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ME112 Crawler Final Report Aaron Oro, Alex Le Roux, Jamie Young, Jeff Sarsona February 7th, 2016

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Contents 1 Executive Summary

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2 Background

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3 Design Description 6 3.1 Motor Design Goals . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Transmission Design Goals . . . . . . . . . . . . . . . . . . . . 7 3.3 Crawler Mechanical Design . . . . . . . . . . . . . . . . . . . . 8 3.4 Dynamic Movement Design Goals . . . . . . . . . . . . . . . . . 10 3.5 Free Body Diagrams . . . . . . . . . . . . . . . . . . . . . . . 11 4 Crawler Demo Logistics

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5 Analysis of Performance 13 5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5.2 Motor Performance . . . . . . . . . . . . . . . . . . . . . . . 13 5.3 Transmission Performance . . . . . . . . . . . . . . . . . . . . 16 5.4 Rolling Resistance . . . . . . . . . . . . . . . . . . . . . . . . 17 5.5 Overall Performance . . . . . . . . . . . . . . . . . . . . . . . 17 6 Strength Estimate

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7 Conclusions

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A Appendices

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Executive Summary For this project, our challenge was to create a small Lego “crawler” that could ascend a narrow pyramid shaft (modeled as a 60° inclined track), depress a bumper button at the top of the shaft and descend back down the shaft while using as little energy as possible. Furthermore, in order to model a core-drill to be attached, the crawler also needed to carry a payload in the form of a steel bolt. After iterating through designs by taking into account factors such as gear ratio, wheel placement, driving orientation and general shape, we decided upon a back-driven crawler that drove up the side walls of the track as seen in Figure 1.1. This design minimized the contact forces the wheels imparted on the sidewalls, reducing rolling resistance and allowing our crawler to simply roll down the inclined track when power was disconnected. The design also biased our crawler to roll into the track bottom by incorporating clever wheel alignment and weight distribution. When combined with Lego bumpers added to the bottom of the crawler, this allowed us to keep our crawler moving along the bottom of the track in a set orientation . Although incur some frictional power losses, this guiding allowed our crawler to dependably achieve its functionality.The transmission for our crawler drove a single back wheel with a speed reduction of 75 and operated at a calculated 13.5% efficiency. This indicates that we saw an efficiency loss of 5.8% due to rolling resistance and friction. During presentation, our crawler comfortably crawled both up and down the track while depressing the button at the tracks apex. Quantitatively, our crawler ascended a 1m section of the track in 9.7 seconds at 6.0V and 0.44 A. Since the crawler needed no power input to descend this section, this lead to a total energy expenditure of 25.6 J and an overall efficiency of 7.8%. Although this energy expenditure was well under the desired value of 60J, if allowed further iteration our group would have moved to a higher gear ratio (150:1) in order to get our crawler closer to its maximum efficiency. We also would have redesigned the protective bumpers contacting the track bottom so as to reduce power losses due to friction and lubricated our transmission so as to increase its efficiency.

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Background Inspired by the work of Dr. Zahi Hawass, the goal of this project was to create a small “crawler” that could be used to explore narrow passages and shafts often found in Egyptian Pyramids. Furthermore, this crawler needed to be able to carry a payload representing a core drill as many of these pyramidal shafts are blocked off and need be excavated. In order to achieve this functionality, the crawler was tasked with ascending a 60° inclined track, depressing a button at its top, and then descending back down to the bottom of the track, all the while carrying a steel bolt as its payload. Note that the track itself was 3m long and in the shape of a 3-sided rectangular prism with a width of 13.5 cm. In order to meet these requirements, we were limited to using a Lego kit, readily available office supplies, and a small motor that could be driven from 0-9 V. Finally, as in a real life application a battery would need be used, the crawler needed to minimize its energy consumption and maximize its overall efficiency. For our application, our crawler needed to use no more than 60 J of power while ascending and descending a 1m section of the track.

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Design Description Motor Design Goals The first step in the team’s design process was to understand the limitations and strengths of our motor. The team characterized our motor’s three essential constants (R, k, ) by testing it under no load and stall conditions and using the following motor mechanical and electrical equations: −

− =

=0 −

At stall, đ?œ” = 0 and therefore equation (1) can be reduced to

(1) (2) =

. When no load is

applied to the motor, we can determine đ?œ” and back out the k value for our motor. In addition, by definition = 0at the no load condition. This reduces equation (2) to = = .Using this logic, we determined the following constants for our motor: = 0.0003 [ ] = 0.0037 [ / ] = 8.0639 Using these motor constant values and the voltage preset values to be used for the challenge (1.5V, 3V, 6V and 9V), the team developed a MatLab script to plot motor efficiency and power versus the angular velocity of the motor. We decided to design for maximum motor efficiency. As seen in the plot below, efficiency scales positively with input voltage. Within the range of preset voltages, the higher the voltage, the higher the potential motor efficiency.

While running the

motor at the 9V 6


preset would ensure a higher efficiency, the motor was specified to operate at 3-6V and our group opted to run at 6V to avoid thermal and performance breakdowns at maximum efficiency. As seen in the graph below for motor output power and efficiency versus omega, the motor angular velocity that maximizes motor efficiency occurs at approximately 1035 [rad/sec]. The motor angular velocity that maximizes motor power out is approximately 730 [rad/sec]. Ideally, to maximize both power and efficiency, our group hoped to be in the 900 - 1035 [rad/sec] range for a maximum theoretical motor efficiency of 44.5%.

Transmission Design Goals We initially prototyped several transmission designs with different number of stages, gear ratios and locations. Our transmission design was formed around 3 basic concepts: (1) use a compact, rigid, minimal design (2) use the fewest number of total gears possible (3) maximize functional output torque. We wanted to reduce weight (and therefore the amount of shafts, supporting pieces and connectors) as much as possible. As the Lewis Stress on the gears is proportional with the mounting factor, our group ensured that our gear shafts were as rigidly and accurately mounted as possible. Our team also attempted to reduce idlers and the number of gear train stages in order to reduce losses among imperfect contact between ABS plastic Lego gears. While loaded with the approximate weight of our crawler, we also wanted to

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ensure that the transmission could apply enough torque and operate in the efficient angular velocity range as detailed above. We settled on a 75:1 gear ratio using a 3 stage gear reduction with spur gears. This allowed us to create a compact transmission with the fewest number of gears possible will delivering an ample output torque of ~0.0465 [Nm]. A detailed view of our transmission ratios and torques can be found in Appendix ?. More about the required output torque and transmission performance will be discussed later.

Crawler Mechanical Design The basic design of our crawler consists of two bodies that are connected by both a pin joint and a linkage. The bodies themselves are both long rectangular frames with stabilizing pieces added across their spans. One of these bodies (from here on ostensibly referred to as the main body) houses our motor/transmission as well as two wheels; a large, driven wheel at the body’s rear and a smaller, neutral wheel at its front. This main body also incorporates lego bumpers (wrapped in tape) on one of its sides that are used to guide the crawler along the bottom of the track in a set orientation. Finally, this main body also houses the metal bolt meant to represent a core drill. This payload is placed near the front of the main body and at the center of its span. It was placed there as we wanted our crawlers center of mass to be as close to the crawlers absolute center as possible, and the majority of the crawlers weight (i.e. motor/transmission) was at the back of the crawler. The other body simply contains one more smaller wheel at its length. As can be seen in the figure 2.5 below, when placed in the track the crawler is oriented so that the two smaller wheels contact one of the side walls, while the larger wheel driven by the transmission contacts the other side wall. This orientation was prefered as when we tested designs that incorporated a driven wheel and a neutral wheel contacting the same sidewall, the torque caused by the driven wheel tended to pull the neutral wheel of the wall, rendering it useless. Furthermore, you can see that this larger wheel is oriented towards the back of the crawler, but still within the range of the two smaller wheels so as to avoid unwanted rotation of the crawler off the wall and make sure that all 3 wheels are constantly contacting the sidewalls. The weight of the crawler was measured as 234 grams during presentation, its overall length when fully stretched out measured at 29cm, and its length when compressed in the track measured at 18 cm. In order have the two bodies oppose each other and allow the wheels to apply a contact force to the track’s sidewalls, a two bar linkage tensioned by rubber bands was connected between the bodies. This allowed us relative control over the contact force applied by the wheels to the sidewalls as it was simply a function of how strongly we tensioned the linkage. Furthermore, this allowed us to descend the track without applying power as our crawler simply rolled down the side walls when power was cut, a phenomenon that will be further

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explained in Dynamic Movement Design Goals section. Also, in order to avoid unwanted wander along the sidewalls of the track, the wheels were all intentionally placed in line with one another. This wheel placement, combined with the bottom bumpers previously described, resulted in a slight downward bias in crawler that caused it to move down into the track. This allowed our crawler to skirt along the bottom of the track without the unwanted wander up and down the sidewalls. One unfortunate byproduct of this implementation was increased friction caused by these bumpers, however we felt this loss in efficiency to be necessary as it pretty much guaranteed that our crawler would dependably work every time. As a final note, our front wheel was used to depress the bumper at the top of the shaft, simply because it worked reliably and we never felt the need to implement another solution.

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Dynamic Movement Design Goals In order for the crawler to navigate the 60 degree incline, large normal forces are required to prevent the crawler from rolling back down the ramp and from rotating in the Z plane. These large, induced normal forces create frictional forces that secure the crawler in the ramp channel. From the onset of the project, we wanted to create a crawler that was backdrivable down the ramp without any inputted power. This would conserve power and theoretically allow us to generate energy. More broadly, being backdrivable at a constant speed would mean that our statically exerted forces were less than the weight of our crawler down the ramp (i.e. 10


mgsin(60)). However, in order to achieve this, our crawler needed to have enough frictional force during movement to ensure proper drive wheel engagement with the side of the ramp to avoid slipping. Therefore, we aimed to design our crawler to have high normal forces while driving up the ramp induced by the motor torque on the drive wheel and the allowed rotation or the crawler in the X plane. However, when no torque was applied from the motor, the crawler would induce a very low normal force thereby creating as little friction as possible and allowing unpowered movement back down the ramp. This force balance can be seen in the FBDs below.

Free Body Diagrams

insert FBDs here and CAD.

Crawler Demo Logistics On final demonstration day, the crawler had to perform a series of tasks with measurements taken to gauge the performance of our design. The basic functionality of our crawler was tested by successfully ascending and descending a 60 degree incline shaft while carrying a bolt representing a core drill. The shaft was constructed of wood and was open from the top, having the bottom floor and two sidewalls but lacking a top ceiling.

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Successful ascent of the shaft was indicated by the crawler depressing a bumper at the top that switches on an LED. Upon reaching the top, the crawler must then descend the shaft. During both ascent and descent, power was supplied to the crawler’s motor to drive it up and down, and the input voltage and current drawn were recorded for efficiency calculations. For an additional challenge, crawlers could be designed to maneuver the 60 degree transition from the flat section to the inclined section of the shaft. To accomplish these tasks, our team designed the crawler to drive up the side walls of the shaft rather than drive on its floor with sidewall bracing arms. Our design focused on reliably ascending the incline section with a 6V input voltage, but descending the shaft with no power supply, using only the weight of the crawler to force it back down. In order to achieve this, we carefully designed the geometry of the crawler and the location of the wheels to reduce rolling resistance due to excessive normal forces. We did not design to accommodate the 60 degree transition, but by designing for no power during the descent, we greatly reduced the total energy consumption of our crawler.

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Analysis of Performance Abstract The analysis of our crawler performance is detailed in this section. The analysis is based on data collected before and during the final presentation and is completely detailed in Appendix ?. In addition, for our analysis of design improvement detailed below, we made 3 main assumptions: (1) the mass of the crawler stays constant (2) the drive output torque stays constant (3) the friction stays constant.

Motor Performance We measured the angular velocity of the motor input shaft during the motor winch test. As our design goal was to have a motor angular velocity of approximately 1035 [rad/sec] to maximize efficiency and output power [given in the Design Description -- Motor Design Goals section], we wanted to compare our actual crawler motor performance to our designed value. When loaded with the dynamic weight of our crawler (~414.2 grams) from the frictional drag on the bottom of the ramp, we found from our measurements that our motor was spinning at ~625 [rad/sec]. Our motor was performing at 31% efficiency. This value is well below our designed value and means that our efficiency was 13.5% less efficient than our designed ideal case.

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With our measured data added to our motor performance plot, we can see that there was definite room for improvement in our motor efficiency. Our high frictional force rubbing on the bottom of the track increases the load torque on our motor and hence the angular velocity of our motor. This load torque on the motor is coupled to the torque at the drive wheel by the gear ratio as detailed in the equations below. = − =

1

∗ =0

=

As seen in the motor equations above, the load torque on the motor is proportional to the motor current. Because we know the motor constants and we can illustrate how load torque on the motor affects the current drawn:

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As seen in the plot above, the smaller the load torque on the motor the smaller the current draw. This translates to a more energy-lean design. If we assume that we need the same output torque on the drive wheel as detailed in the abstract, we can see that if we increase the gear ratio, the motor will have a smaller motor load torque. In addition, drawing less current will increase the motor angular velocity as seen in the equation above. This will allow the motor to draw less current, use less power, and be more efficient. Therefore, in order to increase motor omega to our desired omega at dynamic load, we could increase our gear ratio to bring us back up to our most efficient motor omega and reduce the load torque on our motor. Assuming that we keep our drive wheel motor torque constant, we can see how increasing gear ratio would affect our motor efficiency in the plot below.

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From the plot, we can see that a gear ratio of 150:1 could increase our motor efficiency to our ideal design angular velocity value. This could mean that we would have to add an additional compound stage to increase our gear ratio by a factor of 2. While there is not a perfect Lego gear combination to accomplish this ratio, we could use a 40 tooth and 24 tooth gear to get close. While this design change would boost the motor efficiency, there could be consequences in our transmission efficiency with the addition of an additional gear stage. More on the consequences of this additional gear stage will be discussed in the overall performance section.

Transmission Performance Closely tied with the motor efficiency is the efficiency of the transmission. As we are using ABS plastic Lego gears and shafts and supports with less than optimal rigidity, transmission efficiency was something that our group looked to maximize. Our 75:1 gear ratio meant a compact and functional transmission using as few gears as possible. In addition, we lubricated our transmission with graphite to ensure fewer losses from gear friction. Furthermore, we superglued our motor mounting assembly and shaft housings to improve rigidity. We were able to quantify our transmission efficiency using the motor winch test. The diagram setup and

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equations for the test can be found in the Appendix ?. Our team attempted to simulate the load on the drive wheel when crawling up the ramp by increasing the mass being pulled up until the current draw was approximately 0.44 [A] (i.e. the current drawn at 6V while going up the ramp). This resulted in us pulling up 0.414 [kg]. We found that our 75:1 transmission gear train had a 13.75% efficiency. Knowing that our motor efficiency was approximately 31%, we can see that the total efficiency loss in our transmission is: đ?œ‚ = − đ?œ‚ = 0.315 − 0.1375 = 0. = . % , Knowing that we have 6 contacts contained within our transmission (including our idler), this allows us to solve for the efficiency of a single gear contact as: (

)

(#

)

= 1 − đ?œ‚ (

,

)

6

= 1 − 0.1775

= 0.968 = 96.8%

đ?œ‚

This gear contact for a spur gear matches well with what we know for spur gears (ranging 95% - 99% in efficiency). Moving forward, we ideally want to move to a 150:1 gear ratio. Based on the assumptions made in the abstract and our motor analysis, this increased ratio would boost our overall efficiency by 13% as shown by Figure ?. However, this would also require the addition of 2 more gears (i.e. 8 total gear contacts) to our gear train as described in the motor performance section above. This addition would lead to a decreased transmission efficiency, which can be calculated as: ( (.968)

) 8

(#

)

= 1 − đ?œ‚

= 1 − đ?œ‚ ,

đ?œ‚

đ?œ‚

,

=

,

= 0.229

,

− đ?œ‚

,

= 0.445 − 0.229 = 0.

By increasing our gear ratio to 150:1, we can see that our overall transmission efficiency would increase to approximately 21.6% indicating a net overall efficiency gain of 7.8%.

Rolling Resistance

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As detailed earlier, we biased our crawler to follow the bottom of the ramp in order to prevent rotation in Z. This meant that we had a large frictional component opposing the motion of our crawler. Therefore, it was essential that we quantified this rolling resistance. In order to understand the dynamic rolling resistance of the crawler when powered up the ramp, we used the setup detailed in Appendix ?. We increased the load mass until the crawler rested stationary in the track and recorded this weight. We then increased the mass until the crawler slowly moving up the ramp at a constant speed. The difference in this mass was our rolling resistance. We calculated (found in Appendix B). that our total rolling resistance was 1.61 [N]. Our rolling resistance is non-negligible and definitely contributes to energy and efficiency losses. We can approximate that our energy loss to friction was approximately the difference between our transmission efficiency (13.5%) and our calculated crawler efficiency going up the ramp (7.8%). This 5.7% efficiency difference can be attributed to losses from our 1.61 [N] rolling resistance. However, our group was comfortable with this these losses as they allowed our crawler to be oriented in Z and to effectively and reliably ascend and descend the shaft.

Overall Performance Our crawler performed as expected, ascending the shaft smoothly on the first attempt with a 6.0V power supply, drawing 0.44A in 9.7 seconds before reaching the top and pressing the button. We then shut off the power supply and let our crawler roll down the shaft without consuming any additional power. During the descent with no induced power, we read a current of 0.03 [A] with a voltage across of 5 [mV]. This Illustrates that we were generating power. Using the above measurements, our total energy consumption is:

1.99

= ∗ = = ∗ ∗

đ?œ‚

=

/

= (0.44 )(6.0 )(9.7 ) = 25.6 (60 ∘) = (0.234 )(9.81 / 2 )(

(60 ∘)) =

= (1.99 ) / (25.6 ) = 0.0776 = 7.76%

As detailed in Appendix ? we can calculate the overall energy efficiency of our crawler up and down the incline to be 7.76%. As detailed in the rolling resistance analysis, this is a 5.74% decrease in efficiency that can be attributed to frictional losses.

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In the transmission and motor analysis, we detailed how increasing to a 150:1 gear ratio and holding to the assumptions made in the abstract, we would increase our transmission efficiency to 21.6%. As we are assuming that we are applying the same output torque and our crawler weighs the same, the time it takes for our crawler to get up the ramp will be the same at this new gear ratio. Therefore, we can assume that the frictional losses will be the same

However, we will be running at a higher omega and therefore will draw less current. Therefore, our energy efficiency we can we can say that the numerator of our effici, we saw that we could increase our transmission efficiency to 21.6%. Assuming that the losses

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Strength Estimate A thorough gear stress analysis of the drivetrain is difficult to do given our use of ABS plastic Lego gears, which do not have reliable data on lifetime stresses and life cycle fatigue. This means that instead of looking at allowable lifetime stress and contact stress, we compare Lewis stress to the tensile strength of ABS plastic in order to analyze gear strength in the transmission. The crux of the drivetrain is the smaller gear on the last stage of our compound gear train, Gear 5, which suffers the highest stress on its gear teeth making it the most vulnerable component in our transmission. This means if Gear 5 is operating below its load rating, the rest of the gears should likewise be within safe operating ranges. To analyze the strength of this gear, we look at the Lewis stress, which is the bending stress on the gear teeth when treated as cantilevered beams.

=

đ?œŽ

The Lewis stress accounts for gear-specific factors like rigidity of mountings, uniformity of power supply, and how fast the gear is rotating with constants , , , respectively.1 Using Matlab, we calculated the Lewis stress as well as other values pertaining to the transmission and the different stresses acting on the gears. See the Gear Stress Analysis Matlab code and output in Appendix B for reference values.

= 1903

đ?œŽ

,

Comparing the Lewis stress on Gear 5 (đ?œŽ

≈ 7000

,→

<

=1903 psi) with the tensile yield strength of ABS

plastic (đ?&#x153;&#x17D; â&#x2030;&#x2C6;7000 psi) we see that the most vulnerable gear is operating below the yield stress, and therefore our gear train should not be subject to any material failure or deformation during its lifespan within this project. 2

đ?&#x153;&#x17D;

Teeth

Pitch Diam. (in)

Ftan (lbf)

Vtan (in/s)

Vtan (ft/min)

Kv (AGMA)

J_Lewis

N1

8

25.3995

0.0348

170.0875

850.4375

1.1258

0.2

83.442

N2

40

25.3995

0.0348

170.0875

850.4375

1.1258

0.39

42.791

1

(psi)

These K factors, as well as the geometry factor J, were all chosen from tables and curves found in Juvinall and Marshekâ&#x20AC;&#x2122;s Fundamentals of Machine Component Design.

2

http://www.engineeringtoolbox.com/physical-properties-thermoplastics-d_808.html

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N3

8

25.3995

0.1741

34.0175

170.0875

1.0591

0.2

392.47

N4

40

25.3995

0.1741

34.0175

170.0875

1.0591

0.39

201.27

N5

8

25.3995

0.8703

6.8035

34.0175

1.0271

0.2

1903.0

N6 (Idler)

24

25.3995

0.8703

6.8035

34.0175

1.0271

0.26

1463.9

N7

24

25.3995

0.8703

6.8035

34.0175

1.0271

0.36

1057.2

Conclusions The final iteration of our Lego Crawler runs smoothly and consistently performs that tasks required in exploring the narrow shafts of pyramids. Furthermore, the design only consumes 25.6 J in ascending and descending 1 m of the track, leading to a non-ideal but still good efficiency of 7.8%. There is little to no tire slipping, and the crawler dependably makes it up and down the ramp without any intervention, leading our group to view its design as a success. In order to improve on our design, we would mainly want to focus on boosting our overall efficiency. To do so, the first change we would make would be to increase our gear ratio from 75:1 to 150:1. This would effectively reduce the load on our motor, thereby reducing the current it would need to draw and moving us closer to our maximum efficiency rating as seen in Figure. Note that this would also require us to add another stage to our gear train, however we feel that any resultant transmission efficiency losses would be vastly outstripped by overall efficiency gains. The second change we would make would be to redesign the bottom bumpers we use the guide the crawler in order to reduce friction and therefore power consumption. Ideally, we would want no contact with the bottom of the track, however during testing this led to unwanted wander up and down the sides of the track. Therefore, a reasonable solution would be to replace our plastic bumpers with a better bearing surface such as a wheel. A final change we would make would be to lubricate our gears and axles so as to increase our transmission efficiency from its calculated value of 13.5%. As a final note, one of the advantages of our design, the fact that it rolls down the track without power input, might cause problems in real world application, as you would probably want to stop the crawler at some point. For instance, it would be important for the crawler to be at a standstill when drilling. To achieve this, implementation of a braking system would be a good solution. One such system that could be implemented would be a ratchet braking mechanism in which a supported arm could be moved either into a gear to stop its motion or away from the gear to allow it to spin freely.

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Appendix Matlab Gear Strength Estimate code %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Try some gears: %% First Stage - enter values from catalog %% CHANGE these with each new trial! Pressure_angle = 20.0 %degrees pressure angle of gears phi = deg_to_rad*Pressure_angle Pitch1 = 25.3995 %lego gear - metric module of 1[mm] Qv1 = 10 Stage1N1 = 8 Stage1N2 = 40 FaceWidth1 = 0.19685; %5[mm] width approximated by Alex Jlewis1_1 = .2 % Look up from chart, changes with N1, N2 Jlewis1_2 = .39 % Look up from chart, changes with N1, N2 %% Second Stage - enter values from catalog %% CHANGE these with each new trial %% Assume pressure angle same as 1st stage Pitch2 = 25.3995 Qv2 = 10 Stage2N1 = 8 Stage2N2 = 40 FaceWidth2 = 0.19685; %5[mm] width approximated by Alex Jlewis2_1 = .2 % Look up from chart, changes with N1, N2 Jlewis2_2 = .39 % Look up from chart, changes with N1, N2

%% Third Stage %% CHANGE these with each new trial! Pressure_angle = 20.0 %degrees pressure angle of gears phi = deg_to_rad*Pressure_angle Pitch3 = 25.3995 %lego gear - metric module of 1[mm] Qv3 = 10 Stage3N1 = 8 Stage3N2 = 24 Stage3N3 = 24 FaceWidth3 = 0.19685; %5[mm] width approximated by Alex Jlewis3_1_2 = .2 % Look up from chart, changes with N1, N2 Jlewis3_2_1 = .26 % Look up from chart, changes with N1, N2 (use this, worst case) JLewis3_2_3 = .36 % accounting for idler JLewis3_3_2 = .36 % accounting for idler %%Check total speed ratio and torque, power, etc. Looks OK? Omega_m = Rpm*rpm_to_radps %omega motor in radians/second InWatts = (Tmotor/Nm_to_inlbf)*Omega_m %motor power in watts ratio = (Stage1N2/Stage1N1)*(Stage2N2/Stage2N1)*(Stage3N2/Stage3N1) Torque_out = Tmotor*ratio %Want well above 720 inch-lbf Omega_out = Omega_m/ratio cycles_per_second = (Rpm/ratio)/60 %Want 1 to 2 cycles per sec Torque_out_Nm = Torque_out/Nm_to_inlbf

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%%%%%%%Part I: Bending Stress & Contact Ratio %%%%%%%% %% Compute tangential velocities, Kv factors, etc. % Stage1 rp1 = 0.5*Stage1N1/Pitch1 rp2 = 0.5*Stage1N2/Pitch1 Ftan1 = Tmotor/rp1 % Tangential tooth force in lbf Vtan1 = rp1*Omega_m % Tangential velocity in inches/second B1 = 0.25*(12.0-Qv1)^(2.0/3.0) if (Qv1 > 12) B1 = 0 end A1 = 50.0+56.0*(1.0-B1) Kv1 = ((A1+sqrt(Vtan1*inprsec_ftprmin))/A1)^B1 %AGMA velocity factor SigmaLewis1 = (Ftan1*Pitch1*Ko*Km*Kv1)/(FaceWidth1*Jlewis1_1) SigmaLewis2 = (Ftan1*Pitch1*Ko*Km*Kv1)/(FaceWidth1*Jlewis1_2) % Stage2 (accounting for gear ratios) rp3 = 0.5*Stage2N1/Pitch2 rp4 = 0.5*Stage2N2/Pitch2 Ftan2 = Ftan1*(rp2/rp3) % Tangential tooth force, lbf Vtan2 = Vtan1*(rp3/rp2) % Tangential velocity, inches/second B2 = 0.25*(12.0-Qv2)^(2.0/3.0) if (Qv2 > 12) B2 = 0 end A2 = 50.0+56.0*(1.0-B2) Kv2 = ((A2+sqrt(Vtan2*inprsec_ftprmin))/A2)^B2 %AGMA velocity factor SigmaLewis3 = (Ftan2*Pitch2*Ko*Km*Kv2)/(FaceWidth2*Jlewis2_1) SigmaLewis4 = (Ftan2*Pitch2*Ko*Km*Kv2)/(FaceWidth2*Jlewis2_2) % Stage3 (accounting for gear ratios) rp5 = 0.5*Stage3N1/Pitch3 rp6 = 0.5*Stage3N2/Pitch3 Ftan3 = Ftan2*(rp4/rp5) % Tangential tooth force, lbf Vtan3 = Vtan2*(rp5/rp4) % Tangential velocity, inches/second B3 = 0.25*(12.0-Qv3)^(2.0/3.0) if (Qv3 > 12) B3 = 0 end A3 = 50.0+56.0*(1.0-B3) Kv3 = ((A3+sqrt(Vtan3*inprsec_ftprmin))/A3)^B3 %AGMA velocity factor SigmaLewis5 = (Ftan3*Pitch3*Ko*Km*Kv3)/(FaceWidth3*Jlewis3_1_2) SigmaLewis6 = (Ftan3*Pitch3*Ko*Km*Kv3)/(FaceWidth3*Jlewis3_2_1) SigmaLewis7 = (Ftan3*Pitch3*Ko*Km*Kv3)/(FaceWidth3*JLewis3_3_2)

Motor Performance Matlab Detailed view of the 3-stage gear train. The order of power transmission is Motor Input(Pink) -> Red -> Yellow -> Orange(with Green idler) -> Wheel Output

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Ď&#x2030;motor = (r_2/r_1) (r_4/r_3) * (r_6/r_5) * Ď&#x2030;wheel = (40/8) (40/8) (24/8)* Ď&#x2030;wheel = 75 Ď&#x2030;wheel

Motor Winch Measured Results for Crawler Voltage [V]

6.0

đ?&#x203A;Ľ

[sec]

6.23

Current [A]

0.40

dtravel [m]

0.508

MassLoad [kg]

0.414

Gear Ratio

75:1

Calculated Values Calculated Velocity [m/s]

0.0815

Calculated Omega [rad/sec]

81.62

Power In [W]

2.4

Power Out [W]

0.331

Power Loss [W]

2.069

Transmission Efficiency

13.75%

24


Variable

Definition

Units

V

Voltage

Volts

i

Current

Amps

w

angular speed

Radians/second

R

Resistance

Ohms

k

Motor constant

25


26

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