SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015
Design and analysis of Gear Shaft SingiReddy Ravinder#1, Ramesh Banothu*2 #1
M.Tech student, Mechanical, Vathsalya Institute of Science and Technology, Nalgonda Dist, Telangana, India *2 HoD, Mechanical, Vathsalya Institute of Science and Technology, Nalgonda Dist, Telangana, India
Abstract.A reduction gear box is part of a mechanical system of gears and shafts used to reduce the rotational speed of the input shaft to a slower rotational speed of the output shaft. This reduction in output speed helps to increase the torque of a system. Reduction gears are widely used in power transmission devices to reduce the high rotational speeds. Gears have wide variety of applications. Gears are the most important component in power transmission system. The gears generally fail when tooth stress exceed the safe limit. It is essential to determine the maximum stress that a gear tooth is subjected to, under a specified loading. To prevent from failure Analysis is carried on gears. In this study, visualize the forces, torques, and bending moments that are created in the shaft during operation. In the process of transmitting power at a given rotational speed, the shaft is inherently subjected to a torsional moment, or torque. Thus, torsional shear stress is developed in the shaft. Finite element analysis was performed to obtain the variation of the stress magnitude at critical locations. Three dimensional model of the gear shaft was created in Pro-E software. The load was then applied to the FE model and boundary conditions were applied as per the mounting conditions of the engine in the ANSYS. .Also, a shaft usually carries power-transmitting components, such as gears, belt sheaves, or chain sprockets, which exert forces on the shaft in the transverse direction (perpendicular to its axis). These transverse forces cause bending moments to be developed in the shaft, requiring analysis of the stress due to bending. In fact, most shafts must be analysed for combined stress.
Keywords-:Gear shaft, Torque, transmission, Ansys, Pro-E
Stress,
Power-
I. INTRODUCTION Gear box is a speed and torque changing device between the engine and the driving wheels. It serves the following purposes in transmission system of an automobile 1. It exchanges engine power for greater torque and thus provides a mechanical advantage to drive the vehicle at different conditions. 2. It exchanges forward motion for reverse motion. 3. It provides a neutral position to disallow power flow to the rest of the power train.
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Automobile requires high torque when climbing hills and when starting, even though they are performed at low speeds. On the other hand , when running at high speeds at level roads, high torque is not required because of momentum and it would be preferable to have just the wheels alone turning at high speeds. The gear box also called the transmission acts in accordance with the running conditions. When driving power is required, it reduces the engine speed and transmits stronger torque to the wheels. In addition the transmission serves to reverse the vehicle. Since the engine can turn only in one direction, the transmission gear can mesh in such a manner to allow running the vehicle in reverse direction. Located at the junction point of a power shaft, the gearbox is often used to create a right angle change in direction, as is seen in a rotary mower or a helicopter. Each unit is manufactured with a specific purpose in mind and the gear ratio used is designed to provide the level of force required. This ratio is fixed and cannot be changed once the box is constructed. The only possible modification after the fact is an adjustment that allows the shaft speed to increase, along with a corresponding reduction in torque.In a situation where multiple gear speeds are needed, a transmission with multiple gears can be used to increase torque while slowing down the output speed. This design is commonly found in automobile transmissions. The gear transmission mechanism is one of themost widely used transmission mechanism, which canbe used to transmit the motion and force between tworandom shafts in space of transmission, characterizinglarge power range, high efficiency, accuratetransmission ratio, long service life, safe and reliable,has been widely used in various industries (Wang et al.,2010). In which, gear shaft is the main transmissionpart in the most general machinery and its intensity hasa great influence on the service life of the machine.Because the geometric structure of gear shaft is morecomplex than the ordinary transmission shaft, todetermine and check the actual damage location of gearshaft by the conventional method is
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SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015
more cumbersome,it results in a bigger error (Li et al., 2000). In order toprovide the theoretical basis for structural design ofgear shaft, especially for new structural measures takenfor the dangerous position in time, the strength of gearshaft should be clearly understood after the preliminarystructural design is completed. Based on the abovesituation, this paper uses the transmission systemanalysis software MASTA to complete the strengthanalysis and calculation for gear shaft of a certainautomobile transmission.
short shafts or on portions of shafts where no bending or torsion occurs, such stresses may be dominant.
II. THEORETICAL SHAFT DESIGN AND ANALYSIS A shaft is the component of a mechanical device that transmits rotational motion and power. It is integral to any mechanical system in which power is transmitted from a prime mover, such as an electric motor or an engine, to other rotating parts of the system. There are many examples of mechanical systems incorporating rotating elements that transmit power: gear-type speed reducers, belt or chain drives, conveyors, pumps, fans, agitators, household appliances, lawn maintenance equipment, and parts of a car, power tools, machines around an office or workplace and many types of automation equipment. Visualize the forces, torques, and bending moments that are created in the shaft during operation. In the process of transmitting power at a given rotational speed, the shaft is inherently subjected to a torsional moment, or torque. Thus, torsional shear stress is developed in the shaft. Also, a shaft usually carries power-transmitting components, such as gears, belt sheaves, or chain sprockets, which exert forces on the shaft in the transverse direction (perpendicular to its axis). These transverse forces cause bending moments to be developed in the shaft, requiring analysis of the stress due to bending. In fact, most shafts must be analysed for combined stress. Because of the simultaneous occurrence of torsional shear stresses and normal stresses due to bending, the stress analysis of a shaft virtually always involves the use of a combined stress approach. The recommended approach for shaft design and analysis is the distortion energy theory of failure. Vertical shear stresses and direct normal stresses due to axial loads also occur at times, but they typically have such a small effect that they can be neglected. On very
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A. Procedure for Design and analysis of a Shaft 1. Determine the rotational speed of the shaft, n (rpm). 2. Select the material from which the shaft will be made, and specify ultimate tensile strength Su, yield strength Syand its surface condition: ground, machined, hot-rolled and as-forged. At the moment, due to lack of database for endurance strength, this module should be used in the design and analysis of steel shafts only. Use the database in selection of a material. 3. Apply a desired reliability for definition of reliability factor, CR. 4. Apply a design factor, N (we prefer to use ηd). 5. Propose the general form of the geometry for the shaft, considering how each element on the shaft will be held in position axially and how power transmission from each element to the shaft is to take place. Design details such as fillet radii, shoulder heights, and key-seat dimensions must also be specified. Sometimes the size and the tolerance for a shaft diameter are dictated by the element to be mounted there. For example, ball bearing manufacturers' catalogs give recommended limits for bearing seat diameters on shafts. 6. Specify the location of bearings to support the shaft. The reactions on bearings supporting radial loads are assumed to act at the midpoint of the bearings. Another important concept is that normally two and only two bearings are used to support a shaft. They should be placed on either side of the power-transmitting elements if
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SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015
possible to provide stable support for the shaft and to produce reasonably well-balanced loading of the bearings. The bearings should be placed close to the power-transmitting elements to minimize bending moments. Also, the overall length of the shaft should be kept small to keep deflections at reasonable levels. 7. Determine the design of the power-transmitting components or other devices that will be mounted on the shaft, and specify the required location of each device. 8. Determine the power to be transmitted by the shaft. 9. Determine the magnitude of torque at point of the shaft where the power-transmitting element is. T = 30 H/π n [N-m] where: H = transmitted power, W T = torque, N-m. n = rotational speed, rpm. 10. Determine the forces exerted on the shaft. Spur and helical gears, tangential force Wt = 60 000 H / π d n [N] where: d = pitch diameter of gear in [mm]; H = Power in [W]; N = Rotational Speed in [rev/min] Radial force ; Wr = Wt. tan φn / cos ψ [N]
n = normal pressure angle for helical where: gears, and pressure angle for spur gears; and ψ = helix angle 11. Preparing a torque diagram. 12. Resolve the radial forces into components in perpendicular directions, vertically and horizontally. 13. Solve for the reactions on all support bearings in each plane. 14. Produce the complete shearing force and bending moment diagrams to determine the distribution of bending moments in the shaft. 15. Analyze each critical point of the shaft to determine the minimum acceptable diameter of the shaft at that point in order to ensure safety under the loading at that point. In general, the critical points are several and include those where a change of diameter takes place, where
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higher values of torque and bending moment occur, and where stress concentrations occur. If a vertical shearing force V is the only significant loading present, this equation should be used to compute the required diameter for a shaft.
D
2.94 K t V N
S n'
where: Kt = stress concentration factor at the shoulder; 1.5 to 2.5; V = Vertical Shear Force [N]; N = Factor of Safety / Design Factor (you may use ηd); D or d = Diameter of the Shaft at the section considered [mm]; S’n = modified endurance strength [MPa], (Which depends on ultimate tensile strength Su).
S n'
Sn C S CR
where: Cs = size factor; CR = reliability factor; Sn = endurance strength [MPa] In most shafts, the resulting diameter will be much smaller than that required at other parts of the shaft where significant values of torque and bending moment occur. Also, practical considerations may require that the shaft be somewhat larger than the computed minimum to accommodate a reasonable bearing at the place where the shearing force V is equal to the radial load on the bearing.
Most shafts are subjected to bending and torsion. The power being transmitted causes the torsion, and the transverse and radial forces on the elements cause
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SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015
bending. In the general case, the transverse forces do not all act in the same plane. In such cases, the bending moment diagrams for two perpendicular planes are prepared first. Then the resultant bending moment at each point of interest is determined. A design equation is now developed based on the assumption that the bending stress in the shaft is repeated and reversed as the shaft rotates, but that the torsional shear stress is nearly uniform.
D
32 N
Kt M S n'
2
1 2 3
3 T 4 Sy
Where: M = Bending moment (a resultant obtained from bending moment diagrams; (this creates reversed bending stresses on the shaft) [N-mm]; T = Torsion or twisting moment (usually steady) [N-mm]; N = Factor of safety; (We shall usually use η.) D = Diameter of the shaft at the section under investigation; in [mm]. Also, Sy and Sn are to be taken as [MPa] III. DESIGNING OF GEAR SHAFT
mechanical systems incorporating rotating elements that transmit power: gear-type speed reducers, belt or chain drives, conveyors, pumps, fans, agitators, household appliances, lawn maintenance equipment, and parts of a car, power tools, machines around an office or workplace and many types of automation equipment. Preprocessor • Member length. • Member position. • Member material. • Element type -- SOLID 8 NODE 185 • Material model -- AL ALLOY • Real constants -- NONE • Meshing -- TETRA FREE • Loads -- MODAL LOADS Solution • Load position. • Load magnitude. • Load direction. • SOLUTION --- Solve - current L.S (Solves the problem) Post-processor • Get displacement member force detain both graphical and text output. •Plot results – contour plot -- nodal solution
IV. RESULTS OF ANSYS MODEL
A. Shaft Design A shaft is the component of a mechanical device that transmits rotational motion and power. It is integral to any mechanical system in which power is transmitted from a prime mover, such as an electric motor or an engine, to other rotating parts of the system. There are many examples of
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SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015
INPUT GEAR SHAFT ANSYS MODEL SHAFT STRESS INTENSITY
NODE VALUE
MINIMUM VALUES 1542 1542 1542 0.12954 E+06-0
0.16107E+ 06
0.44095E+ 06
MESHED MODEL
VON MISES STRESS SHAFT NODAL SOLUTIONS
V. CONCLUSIONS
MAXIMUM ABSOLUTE VALUES NODE
7061
8212
930
VALUE
0.31897 E-04
0.14851E05
0.15517E03
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.The model that is created in Pro/Engineer wildfire 5.0 and analysed in Ansys V12.1. The model created in Pro/Engineer is transferred to Ansys through IGES (Initial Graphics Exchange Specification) format. The structural analysis has been performed on the model by applying the proposed material properties, boundary conditions and loads. By viewing the results that has been discussed in the early chapter, it can be said that the input gear shaft model can
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SSRG International Journal of Mechanical Engineering (SSRG-IJME) – volume 2 Issue 9 – September 2015
withstand the proposed loads with considering a factor of safety as 1.2. So, thereafter the designed model can be manufactured or fabricated with extensive testing. References 1. Design of machine elements – v.m faires 2. Machine design –schaum series 3. Machine design –Pandya& shah 4. Design data book-psg 5. Mech engg design – j.e shigley 6. Automotive mechanics – kripal singh
BIODATA AUTHOR1 SingiReddy Ravinder has received the B.Tech (MechanicalEngineering) Degree fromAVN institute of Science and Technology, Rangareddy and pursuingM.Tech (Machine Design) in VIST, Bhoingiri, Nalgonda, Telangana, India. AUTHOR2 Ramesh Banothu has 5 years experience in teaching in graduate and post graduate level and he presently working as Associate Professor and HOD of Mechanical Department in VIST, Bhoingiri, Nalgonda, Telangana, India.
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