Design and Analysis of Rotor Shaft Assembly of Hammer Mill Crusher

International Journal of Engineering and Management Research, Volume-3, Issue-2, April 2013 ISSN No.: 2250-0758 Pages: 22-30 www.ijemr.net

E.Vijaya Kumar

Assistant Professor, Department of Mechanical Engineering, Siddhartha Institute of Technology & Sciences, Ghatkesar, Hyderabad, INDIA

ABSTRACT The paper deals with the Design and analysis of shaft and rotor assembly for hammer mill crusher of capacity 0.1 (100kg/hr) tones per hour transmitting 20 B.H.P and a speed of 750 rpm. The design is based on the standard design procedure. In the present work by using the standard design procedure, diameter of rotor shaft of hammer mill crusher has been designed. The design should be safe when the values obtained from the present design procedure were compared with the values and results obtained from the analysis using Ansys package. When the shaft is rotated at rated speed (rpm) and the loads applied to the shaft it should not bend during rotation. When the shaft is rotated under free conditions, deflections will be created due to the critical speed of the shaft. To compare this deflection shaft was designed such that the natural frequency and speed is under limits. In this project the shaft and rotor assembly of hammer mill crusher was modeled using Pro-e modeling package and the FEM model of the shaft was developed using Ansys package. Meshing of the shaft model was done and the loads, stresses that were applied for the shaft to be checked out that the design should be safe one.

I. INTRODUCTION by being crushed into 1/4 inch or smaller size coal. Coal enters from the top and is violently A crusher is a machine designed to thrown against the breaker blocks by the reduce large solid material objects into a smaller hammers. The final crushing is done between the volume, or smaller pieces. Crushers may be used hammer faces and the screen bars. Then the to reduce the size, or change the form, of waste crushed coal goes to the conveyors below and is materials so they can be more easily disposed of carried to the storage bunker. Tramp iron or or recycled, or to reduce the size of a solid mix material that will not go out between the screen of raw materials (as in rock ore), so that pieces of bars is dropped into the iron pocket and is later different composition can be differentiated. removed. The final crushing is done between the Crushing is the process of transferring a force hammer faces and the screen bars. Then the amplified by mechanical advantage through a crushed coal goes to the conveyors below and is material made of molecules that bond together carried to the storage bunker. Tramp iron or more strongly, and resist deformation more, than material that will not go out between the screen those in the material being crushed do. Crushing bars is dropped into the iron pocket and is later devices hold material between two parallel removed. or tangent solid surfaces, and apply sufficient Hammer mill features: force to bring the surfaces together to generate  Material is reduced by impact from enough energy within the material being crushed free-swinging bar hammers so that its molecules separate from (fracturing),  Finished Product size controlled by or change alignment in relation to (deformation), grates or crusher sizes each other. The earliest crushers were hand-held  Materials can be reduced to granular stones, where the weight of the stone provided a powder at high rate. boost to muscle power, used against a stone  Heavy-duty cast-iron or carbon steel anvil. Querns and mortars are types of these construction crushing devices.  Right-hand or left-hand machine available  II. WORKING OF MACHINE Easy access for maintenance and crusher/grate change When coal is delivered to the hammer mill crusher, it is prepared for cyclone furnace firing Applications of Hammer mill crushers:

Material used for Shafts:  Recycling glass The material used for shafts should have the  Feed industry following properties:  Stone crushing 1. It should have high strength  Size reduction of waste materials 2. It should have good machinability.  Electronics recycling 3. It should have low notch sensitivity.  Ceramics 4. It should have good heat treatment  Pulverization of sea shells property.  Minerals 5. It should have high wear resistant  Wood particles for fuel wood property.  Limestone Depending on the requirement, the shafts can be

made of plain carbon steel or alloy steel. III. DESIGN OF SHAFT Designing of Shafts:

A shaft is a rotating machine element, The shafts may be designed on the basis of which is used to transmit power from one place 1) Strength and 2) rigidity and stiffness to another. The power is delivered to the shaft by In designing shafts on the basis of strength, the some tangential force and the resultant torque (or following cases may be considered: twisting moment) set up within the shaft permits 1) Shafts subjected to twisting moment or the power to be transferred to various machine torque only. linked up to the shaft. 2) Shafts subjected to bending moment The following stresses are induced in the only. shafts: 3) Shafts subjected to combined twisting 1. Shear stresses due to the transmission of and bending moment torque (i.e. due to torsional load). 4) Shafts subjected to axial loads in 2. Bending stresses (tensile or addition to combined torsion & compressive) due to the forces acting bending loads upon machine element like gears, pulleys etc. Shafts subjected to twisting moment or 3. Stresses due to combined torsional and torque only: bending loads. When the shaft is subjected to twisting moment (or torque) only, then the diameter of the shaft may be obtained by using the torsion IV. CLASSIFICATION OF equation. We know that

SHAFTS Shafts involved in power transmission may be Where, classified as T=Twisting moment acting on the shaft, 1) Transmission shafts are used to transmit J=Polar moment of inertia of the shaft power between source and the machines using about the axis of rotation, the power. They include line shafts, jackshafts Fs =Torsional shear stress, and and counter shafts. r=Distance from neutral axis to the outer most fiber i) Line shaft is a long continuous shaft, which receives power from =d/2 where the source and distribute to We know for round solid shaft, polar moment of different machines. inertia,

ii) Jackshaft is directly connected to the source of power and from which other shafts are driven. The equation may be written as iii) Counter shafts receive power from 4 T/πd = 2fs /32d line shaft and transmit to a 3 machine. T = fsπd / 16 Twisting moment (T) may be obtain by the 2) Machine Shafts are incorporated within the following relation: machine, such as crank shaft

In S.I units, power transmitted (in watts) by the 1) Guest’s Theory: According to maximum shaft, shear stress theory the maximum shear stress due to combined load is Let P=2πNT/60 or f = Shear stress induced to T=(P х 60)/2πN s twisting moment Where, f = bending stress (tensile or T=Twisting moment in N-m b compressive) induced to Bending moment N=Speed of the shaft in RPM According to Maximum shear stress theory, the In M.K.S units, horse power transmitted by the maximum shear stress in the shaft shaft,

P=2πNT/4500 f max) =√[( f )2 + 4(f )2] T=P х 4500/2πN s ( b s

Where, Substituting the values of f & f as per above T=Twisting moment in N-m and b s equations N=Speed of the shaft in rpm

3 2 2 πd х fs = 16 х √ (M +T ) 3 2 3 Shafts subjected to bending moment only: fs =√ (32M/ πd ) +4(16T/ πd )

When the shaft is subjected to a bending moment only, then the maximum stress (tensile or 3) Rankine’s Theory: According to maximum normal stress theory, the compressive) is given by the bending equation. We know that maximum normal stress in the shaft

2 2 fb (max) = (fb/2) +√ [( fb) +4(fs) ] 3 2 2 Where, fb = (16/ πd ) х (M+√ (M +T )) M=Bending moment, N-mm Shafts subjected to fluctuating loads: In above equations shafts are subjected to I=Moment of inertia of cross-sectional area of the shaft about the constant twisting moment & bending moment Axis of rotation, mm4 but in actual practice shafts are subjected to 2 fluctuating torque & bending moments. In order Fb =Bending stress, N/mm and Y=Distance from neutral axis to the to design such shafts like line shaft &counter outer-most fiber, mm shaft combined shock & fatigue factor to be We know that, Moment of Inertia, for a round considered for calculating33 twisting moment solid shaft and bending moment I = πd4 /64 and Substituting these factors in above equations For maximum shear stress theory y = d/2 3 2 2 Substituting these values in the above equation (πd /16) х fs=√ [(Km хM) + (Kt хT) ] =Te Bending Moment M= (πd3 /32) х fb For maximum normal (tensile or compressive) theory 3 Shafts subjected to combined twisting and (πd /16) х fs= [(Km хM) /2] +√ [(Km хM) 2+ (K хT) 2] =M bending moment: t e Where: When the shaft is subjected to combined M= Bending Moment twisting and bending moment then the shaft must fb = Bending stress be designed on the basis of the two moments T = Twisting moment (Torque) simultaneously. The maximum induced stress upon the shaft can be obtained by considering the following fs = Tensional shear stress theories. Km = Combined shock & 1) Maximum shear stress theory or Guest’s fatigue factor for bending theory. It is used for ductile materials Kt -= Combined shock & such as mild steel. fatigue factor for twisting 2) Maximum normal stress theory or d = diameter of the shaft Rankin’s theory. It is used for brittle materials such as cast iron. Shaft calculations:

Given Data: We know

• Power transmitted by the shaft=75kw or Π /16 х fs х d³ =√ [(Km х M)²+(Kt х T)²] 100hp Π /16 х 650 х d³ • Speed of the shaft =750 rpm =√[(2x54000)²+(2x9549) ²]

• Weight of the rotor shaft =2000kg d=9.5cm (or) 95mm

• Beam length =165cm Deflection of Shaft:

• Arm length =27cm Actual deflection δ = (Wl³/384) х E х I

• Shear stress =650 kg/cm² = 2000/384x2.1x10^6x1198.4 • Bending stress =300 kg/cm² = 0.009246cm Twisting Moment: Allowable deflection = L/1500 Power p=2πNT/4500 = 0.11cm 100= (2π х 750 х T)/4500 Factor of safety = Allowable deflection T=95.49 kg-m (or) 9549 kg-cm / Actual deflection

We know = 0.11/0.009246

T= (π/16) х fs х d³ = 11

9549= π /16 х 650 х d³ Selected diameter of shaft =122.7mm ≈ 125mm d=4.21 cm (or) 42.1mm V. DESIGN OF BEARINGS Bending Moment:

M =Weight of Screen х Arm Length A bearing is a machine element, which supports another moving machine element, = 4500 х 27 knows as journal. It permits a relative motion between the contact surfaces of the member, =54000 kg-cm while carrying the load. The efficiency of the mechanical system depends to a great extent on We know the efficiency of its bearings. A necessity for the efficient working of the M = (π /32) х fb х d³ bearings is that the running surface should be adequately supplied with lubricant. For this 54000= π /32 х 300 х d³ purpose the oil is supplied through a lubricating ring firmly clamped on the shaft at the after end d=12.2cm (or) 122.3mm and a wiper device fitted in the upper part. This device, together with correctly formed oil Combined Bending and Twisting Moment: grooves in the bearing shells ensure that in We know that bearings the oil supply is maintained in all circumstances even at low revolutions.

Π /32 х fb х d³= [M+√M²+T²]/2 VI. SPHERICAL ROLLER Π /32 х 300 х d³= [54000 +√ (54000²+9549²)]/2 BEARING d=12.2cm (or) 122.7 m A spherical bearing is a bearing that Fluctuating Loads: permits angular rotation about a central point in 25 two orthogonal directions within a specified axial direction only. The outer surface of the angular limit based on the bearing geometry. inner ring and the inner surface of the outer ring Typically these bearings support a rotating shaft are collectively considered the raceway and they in the [bore] of the inner ring that must move not slide against each other, either with a lubricant or only rotationally, but also at an angle. a maintenance-free based liner. Some spherical Construction of spherical bearings can be bearings incorporate a rolling element such as a hydrostatic or strictly mechanical. A spherical race of ball bearings, allowing lower friction. bearing by itself can consist of an outer ring and The design of this bearing permits radial load an inner ring and a locking feature that makes the and heavy thrust load in either direction. inner ring captive within the outer ring in the

Fig. Spherical Roller Bearing

VII. BEARING LIFE CALCULATION

Type of bearings used: spherical roller bearings Selected diameter of the shaft=125mm N=speed of the shaft=750 r.p.m Lh=nominal/rated speed in hours =10000 hrs, 10hrs per a day heavy shock load Then life of bearing in millions of revolutions 6 L=60NLh/10 L= (60 х 750 х 10000)/106 L=4500 millions of revolutions Where L is life that 90% of a group of apparently identical group of bearings will complete

Fig Rotor Assembly with Bearings

VIII. ELEMENT USED FOR ANALYSIS BEAM3 is a uni-axial element with tension, compression, and bending capabilities. The element has three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the nodal z-axis. Other 2-D beam elements are the plastic beam.

2D Beam Analysis:

Fig Deformed Shape

Fig Von Mises Stress

3D Shaft Analysis:

Fig Deformed Shape

Fig: Rotor Shaft Assembly Mesh in Ansys

Fig: Deformations in Ansys

Fig. Von Mises Stress Now we can see the stresses in shaft. 10.As per analysis of shaft and rotor Maximum stress developed in shaft is 36.15 assembly done in Ansys, deflection values N/mm2 which is far less than the yield strength of the shaft and rotor assembly are 0.008637 of the material, which is 45 N/mm2. So that shaft and 0.006404. will not fail under these conditions REFERENCES IX. CONCLUSIONS 1. Scham Tickoo, “Pro-Engineer- As per drawings and information provided 2001”, 2nd edition. by Bevcon, 3D models are developed in Pro-e 2. J.N.Reddy, “An Introduction and the shaft of crusher is analyzed in Ansys to Finite Element Method”, 3rd package. edition. 1. Based on calculations and analysis 3. R.K.Allan,“Rolling Bearing “, reports the safe diameter is selected as 3rd edition 125mm, which is safe. 4. S.S.Rao, “Mechanical 2. Factor safety for selected diameter is Vibrations’’, 4th edition. 11. This factor of safety chosen for crusher to address sudden impact and 5. Richard G.Budynas Jata, shock loads created by the material. “Advanced Strength and Applied Stress Analysis”, 2nd 3. Deflection of shaft as per theoretical edition calculations is 0.009mm. . 4. Deflection of shaft in Ansys analysis is 6. V.B. Bhandari, “Introduction 0.007mm (load applied on shaft only). to Machine Design”. 5. Deflection of total rotor assembly in 7. Robert L.Norton, “Machine nd edition Ansys is 0.006mm. Design”, 2 . 6. Selected bearing for this application 8. Hall, Holowenko Laughlin, based on shaft diameter 125mm is “Theory and Problem of heavy-duty spherical roller bearings on Machine Design”, Schanm’s adapter sleeve. series. 7. 3D models developed in pro-e 9. PERRY, r.h., and d.w.Green, & analyzed reports have been “Perrys Chemical Engineers” submitted to Bevcon for their handbook, “7th ed. consideration in their designs 10. F.D.Bond, “Crushing 8. We suggested to consider this analysis Calculations”. report to reduce the bearing diameter 11. Pennsylvania, “Crushing metal for optimizing the rotor design Technologies”. of the hammer mill crusher. 12. P.C.Hayes, “Construction of Hammer 9. Bearing life for selected bearings is 450 Mill Crusher”. Millions of revolutions.