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Project Summary
To design and build a gearbox from laser cut acrylic sheet which will be used to lift a weight (at least 8 kg) from a height (greater than 0.5 m and less than 1 m) as quickly as possible. The gearbox will be powered by a standard DC electric motor at 9000 rpm.
CREATIVITY JOURNEY
Hurdle
What is the input speed and torque?What is the gearbox target output speed or output torque?Will it need to withstand shock and vibration?How overhung is the load on the output shaft?How will the gearing be orientated?
Proposed Concept
Using a reduction gearbox to reduce input rpm while increasing torque to lift a certain amount of load.
Pinion
Pinion Intermediate shaft
Output shaft
GearGear
Motor
Mechanical properties of AcrylicTensile strength, yield 72 MPA
Modulus of elasticity 3.102 GPA
d^2y/dx^2 = M/EI
Reason to choose a Reduction gearbox?
To reduce input speed of 9000 rpm from motor to a much slower speed while increasing output torque.
To reduce speed in stages to avoid damage to gearboxSimple design.
Table 1
Mass (m) (Kg) T(in) (Nm) EfÞciency (%) Gravity (m/s^2) Radius(out) (m) T(out) (Nm) Ratio Speed(in) (RPM) Speed(out) (RPM) Velocity (m/s) Time(for 0.5m) (s) Time(for 1m) (s) Power (W) ((mgh)^2)/(W(t^2)) (h=0.5m)
((mgh)^2)/(W(t^2)) (h=1m)
(m) (T1) (E) (g) (r) (m*g*r) (R=(T2)/(T1*E)) (s1) (s2=s1/R) (v=((2Pi*r)*(s2))/60) ((t0.5)=0.5/v) ((t1)=1/v) (W)
Max EfÞciency 8 0.005884 1 9.81 0.003 0.23544 40.0135961930659 9679 241.892779476724 0.0759928578960493 6.57956568344818 13.1591313668964 5.96 5.96784155294506 5.96784155294506
9 0.005884 1 9.81 0.003 0.26487 45.0152957171992 9679 215.015803979311 0.0675492070187105 7.4020113938792 14.8040227877584 5.96 5.96784155294506 5.96784155294506
10 0.005884 1 9.81 0.003 0.2943 50.0169952413324 9679 193.51422358138 0.0607942863168395 8.22445710431022 16.4489142086204 5.96 5.96784155294506 5.96784155294506
(0.5 < h < 1)m 11 0.005884 1 9.81 0.003 0.32373 55.0186947654657 9679 175.922021437618 0.0552675330153086 9.04690281474124 18.0938056294825 5.96 5.96784155294506 5.96784155294506
12 0.005884 1 9.81 0.003 0.35316 60.0203942895989 9679 161.261852984483 0.0506619052640329 9.86934852517227 19.7386970503445 5.96 5.96784155294506 5.96784155294506
13 0.005884 1 9.81 0.003 0.38259 65.0220938137322 9679 148.8570950626 0.0467648356283381 10.6917942356033 21.3835884712066 5.96 5.96784155294506 5.96784155294506
14 0.005884 1 9.81 0.003 0.41202 70.0237933378654 9679 138.224445415271 0.0434244902263139 11.5142399460343 23.0284798920686 5.96 5.96784155294506 5.96784155294506
15 0.005884 1 9.81 0.003 0.44145 75.0254928619986 9679 129.009482387586 0.0405295242112263 12.3366856564653 24.6733713129307 5.96 5.96784155294506 5.96784155294506
16 0.005884 1 9.81 0.003 0.47088 80.0271923861319 9679 120.946389738362 0.0379964289480247 13.1591313668964 26.3182627337927 5.96 5.96784155294506 5.96784155294506
17 0.005884 1 9.81 0.003 0.50031 85.0288919102651 9679 113.831896224341 0.0357613448922585 13.9815770773274 27.9631541546547 5.96 5.96784155294506 5.96784155294506
18 0.005884 1 9.81 0.003 0.52974 90.0305914343984 9679 107.507901989655 0.0337746035093553 14.8040227877584 29.6080455755168 5.96 5.96784155294506 5.96784155294506
19 0.005884 1 9.81 0.003 0.55917 95.0322909585316 9679 101.849591358621 0.0319969927983366 15.6264684981894 31.2529369963788 5.96 5.96784155294506 5.96784155294506
20 0.005884 1 9.81 0.003 0.5886 100.033990482665 9679 96.7571117906898 0.0303971431584197 16.4489142086204 32.8978284172409 5.96 5.96784155294506 5.96784155294506
21 0.005884 1 9.81 0.003 0.61803 105.035690006798 9679 92.1496302768474 0.0289496601508759 17.2713599190515 34.5427198381029 5.96 5.96784155294506 5.96784155294506
22 0.005884 1 9.81 0.003 0.64746 110.037389530931 9679 87.9610107188089 0.0276337665076543 18.0938056294825 36.187611258965 5.96 5.96784155294506 5.96784155294506
23 0.005884 1 9.81 0.003 0.67689 115.039089055065 9679 84.1366189484259 0.0264322983986259 18.9162513399135 37.832502679827 5.96 5.96784155294506 5.96784155294506
24 0.005884 1 9.81 0.003 0.70632 120.040788579198 9679 80.6309264922415 0.0253309526320164 19.7386970503445 39.4773941006891 5.96 5.96784155294506 5.96784155294506
25 0.005884 1 9.81 0.003 0.73575 125.042488103331 9679 77.4056894325518 0.0243177145267358 20.5611427607755 41.1222855215511 5.96 5.96784155294506 5.96784155294506
26 0.005884 1 9.81 0.003 0.76518 130.044187627464 9679 74.4285475312998 0.023382417814169 21.3835884712066 42.7671769424131 5.96 5.96784155294506 5.96784155294506
27 0.005884 1 9.81 0.003 0.79461 135.045887151598 9679 71.6719346597702 0.0225164023395702 22.2060341816376 44.4120683632752 5.96 5.96784155294506 5.96784155294506
28 0.005884 1 9.81 0.003 0.82404 140.047586675731 9679 69.1122227076356 0.021712245113157 23.0284798920686 46.0569597841372 5.96 5.96784155294506 5.96784155294506
Max Power 8 0.007845 1 9.81 0.003 0.23544 30.0114722753346 7845 261.4000382263 0.0821212439739834 6.08855852400876 12.1771170480175 6.44 6.44975414481467 6.44975414481467
9 0.007845 1 9.81 0.003 0.26487 33.7629063097514 7845 232.355589534489 0.0729966613102075 6.84962833950986 13.6992566790197 6.44 6.44975414481468 6.44975414481468
10 0.007845 1 9.81 0.003 0.2943 37.5143403441683 7845 209.12003058104 0.0656969951791867 7.61069815501095 15.2213963100219 6.44 6.44975414481468 6.44975414481468
11 0.007845 1 9.81 0.003 0.32373 41.2657743785851 7845 190.109118710036 0.0597245410719879 8.37176797051205 16.7435359410241 6.44 6.44975414481467 6.44975414481467
12 0.007845 1 9.81 0.003 0.35316 45.0172084130019 7845 174.266692150866 0.0547474959826556 9.13283778601315 18.2656755720263 6.44 6.44975414481467 6.44975414481467
13 0.007845 1 9.81 0.003 0.38259 48.7686424474187 7845 160.861561985415 0.0505361501378359 9.89390760151424 19.7878152030285 6.44 6.44975414481468 6.44975414481468
14 0.007845 1 9.81 0.003 0.41202 52.5200764818356 7845 149.371450415028 0.0469264251279905 10.6549774170153 21.3099548340307 6.44 6.44975414481467 6.44975414481467
15 0.007845 1 9.81 0.003 0.44145 56.2715105162524 7845 139.413353720693 0.0437979967861245 11.4160472325164 22.8320944650329 6.44 6.44975414481468 6.44975414481468
16 0.007845 1 9.81 0.003 0.47088 60.0229445506692 7845 130.70001911315 0.0410606219869917 12.1771170480175 24.3542340960351 6.44 6.44975414481467 6.44975414481467
17 0.007845 1 9.81 0.003 0.50031 63.774378585086 7845 123.011782694729 0.0386452912818745 12.9381868635186 25.8763737270372 6.44 6.44975414481468 6.44975414481468
18 0.007845 1 9.81 0.003 0.52974 67.5258126195029 7845 116.177794767244 0.0364983306551037 13.6992566790197 27.3985133580394 6.44 6.44975414481468 6.44975414481468
19 0.007845 1 9.81 0.003 0.55917 71.2772466539197 7845 110.063173990021 0.0345773658837825 14.4603264945208 28.9206529890416 6.44 6.44975414481468 6.44975414481468
20 0.007845 1 9.81 0.003 0.5886 75.0286806883365 7845 104.56001529052 0.0328484975895934 15.2213963100219 30.4427926200438 6.44 6.44975414481468 6.44975414481468
21 0.007845 1 9.81 0.003 0.61803 78.7801147227534 7845 99.5809669433522 0.0312842834186603 15.982466125523 31.964932251046 6.44 6.44975414481467 6.44975414481467
22 0.007845 1 9.81 0.003 0.64746 82.5315487571702 7845 95.0545593550181 0.029862270535994 16.7435359410241 33.4870718820482 6.44 6.44975414481467 6.44975414481467
23 0.007845 1 9.81 0.003 0.67689 86.282982791587 7845 90.921752426539 0.0285639109474725 17.5046057565252 35.0092115130504 6.44 6.44975414481468 6.44975414481468
24 0.007845 1 9.81 0.003 0.70632 90.0344168260038 7845 87.1333460754332 0.0273737479913278 18.2656755720263 36.5313511440526 6.44 6.44975414481467 6.44975414481467
25 0.007845 1 9.81 0.003 0.73575 93.7858508604207 7845 83.6480122324159 0.0262787980716747 19.0267453875274 38.0534907750548 6.44 6.44975414481468 6.44975414481468
26 0.007845 1 9.81 0.003 0.76518 97.5372848948375 7845 80.4307809927076 0.025268075068918 19.7878152030285 39.575630406057 6.44 6.44975414481468 0
27 0.007845 1 9.81 0.003 0.79461 101.288718929254 7845 77.4518631781629 0.0243322204367358 20.5488850185296 41.0977700370591 6.44 6.44975414481468 0
28 0.007845 1 9.81 0.003 0.82404 105.040152963671 7845 74.6857252075142 0.0234632125639953 21.3099548340307 42.6199096680613 6.44 6.44975414481467 0
0
!1
GEARBOX TORQUE TABLE
Design Limitations
Face width of the gear is 3mm
Gears will be laser cut on Acrylic sheet.
Spur gears is the only choice for the project as teeth are cut parallel to shaft.
Axial length of gearbox housing will have to be as minimal as possible to achieve a greater performance.
Addendum diameter of pinion gear on motor is approximately 18.22 mm
Super glue will be used to connect the shaft and the gears
Mechanical properties of AcrylicTensile strength, yield 72 MPA
Modulus of elasticity 3.102 GPA
Pro�le for motor connection to Input shaft of gearbox
Areas of improvement involve gear arrangement.
Speed and torque of the gearbox output.
Calculating most e�cient torque required to lift weight.
Stacking acrylic gear next to each other for greater strength.
Experimentation with gear ratio
Possible Improvements
Table 1
Mass (m) (Kg) T(in) (Nm) EfÞciency (%) Gravity (m/s^2) Radius(out) (m) T(out) (Nm) Ratio Speed(in) (RPM) Speed(out) (RPM) Velocity (m/s) Time(for 0.5m) (s) Time(for 1m) (s) Power (W) ((mgh)^2)/(W(t^2)) (h=0.5m)
((mgh)^2)/(W(t^2)) (h=1m)
(m) (T1) (E) (g) (r) (m*g*r) (R=(T2)/(T1*E)) (s1) (s2=s1/R) (v=((2Pi*r)*(s2))/60) ((t0.5)=0.5/v) ((t1)=1/v) (W)
Max EfÞciency 8 0.005884 1 9.81 0.003 0.23544 40.0135961930659 9679 241.892779476724 0.0759928578960493 6.57956568344818 13.1591313668964 5.96 5.96784155294506 5.96784155294506
9 0.005884 1 9.81 0.003 0.26487 45.0152957171992 9679 215.015803979311 0.0675492070187105 7.4020113938792 14.8040227877584 5.96 5.96784155294506 5.96784155294506
10 0.005884 1 9.81 0.003 0.2943 50.0169952413324 9679 193.51422358138 0.0607942863168395 8.22445710431022 16.4489142086204 5.96 5.96784155294506 5.96784155294506
(0.5 < h < 1)m 11 0.005884 1 9.81 0.003 0.32373 55.0186947654657 9679 175.922021437618 0.0552675330153086 9.04690281474124 18.0938056294825 5.96 5.96784155294506 5.96784155294506
12 0.005884 1 9.81 0.003 0.35316 60.0203942895989 9679 161.261852984483 0.0506619052640329 9.86934852517227 19.7386970503445 5.96 5.96784155294506 5.96784155294506
13 0.005884 1 9.81 0.003 0.38259 65.0220938137322 9679 148.8570950626 0.0467648356283381 10.6917942356033 21.3835884712066 5.96 5.96784155294506 5.96784155294506
14 0.005884 1 9.81 0.003 0.41202 70.0237933378654 9679 138.224445415271 0.0434244902263139 11.5142399460343 23.0284798920686 5.96 5.96784155294506 5.96784155294506
15 0.005884 1 9.81 0.003 0.44145 75.0254928619986 9679 129.009482387586 0.0405295242112263 12.3366856564653 24.6733713129307 5.96 5.96784155294506 5.96784155294506
16 0.005884 1 9.81 0.003 0.47088 80.0271923861319 9679 120.946389738362 0.0379964289480247 13.1591313668964 26.3182627337927 5.96 5.96784155294506 5.96784155294506
17 0.005884 1 9.81 0.003 0.50031 85.0288919102651 9679 113.831896224341 0.0357613448922585 13.9815770773274 27.9631541546547 5.96 5.96784155294506 5.96784155294506
18 0.005884 1 9.81 0.003 0.52974 90.0305914343984 9679 107.507901989655 0.0337746035093553 14.8040227877584 29.6080455755168 5.96 5.96784155294506 5.96784155294506
19 0.005884 1 9.81 0.003 0.55917 95.0322909585316 9679 101.849591358621 0.0319969927983366 15.6264684981894 31.2529369963788 5.96 5.96784155294506 5.96784155294506
20 0.005884 1 9.81 0.003 0.5886 100.033990482665 9679 96.7571117906898 0.0303971431584197 16.4489142086204 32.8978284172409 5.96 5.96784155294506 5.96784155294506
21 0.005884 1 9.81 0.003 0.61803 105.035690006798 9679 92.1496302768474 0.0289496601508759 17.2713599190515 34.5427198381029 5.96 5.96784155294506 5.96784155294506
22 0.005884 1 9.81 0.003 0.64746 110.037389530931 9679 87.9610107188089 0.0276337665076543 18.0938056294825 36.187611258965 5.96 5.96784155294506 5.96784155294506
23 0.005884 1 9.81 0.003 0.67689 115.039089055065 9679 84.1366189484259 0.0264322983986259 18.9162513399135 37.832502679827 5.96 5.96784155294506 5.96784155294506
24 0.005884 1 9.81 0.003 0.70632 120.040788579198 9679 80.6309264922415 0.0253309526320164 19.7386970503445 39.4773941006891 5.96 5.96784155294506 5.96784155294506
25 0.005884 1 9.81 0.003 0.73575 125.042488103331 9679 77.4056894325518 0.0243177145267358 20.5611427607755 41.1222855215511 5.96 5.96784155294506 5.96784155294506
26 0.005884 1 9.81 0.003 0.76518 130.044187627464 9679 74.4285475312998 0.023382417814169 21.3835884712066 42.7671769424131 5.96 5.96784155294506 5.96784155294506
27 0.005884 1 9.81 0.003 0.79461 135.045887151598 9679 71.6719346597702 0.0225164023395702 22.2060341816376 44.4120683632752 5.96 5.96784155294506 5.96784155294506
28 0.005884 1 9.81 0.003 0.82404 140.047586675731 9679 69.1122227076356 0.021712245113157 23.0284798920686 46.0569597841372 5.96 5.96784155294506 5.96784155294506
Max Power 8 0.007845 1 9.81 0.003 0.23544 30.0114722753346 7845 261.4000382263 0.0821212439739834 6.08855852400876 12.1771170480175 6.44 6.44975414481467 6.44975414481467
9 0.007845 1 9.81 0.003 0.26487 33.7629063097514 7845 232.355589534489 0.0729966613102075 6.84962833950986 13.6992566790197 6.44 6.44975414481468 6.44975414481468
10 0.007845 1 9.81 0.003 0.2943 37.5143403441683 7845 209.12003058104 0.0656969951791867 7.61069815501095 15.2213963100219 6.44 6.44975414481468 6.44975414481468
11 0.007845 1 9.81 0.003 0.32373 41.2657743785851 7845 190.109118710036 0.0597245410719879 8.37176797051205 16.7435359410241 6.44 6.44975414481467 6.44975414481467
12 0.007845 1 9.81 0.003 0.35316 45.0172084130019 7845 174.266692150866 0.0547474959826556 9.13283778601315 18.2656755720263 6.44 6.44975414481467 6.44975414481467
13 0.007845 1 9.81 0.003 0.38259 48.7686424474187 7845 160.861561985415 0.0505361501378359 9.89390760151424 19.7878152030285 6.44 6.44975414481468 6.44975414481468
14 0.007845 1 9.81 0.003 0.41202 52.5200764818356 7845 149.371450415028 0.0469264251279905 10.6549774170153 21.3099548340307 6.44 6.44975414481467 6.44975414481467
15 0.007845 1 9.81 0.003 0.44145 56.2715105162524 7845 139.413353720693 0.0437979967861245 11.4160472325164 22.8320944650329 6.44 6.44975414481468 6.44975414481468
16 0.007845 1 9.81 0.003 0.47088 60.0229445506692 7845 130.70001911315 0.0410606219869917 12.1771170480175 24.3542340960351 6.44 6.44975414481467 6.44975414481467
17 0.007845 1 9.81 0.003 0.50031 63.774378585086 7845 123.011782694729 0.0386452912818745 12.9381868635186 25.8763737270372 6.44 6.44975414481468 6.44975414481468
18 0.007845 1 9.81 0.003 0.52974 67.5258126195029 7845 116.177794767244 0.0364983306551037 13.6992566790197 27.3985133580394 6.44 6.44975414481468 6.44975414481468
19 0.007845 1 9.81 0.003 0.55917 71.2772466539197 7845 110.063173990021 0.0345773658837825 14.4603264945208 28.9206529890416 6.44 6.44975414481468 6.44975414481468
20 0.007845 1 9.81 0.003 0.5886 75.0286806883365 7845 104.56001529052 0.0328484975895934 15.2213963100219 30.4427926200438 6.44 6.44975414481468 6.44975414481468
21 0.007845 1 9.81 0.003 0.61803 78.7801147227534 7845 99.5809669433522 0.0312842834186603 15.982466125523 31.964932251046 6.44 6.44975414481467 6.44975414481467
22 0.007845 1 9.81 0.003 0.64746 82.5315487571702 7845 95.0545593550181 0.029862270535994 16.7435359410241 33.4870718820482 6.44 6.44975414481467 6.44975414481467
23 0.007845 1 9.81 0.003 0.67689 86.282982791587 7845 90.921752426539 0.0285639109474725 17.5046057565252 35.0092115130504 6.44 6.44975414481468 6.44975414481468
24 0.007845 1 9.81 0.003 0.70632 90.0344168260038 7845 87.1333460754332 0.0273737479913278 18.2656755720263 36.5313511440526 6.44 6.44975414481467 6.44975414481467
25 0.007845 1 9.81 0.003 0.73575 93.7858508604207 7845 83.6480122324159 0.0262787980716747 19.0267453875274 38.0534907750548 6.44 6.44975414481468 6.44975414481468
26 0.007845 1 9.81 0.003 0.76518 97.5372848948375 7845 80.4307809927076 0.025268075068918 19.7878152030285 39.575630406057 6.44 6.44975414481468 0
27 0.007845 1 9.81 0.003 0.79461 101.288718929254 7845 77.4518631781629 0.0243322204367358 20.5488850185296 41.0977700370591 6.44 6.44975414481468 0
28 0.007845 1 9.81 0.003 0.82404 105.040152963671 7845 74.6857252075142 0.0234632125639953 21.3099548340307 42.6199096680613 6.44 6.44975414481467 0
0
!1
Observations (HCR)
The maximum tooth load is ~63% of transmitted load due to the sharing of teethVibration-signature amplitude is approximately ½ for equivalent for gears not in contact and that are at the same load and speed.With HCR gearing�three pairs of teeth share the load: Entrace� Through the pitch point� at the exit of the mesh
Applications Possible gear designElectric fork lift truck transmission Noise reductionHeavy lift helicopter HCR gearingPropeller reduction drive gear (aircraft) HCR gearing
Gear optimization�Contact ratio
Gear Parameter Changes Contact RatioIncreased Ratio DecreasesIncreased Addendum IncreasesIncreased Centre Distance IncreasesIncreased pitch diameter IncreasesIncreased Centre distance IncreasesAmount of Pro�le Modi�cation Decreases
C.R = OD° −TIF° 360 ° /N
No. T = 360 ° C.R OD ° - TIF °
Pros:Can handle extremely large reductionsGood load distribution, giving huge torque capabilityHigh e�ciency, with a general loss of only 3% per trainHigh power density�Cons:More di�cult to manufactureHigh precision requiredLoud at high speedsHigh stress at the output shaftHigh bearing loads
Reduction Gearbox
Pros:Easy to manufactureE�cient (rolling tooth engagement)Low heat generated
Cons:Low tooth engagement Loud operationLower torque handling capabilities
Referencing:
http://www.motioncontroltips.com/2012/08/24/how-to-select-a-gearbox/https://www.youtube.com/watch?v=Lt_FLicYejU
http://lcamtuf.coredump.cx/gcnc/ch6/ http://www.smex.net.au/reference/Ratios02.php
http://lcamtuf.coredump.cx/gcnc/ch6/ http://www.plexiglas.com/export/sites/plexiglas/.content/medias/downloads/sheet-docs/plexiglas-g.pdf
http://www.chiefdelphi.com/media/photos/37186http://www.zwgearbox.com/LatestNews/Whataretheadvantages_1.html
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