Natural Frequency & Mode Shape Analysis of Rotordisc With Diametralslots

Transcription

1 ISSN Frequency & Mode Shape Analysis Rotordisc With Diametralslots #1 Miss. Varsha Waikar, #2 Pr.V.B.Ghagare. #1 M.E.Mech. design-ii, trinity college Engg, Kondhawa, Pune. #2 Asst Pr. Mech. Engg., trinity college Engg, Kondhawa, Pune. ABSTRACT Rotordiscs with different diametral slots are extensively used in the construction aircraft, ships, automobiles, flywheels, clutch plates, circular saw plates, pressure vessel, missiles, liquid containers, and ship structures & other vehicles.the turbine is a well-known example for the industrial application the rotordisc. The knowledge natural frequencies components is great interest in the study response structures to various excitations. Hence one the application rotordisc i.e. tilecutter with central hole, fixed at inner edge and free at outer edge is chosen and its dynamic response is investigated. The objective current dissertation work is optimization existing tilecutters for better performance in vibration. It is done by analyzing the vibration characteristics like natural frequency, mode shapes tilecutters with free boundary condition through optimization no. diametral slots, diameter slot end & no. cooling holes. The clamped tilecutter will be mounted on exciter and different resonance s will be detected by varying the exciting frequency. As before response will be measured by an accelerometer.also FEM stware package is used for vibration analysis circular tilecutters with same boundary condition for determining different parameters like frequency, Mode shapes. Thus, Stware and experimental results obtained are to be compared. ARTICLE INFO Article History Received: 28 th February 2016 Received in revised form : 1 st March 2016 Accepted: 3 rd March 2016 Published online : 5 th March 2016 I. PROBLEM DEFINATION The study the dynamic behavior tilecutter with free boundary condition but having different design optimisation is important, as used in several cutting machines. Unwanted cutting process noise, vibration & accidental failure associated with the cutting process has become an important economic and technological problem in the industry that can be solved by this dissertation work. II.EXPERIMENTAL WORK It is done by two types.1)using FFT analyzer, natural frequencies are detected by hitting the tilecutter with impact hammer; the response at a point is measured by using an accelerometer.fft analyzer analyzed the output accelerometer. 2)The clamped tilecutter will be mounted on exciter and different resonance s will be detected by varying the exciting frequency. Mode shapes are investigated using sea shore sand, coal dust or salt to compare with FEM mode shapes same test specimens. III.INTRODUCETION Three Specimens circular annular cutters S.S. are chosen for testing. Following are the material properties for the specimen plates. Young s modulus (E) = 2.1 X N/m 2,, Poisson s ratio (γ) = 0.3, Density material (ρ) = 6250 N/m 3. In analysis, annular cutters are used for investigating the bending modes. The structure is axisymmetric and formed an isotropic homogeneous elastic material. Three dimensional parameters represents the disk's inner radius (b),outer radius (a) and thickness (h) respectively. IV.FIXTURE MADE FOR TEST Bolt is used to restrict the movement at inner edge cutter in x and y and z direction. The fixture was held in bench vice, which is rigidly fixed on rigid foundation with nut bolts. Clamping was obtained by using two 20mm diameter nuts and one bolt with two washers are fastened above and below the cutter as shown Secondly cutter with annular plate assembly was mounted on exciter & pressed by a set nut and clamping bolts. Sufficient care is exercised to 2015, IERJ All Rights Reserved Page 1

2 tighten the bolts with 3kg-m constant torque provided by torque range spanner, uniformly to achieve the fixed end condition. the clamped disk cutters were excited by electrodynamic exciter. V.EXPERIMENTATION Photographs and Figs. shows schematic representation the experimental set up to be used, both for impact hammer test along with specialized mounting to simulate the clamped end condition at the inner boundary. The annular plate cutter thickness 1.5 mm. The inner diameter the plate is 25.4 mm and outer diameter is variable with same boundary condition. Specimens prepared were rigidly fixed in fixture to obtain correct boundary conditions. Analysis is done experimentally with the help FFT analyzer, accelerometer, impact hammer. frequencies are detected by hitting the plate with hammer; the response at a point a plate is measured by using an accelerometer. FFT analyzer analyzed the output accelerometer. FFT test output graphs are shown below. Comparison vibration results is done after experimentation with analysis by three methods as below: i)to find natural frequency & modes by FEM,ii) To find natural frequency by FFT, iii) To find modes by exciter. Discussion on results obtained by FEM,& FFT analysis are compared here. Also mode shapes will be compared with exciter & FEM modes to reach the conclusion. Comparison on ANSYS & experimental results cutter no.1 with its optimized cutter no 2. : Table :Test specimen Type I dimensions Non Toothed cutter, thickness = 1.5 mm Use : To cut Wood. Number Aspect Inner Outer holes Specimen ratio diameter diameter dia.5 b/a in mm in mm mm 1 st feq.by 2nd optimised % change 371% 356% 367% 650% 609% Graph Comparison graph natural frequency results to show the effect adding cooling holes in cutter no.1 (Frequency vs modes) Concluding Remark:-FFT and FEM natural frequency results are matched to average 3% error which is acceptable.natural frequency decreases if air cooling holes are added to circular annular cutters. Table Test specimen type-ii dimensions Non Toothed cutter, thickness = 1.5 mm Use : To cut Wood Specimen Aspect ratio b/a Inner diameter in mm Outer diameter in mm Number cracks length 17.5 mm. Crack end hole dia.mm 3rd freq. by freq. by th optimised feq. by % change Concluding Remark : frequency increases as the no. diametral cracks increases.10% rise in the no. diametral cracks gives 7% to 40% rise in natural frequency variable as per modes. 2015, IERJ All Rights Reserved Page 2

3 th optimise d feq.by Graph : Comparison graph FEM natural frequency results to show the effect change in no. diametral slots, For cutter no.3 & 4(Frequency vs modes) % change 3 in FEM 5 15 freq Test specimen and fixture in vice for impact hammer FFT test We shall now attempt to compare the predicted and measured results for individual modes or pairs modes. As these are the modes with a low number diameter, which are most readily identified to concentrate our interest on those with 2, 3 or 4 nodal diameters. Comparisons on the results, concern the natural frequencies and the mode shapes is done here. Experimental results shows that values natural frequencies determined experimentally are less than those obtained by FEM analysis due to certain parameters discussed below as It is important to highlight the reasons are: Boundary condition Damping, Rotary inertia, Impact hammer double hit Table: Test specimen Type III,thickness = 1.5 mm,use : To cut Wood Speci men Asp ect rati o b/a Inner diamet er in mm Outer diamete r in mm Numb er cracks length 17.5 mm. Crack end hole dia.mm Graph: Comparison graph FEM natural frequency results for cutter showing effect increased hole diameter radial slot end. For cutter no.5&6(frequency vs modes) Concluding Remark:-.natural frequency decreases as crack end hole diameter increases. 3 to34%reduction in natural frequency is achieved by 100% enlargement crack end hole diameter Analysis method iii) To find modes by exciter: Comparison mode shapes annular disk cutter no.1through exciter results and FEM(ANSYS) results showing similarity are given below: 5th 10 5 Matching Mode shapes for cutter no , IERJ All Rights Reserved Page 3

4 Showing 4th mode shape (0,2) Showing 2nd mode shape (1,0) VI.EXPERIMENTATION Conclusion results common for all specimen types:: frequency increases with increase in nodal diameter and both results FFT & FEM are matched to average 4% error which is acceptable. Comparison Mode shapes is done for annular disk cutters through exciter results and FEM- ANSYS results which found,similar modes shapes. Conclusion results specimen type I) : natural frequency decreases if air cooling holes are added to circular annular cutters. Conclusion results specimen type II) : frequency increases as the no. diametral cracks increases. increases. 10% change in the no. diametral cracks gives 7% to 40% change in natural frequency variable as per modes. Conclusion results specimen type III) : natural frequency decreases as crack end hole diameter increases. 3 to34%reduction in natural frequency is achieved by 100% enlargement crack end hole diameter sothat it is recommended that stress concentration hole diameter must be smaller than 5mm.Hence outcome we received is to increase the natural frequency by 1% we have to reduce the slot end stress cons. hole diameter by 30%approx. 2015, IERJ All Rights Reserved Page 4

5 REFRENCES [1].Weisensel G. N. Frequency information for circular and annular Plates,Journal sound and vibration, 1989, vol. 133, pp [2]..D.V.Bambill, S.La.Malfa, C.A.Rossit, P.A.A.Laura, Analytical and Experimental investigation on transverse vibration solid, circular and Annular plates carrying a concentrated mass at an arbitrary position with Marine applications, Journal ocean Engineering, vol31,pp [3].J.C. Bae and J.A. Wickert, free vibration coupled disk-hat Structures, Journal sound and vibration, (2000) 235(1), [4].M.Ambali, G.frosali, M.K.Kwak., Free vibrations annular plates coupled with fluids, Journal sound and vibration, 1996 vol.191(5),pp [5].S. S. Rao and A. S. Prasad, Vibrations annular plates including the Effects rotary inertia and transverse shear deformation, Journal Sound and Vibration, 1975, vol 42, [6].Vogel S. M. & Skinner D.W., Frequencies Transversely Vibrating Annular Plates, Journal Applied Mechanics, December, 1965, [7].Leissa Arthur W., 1969, Vibration Plates, NASA P160 Watson, GN, [8].K. Ramesh, D.P.S. Chauhan and A.K. Mallik, Free vibration annular plate with periodic diametral cracks, Journal sound and vibration, 1997, 206(2) [9].Murari P. singh, Bhabesh K.Thakur,Willam E. Sullivan, George Donald, Resonance identification for impellers,2003, Proceeeding thirty second Turbo machinary symposium. 2015, IERJ All Rights Reserved Page 5