration. Lastly after these two considerations, acceleration is ranked as the third chief consideration.
Using these series of rankings, first the most efficient RPM range of the motor was determined. This was done by using the drive motors curve which is shown here in Figure 2-1:
The complete motor and motor transmission specification sheets can be found in the specifications section.
The angular speed value attained is approximately 4875 RPM for most efficient operation (≈60%). Using a 5% upper and lower bound a speed range of ≈4600 - 5120 RPM would be deemed acceptable. These values are denoted by the green range on the motor curve.
The most efficient motor RPM defines the angular speed of the motor and transmission, but to get the highest speed from the module we can alter the gear ratios. This is done while considering the effects of the drivetrain on the yoke. Using a gear ratio increase of 1:2 through the bevel gear and 1:2 through the pulleys a 1:4 overall gear ratio can be attained. This slightly increases the width of the yoke by less then an inch, but substantially increases the attainable speed of the robotic module.
Knowing the speed that we will run the robot we can use a variety of acceleration values and still meet the speed metric requirement. The motor will not be able to operate at efficient conditions while acceleration regardless of the acceleration value. The maximum acceleration is calculated in the analysis section by using a 100% duty cycle, but this can be changed depending on required acceleration needs by changing the value of the duty cycle in our software.
An in-depth system response simulation is done for the motor in both Microsoft Excel and Simulink. The results from the model are in the simulation analysis section and the complete excel analysis is located in the appendix.
Drivetrain Part Replacement Time:
This very applicable concern largely deals with the yoke subsystem in conjunction with the drivetrain subsystem. With our current yoke design it is believed that the drivetrain belt, bevel gear, and wheel can be replaced faster than on RP10. There are simply a lot less fasteners on our current yoke design and removing the yoke will offer total access to all the drivetrain components.
Refined Overall Drivetrain Design:
Initial Drivetrain Concept:
Problems associated with the initial concept design are the cantilevered shaft off a bearing, bevel gear meshing problems, and the motor operating speed in steady state conditions.
Refined Drivetrain Concept Overview:
Refined Drivetrain Isometric View (no yoke):
C. Risk Identification/Mitigation:
Critical Dimensions:
In order for the drivetrain to operate smoothly and without problems a high level of accuracy is needed in fitting the parts. Notable critical dimensions are the drive axle alignment, the bracket holes for the bevel gears, and the motors fixed position. A possibility for reducing the critical dimensions is by using a flexible coupling to mount the motor to the axle. This will alleviate misalignment with the motor and the bevel gear bracket.
Bevel Gear/Cantilever axle:
This risk identification and mitigation was previously addressed in the action items section.
Drive Belt:
Proper care must be made in sourcing the correct length belt with the same pitch as the pulleys. If the belt length is off there is the potential for problems with the belt slipping and coming off the pulleys.
Drive Axle Robustness:
In order to ensure that a ¼” diameter shaft is sufficient for the wheel axle in a table top drop a finite element analysis will be conducted by the next week Friday (2/8/2008). This is an important consideration since robustness is a prime concern for our robotic module.
Bearings:
A more in depth analysis needs to be done as to selecting appropriate bearings. A comparison between ball bearings and journal bearings should also be done to justify the use of the journal bearings. Currently nylon journal bearings are selected to be used due to the light loads encountered on our design, low operating speeds, as well as the good value that these bearings have. A nylon journal bearing is 0.39 cents a piece where as a ball bearing is around $8.00 each for ¼” shaft.
Interfacing with other Subsystems:
The yoke subsystem is highly integrated into the drive system. Great care was taking when selecting components to minimize the size. The larger the size of the drivetrain components the bigger the yoke will be and this will aide in conflicting with the size engineering metric. For this reason we went with a 1:4 gear ratio as the maximum gearing up ratio. Backlash must also be minimized in the wheel axle and make sure the wheel is aligned when it is being built to ensure that the steering will be true.
Cost:
The bevel gear cost is very high relative to the price of other components on the drivetrain. Most alternative to the current bevel gears are cheap plastic miter gears that will compromise our system reliability. Further effort will be placed into sourcing cheaper bevel gears that still meet our requirement.
Manufacturability/Assembly:
With the addition of the bracket on the bevel gears there is a very tight space to work in to assembly the drive system. To aide in easing this risk the yoke has been designed so it can be easily removed and the whole drive system can be put together loose making it easier to assembly.
Mounting:
The way in which we will mount the axles, wheels, pulleys, and gears need to be better researched. The current setup utilizes techniques used previously in RP10. A search should be done to verify that these are the best techniques for mounting the components.
Accurateness of Systems Modeling:
The robotic module systems acceleration, velocity, and displacement simulation model needs to be verified by experimental tests in order to ensure that the robotic module will meet our engineering metrics. Points of concern about the precision of the analytical model is the accurateness of the provided motors torque curve, the friction in the bearings was not taking into consideration in the simulation, and the moment of inertia of smaller components were ignored in the analytical simulation.
D. Simulations Analysis
System Response Calculation Summary:
Specifications:Wheel Radius (in) / 1 / Gear Ratio: / 1:4
Mass of module (lbs) / 5 / Wheel Radius (m) / 0.0254
Mass of Platform (lbs) / 4 / Coefficient of Friction
(Rubber & Steel) / 0.7
Mass of Payload (lbs) / 2.2 / Mass of module (kg) / 2.27
Mass of Idler (lbs) / 3 / Mass of Platform (kg) / 1.81
Mass of Wheel (oz) / 1.2 / Mass of Payload (kg) / 1.00
Mass of Wheel (lbs) / 0.075 / Mass of Idler (kg) / 1.36
g(ft/s^2) / 32.2 / Mass of Wheel (kg) / 0.034
g(in/s^2) / 386.4 / g(m/s^2) / 9.81
Efficiency
(≈Mechanical Efficiency) / 0.80
Summary of Results:
Most Ideal Operation: / 100% Duty Cycle
Angular Speed (RPM) / Velocity (in/s) / Distance (in) / Time (s)
275 / 28.80 / 9.72 / 0.55
Highest Efficiency Motor RPM
4875
High Efficiency Motor RPM Range
4600-5120
High Efficiency Wheel RPM Range
259-288
Max acceleration
capable with no slip (in/s^2)
159.53
Average Acceleration to efficient RPM (in/s^2)
50.47
Max Attainable Wheel RPM
365
Note: The complete analysis for the system response is in the appendix, only the summary is shown here.
System Response Graphs at 100% duty cycle to most efficient RPM:
Simulink System Response:
Simulink Model:
System Response Graphs:
Power and Torque Characteristics:
Simulation Notes: The response curves depict accurate relationships for acceleration, velocity, and displacement. The curves show values up too the most efficient rpm for the motor. The speed will try to be kept at the most efficient RPM within the specified 5% range. The values seem high and need to be verified by experimental testing. The graph in Figure 4-1 shows the max acceleration capable by the robotic platform and the acceleration attained with our current motor with a 1:4 drive ratio. This graph shows that the acceleration is within max limits, so there should be no wheel slip on acceleration. The Simulink simulation model values are very similar to the excel model values. Finding the system response using two different techniques helps to improve confidence in the results. When the motor is operating at its most efficient value it is producing a good amount of power as can be seen by figure 4-9, the line represents the efficient speed value.
E. Preliminary Bill of Materials:
Item Description / Quantity / Cost / Company / Item Total CostStainless Steel Bevel Gears 1:2 / 1 / $70.18 / WM Berg / $70.18
Stainless Steel 1/4" Axle, 36" / 1 / $13.37 / WM Berg / $13.37
1.528" PD, 0.08" Pitch, Aluminum Pulley / 1 / $13.95 / McMaster Carr / $13.95
0.764" PD, 0.08" Pitch, Aluminum Pulley / 1 / $9.51 / McMaster Carr / $9.51
1/4" Synchronous Belt, 0.08" Pitch / 1 / $3.00 / McMaster Carr / $3.00
Nylon Journal Bearing / 2 / $1.96 / McMaster Carr / $3.92
Total Cost: / $113.93
F. Conclusion
Two of the large concerns, bevel gears and motor operating speed, are thoroughly addressed here due to there importance. The risk of the bevel gears was assessed and mitigated as best as possible. In addition to these major concerns a selection of other potential risks are identified. System simulations where then run in order to verify that our engineering metrics could be attained.
F. Appendix:
Complete Motor System Response Analysis:
Drivetrain Motor Specs:Specifications:
Standard / Metric / System Parameters:
Wheel Radius (in) / 1 / Wheel Radius (m) / 0.0254 / Gear Ratio: / 4:1
Mass of module (lbs) / 5 / Mass of module (kg) / 2.27 / Coefficient of Friction
(Rubber & Steel) / 0.7
Mass of Platform (lbs) / 4 / Mass of Platform (kg) / 1.81 / Efficiency
(≈Mechanical Efficiency) / 0.80
Mass of Payload (lbs) / 2.2 / Mass of Payload (kg) / 1.00
Mass of Idler (lbs) / 3 / Mass of Idler (kg) / 1.36
Mass of Wheel (oz) / 1.2 / Mass of Wheel (kg) / 0.034
Mass of Wheel (lbs) / 0.075
g(ft/s^2) / 32.2 / g(m/s^2) / 9.81
g(in/s^2) / 386.4
RPM / Torque (lb*in) / Acceleration (in/s^2) / Speed (in/s) / Distance (in) / Time (s)