Design of single stage reduction gearbox
Introduction Designing a mechanical power transmission such as a single stage spur gear gearbox is very complex. The complexity arises from strong and often intractable interdependencies between the design variable and system requirements. The optimal reducer is generally not an assembly of components optimized in isolation a fact overlooked by many conventional designs. It is known that designing of a reducer is an iterative process in which it is necessary to make some tentative choices and to determine which parts of the design are critical For example, the impact of certain choice of the coefficient of face width of the gear may yield to a minimum, mass of gearing, but the selection of this coefficient may cascade through subsequent steps of the design process (sizing of shafts, radial seals, ball bearings, housing etc.) that ultimately lead to a heavier reducer than if a slight compromise had been made on the choice of the gearing.
Reduction gearbox design description The design was made to accommodate a power transfer of 30kw at a drive speed of 1500 rpm and the gearbox is to reduce the speed to 750 rpm. The design was made to give an overall efficiency of 95% and it has a life span of approximately twenty thousand hours.
The parameters of for each gear
Parameters
Gear 1
Gear 2
Number of teeth(N) Form of teeth Module (m) Face with of teeth(F) (mm) Pitch diameter(dp)(mm)
24 Involute 5.5 65 132
48 Involute 5.5 65 264
Diameter gear (mm)
142.035
275.418
Mass of gear (Kg)
4.478
25.753
Pressure angle (deg.)
20
20
The single stage reduction gearbox The single-stage spur gear unit we are considering in this work is highly standardized, both in terms of its layout and in terms of design of its gearings, shafts, radial sealing and tapered roller bearings. The set of genes that define the single-stage spur gear unit unequivocally reflects this, with standardization imposing discrete values sets on most of them. The problem of minimum mass design of simple and multi-stage spur gear trains has been a subject of considerable interest, since many high-performance power transmission applications (e.g. automotive, aerospace, machine tools, etc.) require low mass. For this reason, in this study, minimization of single-stage spur gear unit mass is the objective function. This system consists of two gears supported by a two shaft. The bearings, the gears, the shaft, and the keys need to be designed and analyzed. The first components analyzed were the gears. The reason behind this is that there’s more information from which to attain, and this speeds up the design process.
Results of test and calculations
Gears The gears were made from a material called EN C50 (tooth face hardened) which has a allowable bending stress of 152 MPa , allowable contact stress of 1170 MPa, modulus of elasticity 206000 MPa, and a Poisson’s ratio(µ) of 0.3. The overall efficiency of the two gears is 98%.
Tangential force (N) Radial force (N) Axial force (N) Normal force (N) Velocity (m/s) Factor of safety form pitting Factor of safety from tooth breakage Torque (Nm)
Gear 1 (Pinion) 2864.8 1129.6 0 3079.4 10.367 2.7 7.6 190.99
Gear 2 2864.8 1129.6 0 3079.4 10.367 2.79 6.065 374.33
Shafts The shaft holds everything together and it withstands most of the loads. Therefore, a thorough statics analysis is required in order to design this component. Borrowing the statics analysis already performed on the bearings, the shafts were analyzed. Shear Force and Bending Moment diagrams were developed in order to determine the maximum points. The material selected for the shaft is steel which has a modulus of elasticity of 206000MPa, modulus of rigidity of 8000MPa and a density of 7860Kg/m3. The shaft and gear was fastened by the use of keyway and the gear is held into place by circlips.
Length of shaft (mm) Mass of shaft (Kg) Maximal bending stress(MPa) Maximal shear stress(MPa) Maximal reduce stress(MPa) Maximal Defection (µm) Torque (Nm)
Shaft 1 (Pinion Shaft) 391 10.74 0.274 0.023 0.275 0.236 191
Shaft 2 (Gear Shaft) 388 11.85 0.166 0.02 0.166 0.15 374
Bearings The bearings are critical components that allow the system to move smoothly. They should also withstand loading in the radial direction and thrust in the axial direction. In many application roller bearings are used back to back in pairs for axial load . A statics analysis had to be performed in order to find the reactions and determine the loads on the bearings. Two different planes had to be evaluated in order to do so. The system should be steady and not move in any direction, so the forces must cancel out. The reason for the use of roller bearings it that it can simultaneously cope for large vertical and horizontal forces. The load capacity and bearing life was determine to make sure that the bearing life will have exceed 20000 hours .
Bearing properties and parameters Properties and parameters
Bearing 1
Bearing 2
Bearing 3
Bearing 4
Radial load (N) Speed (RPM) Outside diameter(mm) Inside diameter(mm) Bearing width(mm) Contact angle (Deg.) Basic dynamic load rating (N) Static loading(N) Require life (Hrs.) Max Working temperature(°C)
184.4 750 130 60 46 15 86800 27500 20000 100
184.4 750 130 60 46 15 86800 27500 20000 100
74.6 1500 110 50 40 15 64500 19800 20000 100
74.6 1500 120 55 43 15 75200 23500 20000 100
Bearing 3 25000 44.6 1.6
Bearing 4 25000 52.9 1.7
Bearing calculation
Rating life (Hrs.) Static safety factor Frictional loss (W)
Bearing 1 25000 42.1 1.3
Bearing 2 25000 42.1 1.3
Conclusion and recommendation The critical features involved in the design of the gear reduction system have been determined through the use of statics, strength, and fatigue analyses. The calculation of the safety factor under various conditions and loadings has made it clear that the system will not fail. The gears have very large safety factors under bending, which indicates that our selection of materials is extremely safe and conservative. For wear, the safety factor was smaller, on the average safety factor range, indicating that our selection is good. The bearings were carefully decided upon to be very safe as well, and to withstand the loads to which the system is subjected. The shaft is made of a very strong material that can withstand a lot of fatigue and stress. The determination of our safety factor under fatigue proves that the shaft will not fail and our selection is good. For static and tensile loading, our shaft is very strong, and the safety factors were big, meaning that our selection is safe and conservative. During the analysis of this system, one of the most important things that were considered was the reliability.
