Optimization of Design Based on Tip Radius and Tooth Width to Minimize the Stresses on the Spur Gear with FE Analysis.

Transcription

1 Optimization of Design Based on Tip Radius and Tooth Width to Minimize the Stresses on the Spur Gear with FE Analysis. K.Ruthupavan M. Tech Sigma Consultancy Service /C/A/1, 104, First Floor Rajaiah Complex, Near Yellamma Temple, Balkampet Hyderabad Y.Sandeep Kumar M. Tech Sri Kalahastheswara Institute of Technology, Sri Kalahasthi Chittor Abbreviations: AGMA-American Gear Manufacturing Association Keywords: Spur Gear, Contact Stress, Fillet Stress Abstract Gears are one of the most critical components in mechanical power transmission system. Spur gears are mostly used in the applications varying from domestic items to heavy engineering applications. The contact stress and tooth stresses due to transmission depends on some parameters. In this thesis the effect of tip radius, tooth width is considered and how the contact stress results vary with these parameters are studied. The Gear design is optimized based on FE analysis and also finally the gear design is optimized based on the stresses. The stresses were calculated using the Lewis equation and then compared with the FE model. The Bending stresses in the tooth root and at mating region were examined using 3D FE model. Introduction Spur gears are the simplest type of gear. They consist of a cylinder or disk with the teeth projecting radially, the edge of each tooth is straight and aligned parallel to the axis of rotation. These gears can be meshed together correctly only if they are fitted to parallel shafts. The main reason for the popularity of spur gears is their simplicity in design and manufacturing. In Spur gears the design parameters play a major role in determination of stresses. The AGMA Standards set by American Gear Manufacturing Association are usually followed in design of Spur gear. In this thesis the two parameters, tip radius and tooth width which play a key role in gear design are studied. These parameters are varied and their effects on the final stress are observed at the root and mating regions of the gear. A gear was considered which was mating with similar kind of the gear and then FE Model was built in HYPERMESH. Using Lewis Equation and AGMA Standards the stresses were calculated and the FE model was solved using RADIOSS solver and results were compared. The results were optimized for best results with the variation of two parameters tip radius and tooth width so that the stresses are minimized. Simulation Driven Innovation 1

2 Process Methodology The Gear with the following specifications was modeled using HyperMesh Number of teeth 20 Module(m) 4 Pitch Circle diameter 80 Base circle diameter 70 Pressure angle 20 Addendum circle diameter 88 Circular pitch Thickness of tooth 6.25 Table 1.1 Gear specifications Material assigned to gear was steel with following material properties Modulus of elasticity E= MPa Poisson s ratio v= 0.3 Finite Element model of the Spur Gear: A finite element model with a segment of one tooth is considered for analysis. The gear tooth was meshed with hexa and penta elements. The nodes were identified at pitch circle where the gear transmission force was applied. The nodes at the plane cut were considered for applying the symmetric boundary conditions. Fig 1.1 FE Model representation with Boundary conditions and CLOAD at Pitch Circle Simulation Driven Innovation 2

3 Lewis Equation: This bending stress equation was derived from the Lewis equation. Fig 1.2 Forces acting on teeth σ w = M y/i M = Maximum bending moment at the critical section BC, = W T h W T = Tangential load acting at the tooth, h = Length of the teeth, y = Half the thickness of the tooth (t) at critical section BC, = t/2 I = Moment of inertia about the centre line of the tooth, = bt 3 /12 b = Width of gear face. Equation 1.1 Calculations based on AGMA Standards: The stress is calculated based on AGMA Standrds as follows Equation 1.2 Simulation Driven Innovation 3

4 Where C p = Form factor K v = Velocity or Dynamic factor = (6+V)/6 K 0 = Overload factor which reflects the degree of non-uniformity of driving and load torques. Km = load distribution factor which accounts for non uniform spread of load across the face width. It depends on the accuracy of mounting, bearing, shaft deflection and accuracy of gear. Results & Discussions Equation 1.3 Fig 1.3 Stress Contour Results with the variation of face width and with change of fillet radius are represented below. The fillet radius of 4, 3, 2 mm and no fillet are considered. The Results are presented as follows which shows the Fillet = 4 mm radius Simulation Driven Innovation 4

5 Fillet =3 mm radius Graph 1.1 Graph 1.2 Graph 2.1 Graph 2.2 Fillet = 2 mm radius No Fillet Graph 3.1 Graph 3.2 Graph 4.1 Graph 4.2 Simulation Driven Innovation 5

6 Comparision of the Results for Fillet radius 3 mm: The FEA results of bending stress are compared with the stress calculated Table 6.1 using the gear related procedure specified in AGMA standards. The FEA results are found to be in close agreement with the calculated stresses based on AGMA Standards for the specific geometry configuration of the gear. From the Equation (4.2) σ w = ( )/20 (6.25) 2 = 96 Mpa Face width Lewis equation AGMA FEA % of error (AGMA And FEA) % of error (Lewis equation and FEA) Table 8.1 Comparison of results Conclusions: 1. The FEA results are found to be in close agreement with the calculated stresses based on AGMA standards and Lewis Equation. 2. The Stresses at the contact and fillet region decreases with the increase of face width. 3. Gradual decrease of stresses with increase of fillet radius. ACKNOWLEDGEMENTS The authors would like to thank the Altair Support team for helping to solve the issues related with RADIOSS. REFERENCES [1] Robert Basan, Marina Franulovic, and Bozidar Krizan. Numerical model and procedure for determination of stresses in spur gear teeth flanks -XII International Conference on Mechanical Engineering-Nov 2008, [2] M.S. Hebbal, V.B. math, B.G. Sheeparamatti- A Study on reducing the root fillet stress in spur gear using Internal Stress Relieving Feature of Different Shapes - International Journal of Recent Trends in Engineering, Vol.1, no.5, may 2009, [3] Pankaj kumar jena, prof. S.C.Mohanthy A Project Report on static and dynamic analysis of HCR spur gear drive using finite element analysis [4] prof. Gopinath, prof. M.M. Mayuram spur gear design - Indian Institute of Technology Madras [5] HyperMesh user Guide, [6] Gear Reference Guide Berg Manufacturing, [7] R.S Kurmi- S.Chand publications A text book on Machine Design pg.n.1036 to 1039, Simulation Driven Innovation 6