Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 123 Rigidity and Dynamic Analysis of Lathe Bed P. Karunakar, A. Ramesh and S. Vidya Sagar Abstract--- Lathe is the most important machine tool, It is used to perform number of operations. The requirements of lathe are zero deflection & high rigidity heavy type lathe beds. The main objective of this paper is to develop geometric model of lathe structure, stress and deflection analysis of lathe bed structure by considering the specifications of Lathe bed. Here we determine the natural frequencies of lathe structure and observed mode shapes and also we found the amplitudes at various critical location ie., A 1 120, A 2 203 by two methods(1) Model Analysis (2) Hermonic Analysis with respect to lathe speed by finite element approach. Expected Results--- Highest Rigidity and Dynamic Stability Keywords--- Lathe Rigidity, Mode Shapes & Natural Frequencies I. INTRODUCTION Machine tools are power driven devices designed to produce a required geometrical surface. The purpose of machine tools is to produce components with greater precision and more complex forms than is possible by the hand tools (or) by the primary forming processes. Various machine tools are employed to shape many commercial products from raw materials by cutting away the excess materials. The lathe is the most important of all machine tools employed in industry (or) workshops. The most significant factor in evolution of the lathe as a machine tool for turning metal was the development of the slide rest by HENRY MAUDSLEY shortly before 1800. For the first time the cutting tool could be firmly fixed to a carriage and constrained to slide along a surface in a direction parallel to the axis of the work. II. LITERATURE REVIEW The function of lathe is to remove excess material in the form of chips by rotating the work piece against a cutting tool. Feeding the tool into the work piece parallel to the axis of the rotation results in the formation of cylindrical shape and is referred as turning. If the tool moves perpendicular to the axis it produces a flat surface and is referred as facing. Thus the lathe can be used to generate both a cylindrical surface and flat surface. Besides turning and facing, a wide range of works can be performed on it, including taper turning, drilling, boring P. Karunakar, B.Tech, M.Tech., Assistant Professor, Christhu Jyothi Institute of Technology and Science (CJITS), Jangaon, Warangal, AP, India. E-mail: karunakarkanna@gmail.com A. Ramesh, B.Tech. M.Tech., Assistant Professor, Christhu Jyothi Institute of Technology and Science (CJITS), Jangaon, Warangal, AP, India. E-mail: ramesh340mech@gmail.com S. Vidya Sagar, B.Tech. M.Tech., Assistant Professor, BITS., Narsampet, Warangal, AP, India. and thread cutting. Milling and grinding may also be done on it by suitable attachments. III. TYPES OF LATHE Lathes are versatile machines and are manufactured in a variety of types and sizes but they operate on same principles and perform same function. According to the design and construction, the lathes are classified as: 1. Speed lathe 2. Engine lathe 3. Bench lathe 4. Tool room lathe 5. Capstan and turret lathes 6. Special purpose lathe 7. Automatic lathe 1. The Speed Lathe The speed lathe, in construction and operation, is the simplest of all types of lathe. It consists of a bed, a headstock, a tailstock and a tool post mounted on an adjustable slide. There is no feed box, lead screw (or) conventional type of carriage. The tool is mounted on the adjustable slide and is fed in to work purely by hand control. This characteristic of the lathe enables the designer to give high spindle speeds which usually range from 1200 to 3600 rpm. As the tool is controlled by hand, the depth of cut and thickness of chip is very small. The headstock construction is very simple and only two (or) three speeds are available. Light cuts and high speeds necessitate the use of this type of machine where cutting force is minimum such as in wood working, spinning, centering, polishing, etc. The Speed lathe has been so named because of the very high speed of the headstock spindle. 2. The Engine Lathe (Or) Center Lathe This lathe is the most important member of the lathe family and is the most widely used. The term engine is associated with the lathe owing to the fact that early lathe were driven by steam engines. Similar to the speed lathe, the engine lathe has got all the basic parts, e.g. bed, headstock, and tailstock. But the headstock of an engine lathe is much more robust in construction and it contains additional mechanism for driving the lathe spindle at multiple speeds. Unlike the speed lathe, the engine lathe can feed the cutting tool both in cross and longitudinal direction with reference to the lathe axis with the help of a carriage, feed rod and lead screw. With these additional features an engine lathe has proved to be a versatile machine adapted for every type of lathe work. 3. The Bench Lathe This is a small lathe usually mounted on a bench. It has practically all the parts of an engine (or) speed lathe and it performs almost all the operations, its only difference being in the size. This is used for small and precision work.
Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 124 4. The Tool Room Lathe A tool room lathe having features similar to an engine lathe is much more accurately built and has a wide range of spindle speed ranging from a very low to a quite high speed up to 2500 rpm. This is equipped, besides other things, with a chuck, taper, turning attachment, draw in collect attachment, thread chasing dial, relieving attachment, steady and follower rest, pump for coolant etc. This lathe is mainly used for precision work on tools, dies, gauges and in machining work where accuracy is needed. The machine is costlier than an engine lathe of the same size. 5. The Capstan and Turret Lathe These lathes are development of the engine lathe and are used for production work. The distinguishing feature of this type of lathe is that the tailstock of an engine lathe is replaced by a hexagonal turret, on the face of which multiple tools may be fitted and fed in to the work in proper sequence. The advantage is that several different types of operations can be done on a work piece without re-setting of work (or) tools, and a number of identical parts can be produced in the minimum time. 6. Special Purpose Lathe As the name implies, they are used for special purposes. They are classified as follows. (a)wheel lathe (b)gap bed lathe (c)t-lathe (d)duplicating lathe The wheel lathe is made for finishing the journals and turning the thread on railroad car and locomotive wheels. The gap bed lathe, in which a section of the bed adjacent to the headstock is recoverable, is used to swing extra-large diameter pieces. The T-lathe, a new member of the lathe family, is intended for machining of rotors for jet engines. The axis of the lathe bed is at right angle to the axis of the headstock spindle is the form of a T. The duplicating lathe is one for duplicating the shape of a flat (or) round template on to the work piece. Mechanical, air and hydraulic devices are all used to coordinate the movements of the tool to reproduce accurately the shape of the template. 7. Automatic Lathe These are high speed, heavy duty, mass production lathes with complete automatic control. Once the tools are set and the machine is started it performs automatically all the operations to finish the job. The changing of tools, speeds, and feeds are also done automatically. After the job is complete, the machine will continue to repeat the cycles producing identical parts even without the attention of an operator. An operator who has to look after five (or) six automatic lathes at a time will simply look after the general maintenance of the machine and cutting tool, load up a bar stock and remove finished products from time to time. Force System during Turning The force system in the general case of conventional turning process is shown in figure (a). The resultant cutting force R is expressible by its components. P x known as the feed force in the direction of the tool travel. P y called as thrust force in the direction perpendicular to the produced surface and P z is the cutting force (or) Main force acting in the direction of cutting velocity vector. These directions have been chosen for their suitability of being determined by properly designed tool force dynamometers. After determining the individual components P x, P y and P z, the resultant force, R can be evaluated. R=(P 2 x +p 2 y +p 2 z ) 1 / 2 (1) This three-dimensional force system can be reduced to a two dimensional force system if in the orthogonal planeπ 0 the forces are considered in such a way that the entire force system is contained in the considered state, when R=(P 2 z +P 2 xy ) 1 / 2 (2) R=( P x 2 +P y 2 ) 1 / 2 (3) a) Cutting Forces in Conventional Turning Process This is possible when the force P xy is contained in plane π 0 which is possible only under consideration of free orthogonal cutting. This corresponds to orthogonal system of the first kind for which the conditions are: (1) 0<φ<90 0 (2) λ=0 (3) The chip flow direction lies on the plane π 0 (4) Figure (b) shows the cutting force for the case of orthogonal system of first kind. b) Reduced two dimensional force system π o for orthogonal system of the first kind with λ=0 and 0<φ<90 0 An orthogonal two-dimensional system of second kind can be obtained by choosing λ and φ in such a manner that either P x (or) P y can be made zero.
Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 125 For an orthogonal system of the second kind, P y is made zero by having λ=0 and φ=90 0. When the two-dimensional force system is R= (P z 2 +P x 2 )1/2 (4) Figure (C) shows the disposition of cutting forces in plane orthogonal turning with λ=0 and φ=90 0. Fig Force System at the Shear Plane Let P s be the force cutting tangentially at the hypothetical single shear plane causing slip and deformation. P n is the compressive load on the shear plane. From the geometry of figure (d) P s = ON-QN = ON-MS = P z cosβ - P xy sinβ (5) 3-D Model of Lathe AutoCAD package is used to model the lathe bed structure. Lathe Bed Considered for the Analysis has to Following Dimensions Dimensions of Manufacturer: PANTHER ENGG. & CO. Dimensions of the lathe bed: Total length of the lathe bed = 1945mm Total width of the lathe bed = 255mm Total height of the lathe bed = 306mm The distance between the ribs = 190mm Dimensions of the RIB: Height of the rib = 160 mm Width of the rib = 100 mm Thickness of rib = 20 mm Finite Element Modeling of Lathe Bed in Ansys After modeling the lathe in Auto CAD, it is stored in the form of SAT files and exported to the ANSYS package. ANSYS is an analysis type software package in which forces, stresses, strains, deformations, vibration and also heat transfer can be analyzed. The following procedure shows the Static Analysis of the lathe bed in ANSYS. When the modeled component is imported in to the ANSYS, only wire frame model can be viewed. So this wire frame model is first converted in to Solid model by using the plot controls volumes command. Figure show the wire frame and the solid model as the model of the lathe bed is imported to ANSYS. And P n = QT = QS + ST= MN + ST = P z sinβ + P xy cosβ (6) Hence = (7) Further P n =P s tan (β+η-ϒ 0 ) (8) Modeling of the Lathe Bed in Autocad For the analysis of the lathe bed, solid model of the lathe is required. There are different types of modeling software s such as AutoCAD, Pro-E and CATIA etc. ANSYS software also facilitates to model some simple components having simple geometry. If the component s geometry is complex other modeling software s are used. AutoCAD is one of the modeling software in which we can model components of moderate complexity. If the complexity of the component is more, Pro-E and CATIA software s are used. Solid Model Converted in ANSYS Wire Frame Model in ANSYS
Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 126 Material Properties The bed is made up of Cast Iron (Grey cast iron). Hence, the following properties are adopted. i) Young s modulus for lathe bed (Eφ) =1*10 5 N/mm 2 ii) Poisson s ratio for lathe bed (μ) =0.23 iii) Density of material (ρ) =7800*10-9 Kg/mm 3 Meshing of the Component Meshing is defined as creation of nodes and elements on the component. There are two types of meshing options. One is Auto Meshing in which the nodes and the elements are created automatically. By this method we cannot control the size and the number of the nodes and elements of the component. The other is the Manual Meshing in which the size and number of the nodes and elements can be controlled. The procedure for generating a mesh of nodes and elements consists of three main steps: i) Set the element attributes. ii) Set Mesh Control (optional). ANSYS offers a large number of mesh controls, which you can choose from to suit your needs for description of these Mesh Controls. Mesh Model of Lathe Bed in ANSYS Displacement Constraints The bottom end of the lathe bed is fixed in all the directions i.e. the displacement to the nodes on the bottom end is zero. This is made in order to provide support to the component when the forces are applied. To apply the displacement constraint, the surface area of the lathe bed i.e. A 1 120, A 2 203 are selected. The nodes on this are selected and the DOF command is applied. This displacement constraint is applied to the lathe bed. The displacement constraints are given at the bottom of the bed and this is seen in figure. Generate the Mesh The second step, setting mesh controls, is not always necessary because the default Mesh Controls are appropriate for many models, if not control are specified, the program will use the default settings on the DE SIZE command to produce a free mesh. As an alternative, you can use the smart size feature to produce a better quality. Free (Or) Mapped Mesh Before meshing the model, and even before building the model, it is important to think about whether a free mesh (or) a mapped mesh is appropriate for the analysis. A free mesh has no restrictions in terms of element shapes, and has no specified pattern applied to it. Compared to a free mesh, a mapped mesh is restricted in terms of the element shape it contains and the pattern of the mesh. A Mapped area mesh contains either only quadrilateral (or) only triangular elements, while a mapped volume mesh contains only hexahedron elements. In addition, a mapped mesh typically has a regular pattern, with obvious rows of elements. If you want this type of mesh, you must build the geometry as a series of fairly regular volumes and areas that can accept a mapped mesh. So for accurate analysis, the lathe bed require fine meshing i.e. small element size and the regions where the loads are not required their normal sized elements are sufficient. The meshed model in the ANSYS can be seen in figure. Displacement constraints For applying the loads, the nodes on the guide ways are selected and load is applied to these nodes. Force The force acting on the lathe bed can be calculated in the following way. The specifications of the PANTHER ENGG.CO are as follows, i) Motor HP/KW = 2/105 ii) Spindle speed range = 45-938 rpm iii) Spindle hollow (D) = 42mm. iv) Power (P) = 2πNT/60 Where, N Spindle speed in R.P.M T Torque in N-m. From above formulae Torque can be calculated as: T = P*60/2πN N-m. T = 1.5*1000*60/2π*45,T = 318.30 N-m. T = 318.308*10 3 N-mm. We know that Torque = F * r F is the force, r is the radius of hollow spindle. r = D/2= 42/2, r = 21mm.
Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 127 F = T/r = 318.30*10 3 /21, F = 15157.142 N. This is the force acting on the lathe bed. This force is divided equally and applied on selected nodes of the lathe bed. So the force on each node (F N ) is given as F N = 15157.142/1063, F N = 14.258 N/node. This force is applied on the selected nodes of the lathe bed which are selected from head stock side of the lathe bed. The load applied on the bed can be seen in the figure. Deflection along Load Applied a) Nodes with applied Loads b) Lathe Bed Model with all the Displacement Constraints IV. REVIEW OF THE RESULTS After solving the problem the result can be viewed by the help of Plot Results Command in the Post Processor. Figure shows the Von-Mises stress acting on the surface of the lathe bed. The scale shown in the figure represents the variation of the stresses acting on the surface of the lathe bed. The Blue colored portion indicates the maximum stressed part of the lathe bed and the Yellow colored portion indicates the minimum stressed part of the lathe bed. Maximum Stress = 6594 N/mm 2 Minimum Stress = 0.729 N/mm 2 Deformed & Un-deformed Shape of Lathe Bed Modal Analysis Modal Analysis is used to determine the vibration characteristics (natural Frequencies, mode shapes) of a structure (or) a machine component while it is designed it is also can be starting point for another more detailed dynamic analysis, such as transient dynamic analysis, harmonic analysis (or) a spectrum analysis. Modal Analysis Inputs Lathe bed modal analysis options: i) Method of Extraction: Bloc Lanczos Method ii) Number of modes to extract: 3 iii) Frequency (range) :0-500 Hz With these options as specified the modal analysis is hence solved and the following table shows the natural frequencies. Table Modal Frequencies S.No Mode No. Frequency (Hz) 1 1 39.424 2 2 75.570 3 3 82.091 Modal analysis also derives the deformed shape when exited at mode frequencies. These can be seen in the figure. Deformed & Un-deformed Shape (First Frequency) von-mises Stress plot(inset the Maximum Stress Zone) The deflection along the axis of load applied direction of lathe bed is also plotted and found to be 0.2603 mm
Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 128 Deformed & Un-deformed Shape (Second Frequency) Deformed & Un-deformed Shape (Third Frequency) Harmonic Analysis Harmonic response analysis is the ability to predict the sustained dynamic behavior of structure, thus enabling to verify whether (or) not design will successfully over comes the resonance fatigue and other harmful effects of forced vibrations. The idea is to calculate the structures response at several frequencies and obtain a graph of some response quantity (usually displacement versus frequencies. Peak responses are than identified on the graph. Harmonic Analysis Inputs Apart from the loading of the model inputs such as frequency and the number of sub steps have to be defined. The following are the options to be given: No. of sub steps : 5 Frequency (Range) : 40-80 Hz The frequency range that is taken here as input is based on the results observed form the modal analysis natural frequencies. Frequency and Amplitude Frequency Amplitude Phase 40 0.382241 180 50 0.915262 180 60 1.92860 180 70 5.83142 180 80 5.49736 180 The variation of the amplitude with the change in frequency is plotted and hence can be seen in figure Amplitude vs. Frequency graph Amplitudes that are observed are maximum at node number 9126. Comparison of Two Types of Lathe Beds (Lathe bed with ribs & Lathe bed without ribs.): Von-mises Stress with Ribs Deformed & Un-deformed Shape with Ribs Von-mises Stress without Ribs Deformed & Un-deformed Shape without Ribs Modal Frequencies of Lathe Bed with Ribs: S. No Mode No Frequency (Hz) 1 1 39.424 2 2 75.510 3 3 82.09 Modal Frequencies of Lathe Bed without Ribs: S. No. Mode No Frequency (Hz) 1 1 31.902 2 2 33.510 3 3 77.863 Amplitude & graph (with ribs) at Maximum stress acting node i.e.-9126 Frequency Amplitude Phase 40 0.382241 180 50 0.915262 180 60 1.92860 180 70 5.831418 180 80 5.49736 180
Advance Research and Innovations in Mechanical, Material Science, Industrial Engineering and Management - ICARMMIEM-2014 129 P. Karunakar, B.Tech, M.Tech., Assistant Professor, Christhu Jyothi Institute of Technology and Science (CJITS), Jangaon, Warangal, AP, India. E-mail: karunakarkanna@gmail.com Amplitude vs. Frequency Amplitude & graph (without ribs) at maximum stress acting node i.e.-6483. Frequency Amplitude Phase 40 0.382241 180 50 0.898673 180 60 1.63101 180 70 2.9443 180 80 6.78063 180 V. RESULTS AND CONCLUSION The solid model of the lathe bed has been modeled in the solid modeling software AutoCAD. This solid model is exported to the ANSYS as SAT file format. General purpose finite element analysis software. Conclusion from Above Study Type With ribs Without ribs Von-Mises stress (max) 6594N/mm 2 9123N/mm 2 Von-Mises stress (min) 0.729N/mm 2 0.7236Nmm 2 Maximum deflection 1.42mm 2.078mm Deflection at resonance frequency 5.8314mm (At 70Hz) 6.78064mm (At 80 Hz) By observing the above values, stress distribution, deflection and amplitudes are less in case of lathe bed having ribs. Hence good surface finish, dimensional accuracy etc, can be achieved. Hence lathe beds must have the ribs. A. Ramesh, B.Tech. M.Tech., Assistant Professor, Christhu Jyothi Institute of Technology and Science (CJITS), Jangaon, Warangal, AP, India. E-mail: ramesh340mech@gmail.com S. Vidya Sagar, B.Tech. M.Tech., Assistant Professor, BITS., Narsampet, Warangal, AP, India. VI. CONCLUSION Static and dynamic analysis on the lathe bed is performed by using ANSYS 10.0 software. The maximum Von-Mises stress acting on the lathe bed are found. Deformation accruing in the lathe bed during the force observed. Natural frequencies and mode shapes of the lathe bed are found. Deflections at resonance frequency at various critical locations with respect to the lathe speed are found. Lathe with ribs and without ribs are compared and found that with ribs offers more rigidity. REFERENCES [1] Chandrupatla T.R., Ashok D.B., Introduction to Finite Element in Engineering, 3e, PHI, 2002. [2] ANSYS 10.0 Users manual, Swanson Int, 2007. [3] S.K. Hajra Choudhury, A.K. Hajra Choudhury Nirjhar Roy Elements of workshop technology (Vol.: II Machine tools) [4] S.K. Basu and Battacharya theory of metal cutting, Metropolitan Publisher.