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Gearbox Design as Seen Through the Toughbox

Or

Gear UpGear Up

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Toughbox Gear Pairs

● Diametral Pitch (DP): 20 per inch

● Pressure angle: 14.5 degreesOutside Diameter (mm) Pitch Diameter (mm) Input:Output Ratio

Gear Teeth Small Large Small Large Sum of Radii (mm) Center Distance (mm) Small to Large Large to Small14 50 20.32 66.04 17.78 63.50 43.18 40.64 3.57 0.2816 48 22.86 63.50 20.32 60.96 43.18 40.64 3.00 0.3319 45 26.67 59.69 24.13 57.15 43.18 40.64 2.37 0.4224 40 33.02 53.34 30.48 50.80 43.18 40.64 1.67 0.6028 35 38.10 46.99 35.56 44.45 42.55 40.01 1.25 0.80

Pitch Diameter (PD)=NDP

Center Distance (C)=(N 1+N 2)2∗DP

Toughbox Overall Gear RatiosGears 14:50 16:48 19:45 24:40 28:35

Gears Gear Ratio 3.57 3.00 2.37 1.67 1.2514:50 3.57 12.76 10.71 8.46 5.95 4.4616:48 3.00 10.71 9.00 7.11 5.00 3.7519:45 2.37 8.46 7.11 5.61 3.95 2.9624:40 1.67 5.95 5.00 3.95 2.78 2.0828:35 1.25 4.46 3.75 2.96 2.08 1.56

N = 50

N = 14

Not really a Toughbox gear pair

not to scale

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Toughbox Motor Plate

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Who Doesn't Like An Explosion?

Toughbox – Exploded View

CIMs mount directly to the motor plate, requiring the plate to react the motor torque

Bearings reduce the motor torque transmitted to the gearbox

½ inch output shaft and ⅜ inch input shaft

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Gear Selection

● Transmission gears on AndyMark

– Diametral pitch of 20 per inch

– 14.5 degree pressure angle

● CIM gears

– 8 mm bore

– 2 mm keyway

● Cluster gear

– 9.58 mm hex hole

– Steel or aluminum

● Output gear

– 12.75 mm hex hole

– Steel or aluminum

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Thrust Bearings

● Thrust bearings allow two parts in contact and producing axial load to rotate relative to each other with little friction generated

– Thrust bearings work between two surfaces spinning at different speeds including one surface spinning and the other stationary

– Lower friction means reduced energy loss to waste heat

● Thrust bearings come in many varieties, but our designs will most likely use needle bearings or roller bearings

– Needle bearings

● High axial load bearing capability, but tend to wear unevenly

● Compact packaging

– Ball bearings wear well, but have less axial load capability than needle bearings

● When using needle bearings, consider using the mating washers as well to provide a smooth rolling surface

● Many online retailers sell thrust bearings, including Amazon

Thrust Ball Roller Bearing

Thrust Needle Roller Bearing

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Design Process

● We need some additional requirements to narrow our design space and allow us to start designing the gearbox. We'll use these:

– CIM motors

– Efficient sustained speed of 3.0 m/s

– 152.4 mm diameter wheels

– 20 diametral pitch gears

● Select our motor drive speed

– We will set our sustained speed as the normal load rotor speed of the CIM motor

– Using the table below, we select 4,320 rpm or 452.4 rad/s as our design motor speed

Load Torque (N-m)

Speed (rpm)

Current (amps)

Power (watts)

Efficiency (%)

Free 0.00 5,310 2.7 0 0

Normal 0.45 4,320 27.0 205 63

Max efficiency 0.32 4,614 19.8 154 65

Max power 1.21 2,655 67.9 337 41

Stall 2.42 0 133.0 0 0

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Design Process

● Calculate the rotational speed of our wheels when the robot is traveling at 3.5 m/s

vtangential=wheel radius∗wheel angular velocity (rad / s)

wheel angular velocity (rad /s)=v tangential

wheel radius

wheel angular velocity (rad /s)=3.5m /s0.1524m

wheel angular velocity (rad /s)=22.96

● Calculate the required gear ratio to match desired motor speed, 452.4 rad/s, to desired wheel speed 22.96 rad/s

gear ratio=input speedoutput speed

gear ratio=452.422.96

gear ratio=19.70

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Design Process

● A 19.70 speed reduction is fairly significant

– AndyMark gears max out at 14:50 (3.57 to 1) on a 9.58 mm hex shaft

– Two stages of reduction of 14:50 gears, as the Toughbox comes pre-configured, only yields an overall reduction of 12.56 to 1

– Let's see what we can do with three stages of reduction

● Three reduction stages

– Stage 1: 14 tooth, 8 mm CIM gear and 40 tooth, 9.58 mm hex; 2.86 to 1 reduction

– Stage 2: 14 tooth, 9.58 mm hex and 45 tooth, 12.75 mm hex, 3.21 to 1 reduction

– Stage 3: 24 tooth, 12.75 mm hex and 50 tooth, 12.75 mm hex, 2.08 to 1 reduction

– Overall reduction is 19.13 to 1

● Calculate the center distances for each gear pairing

– 14:40 is 34.29 mm center distance

– 14:45 is 37.47 mm center distance

– 24:50 is 46.99 mm center distance

Center Distance (C)=(N 1+N 2)2∗DP

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Design Process

● In the Toughbox, AndyMark adds 0.05 mm to the center distance to provide clearance between the peak of the tooth and the trough of the mating gear

● With the center distances known, we can layout the gear shaft and CIM locations

● Check to make sure that gears and shafts do not clash between subsequent stages of reduction

● VexPro has drawings and STEP files of the CIM and min-CIM motors available for download

● Mount points for the gearbox to the drive base should take into consideration the drive base design and locations of other drive and subsystem components

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Considerations

● The gear reduction we need is a strong function of the linear speed capability that we want for the robot and the nominal speed we select for the motor. Play with the increase and decrease either or both and see how gear reduction changes

● As we increase gear reduction, we increase torque available on the output shaft. We will need to verify that 12.75 mm steel shafts can handle the torque without failure or excessive flexure.

● We may elect to cantilever the motor off of the gearbox frame. Make sure sufficient material is available at the motor bolts to react motor torque and weight in motion without failure or excessive flexure.

● AndyMark uses a square polycarbonate plate for the motor mount on the Toughbox. More abstract motor mount designs are probably best executed in ¼ inch aluminum or similar.

● Have fun!

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Questions

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