# Nine speed transmission design

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Complete process of designing a nine speed lathe transmission from gears to shafts and bearings.

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### Nine speed transmission design

1. 1. POLITECHNIC UNIVERSITY OF PUERTO RICO DEPARTMENT OF MECHANICAL ENGINEERING HATO REY, PUERTO RICO ME5240; MACHINE DESING ELEMENTS II SP-13 Nine Speed TransmissionDesign Final Project Carlos J. Gutiérrez Román #54543 Submitted to: Dr. Skrzypinski May 28, 2013 1|Page
2. 2. Abstract Atransmission as we know isthe system transmitsthe power fromone engineto the point thatis to be used. Withthe initial parametersset, we conduct a comprehensive processof analysis,including the calculation ofpartialrelations, speed, shaft distance,acting forces and both shear and momentdiagrams. For this casethe transmissiondesignbasedon theorieslearnedin class andalsouseknowledge learned inotherclassespassed assolidmechanicsIIwhichappliesin this design. 2|Page
3. 3. Table of Contents Abstract ............................................................................................................................................ 2 Introduction ..................................................................................................................................... 6 Theory .............................................................................................................................................. 7 Calculations .................................................................................................................................... 12 Partial Relations ......................................................................................................................... 13 Total Relations ........................................................................................................................... 14 Gear Analysis.............................................................................................................................. 15 Torque ........................................................................................................................................ 15 Real Forces ................................................................................................................................. 16 Lewis Forces ............................................................................................................................... 17 Results ............................................................................................................................................ 18 Conclusions .................................................................................................................................... 48 References ..................................................................................................................................... 49 Appendices..................................................................................................................................... 50 3|Page
4. 4. Tables and Figures Table 1 Partial Relations ................................................................................................................ 18 Table 2 Output gear relation.......................................................................................................... 18 Table 3 Total Relations and Output speeds ................................................................................... 19 Table 4 Shaft Speeds, and distances between shafts .................................................................... 20 Table 5 Reducer Gear Analysis ....................................................................................................... 21 Table 6 Real Forces and Lewis Forces comparison ........................................................................ 22 Table 7 Real Forces and Lewis Forces Comparison........................................................................ 23 Table 8 Lewis Form Factor for N-Teeth.......................................................................................... 24 Table 10 Gear Analysis ................................................................................................................... 25 Table 11 Real Forces ...................................................................................................................... 25 Table 12 Failure Theories, deflection and shaft diammeter .......................................................... 26 Table 13 Bearing Design................................................................................................................. 46 Figure 1 Lewis Form Factor diagram .............................................................................................. 24 Figure 2 Shaft I FBD ........................................................................................................................ 28 Figure 3 Shaft I Shear Diagram x-y ................................................................................................. 28 Figure 4 Shaft I Moment Diagram x-y ............................................................................................ 29 Figure 5 Shaft I FBD x-z .................................................................................................................. 29 Figure 6 Shaft I Shear diagram x-z ................................................................................................. 30 Figure 7 Shaft I Moment diagram x-z............................................................................................. 30 Figure 8 Shaft II FBD x-y ................................................................................................................. 31 Figure 9 Shaft II Shear Diagram x-y ................................................................................................ 31 Figure 10 Shaft II Moment diagram x-y ......................................................................................... 32 Figure 11Shaft II FBD x-z ................................................................................................................ 32 Figure 12 Shaft II Shear diagram x-z .............................................................................................. 33 Figure 13 Shaft II Moment diagram x-z.......................................................................................... 33 Figure 14 Shaft III FBD x-y .............................................................................................................. 34 Figure 15 Shaft III Shear diagram x-y ............................................................................................. 34 Figure 16 Shaft III Moment diagram x-y ........................................................................................ 35 Figure 17 Shaft III FBD x-z .............................................................................................................. 35 Figure 18 Shaft III Shear diagram x-z ............................................................................................. 36 Figure 19 Shaft III Moment diagram x-z......................................................................................... 36 Figure 20 Shaft IV FBD x-y .............................................................................................................. 37 Figure 21 Shaft IV Shear diagram x-y ............................................................................................. 37 Figure 22 Shaft IV Moment diagram x-y ........................................................................................ 38 Figure 23 Shaft IV FBD x-z .............................................................................................................. 38 Figure 24 Shaft IV Shear diagram x-z ............................................................................................. 39 4|Page
5. 5. Figure 25 Shaft IV Moment diagram x-z ........................................................................................ 39 Figure 26 Shaft V FBD x-y ............................................................................................................... 40 Figure 27 Shaft V Shear diagram x-y .............................................................................................. 40 Figure 28 Shaft V Moment diagram x-y ......................................................................................... 41 Figure 29 Shaft V FBD x-z ............................................................................................................... 41 Figure 30 Shaft V Shear diagram x-z .............................................................................................. 42 Figure 31 Shaft V Moment diagram x-z ......................................................................................... 42 Figure 32 Shaft VI FBD x-y .............................................................................................................. 43 Figure 33 Shaft VI Shear diagram x-y ............................................................................................. 43 Figure 34 Shaft VI Shear diagram x-y ............................................................................................. 44 Figure 35 Shaft VI FBD x-z .............................................................................................................. 44 Figure 36 Shaft VI Shear diagram x-z ............................................................................................. 45 Figure 37 Shaft VI Moment diagram x-z ........................................................................................ 45 5|Page
6. 6. Introduction A transmission is the system that transmits the power generated by the engine or motor to the point where it is to be used. This document presents the design process of a transmission meeting pre-established requirements, nine output velocities, a power input of 30 kW, the motor’s angular velocity of 1600RPM, lowest angular velocity of 25 RPM and the geometric relation of 1.6. With the initial parameters already established, a complete process of analysis was done, including but not limited to calculation of partial relations, speed, distance between shafts, Lewis Forces and Shear and Moment diagrams. The material selected to analyze the shaft was Steel A350. In this paper we resume some theoretical background of a transmission, the mathematical procedure made for the design, and a complete mechanical drawing, which specifies the transmission design. 6|Page
7. 7. Theory In mechanics, a transmission or gearbox is the gear and/or hydraulic system that transmits mechanical power from a prime mover (which can be an engine or electric motor), to some form of useful output device. Early transmissions included right angle drives and other gearing in windmills, horse-powered devices, and steam engines, mainly in support of pumping, milling, and hoisting applications. Typically, the rotational speed of an input shaft is changed, resulting in a different output speed. However, some of the simplest gearboxes merely change the physical direction in which power is transmitted. In daily life, individuals most often encounter the transmissions used in automobiles, which cover an ever-expanding array of specific types. However, gearboxes have found use in a wide variety of different-often stationary-applications. Most mechanical transmissions function as rotary speed changers; the ratio of the output speed to the input speed may be either constant (as in a gearbox) or variable. On variable-speed transmissions, the speeds may be variable in individual steps (as on an automobile or some machine-tool drives) or continuously variable within a range. Step-variable transmissions, with some slip, usually use either gears or chains and provide fixed speed ratios with no slip; step less transmissions use belts, chains, or rolling-contact bodies. Simple transmission The simplest transmissions, often called gearboxes to reflect their simplicity (although complex systems are also called gearboxes on occasion), provide gear reduction (or, more rarely, an increase in speed), sometimes in conjunction with a rightangle change in direction of the shaft. These are often used on PTO-powered agricultural equipment, since the axial PTO shaft is at odds with the usual need for the driven shaft, which is either vertical (as with rotary mowers), or horizontally extending from one side of the implement to another (as with manure spreaders, flail mowers, 7|Page
8. 8. and forage wagons). More complex equipment, such as silage choppers and snow blowers, has drives with outputs in more than one direction. Regardless of where they are used, these simple transmissions all share an important feature: the gear ratio cannot be changed during use. It is fixed at the time the transmission is constructed. Automotive basics The need for a transmission in an automobile is a consequence of the characteristics of the internal combustion engine. Engines typically operate over a range of 600 to about 6000 revolutions per minute (though this varies from design to design and is typically less for diesel engines), while the car's wheels rotate between 0 rpm and around 2500 rpm. Furthermore, the engine provides its highest torque outputs approximately in the middle of its range, while often the greatest torque is required when the vehicle. Multi-ratio systems Many applications require the availability of multiple gear ratios. Often, this is to ease the starting and stopping of a mechanical system, though another important need is that of maintaining good fuel economy. e is moving from rest or traveling slowly. Therefore, a system that transforms the engine's output so that it can supply high torque at low speeds, but also operate at highway speeds with the motor still operating within its limits, is required. Transmissions perform this transformation. Most transmissions and gears used in automotive and truck applications are contained in a cast iron case, though sometimes aluminum is used for lower weight. There are three shafts: a main shaft, a countershaft, and an idler shaft. The main shaft extends outside the case in both directions: the input shaft towards the engine, and the output shaft towards the rear axle (on rear wheel drive cars). The shaft is suspended by the main bearings, and is split 8|Page
9. 9. towards the input end. At the point of the split, a pilot bearing holds the shafts together. The gears and clutches ride on the main shaft, the gears being free to turn relative to the main shaft except when engaged by the clutches. The countershaft is generally below the main shaft and turns in the opposite direction, driven by a bevel gear on the input shaft. Manual transmission Manual transmissions come in two basic types: a simple unsynchronized system where gears are spinning freely and must be synchronized by the operator to avoid noisy and damaging "gear clash", and synchronized systems that will automatically "mesh" while changing gears. It is hard and takes a long time to become familiar with operating manual transmissions. A small mistake can lead to the car stalling or jumping or to irreparable damage of the transmission. Manual transmissions tend to distract the driver's attention from traffic and are associated with higher accident rates in cities and stop and go traffic. For that reason insurance premiums are higher for cars with manual transmissions in some countries. Manual transmissions have been popular in [Europe] and less developed countries for the longest time. Automatic transmission Most modem cars have an automatic transmission that will select an appropriate gear ratio without any operator intervention. They are primarily using hydraulics to select gears, depending on pressure exerted by fluid within the transmission assembly. Rather than using a clutch to engage the transmission, a torque converter is put in between the engine and transmission. It is possible for the driver to control the number of gears in use or select reverse, though precise control of which gear is in use is not 9|Page
10. 10. possible. Automatic transmissions are easy to use. In the past, automatic transmissions of this type have had a number of problems, they were complex and expensive, and sometimes had reliability problems (which sometimes caused more expense in repair), and often have been less fuel-efficient than their manual counterparts. With the advancement of modem automatic transmissions this has changed. With computer technology, considerable effort has been put into designing gearboxes based on the simpler manual systems that use electronically-controlled actuators to shift gears and manipulate the clutch, resolving many of the drawbacks of a hydraulic automatic transmission. Automatic transmissions have always been extremely popular in the United States, where perhaps 19 of20 new cars are sold with them (most vehicles are not available with manual gearboxes anymore). In Europe automatic transmissions are finally gaining popularly as well. Attempts to improve the fuel efficiency of automatic transmissions include the use of torque converters which lock-up beyond a certain speed eliminating power loss, and overdrive gears which automatically actuate above certain speeds; in older transmissions both technologies could sometimes became intrusive, when conditions are such that they constantly cut in and out as speed and such load factors as grade or wind vary slightly. Current computerized transmissions possess very complex programming to both maximize fuel efficiency and eliminate any intrusiveness. For certain applications, the slippage inherent in automatic transmissions can be advantageous; for instance, in drag racing, the automatic transmission allows the car to be stopped with the engine at a high rpm (the "stall speed") to allow for a very quick launch when the brakes are released; in fact, a common modification is to increase the stall speed of the transmission. This is even more advantageous for turbocharged engines, where the turbocharger needs to be kept spinning at high rpm by a large flow of exhaust in order to keep the boost pressure up and eliminate the turbo lag that occurs when the engine is idling and the throttle is suddenly opened. 10 | P a g e
11. 11. Semi-automatic transmission The creation of computer control also allowed for a sort of half-breed transmission where the car handles manipulation of the clutch automatically, but the driver can still select the gear manually if desired. This is sometimes called "clutch less manual". Many of these transmissions allow the driver to give full control to the computer. There are some specific types of this transmission, including Triptronic and Direct Shift Gearbox. There are also sequential transmissions which use the rotation of a drum to switch gears. A great example of this is the 7 -speed sequential transmission on the Bugatti Veyron, a super car that puts out 1,001 horsepower (746 kW) and goes 254 miles per hour (409 km/h). You can see this at howstuffworks.com. Follow this link to get to the howstuffworks.com article on sequential transmissions. 11 | P a g e
12. 12. Calculations 12 | P a g e
13. 13. Partial Relations (Number of Teeth was assumed) 13 | P a g e
14. 14. Total Relations 14 | P a g e
15. 15. Gear Analysis  Gear I  ; ; Same procedure was done to obtain other gear dimensions Torque → (  ) ; Shaft I Same procedure was done to obtain torques acting on other shafts 15 | P a g e
16. 16. Real Forces Same procedure was done to obtain real forces for the remaining gear pairs 16 | P a g e
17. 17. Lewis Forces From table 2a and a BHN 302-351 ;  Bending ; Same procedure was done to obtain Lewis forces for other gears. 17 | P a g e
18. 18. Results Table1PartialRelations Input RPM Shaft 1 & 2 1st Gear Pair M 5 400 Puley ratio Reducer gear ratio 30 0.5 0.5 120 2nd Gear Pair Given: Z1=21, Z2=42, Engine RPM 42 1600 Power [kW] 108 3rd Gear Pair 30 58 θ 92 1.6 Min output [rpm] i1 0.250 M 5 i2 0.389 M 5 i3 0.630 Shaft 2 & 3 4th Gear Pair 30 120 5th Gear Pair 77 73 6th Gear Pair M 5 i4 0.250 M 5 i5 1.055 M 5 89 61 i6 4.684 19 25 Max output [rpm] 1073.741824 Table2 Output gearrelation output gear 38 42 M 5 i7 0.905 18 | P a g e
19. 19. Table 3Total Relations and Output speeds 1st Gear Pair 2nd Gear Pair tooth 30 120 120 30 77 120 73 30 89 120 61 42 30 108 120 42 77 108 73 42 89 108 58 92 58 92 58 92 61 30 120 77 73 89 19 Actual Actual rpm w/output tooth 30 Total ratioTotal ratio rpm in order J1 0.063 0.063 25.0 1068.7 J2 0.264 0.264 105.5 659.3 J3 1.171 1.060 423.8 423.8 J4 0.097 0.097 38.9 266.0 J5 0.410 0.410 164.1 164.1 J6 1.822 1.648 659.3 105.5 J7 0.158 0.158 63.0 63.0 J8 0.665 0.665 266.0 38.9 J9 2.953 2.672 1068.7 25.0 19 | P a g e
20. 20. Table 4 Shaft Speeds, and distances between shafts Speed per shaft Rpm Torque Max Shaft 1 n1 400.0 Shaft 2 n1 100.0 n2 155.6 n3 252.2 n1 25.0 n2 105.5 1st Gear Pair 375 n3 423.8 2nd Gear Pair 375 n4 38.9 3rd Gear Pair 375 n5 164.1 n6 659.3 4th Gear Pair 375 n7 63.0 5th Gear Pair 375 n8 266.0 6th Gear Pair 375 n9 1068.7 Shaft 3 11464.97 [N.m] Torque Min 268.19 Distance Between Shafts [N.m] Shaft 1 & 2 [mm] Shaft 2 & 3 [mm] 20 | P a g e
21. 21. Table5ReducerGearAnalysis Reducer Gear Cálculo de Fuerzas de Lewis Potencia [W] 30000 Z1 21 N0 [RPM] 1600 Z2 42 N1 [RPM] N2 [RPM] 800 400 dp1 5 0.105 degree] 20 dp2 0.21 Torque I [N.m] Torque II [N.m} M 358.1 716.2 FuerzasReales Fuerza B Fuerza W Fuerza R Fuerzas de Lewis [psi] [MPa] b = #*m ( 9 to 14) P Y dp1 6820.9 7258.7 2482.6 22000 151.7 9 15.7 0.102 105 Q K [MPa] Fuerza BL 1.333 4.49 10939.2 Fuerza WL 55000 379.3 28287.0 21 | P a g e
22. 22. Table 6 Real Forces and Lewis Forces comparison Fuerzas Reales [N] & Fuerzas de Lewis [N] [N] [N] Shaft 1 & 2 1st Gear Pair Fuerza B 30 120 Fuerza W Fuerza R P 15.708 2nd Gear Pair Fuerza B 42 108 Fuerza W Fuerza R P 15.708 3rd Gear Pair Fuerza B 58 92 Fuerza W Fuerza R P 15.708 9549.3 Fuerza BL 13465.5 10162.1 3475.7 Fuerza WL y 0.1130 53880.0 Q 1.6 b 50.0 6820.9 Fuerza BL 14413.8 7258.7 2482.6 Fuerza WL y 0.1210 67888.8 Q 1.4 b 50.0 4939.3 Fuerza BL 15741.4 5256.3 1797.8 Fuerza WL y 0.1321 79862.1 Q 1.226667 b 50.0 Shaft 1 & 2 , 1st, 2nd, 3rd Gear Pairs PASS PASS PASS PASS PASS PASS Torque at Shaft 2 for 1st Gear Pair 2864.8 [N.m] Torque at Shaft 2 for 2nd Gear Pair 1841.7 [N.m] Torque at Shaft 2 for 3rd Gear Pair 1136.0 [N.m] 22 | P a g e
23. 23. Table 7 Real Forces and Lewis Forces Comparison With 1st Gear Pair Torque Shaft 2 & 3 [N] Fuerza B 38197.2 4 Gear Pair Fuerza W 40648.6 30 Fuerza R 13902.6 120 y 0.1130 15.70796 th 5th Gear PairFuerza B 14882.0 Fuerza W 15837.1 77 Fuerza R 5416.6 73 y 0.1369 15.70796 Fuerza BL 40396.5517 Fuerza W L 64656 b 60 Q Torque at Shaft 3 for 4th Gear Pair 11459.2 [N.m] 1.6 Fuerza BL 16310.3448 Fuerza W L 84127.6333 b 50.0 Q PASS PASS PASS PASS Torque at Shaft 3 for 5th Gear Pair 2716.0 [N.m] 0.97333333 6th Gear PairFuerza B 12875.5 Fuerza BL Fuerza W 13701.8 Fuerza W L 89 61 Fuerza R 4686.3 b 20 y 0.1385 Q P 15.70796 With 2nd Gear Pair Torque Shaft 2 & 3 [N] th Fuerza B 24555.3 Fuerza BL 4 Gear Pair Fuerza W 26131.2 Fuerza W L 30 Fuerza R 8937.4 120 b y 15.70796 0.1130 Q 5th Gear PairFuerza B 9567.0 Fuerza BL Fuerza W 10181.0 Fuerza W L 77 Fuerza R 3482.1 73 b 15.70796 y 0.1369 Q 16500 81254.0333 50.0 0.8133 PASS PASS 40396.5517 64656 60 1.6 PASS PASS 16310.3448 84127.6333 50 0.97333333 PASS PASS 6th Gear PairFuerza B 8277.1 Fuerza BL Fuerza W 8808.3 Fuerza W L 89 61 Fuerza R 3012.6 b 20 y 0.1385 Q P 15.70796 With 2nd Gear Pair Torque Shaft 2 & 3 [N] 4th Gear PairFuerza B 15147.2 Fuerza BL Fuerza W 16119.3 Fuerza W L 30 Fuerza R 5513.1 120 b y 15.70796 0.1130 Q 5th Gear PairFuerza B 5901.5 Fuerza BL Fuerza W 6280.2 Fuerza W L 77 Fuerza R 2148.0 73 b y 15.70796 0.1369 Q 6th Gear PairFuerza B 5105.8 Fuerza BL Fuerza W 5433.5 Fuerza W L 89 61 Fuerza R 1858.4 b 20 y 0.1385 Q P 15.70796 16500 81254.0333 50 0.8133 PASS PASS 40396.5517 64656 60 1.6 PASS PASS 16310.3448 84127.6333 50 0.97333333 PASS PASS 16500 81254.0333 50 0.8133 PASS PASS Torque at Shaft 3 for 6th Gear Pair 643.8 [N.m] Torque at Shaft 3 for 4th Gear Pair 7366.6 [N.m] Torque at Shaft 3 for 5th Gear Pair 1746.0 [N.m] Torque at Shaft 3 for 6th Gear Pair 413.9 [N.m] Torque at Shaft 3 for 4th Gear Pair 4544.1 [N.m] Torque at Shaft 3 for 5th Gear Pair 1077.0 [N.m] Torque at Shaft 3 for 6th Gear Pair 255.3 [N.m] 23 | P a g e
24. 24. Table 8 Lewis Form Factor for N-Teeth Lewis Form Factor for N-Teeth N teeth Y y 30 0.355 0.11300001 43 0.38 0.12095776 58 0.415 0.1320986 77 0.43 0.13687325 89 0.435 0.1384648 Figure 1 Lewis Form Factor diagram 24 | P a g e
25. 25. Table9GearAnalysis M= 5 Number of teeth 21 42 108 30 120 58 92 89 61 19 38 42 30 120 77 73 Z 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 θ= 20 dp 105 210 540 150 600 290 460 445 305 95 190 210 150 600 385 365 Pd 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 db 98.66772518 197.3354504 507.4340152 140.9538931 563.8155725 272.51086 432.2586056 418.1632162 286.6062493 89.27079897 178.5415979 197.3354504 140.9538931 563.8155725 361.781659 342.9878066 All in mm da 115 220 550 160 610 300 470 455 315 105 200 220 160 610 395 375 dd 92.5 197.5 527.5 137.5 587.5 277.5 447.5 432.5 292.5 82.5 177.5 197.5 137.5 587.5 372.5 352.5 width 45 45 45 45 45 45 45 45 45 45 45 45 60 60 45 45 Table10 Real Forces Shaft I II II II III V VI III III IV Fuerzas Reales Engine Torque= 358.1 Torque Fb Par 1 (z1 y z2) 358.1 6820.926133 Par 2 (z2 y z3) 716.1972439 6820.926133 Par 3 (z4 y Z5) 716.1972439 9549.296586 Par 4 (z6 y z7) 716.1972439 4939.291337 Par 5 (z8 y z9) 2864.788976 12875.45607 Par 6 (z9 y z10) 1963.507051 12875.45607 Par 7 (z11 y z12) 611.5841633 6437.728035 Par 8 (z13 y z14) 2864.788976 38197.18634 Par 9 (z15 y z16) 2864.788976 14882.02065 11459.1559 38197.18634 Fw 7258.677978 7258.677978 10162.14917 5256.284053 13701.77416 13701.77416 6850.88708 40648.59668 15837.11559 40648.59668 Fr 2482.614082 2482.614082 3475.659715 1797.755025 4686.282762 4686.282762 2343.141381 13902.63886 5416.612543 13902.63886 25 | P a g e
26. 26. Shaft Table 11 Failure Theories, deflection and shaft diammeter Mt 358.1 716.2 2864.78 11459.16 1963.5 611.58 Mb 226.829405 I dia. (mm) 1521.20131 II dia. (mm) 8737.51681 III dia. (mm) 5681.47868 IV dia. (mm) 565.183245 V dia. (mm) 983.929576 VI dia. (mm) Failure Theories for Shaft Design Torsional Rigidity 30.6 36.3 51.4 72.7 46.8 34.9 ASME Code for Shaft 23.2 39.2 69.6 71.1 37.8 34.3 Max Principal Max Shear Stress Theory Stress Theory 20.6 22.5 35.0 35.5 62.0 62.6 62.7 69.8 32.6 37.9 30.6 31.4 Minimal Allowed deflection: (0.010)module = 0.05mm 4141 Properties To comply with minimal deflections the following diameters were used: SF 1.75 Shaft D (mm) Spline d (mm) a b Sy 6.75E+08 I 28.00 14.0124 62.50 62.50 tmax 192857143 II 84.00 82.1960 245.00 245.00 S1 385714286 III 120.00 118.0647 253.00 1022.50 Splines 6 IV 132.00 115.2475 317.50 250.00 E (Gpa) 205 V 40.00 #NUM! 82.50 82.50 Pm (N/mm2) 6.5 VI 58.00 54.7995 272.50 75.00 Length (mm) Deflection (mm) 125.00 0.04775 490.00 0.04972 1275.50 0.34069 567.50 0.04924 165.00 0.04978 347.50 0.04821 26 | P a g e
27. 27. Shaft I x-y x-z 27 | P a g e
28. 28. Shaft I  Plane X-Y Figure 2Shaft I FBD Figure 3 Shaft I Shear Diagram x-y 28 | P a g e
29. 29. Figure 4 Shaft I Moment Diagram x-y Shaft I  Plane X_Z Figure 5 Shaft I FBD x-z 29 | P a g e
30. 30. Figure 6 Shaft I Shear diagram x-z Figure 7 Shaft I Moment diagram x-z 30 | P a g e
31. 31. Shaft II  Plane X-Y Figure 8 Shaft II FBD x-y Figure 9 Shaft II Shear Diagram x-y 31 | P a g e
32. 32. Figure 10 Shaft II Moment diagram x-y Shaft II  Plane X-Z Figure 11Shaft II FBD x-z 32 | P a g e
33. 33. Figure 12 Shaft II Shear diagram x-z Figure 13 Shaft II Moment diagram x-z 33 | P a g e
34. 34. Shaft III  Plane X-Y Figure 14 Shaft III FBD x-y Figure 15 Shaft III Shear diagram x-y 34 | P a g e
35. 35. Figure 16 Shaft III Moment diagram x-y Shaft III  Plane X-Z Figure 17 Shaft III FBD x-z 35 | P a g e
36. 36. Figure 18 Shaft III Shear diagram x-z Figure 19 Shaft III Moment diagram x-z 36 | P a g e
37. 37. Shaft IV  Plane X-Y Figure 20 Shaft IV FBD x-y Figure 21 Shaft IV Shear diagram x-y 37 | P a g e
38. 38. Figure 22 Shaft IV Moment diagram x-y Shaft IV  Plane X-Z Figure 23 Shaft IV FBD x-z 38 | P a g e
39. 39. Figure 24 Shaft IV Shear diagram x-z Figure 25 Shaft IV Moment diagram x-z 39 | P a g e
40. 40. Shaft V  Plane X-Y Figure 26 Shaft V FBD x-y Figure 27 Shaft V Shear diagram x-y 40 | P a g e
41. 41. Figure 28 Shaft V Moment diagram x-y Shaft V  Plane X-Z Figure 29 Shaft V FBD x-z 41 | P a g e
42. 42. Figure 30 Shaft V Shear diagram x-z Figure 31 Shaft V Moment diagram x-z 42 | P a g e
43. 43. Shaft VI  Plane X-Y Figure 32 Shaft VI FBD x-y Figure 33 Shaft VI Shear diagram x-y 43 | P a g e
44. 44. Figure 34 Shaft VI Shear diagram x-y Shaft VI  Plane X-Z Figure 35 Shaft VI FBD x-z 44 | P a g e
45. 45. Figure 36 Shaft VI Shear diagram x-z Figure 37 Shaft VI Moment diagram x-z Bearings Assumptions 45 | P a g e
46. 46. The value of Bore, Outside Diameter (OD), Series and Width are obtain of the Table 11-3 of our textbookShigley’s Mechanical Engineering Design 9th Edition. Table12BearingDesign Bearing Design Shaft C10 ND FD Bore Series OD Width I 45108.8 800 7258.67 35 03-Series 80 17 II 50124.3 400 10162.2 60 02-Series 110 22 III 161512.2 252 38197.19 100 02-Series 180 34 IV 278148.3 1068 40648.6 130 02-Series 230 40 V 65710.9 367.67 13701.8 45 03-Series 100 25 VI 46882.4 1068.2 6850.9 55 03-Series 100 21 Belt Drive Design Power 46 | P a g e
47. 47. , , , 47 | P a g e
48. 48. Conclusions After calculations and analysis we have designed a transmission that is fully functional complying with the initial requirements. The 9 shift transmission design is composed of 6 shafts and 16 gears. At the same time the transmission will have a minimum output of 25RPM and a maximum of around 1,068 RPM. This explains the proper function of the mechanism. On the other hand, it was necessary to analyze the mechanism in order to draw out the manner in which the transmission will look in a blue print. This drawing shows the compilation of our analysis in one page were one can visualizes the behavior and “connectivity” between the gears, shaft, pulleys, motor, etc. further explaining our design. 48 | P a g e
49. 49. References  Shigley’s Mechanical Engineering Design 9th Ed. (Budynas, Nisbett, 2010)  www.matweb.com  www.wikipedia.com 49 | P a g e
50. 50. Appendices 50 | P a g e