International Journal of Management, Technology And Engineering ISSN NO : 2249-7455
Modelling, Static and Dynamic Analysis Of
Chittiboyina Kiran Kumar Asst.Professor, Visakha Institute of Engineering and Technology, Visakhapatnam
S. Ananth Asst.Professor, Baba Institute of Technology and Sciences, Visakhapatnam
Abstract- A rolling element is often pressed onto an shaft and mounted directly on a locomotive or indirectly on a bogie. A railroad wheel generally consists of 2 main parts: the wheel itself, axle. A rail wheel and shaft are typically made of steel, and typically heated and pressed onto the wheel, wherever it remains firmly because it shrinks and cools. Over 160 years past failures of iron railway axles led to analysis into what we currently understand as metal fatigue. Today’s railways consider a wide kind of materials from all the foremost classes of materials. in this project so as to get the dynamic forces on the locomotive shaft, it had been recognized that axles suffer many dynamic load cycles as they rotate and in the past several fanciful theories were projected to elucidate why failures occurred after periods of productive service. The dynamic characteristics analysis of wheel shaft of the locomotive is especially concerned in the calculation concerning natural frequency and operational frequency. the objective is to calculate the natural frequency and operational frequency of wheel axle of the locomotive is modulating those frequencies and avoiding resonance by the use of the harmonic response, so the vibrations of wheel axle of the locomotive might scale back. Resonance is vibration development that happens at bound rotor speeds once the wheel axle of the locomotive is on the work. The influence of wheel shaft of the locomotive design resonance development is investigated by ANSYS software system. In this project, the 3D model of wheel shaft of the locomotive is modelled in NX-CAD and imported into ANSYS software system to perform static and dynamic analysis to investigate strength and dynamic characteristics of wheel shaft of the locomotive and optimize if required.
Keywords: locomotive wheel shaft, natural frequency, operational frequency, resonance. NX-CAD, ANSYS.
INTRODUCTION A train wheel or rail wheel is kind of wheel specially designed to be used on rail tracks. A rolling element is often pressed onto shaft and mounted directly on a rail or locomotive or indirectly on a bogie, known as a truck. Wheels are forged or cast (wrought) and are heat-treated to possess a particular hardness. New wheels are trued, employing a lathe, to a particular profile before being pressed onto axle. All wheel profiles got to be sporadically monitored to insure correct wheel-rail interface. Improperly trued wheels increase rolling resistance, scale back energy potency and will create unsafe operation. A railroad wheel generally consists of 2 main parts: the wheel itself, and therefore the tire (or tyre) round the outside. A rail tire is sometimes made of steel, and is typically heated and pressed onto the wheel, wherever it remains firmly because it shrinks and cools. Mono block wheels don't have peripheral tires, whereas resilient rail wheels have a resilient material, like rubber, between the wheel and tire. Most train wheels have a conical geometry, that is the primary means of keeping the train's motion aligned with the track. Train wheels have a projection on one facet to stay the wheels, and therefore the train, running on the rails, once the bounds of the pure mathematics based mostly alignment area unit reached, e.g. because of some emergency or defect. See hunting oscillation. Some wheels have a cylindrical pure mathematics, wherever flanges area unit essential to stay the train on the rail track.
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Table 1.1 shows Locomotive wheel data table All dimensions in mm Wheel type W61, W63, W64 New wheel diameter (mm) 1016 Condemn wheel diameter (mm) 930 Thickness of Rim at Condemn on Back Flange (mm) 38 Thickness of Tread at Condemn on Back Flange (mm) 6 Minimum flange width (mm) 19 Maximum flange height (mm) 35 Maximum tread hollowing (mm) 3 Wheel width (mm) 130 Wheel drawing W61 – 206-328/1 W63 – 206- 328/3 W64 – 206-328/4 Clearance to structure gauge (mm) 40
OBJECTIVE
In this paper, main objective is to get the dynamic forces on the locomotive shaft. It was recognized that axles suffer a good several dynamic load cycles as they rotate and in the past several fanciful theories were projected to elucidate why failures occurred after periods of prosperous service.
The target is to calculate the natural frequency and operating frequency of wheel shaft of the locomotive is modulating those frequencies and avoiding resonance by making use of the harmonic response, so the vibrations of wheel axle of the locomotive could scale back. Resonance is vibration development that happens at bound rotor speeds once the wheel shaft of the locomotive is on the work.
During this project, the 3D model of wheel shaft of the locomotive is modelled in NX-CAD and imported into ANSYS software system to perform static and dynamic analysis to investigate strength and dynamic characteristics of wheel axle of the locomotive and optimize if needed.
METHODOLOGY:
3d Modeling Of Rail Wheel Axle:
The 3D model of the Rail wheel axle is made through UNIGRAPHICS NX software system from the 2 D drawings. UNIGRAPHICS NX is world’s leading 3D development resolution. This software system allows designers and engineers to bring good product to the market quicker. It takes care of the entire product definition to utility. NX delivers measurable worth to manufacturing firms of all sizes and all told industries.
NX is employed in a very large range of industries from producing of rockets to pc peripherals. With over 1 100000 seats put in in worldwide several cad users are exposed to NX and revel in using NX for its power and capability.
Fig. 3.1 The 3D model of Rail wheel shaft (Right facet view)
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Fig. 3.2 The 3D model of Rail wheel axle (top view)
Isometric View of Rail Wheel Axle
Fig. 3.3 The 3D model of Rail wheel axle (isometric view)
MATERIAL PROPERTIES:
30 NiCrMoV12 steel properties are used to Rail wheel axle:
Young’s Modulus (E) =180GPa Poisson’s Ratio = 0.3 Density = 8900Kg/mm3 Yield Strength = 490MPa In the follwing, chemical composition and main mechanical charecteristics of 30NiCrMoV12 steel ae shown.
Table:4.1 Chemical compostion and mechanical properties:
C S M P S C C M N V i n a r u o i
30Ni 0 - 0 - - 0 - 0 2 0 CrMo 2 . . . . . 0 0 0 0 v12 6 4 6 4 7 0 . . . . 0 0 0 0 8 0 4 0 0 2 . 0 0 2 1 1 0 0 3 0 3 . 0 5 . . . . 2 7 0 6 3 1 0 0 0 0 3
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Ra(N/m Rm(N/m As KU KU m²) m²) % longitudinal transverse (J) (J)
30NiCrMov ≥834 932-1079 ≥1 ≥47 ≥22 12 5
Mechanical Properties: s in the Tensile strength, [MPa] s T The limit of proportionality (Yield strain) [MPa] 5 d Specific elongation at fracture, [%] y Reduction of area, [%] KCU Impact strength, [kJ/m2] HB Brinell hardness, [MPa] Physical property: T The temperature at which the properties of the obtained data, [Grade] E Modulus [MPa] a Coefficient (linear) expansion (range 20oT), [Grade] l Thermal conductivity (heat), [W / (m · Grade)] r Density[kg/m3] C Specific heat (range 20o T), [J / (kg · Grade)] R Electrical resistance, [Ohmm] Weld ability: Without limitations – welding is done without heating and subsequent heat treatment. Limited weld ability- welding is feasible below heating up to 100120 degrees. And subsequent heat treatment Element Type Used:
Element type: Solid92 No. of nodes: Ten Degrees of freedom: Six
Structural Analysis
Finite part Modelling (FEM) and Finite part Analysis (FEA) are 2 preferred technology applications offered by existing CAE systems. this is often attributed to the very fact that the FEM is probably the most popular numerical technique for resolution engineering issues. The method is general enough to handle any complicated form of pure mathematics (problem domain), any material properties, any boundary conditions and any loading conditions. The generality of the FEM fits the analysis necessities of today’s complicated engineering systems and styles wherever closed type solutions area unit governing equilibrium equations are not offered. In addition it's AN economical design tool by that designers will perform constant quantity design finding out numerous cases (different shapes, material hundreds etc.) analyzing them and choosing the optimum style.
BOUNDARY CONDITIONS
shaft was in remission all told Dof at the first ending of the shaft mounted with wheel. Allowable axial load of 587N has been applied at the second ending of the shaft mounted with wheel.
Allowable Axle Load calculation Analytical calculation of Rail wheel shaft to style the Rail wheel shaft first we opt the diameter of the shaft which might bear the applied stress at a secure vary. we all know that shaft load formula
------>Eq. 4.1 *2
Where, P= Allowable Axle load
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n = number of fixed points E= Young’s modulus of material l = length between the fixed points I= moment of inertia
------>Eq. 4.2
d =Diameter of the axle= 180mm n = number of fixed points = 2 E= Young’s modulus of material = 180000 N/mm2 l = length between the fixed points = 1684mm
I= moment of inertia
I = 51503880 mm2
*2
P=32232004 N We know, Area of load acting location A= 2πrL Where, A = Surface area (mm2) r = radius of axle loading area (mm) L = length of axle loading area (mm)
A= 2*3.14*110*194
We know, Axle Force (F) = P/A F = 587.9N/mm2 DEFLECTION
5.1.1 The Maximum deformation determined 1.5mm on Rail wheel shaft in X-dir:
Fig. 5.1 the deformation of Rail wheel shaft in X-dir
5.1.2 The Max. Deformation determined 0.049mm on Rail wheel shaft in Y-dir:
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Fig. 5.2 the deformation of Rail wheel shaft in Y-dir
5.1.3 The Max. Deformation determined 0.8mm on Rail wheel shaft in Z-dir:
Fig. 5.3 shows the deformation of Rail wheel shaft in Z-dir
5.1.4 The Max.Displacement resultant observed 1.6mm on Rail wheel shaft:
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Fig. 5.4 shows the Max. Deformation of Rail wheel axle
STRESS
5.2.1 1st principle Stress observed 97MPa on Rail wheel axle in X- Dir:
Fig. 5.5 shows the 1st principle Stress of Rail wheel axle
5.2.2 2nd principle Stress observed 4.3MPa on knuckle joint in Y- Dir:
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Fig. 5.6 the 2nd principle Stress of Rail wheel axle
5.2.3 3rd principle Stress observed 0.01MPa on Rail wheel axle in Z- Dir:
Fig. 5.7 shows the 3rd principle Stress of Rail wheel axle
5.2.4 The Max. Von Mises Stress observed 163MPa on Rail wheel axle:
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Fig. 5.8 the Von Mises stress of Rail wheel axle
Table.5.1 The Max. Deflection and Max. Stress:
DEFLECTION (mm) STRESS(MPa) S. N U O. U U U S Von X Y Z U mises M ơX ơY ơZ
1. 0. 0. 1. 4. 0. 1 5 04 8 6 97 3 01 163
From the above analysis:
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The Max Deflection and the Max Avg. VonMises Stress observed on the Rail wheel axle for axial loads is 1.6mm and 163MPa with respectively. And the Yield strength of the material stainless steel is 490 MPa. Therefore in step with the Maximum Yield Stress Theory, the VonMises stress is a smaller amount than the yield strength of the material. the look of Rail wheel shaft is safe for the on top of in operation loads. But the factor of safety is (490/163=3).
Table.5.2 Frequencies in the range of 0-1000Hz MO FREQUEN PARTIC.FACTOR EFFECTIVE MASS DE CY X Y Z X Y Z - 0.8 0.7 0.1 0.4 0.3 0.2 1 468 E- E- E- 5 E-3 07 05 10 01 - 0.1 0.1 0.3 0.3 0.2 2 469 0.4 E- E- E- E- 07 01 08 03 04
The mode shapes for the above frequencies are plotted below: A) Results –Mode1 @ 468 Hz
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Fig. 5.3 Shows Mode shape 1@468 Hz for Rail wheel axle
B) Results –Mode2 @ 469 Hz
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Fig.5.4 Shows Mode shape 2@ 469 Hz for Rail wheel axle
GRAPHS: Amplitude v/S Forcing Frequency:
1. Harmonic response at face
Fig. 6.1 harmonic response at 1st fixed end of Rail wheel axle liner scale
Fig.6.2 harmonic response at 2nd fixed end of Rail wheel axle liner scale
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Fig.6.3 harmonic response at mid location of Rail wheel axle liner scale
From the above graphs, the subsequent amplitude were observed: Amplitude of 0.0002mm is observed on the 1st fixed end of Rail wheel axle at a frequency of 465Hz. Amplitude of 0.079mm is observed on the 2nd fixed end of Rail wheel axle at a frequency of 465Hz. Amplitude of 0.42 mm is observed on the mid location of Rail wheel axle at a frequency of 465Hz. 6.1 MAX. DEFLECTION AND STRESS OF FREQUENCY @ 468HZ Max. Deflection:
Fig. 6.4 shows the max. Deflection of Rail wheel axle Von-Mises stress:
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Fig.6.5 shows the Von-Mises stress of Rail wheel axle.
6.2 Max. Deflection And Stress Of Frequency @ 469hz Max. Deflection:
Fig.6.6 shows the max. Deflection of Rail wheel axle
Von-Mises stress:
Fig.6.7 shows the Von-Mises stress of Rail wheel axle. Table 6.3 Deflections and von-mises stress for critical frequencies
S FREQUENCY( DEFLEC VON MISES STRESS .no Hz) TIONS (mm) (MPa)
1 468 1.8 336
2 469 1.7 333
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From the above results it's determined that the crucial frequencies 468Hz and 469Hz are having stress 336MPa and 333MPa. The yield strength of the material (stainless steel) used for gear is 490MPa.
In step with the Von-Mises Stress Theory, the Von-Mises stress of drugs at frequencies 468Hz and 469Hz having stresses less than the yield strength of the fabric. Hence the design of Rail wheel shaft is safe for the above in operation loading conditions.
CONCLUSION
NX-CAD model of the wheel axle is generated in solid works and this model is imported to ANSYS for processing work. An axial load of 587N is applied on the circumference of the wheel shaft and track is mounted. Following are the conclusions from the results obtained: Maximum stress by ANSYS is lower than the yield stress of material. Von-Mises stresses are less than ultimate strength. Since the Von-Mises stresses are less than the ultimate strength, taking deflections under consideration, 30 NiCrMoV12 steel is preferred as best material for designed Rail wheel axle. So as to get the forces working on the shaft, a dynamic model with six Dof is made. Then, a discussion on dynamic forces working on the shaft is given very well. From the above results it's determined that the crucial frequencies 468Hz and 469Hz are having stress 336MPa and 333MPa. The yield strength of the material (stainless steel) used for gear is 490MPa. The Von-Mises stress at frequencies 468Hz and 469Hz having stresses less than the yield strength of the material. Hence the design of Rail wheel axle is safe for the above operating loading conditions.
SCOPE FOR FUTURE WORK
In the above projected work solely force acting circumferentially on the wheel shaft is just thought of, this may be extended to different forces that act on the wheel rim and structural analysis is administered, this can be extended to Transient Analysis. If it's potential, damping ought to be other to the system. Because, it's clear that within the damping case, abrupt force rise may be avoided and additionally, dynamic forces for different speeds may be decreased.
REFERENCES
[1]. Bayraktar M, Guclu R, Metin M and Yazici H 2009 The vibration analysis of light rail vehicle with axle modelling, 14. National Machine Theory Symposium (UMTS 2009), 02–04 June 2009, Guzelyurt,Cyprus (In Turkish). [2]. Dikmen F 1989 Axle fractures and precaution in rail vehicles: computer based dynamic analysis and constructive approach, PhD Thesis,Yildiz Technical University, Institute of Natural Science, Istanbul(In Turkish). [3]. Docoquier N, Fisette P and Jeanmrt H 2007 Multiphysics modelling of railway vehicles equipped with pneumatic suspensions. Vehicle System Dynamics 45(6): 505–524. [4]. Guclu R and Metin M 2009 Fuzzy logic control of vibrations of a light rail transport vehicle in use in Istanbul traffic. J. Vibr. Control 15(9): 1423–1440. [5]. Hanchen R and Decker K H 1967 Neue festigkeitberechnung für der maschinenbau, ZEV, C. Hanser Verlag Joly R 1986 Schwingungsverhalten eines eisenbahnfahrzeugs, Schienen der Welt, 23–26, Marz. [6]. Kruse H and Popp K 2001 A modular algorithm for linear, periodic, train-track models. Archive of Applied Mechanics 71: 473–486 [7]. Mitschke M and Helms H 1975 Schwingungen von schienen-und straaefahrzeungen. ETR: Eisenbahntechnische Rundschau 24(10): 371– 377 [8]. Platin B E 1983 The common effect of dry and viscous friction in railway load wagon systems, 3rd National Mechanic Conference (In Turkish [9]. Popp K, Kruse H and Kaiser I 1999 Vehicle-track dynamics in the mid-frequency range. Vehicle System Dynamics 31: 423–464 [10]. Stichel S and Knothe K 1998 Fatigue life prediction for a S-train. Vehicle System Dynamics 28: 390–403 Stribersky A, Moser F and Rulka W 2002 Structural dynamics and ride comfort of a rail vehicle system. [11]. Thompson, D., and Wu, T.X., “The effect of nonlinearity on wheel/rail impact” Journal of Rail and Rapid transit, volume 218, part F, 2003, p1-15. [12]. Sun, Y. Q., Dhanasekar, M., and Roach, D., “A threedimensional model for the lateral and Vertical Dynamics of wagon-track system.” Proceedings of the institution of Mechanical Engineers, Part F: Rail and Rapid Transit. Vol. 217 (1), 2003, p 31-45. [13]. Hou, K., Kalousek, J., Dong, R., “A dynamic model for an asymmetrical vehicle/track system” Journal of Sound and Vibration 267 (2003) 591–604. [14]. Knothe, K., and Grassie, S.L., “Modeling of railway track and vehicle/track interaction at high frequencies”, Vehicle System Dynamics 22 1993, pp. 209 – 262.
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[15]. Wen, Z., Jin, X., and Zhang, W., “Contact-impact stress analysis of rail joint region using the dynamic finite element method” Wear 258 (2005) p1301–1309. [16]. Zhai, W. M., Cai, C. B., Wang, Q. C., Lu, Z.W., and Wu., X. S., “Dynamic Effects of Vehicles on Tracks in the Case of Raising Train Speed” Proceedings of the Institution of Mechanical Engineers, Part F, v 215, 2001, p125-135. [17]. Jin, X., Wen, Z., Wang, K., and Xiao, X., “Effect of passenger car curving on rail corrugation at a curved track” Volume 260, Issue 6, 10 March 2006, p619-633. [18]. Zhai, W., and Cai, Z., “Dynamic interaction between a lumped mass vehicle and a discretely supported continuous rail track” Computers and Structures Vol.63, No. 5, pp. 987-997, 1997. [19]. Nielsen, J.C.O., and Oscarsson, J., “Simulation of dynamic train–track interaction with state-dependent track properties” Journal of Sound and Vibration, vol. 275 (2004) 515–532. [20]. Sun, Y. Q., and Dhanasekar, M., “Importance of the track modeling on the determination of the critical speed of wagons” Vehicle system Dynamics Supplement 41 (2004), p232-241. [21]. Rajib Ul Alam Uzzal, “Role of Railway Vehicle- Track System and Design Parameters on Flat-Induced Impact Load” M. A. Sc thesis, Dept. of Mechanica & Industrial Engineering, Concordia University, Montreal, Quebec, Canada 2007. [22]. Cai, Z., “Modelling of Rail track dynamics and wheel rail interaction” Ph D thesis, Dept. of Civil Engineering, Queen’s University, Kingston, Ontario, Canada 1992 [23]. Lonsdale, C., Dedmon, S.,and Pilch, J., “Effects of increased gross rail load on 36-inch diameter freight monobloc wheels”. [24]. Transport Canada “Railway Freight Car Inspection and Safety Rules” available at http://www.tc.gc.ca/railway/Rules/TC_0-06-1.ht [25]. Reilly, K., “Railway Wheel sets”, Rail Safety and Standards Board, London, UK, June 2003.
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