Vibration analysis of lathe structrure due to gear defect using fem 02

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Vibration analysis of lathe structrure due to gear defect using fem 02

  1. 1. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 CHAPTER 1 I TRODUCTIO 1.1 GE ERAL I TRODUCTIO Machine condition monitoring (MCM) involves the continuous analysis of operational equipment and the identification of problems before component breakage or machine failure. One of the main challenging problems of present day machine tools is the development of machine tools with high vibration proof qualities. Vibration ranks among the most destructive forces in the machine tools. Vibration influences the operation, performance and life expectancy of the machine tools. Deterioration in the machine running conditions always produces a corresponding increase in the vibration level. By monitoring vibration level it is possible to obtain information about the machine condition. Excessive vibration in the rotating machineries is the major cause of premature bearing failure and can lead to disastrous machinery breakdown. The end result is a costly unscheduled plant shutdown. Vibration can be caused by a variety of factors. This includes unbalance-rotating elements, misalignment of bearings, looseness of parts and resonance from machineries. However, the most common cause of machine vibration is unbalance. It is the most damaging one and informs most about the machines condition. Hence there is a need to have a predictive maintenance program for rotating machineries. The objective is to detect a change in the vibration levels over a period of time and to act on that information which results in increased productivity, improved product quality etc. Most of the basic information required for the diagnosis of vibration problems is provided by the frequency analysis of the vibration. The major characteristic, which must be identified in the investigation of a vibration problem, is the frequency at which vibration is occurring and for this purpose frequency domain analysis of the vibration present is considered. Useful information can also be obtained by time domain analysis wherein the recording and the study of the vibration is analyzed which varies with time. Lathe is one of the most versatile and complex machine tool used in manufacturing industries for producing cylindrical work pieces. The quality of the finished products M-Tech Thesis 1 P.E.S.C.E., Mandya
  2. 2. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 depends mainly on the stability and rigidity of different machine components of a lathe. The resulting markings on the finished work piece are related to the amplitude and frequency content of the vibration present. A bearing is the most common critical component in a lathe. Proper performance and functioning of bearings has always been a major concern in rotating machinery. The shaft in the gearbox rotates at various speeds by combination of the different meshing gears and hence the gear loads and the bearing loads vary leading to innumerable computations. Thus the spindle bearings and the gearbox are found to be the critical elements of the lathe on which condition monitoring has to be concentrated. The Finite Element Analysis has become the most popular choice of practicing engineers to solve the real life problems of vibration, stress and heat flow analysis of machine tools. General-purpose finite element software’s provide the necessary tools to perform such analysis for a wide variety of problems without compromising accuracy. The finite element model of a lathe was developed by using finite element package A SYS 7.1.The lathe model was made up of elastic shell elements SHELL 63, structural mass element MASS 21, beam elements BEAM 188 and spring elements MATRIX 27. The finite element software A SYS 7.1 provides the necessary tools to perform modeling as well as analysis. The objective of the present work deals with the study of the unbalance forces generated by the various machine elements like spindle, chuck, pulley shafts, spindle shafts, gear shafts and the effect of gear mesh frequencies. The effect of these unbalance forces on the machine structure was analyzed by frequency domain and time domain approach. Transient dynamic analysis was also carried to study the effect of defect present in the gear. The experimentation will be carried out on the lathe by using the instrument Machine Condition Tester T 30 that was compatible with the computer. Vibration velocities were measured on the bearing housing by placing vibration transducer on the critical points for the different spindle speeds. The experimental data obtained from Machine Condition Tester T 30 were used to analyze the condition of the machine elements and also the effects of the vibration level on the structure. M-Tech Thesis 2 P.E.S.C.E., Mandya
  3. 3. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 1.2 OBJECTIVE OF THE WORK The objective of the present work was to conduct theoretical and experimental analysis to monitor the machine elements in the lathe. Finite Element Modeling and analysis I Modeling of a lathe structure by using elements like elastic shell elements SHELL 63, structural mass element MASS 21, beam elements BEAM 188 and spring elements MATRIX 27. II To carry out the Modal analysis of a lathe structure. Determine mode shapes of the structure, and its corresponding natural frequencies. III To carry out the Harmonic Response Analysis by using both the frequency domain and time domain for the various unbalance forces present on the rotating machineries. IV To carry out the Transient response analysis and to know the response of the structure for the induced defect in gear. Experimental Method I Measurement of RMS vibration velocity from the Gear box of an E TERPRISE 1330 lathe for different spindle speeds by using MACHI E CO DITIO TESTER T 30 equipment. 1.3 ORGA IZATIO OF THE THESIS The thesis has been organized in the following manner: Chapter 2 deals with the brief literature survey carried out related to the present work, Introduction to condition monitoring, types of condition monitoring, advantages of condition monitoring, vibration monitoring and an characteristics of gear defects. Chapter 3 deals with the finite element method and analysis, steps involved in doing finite element analysis, finite element modeling and analysis procedures. Chapter 4 will discuss about the experimental procedure, specification of enterprise lathe 1330, machine condition tester T30 vibration measurement procedure. Chapter 5 deals with the results and discussion of both the experimental and theoretical analysis. Chapter 6 explains the conclusion of the project work and scope for further improvement. M-Tech Thesis 3 P.E.S.C.E., Mandya
  4. 4. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 CHAPTER 2 LITERATURE SURVEY 2.1 REVIEW OF PAPERS Several researches have been done in the field related to condition monitoring. Condition monitoring is applied as a technique to improve productivity, efficiency and reliability of the machine tool and its operations. Following are the papers related to the field of condition monitoring of gearboxes. Dr. Ramachandra A. et.al [1] have discussed about the vibration analysis of machines and various types and methods of condition monitoring. They also dealt with various methods of condition monitoring of ball and roller bearings and presented some case studies wherein the SPM was useful in finding the condition of the bearing thereby saving the cost, work of replacement and loss of production. Grzegorz Litak and Michael I. Friswell [2] gave the information about Dynamics of a Gear System with Faults in Meshing Stiffness. Gearbox dynamics is characterized by a periodically changing stiffness. In real gear systems, a backlash also exist that can lead to a loss in contact between the teeth. Due to this loss of contact the gear has piecewise linear stiffness characteristics, and the gears can vibrate regularly and chaotically. In this paper we examine the effect of tooth shape imperfections and defects. Using standard methods for nonlinear systems we examine the dynamics of gear systems with various faults in meshing stiffness. J. Antoni Randall [3] in the paper titled “Differential Diagnosis of Gear and Bearing faults” discusses the vibration-based diagnosis of rolling element bearings in the presence of strong interfering gear signals from the gearboxes. A strong emphasis is placed on how to distinguish between gear and bearing faults where the two signals may interact through the analysis of their vibration signals. The key idea consists in recognizing gear signals as purely periodic, whereas bearing signals experience some randomness. This is demonstrated by introducing a comprehensive model for the vibration generating process of bearing faults and the distributed faults. M-Tech Thesis 4 P.E.S.C.E., Mandya
  5. 5. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 W. J. Wang and P. D. Mc Fadden [4] describe the decomposition of gear motion and the related dynamic measurements for the condition monitoring and fault diagnosis of gearboxes. In the case of gearbox monitoring, the teeth of the gears are the components to be monitored. The important signal generated in a gearbox is the meshing vibration, which propagates through all kinds of media and via all possible routes. The vibration signal measured carries the information describing the condition of the gears. In gear condition monitoring, a kinematics analysis can be performed by applying the various static and dynamic loads on the gear. Any change in the condition such as wear, a fatigue crack will cause some change in the motion of the gear. It is known that the tooth meshing vibration of the gears is caused by the motion errors. The motion errors of the gear in quantified by several motion error functions, which may be taken as indicators of the condition of the gear. The motion error signal is separated according to fundamental frequencies into the harmonic error and the residual error, which are used to quantify the gear condition. Analysis of the time domain average of a gearbox casing vibration signal enables early detection of gear damage. Zeping Wei [5] discuses about Current methods of calculating gear contact stresses use Hertz’s equations, which were originally derived for contact between two cylinders. To enable the investigation of contact problems with FEM, the stiffness relationship between the two contact areas is usually established through a spring placed between the two contacting areas. This can be achieved by inserting a contact element placed in between the two areas where contact occurs. The results of the two dimensional FEM analyses from A SYS are presented. These stresses were compared with the theoretical values. Both results agree very well. This indicates that the FEM model is accurate. Paula J. Dempsey and James J. Zakrajsek of Load Effects on ASA [6] discuses about Minimizing A4 Gear Vibration Diagnostic Parameter and expressed formulation and fluctuation load during destructive pitting. A change to the calculation of A4 is required to minimize the effect of a fluctuating load on A4. This change, A4 reset, is made when the load increases or decreases by a given percentage. For this application, a 10 percent load change was used. For A4 reset, when the load changes by 10 percent, the denominator resets to the square of the variance of the same reading, and a new average variance is calculated starting with the reading measured when the load changed. Each time the load changes by 10 percent, the first reading in the average variance resets to the first reading M-Tech Thesis 5 P.E.S.C.E., Mandya
  6. 6. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 when the load changed. For the purpose of this paper, damage is defined as destructive pitting if the depth is greater than 1/64 inches and the diameter is less than 1/16 inches. Paula J. A [7] of ASA Discussed about Comparison of Vibration and Oil Debris Gear Damage Detection Methods Applied to Pitting Damage, Two vibration diagnostic parameters were used in this analysis, FM4 and A4. FM4 was developed to detect changes in the vibration pattern resulting from damage on a limited number of teeth. Initial pitting for the purpose of this paper is defined as pits less than 1/64 inch in diameter with a depth less than 1/64 inches. At the completion of the test, the gears were inspected for damage Tadashi and Kazuhide [8] discussed about Gear Whine Analysis with Virtual Power Train Meshing transmission error (TE) is well known as a contributing factor of gear whine, but system- level prediction of transmission error and quantitative analysis of dynamic meshing vibromotive force have not been analyzed adequately until now. This paper describes the use of a computer- aided-engineering (CAE) model for the analysis of the dynamic gear meshing behavior and for the prediction of dynamic transmission error from the input torque of the system. This paper also describes the analysis of a dynamic vibromotive force at a bearing location where vibration is transmitted to the vehicle body. The gear whine critical frequency can be predicted with the proposed method at an early stage of passenger-car development when no prototype is available. J.J. Zakrajsek and D.P. Townsend [9] discussed about Transmission Diagnostic. A number of previously published and newly developed methods to specifically detect damage on gear teeth were applied to vibration data from the spur gear, spiral bevel gear, and face gear fatigue tests. The primary purpose was to verify the various methods with naturally occurring faults and to determine their relative performance. Of the various techniques investigated, only methods FM4, A4, and B4 responded to gear damage on a relatively consistent basis over the various gear types and failure modes. Timothy S Irwin [10] gave discussions on Gearbox Spectral Components and Monitoring Methods; gave information’s about Five Fundamental Gear Frequencies, Additional Component Frequencies, Fundamental Frequency Analysis, Transducer Selection and Monitoring M-Tech Thesis 6 P.E.S.C.E., Mandya
  7. 7. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.2 I TRODUCTIO TO CO DITIO MO ITORI G Condition monitoring is applied as a technique for improving productivity, efficiency and reliability of the machine components. It is the recent development in the field of maintenance engineering. It involves monitoring the health of the machinery through measurement by using parameters such as vibration, shock pulse, speed, temperature, pressure etc. Condition monitoring systems are becoming increasingly necessary in improving the efficiency of the manufacturing system. The main demand made of these monitoring systems is the detection of bearing failure, estimation of the bearing wear and wear rate. Unless condition-monitoring technology is implemented in all its aspects no fruitful results or economics can be achieved. Condition monitoring plays a vital role in ensuring the availability of plant machinery. With the proper skills and equipment, plant maintenance technicians not only detect problems before they result in a major machine malfunction or breakdown, but they also perform root cause failure analysis to prevent problems from recurring. Condition monitoring has emerged as a new discipline and is considered as a powerful technique in Modern Maintenance Management. This success has been possible due to the tremendous development and contribution made by Instrumentation, Electronic and Computer Specialists all over the world. Machine failures are now more openly discussed and solutions sought. [12] Condition Monitoring has developed both as a Science and Management with regard to techniques, Computer assistance, Cost benefit and other utilitarian considerations. In the country, there is already a large-scale awareness in most of the Educational Institutions, R&D Laboratories and Industrial Sectors. Unless Condition Monitoring methodology is implemented in all its aspects, no fruitful results or economics can be achieved. Condition Monitoring is taken to mean the use of advanced technologies in order to determine equipment condition, and potentially predict failure. Condition Monitoring is most frequently used as a Predictive or Condition-Based Maintenance technique. The business need that will drive sustainable change in condition monitoring is Asset Effectiveness – the need to extract maximum profits from the minimum investment in plant M-Tech Thesis 7 P.E.S.C.E., Mandya
  8. 8. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 and equipment. We achieve this through the use of Condition Monitoring technologies in the following five ways: • By improving Equipment Reliability through the effective prediction (and then avoidance) of equipment failures. • By minimizing downtime through the integrated planning and scheduling of repairs indicated by Condition Monitoring techniques. • By maximizing component life by avoiding the conditions that reduce equipment life (for example, by ensuring ongoing precision alignment, minimal lubricant contamination etc.) • By utilizing Condition Monitoring techniques to maximize equipment performance and throughput. • By minimizing Condition Monitoring costs. The main function of condition monitoring is to provide the knowledge of machine condition and of its rate of change, which is essential to the operation of this method. The knowledge may be obtained by selecting a suitable parameter such as vibration for measuring deterioration and reading its value at intervals. In recent years improved diagnostic techniques have become available and the condition of plant and machinery can be monitored with sufficient accuracy and consistency to enable condition monitoring to be widely used in the industry. Condition Monitoring involves the measurement or checking of all vital primary and secondary parameters or signals given out by the machine during its operation. Pressure, temperature flow rate etc. are primary parameters whereas vibration, noise, corrosion, wear etc. are secondary parameters. [12] Condition Monitoring is appropriate in situations where failure mechanisms are predominantly time dependent and where breakdown from such mechanisms are fairly frequent over the plant lifetime. These time dependent mechanisms include corrosion, erosion, wear, and fatigue and solids deposition causing excessive dynamic problems. A condition-monitoring program should be evaluated for its reliability and techno economic benefits before implementation in a system. M-Tech Thesis 8 P.E.S.C.E., Mandya
  9. 9. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Before moving on to the practical establishment of a condition monitoring programme, it might be well to keep in mind the basic simplicity of the steps involved. 1. Detection: A periodic vibration check, using a hand-held meter takes only a few seconds per machine. The check points should be clearly marked on each machine by a small metal disc, machine indent or painted circle, so that the pick-up measures at the same spot each time. 2. Analysis: Where periodic checks show an increase in the vibration reading a portable analyser is used to pinpoint the trouble. 2. Correction: As the problems have been discovered at an early stage, correction – including in-place balancing – can be scheduled for a convenient time. 2.3 TECH IQUES OF CO DITIO MO ITORI G There are many techniques available to monitor the health of the machinery. In spite of the large amount of techniques available, there are few techniques of condition monitoring and these are explained below: [13] 1. Visual Monitoring: It involves inspection and recording of surface appearance. Inspection can be done by means of visual testing aids such as magnifying lenses, microscopes, photographs, boroscopes, fiber optic scanners, surface imprinting etc. Inference is made from overall appearance and properties such as color, shape and texture. 2. Vibration Monitoring: Vibration analysis can give useful quantitative idea about the condition of the equipment. This essentially uses vibration pick-up and frequency analyzers. The existence of a problem can be detected from overall vibration levels. Problems can also be diagnosed from frequency content, wave shape, and direction of major component and phase analysis of the vibration signals. 3. Wear Debris Monitoring: This method works on the principle that the working surfaces of a machine are washed by means of lubricating oil, and any damage to them should be detectable from particles of wear debris in the oil. The amount of wear particles in the lubricating oil gives information about the problem existence. M-Tech Thesis 9 P.E.S.C.E., Mandya
  10. 10. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Analysis of the size, shape, density and material composition of wear particles helps to pin point the problem. 4. Performance Trend Monitoring: It involves checking the performance of a machine or component to see whether it is behaving correctly. By monitoring the trend in the performance characteristics such as temperature, pressure, efficiency etc., we will be able to assess the condition of the equipment. This may for example involves the monitoring the performance of a bearing by measuring its temperature to see whether it is carrying out its function of transmitting load. 5. Corrosion Monitoring: Some of methods used for CM are i) Corrosion Coupons ii) Measurement of polarization resistance, which is inversely proportional to rate of corrosion, iii) Electrical resistance method, which makes use of the fact that change in area due to material loss changes resistance. 6. Sound Monitoring: The noise given out from equipment contains useful diagnostic data for condition assessment. Experienced personnel can make intuitive evaluation by directly listening to the sound. Quantifiable diagnostics can be obtained form sound signatures and data processing. 7. on-Destructive Testing: This involves Radiography, ultrasonic flaw detection, acoustic emission technique, Dye-penetrant tests, magnetic particle test etc. Suitable technique is to be selected depending upon the type of defect and nature of data to be obtained. 2.4 VIBRATIO MO ITORI G Vibration monitoring is one of the successful techniques of predicting the health of the machine structures. Vibration monitoring is the process in which the machine components are regularly checked and the condition i.e., whether it is healthy or faulty, is checked on the basis of vibration signals got from the machine components. Vibration analysis can give useful quantitative idea about the condition of the equipment. This essentially uses vibration pick-up and frequency analyzers. The existence of a problem can be detected from overall vibration levels. Problems can also be diagnosed from frequency M-Tech Thesis 10 P.E.S.C.E., Mandya
  11. 11. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 content, wave shape and direction of major component and phase analysis of the vibration signals. As a part of vibration monitoring, vibration signature analysis is based on the following factors. As there is no perfect machine all machines tends to vibrate. When mechanical trouble develops, the vibration level increases. Mechanical trouble causes vibration in different ways. Therefore a periodic vibration check reveals whether the troubles are present or not. Vibration signature analysis reveals which part of the machine is defective and hence vibration monitoring is proved to be one of the most reliable condition monitoring technique to check the machine condition. Application of vibration monitoring includes spindle bearings, couplings, shafts, turbines, compressor and gearboxes. Vibration signature analysis uses the transducers to pickup the signals from the machine structure and the picked up signals are monitored. 2.5 CAUSES OF VIBRATIO The vibration analysis provides a complete machine diagnostic system and is not limited to only a certain number of faults. During the vibration of rotating machinery, many defects will be observed. The most common problems, which produce vibration, are mentioned below: 1) Misalignment 2) Imbalance 3) Mechanical looseness 4) Critical speed excitation 5) Coupling lock-up 6) Uneven loading of a machine 7) Shaft rubbing 8) Cracked shaft 9) Rotor instability 10) Electric motor defects M-Tech Thesis 11) Gear wear 12) Gear defects 13) Gearwheel backlash 14) Bearing defects 15) Tilting pad wear 16) Blade/vane defects 17) Blade fouling 18) Blade rubbing 19) Steam leaks 20) Compressor surge 11 P.E.S.C.E., Mandya
  12. 12. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.6 CHARACTERISTICS OF VIBRATIO A lot can be learnt about the machine conditions & mechanical problems by noting its vibration characteristics. The vibration characteristics are as follows. [14] Vibration displacement Vibration velocity Vibration acceleration Vibration frequency Phase 2.6.1 Vibration Displacement The total distance traveled by the vibrating part from one extreme limit of travel to the other extreme limit of travel is referred to as the “peak to peak” displacement; it is normally expressed in terms of microns. Vibration amplitude i.e., the displacement is an indicator use to determine how good or bad the operation of a machine is. The greater the amplitude, more severe the vibration. Although displacement readings are not widely recommended for determining overall machinery condition, under the condition of dynamic stress, displacement may be the better indicator of severity. Therefore, it is recommended to measure the displacement in those machines, which are subjected to low frequency vibration (below 600 CPM), where stress failure is of significant importance. 2.6.2 Vibration Velocity The velocity of the motion is constantly changing throughout the cycle. The highest or peak velocity is selected for the measurement. Vibration velocity is normally expressed in terms of mm/sec. It provides the best overall indication of machine condition & is a direct measure of vibration severity & appears to be function of displacement, which is significant at medium frequencies (600 to 60000 CPM), where parts are subjected to fatigue. 2.6.3 Vibration Acceleration The velocity of the part approaches zero at the extreme limits of travel each time the parts come to stop at the limits of travel. It must accelerate to pickup speed as it travels towards the other extreme limit. Therefore vibration acceleration is another important characteristic of vibration. Vibration acceleration measurements are closely related to the M-Tech Thesis 12 P.E.S.C.E., Mandya
  13. 13. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 vibratory force being applied to the machine & relatively large forces can occur at high frequencies. Therefore generally vibration acceleration measurements are recommended for vibration frequencies above 60000 CPM. 2.6.4 Vibration Frequency The number of cycles for a given interval of time is the frequency. It is more useful in identifying the cause of vibration. Frequency is normally expressed in hertz. Knowledge of frequency allows use to identify which is at the fault & what the problem is. The forces, which accuse vibration, are generated through rotary motion of the machine parts. Therefore these forces change in magnitude & direction as the rotating parts changes its position with respect to the rest of machine. As a result the vibration produced will have frequency dependent upon the rotating speed of the part, which has the trouble. 2.6.5 Vibration Phase Phase is defined as the position of vibrating part at given instant with references to a fixed point or another vibrating part. In practical sense, phase measurement offers a continent way to compare one vibratory motion with another or to determine how one part is vibrating relative to another. Phase readings are normally expressed in degrees. 2.7 CRITERIA FOR ASSESSME T OF VIBRATIO SEVERITY I ROTATI G MACHI ES International standards on the vibration severity classify all machines into four categories. Table 2.2 lists the classification of machines as per the international standards ISO 2372. Table 2.1 Classifications of Machines as per the International Standards. Class/group I II III IV M-Tech Thesis Description Individual parts of engines and machines integrally connected with the complete machine in its normal operating conditions e.g.: electric motors up to 15KW Medium sized machines Eg: Electric motors up to 15-75 KW Large prime movers and other large machines with rotating masses on rigid and heavy foundations, which are relatively stiff in the direction of measurement. Large prime movers and other large machines with rotating masses on foundations, which are soft in the direction of measurement. 13 P.E.S.C.E., Mandya
  14. 14. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 For each of these categories, the various levels of RMS vibration velocities are divided into four relative quality bands, ranging from good through satisfactory and poor to bad and it is given in the Table 2.3 given below. The particular range selected by the user is based upon a number of parameters like. Type and size of the machines. Type and service expected. Mounting system. Effect of machinery vibration on the surrounding environment. The vibration level measured on the bearing housing is compared with the vibration standards based on ISO 2372 as shown in the Table 2.3 below [16]. It gives condition bands for four classes of machines. Table 2.2 Ranges of Vibration Severity as per ISO2372 Range of RMS Vibration Severity in mm/sec 0.29 Examples of quality judgment for separate classes of machines Small Medium Large Turbo Machines Machines Machines Machines Class – I Class-II Class-III Class-IV A 0.45 A 0.71 B 1.12 A C B A B 1.80 B 2.80 4.50 C 7.10 11.20 C D C 18.00 D 28.00 D D 45.00 A – Good B – Satisfactory C – Poor D – Bad M-Tech Thesis 14 P.E.S.C.E., Mandya
  15. 15. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.8 VIBRATIO FREQUE CY A ALYSIS Vibration, and associated frequency, analysis has become a very popular monitoring technique due to the myriad of information that it can provide about the condition of machinery and structures. Vibration/frequency analysis of machinery has been extensively documented for successfully, and at times automatically, detecting faults Furthermore, vibration analysis is very effective for monitoring of undesirable high vibration levels or foundation looseness, which affect machine health and lead to structural fatigue problems. Methods for monitoring vibrations involve the measurement of three different parameters, although they are all based on the same vibration. These include: Displacement, Velocity, or Acceleration. Measurements of acceleration tend to accentuate higher frequency vibrations, while displacement measurements emphasize the lower frequencies (this may be understood by double-differentiating the displacement relation of a vibration). Consequently, a variety of electrical and magnetic-based sensors have been developed to measure these parameters (i.e., electrical strain gauges, eddy current proximity probes, piezoelectric transducers, etc.) Each technique has a limited frequency range of measurement and is therefore ideally suited for specific applications. ot only is frequency information important for the detection of the incipient faults, but it also enables the cause of the fault to be diagnosed. A frequency analysis reveals the frequencies at which the significant level changes have occurred and these can usually be correlated with a particular mechanical phenomenon: rotation speed of the shaft (unbalance and misalignment), gear meshing frequency, resonances, critical shaft frequency etc. A vibration trouble shooting chart shown in Table 2.3 gives the nature of the faults, its direction and the frequency with which it appears. [17] M-Tech Thesis 15 P.E.S.C.E., Mandya
  16. 16. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Table 2.3 Vibration Trouble-Shooting Chart ature of Frequency of dominant fault vibration (Hz or rpm/60) Rotating 1 x rpm members out of balance Misalignment Usually 1 x rpm Often 2 x and bent shaft rpm. Sometimes 3 and 4 x rpm Damaged Impact rates for the rolling individual bearing component. Also vibrations element bearings (ball, at high frequencies (2 to 60 Hz) often related to radial rotor, etc.) resonance in bearings Journal Sub-harmonics of shaft rpm bearings loose exactly ½ or 1/3 x rpm in housing Oil film whirl Slightly less than half shaft or whip in speed (42% to 48%) journal bearings Hysteresis Shaft critical speed whirl Direction Radial A common cause of excess vibration in machinery. Radial and axial A common fault. Radial and axial Uneven vibration levels, often with shocks. Primarily radial Looseness may only develop at operating speed and temperature (e.g. turbo machines). Applicable to high-speed (e.g., turbo machines). Primarily radial Primarily radial Damaged or Tooth meshing frequencies Radial worn gears (shaft rpm x number of and axial teeth) and harmonics Mechanical 2 x rpm looseness Faulty belt 1, 2, 3 and 4 x rpm of belt drive Unbalanced reciprocating forces and couples Electrically induced vibrations M-Tech Thesis Remarks Radial Vibrations excited when passing through critical shaft maintained at higher shaft speeds. Can sometimes be checking tightness of rotor components. Sidebands around tooth meshing frequencies indication (e.g., eccentricity) at frequency corresponding to spacing. ormally only detectable with very narrow-basis and cepstrum. Also sub and interharmonics, as for loose journal. The precise problem can usually be identified virtual help of a stroboscope. 1 x rpm and/or multiples Primarily for higher order unbalance radial 1 x rpm or 1 or 2 times Radial synchronous frequency and axial 16 Should disappear when turning off the power. P.E.S.C.E., Mandya
  17. 17. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.9 MODES OF GEAR FAILURES From one point of view, causes of gear failure may include a design error, an application error, or a manufacturing error. Design errors include such factors as improper gear geometry as well as the wrong materials, quality levels, lubrication systems, or other specifications. Application errors can be caused by a number of problems, including mounting and installation, vibration, cooling, lubrication, and maintenance. Manufacturing errors may show up in the field as errors in machining or heat-treating. AGMA recognizes four main modes of gear failure, plus a fifth that covers everything else. They are wear, surface fatigue, plastic flow, breakage, and associated gear failures (Fig 2.1). 2.9.1 WEAR FAILURES Moderate wear (Fig 2.1) shows up as a contact pattern in which metal removal occurs from both the addendum and dedendum tooth surfaces, and the operating pitch line remains as a continuous line. This may be caused by lubricant contamination but is often unavoidable due to limitations of lubricant viscosity, gear speed, and temperature. It may occur normally throughout the design life of a gear set, particularly when gears operate near boundary lubrication conditions. Increasing oil film thickness, either by cooling the lubricant, using a higher viscosity lubricant or operating at higher speeds, can sometimes reduce normal wear. Replacing a splash-fed lubrication system with a filtered positive-spray system may improve lubrication by removing particles and delivering a more consistent supply of oil to the working surfaces. Further solutions include reducing the gear loading and changing the gear geometry, materials, or hardness. Extreme wear (Fig 2.1) may appear as the same kind of contact pattern and pitch line visibility that occur with moderate wear, but the progression rate is much faster. Here, a considerable amount of material may be removed uniformly from the gear tooth surfaces, and the pitch line may show signs of pitting. Extreme wear will cause failure to occur before the design life of the gear set is reached. It may cause enough damage to the tooth profile that the resulting high dynamic loads will further accelerate the wear. Causes of M-Tech Thesis 17 P.E.S.C.E., Mandya
  18. 18. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 extreme wear include a lubricating film too thin for the tooth load, fine abrasive particles in the lubrication system, and severe vibratory loads. Shaft seals and air-vent filters, properly installed and maintained, may help reduce wear. Other solutions include oil cooling, higher viscosity lubricants, higher speeds, reduced loads, and possibly reduced vibratory loads if the application permits. Abrasive wear (Fig 2.1) shows up as a lapped surface, with radial scratches or grooves on the tooth contact surfaces. When this occurs shortly after startup of a new installation or on any open gearing, particles in the lubricating system are generally the causes. These may include metal particles from the gears and bearings, weld spatter, scale, rust, and sand, dirt, or other environmental contaminants. Fig. 2 shows severe abrasion. Careful cleaning of the gearbox and lubrication system before use can minimize abrasive wear. With a circulating lubrication system, adding a filter or using a finer replacement filter will help reduce this type of wear. Regular oil changes will help for splash-lubricated drives, and higher viscosity oil also may help protect either type of system with a thicker oil film that will keep the finer particles from scratching. Corrosive wear (Fig 2.1) is visible as surface deterioration, caused by the chemical action of active ingredients in the lubricant. These may include acid, moisture, foreign materials, and extreme-pressure additives. During operation, the oil breaks down and allows corrosive elements present in the oil to attack the gear contact surfaces. This action may affect the grain boundaries and cause fine, evenly distributed pitting. Checking the oil for breakdown and changing it at regular intervals can help minimize corrosive wear. Lubricants with high antiscuff, antiwear additive content must be observed even more carefully because they are chemically active. Gear units that are exposed to salt water, liquid chemicals, or other foreign materials should be sealed from their environment. M-Tech Thesis 18 P.E.S.C.E., Mandya
  19. 19. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.9.2 SURFACE FATIGUE FAILURE Surface fatigue can be noticed by the removal of metal and the formation of cavities. These may be small or large and may grow or remain small. It occurs when the gear material fails after repeated stresses that are beyond the endurance limits of the metal. Here are the main types of surface fatigue, their causes, and cures. Pitting (Fig 2.1) failures depend on surface contact stress and the number of stress cycles. Initial pitting, with areas of small pits from 0.015 in. to 0.030 in. in diameter, occurs in localized parts of the gear teeth that are over-stressed. It is sometimes called corrective pitting because it tends to redistribute the load by progressively removing high contact spots, and often stops once the load has been redistributed. Continued operation may polish or burnish the pitted surface and improve its appearance. Pitting can be monitored by periodically putting some bluing on the affected area, then applying some cellophane tape to lift the pattern and put it in a notebook. Comparing the impressions over time will tell whether the pitting has stopped. While accurate manufacturing control of involute profiles is the best method of preventing pitting, a careful break-in at reduced loads and speeds once the unit is installed also will help minimize pitting by improving gear tooth contact. Destructive pitting (Fig 2.1) appears as much larger pits than initial pitting, often in the dedendum section of the gear teeth. These larger craters usually are caused by more severe overload conditions that cannot be relieved by initial pitting. As stress cycles build up, pitting will continue until the tooth profile is destroyed. To correct the cause of destructive pitting, the load on the surface of the gear needs to be reduced below the material’s endurance limit, or the material hardness needs to be increased to raise the endurance limit to where pitting will not occur. Spalling (Fig 2.1) resembles destructive pitting, except that the pits may be larger, quite shallow, and irregularly shaped. The edges of the pits break away rapidly, forming large, irregular voids that may join together. Spalling is caused by excessively high contact stress levels. Remedies include reducing contact stress on the gear surface or hardening the material to increase its surface strength. M-Tech Thesis 19 P.E.S.C.E., Mandya
  20. 20. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Both Spalling and destructive pitting are indications that the gears do not have sufficient surface capacity and should probably be redesigned if possible. Micro pitting (Fig 2.1) is a type of contact fatigue that appears as frosting or gray staining under thin film conditions. The surface acquires an etch-like finish, with a pattern that sometimes follows the slightly higher ridges left by cutter marks or other surface irregularities. It usually shows up first on the dedendum section of the driving gear, although it may begin on the addendum section as well. When viewed under magnification, the surface is seen as a field of very fine micro pits under 0.0001 in. deep. Causes include high surface loads and heat generation, which thins the lubrication film and leads to marginal lubrication. Improving the surface finish is an effective remedy, through either manufacturing techniques such as hard honing and grinding or a careful break-in cycle. These techniques help lower heat generation by improving conformity of tooth contact and equalizing load distribution. Reducing the lubricant temperature and surface loading will also minimize frosting. Sometimes, frosted areas that appear initially will slowly be polished away during subsequent operation if loads and temperatures are not excessive. Case crushing (Fig 2.1) occurs in heavily loaded case hardened gears, including those that are carburized, nitrided, or induction hardened. It is a subsurface fatigue failure that occurs on material where the case is substantially harder than the core, when surface contact stress at high cycle levels exceeds the material’s endurance limit. Case crushing may appear similar to pitting, if some damage occurs on contacting surfaces. However, it often occurs as longitudinal cracks on the surface of only one or two teeth, and long pieces of the tooth surface may break away. The case material may appear to have chipped away from the core in large flakes. Case crushing occurs when cracks form because stresses in the subsurface area exceed the strength of the core material. High residual stresses may contribute to this effect. The cracks move toward the case-to-core boundary and then to the gear surface, where they may eventually cause large pieces of material to fall off. To prevent case crushing, it may be necessary to in- crease the depth of the case hardening and M-Tech Thesis 20 P.E.S.C.E., Mandya
  21. 21. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 possibly the hardness of the core material. Changes in the material, heat treatment process, or the design itself may be necessary 2.9.3 PLASTIC FLOW FAILURE Plastic flow is a surface deformation that occurs when high contact stresses combine with the rolling and sliding action of the meshing gear teeth to cause cold working of the tooth surfaces. Although usually associated with softer materials, it also can occur in heavily loaded case hardened and through-hardened gears. Plastic flow generally takes one of three distinct forms. Cold flow, rolling, and peening (Fig 2.1) can be identified through evidence of metal flow in the surface and subsurface material. The surface material may have been worked over the tips and ends of the gear teeth, resulting in a finned appearance. Tips of the gear teeth may be heavily rounded over, and a matching depression may appear on the tooth surface. Cold flow occurs under heavy loads and high contact stresses, as the rolling and peening action of the meshing gear teeth cold-works the surface and subsurface material, pushing or pulling it in the direction of sliding. Continued operation during this deterioration increases dynamic loading and results in a dented, battered appearance on the surface, much as if it had been hit with a ball peen hammer. To eliminate the problem it is necessary to reduce contact stress and increase hardness of the contacting surface and subsurface materials. Increasing the accuracy of both tooth spacing and profiles will help reduce dynamic loads, and any mounting deflections or helix angle errors should also be corrected. Rippling (Fig 2.1) is a regular, wave-like formation that occurs at right angles to the direction of motion and has a fish scale appearance. It is most common on hardened gear surfaces and is generally considered a surface failure only when it has progressed to an advanced stage. It usually occurs in slow speed operation with an inadequate oil film thickness. High contact stresses during repeated cycles may then roll and knead the surface, causing it to ripple. Rippling can be prevented by case hardening the tooth surface, reducing the contact stress, increasing oil viscosity, and using an extreme-pressure oil additive M-Tech Thesis 21 P.E.S.C.E., Mandya
  22. 22. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Ridging (Fig 2.1) is a definite series of peaks and valleys that occur across the tooth surface in the direction of sliding. It occurs when high contact compressive stresses and low sliding velocities cause plastic flow of the surface and subsurface material. It is frequently found on heavily loaded worm gear drives, as well as on hypoid pinion and gear drives. Remedies for ridging include reducing contact stress, increasing material hardness, and using more viscous lubricating oil with extreme-pressure additives. 2.9.4 BREAKAGE FAILURE Breakage is the fracture of a whole tooth or substantial part of a tooth. Common causes include overload and cyclic stressing of the gear tooth material beyond its endurance limit. Bending fatigue breakage (Fig 2.1) starts with a crack in the root section and progresses until the tooth or part of it breaks off. It can be recognized by a fatigue “eye” or focal point of the break. The break area itself usually shows signs of fretting corrosion and smooth “beach marks” that resemble patterns in the sand on a beach. A small area will probably have a rough, jagged look where the last portion of the tooth broke away. Most such failures result from excessive tooth loads, which cause repeated root stresses that eventually exceed the endurance limits of the material. Stress risers, such as notches in the root fillet, hob tears, inclusions, small heat treating cracks or grinding burns, may aggravate this condition. To remedy this condition, root fillets can be polished and shot-peened. Material should be properly heat-treated to minimize residual stresses. If redesign is necessary, use a full-fillet radius tooth, which is less prone to breakage and has greater capacity than a tooth with too small a fillet radius. Overload breakage (Fig 2.1) appears as a stringy, fibrous break that has been rapidly pulled or torn apart. In harder materials, the break will have a finer stringy appearance. The eye and beach markings found in fatigue breakage will be missing. This type of breakage is caused by an overload that exceeds the tensile strength of the gear material. Typical overloads that lead to such breakage include a bearing M-Tech Thesis 22 P.E.S.C.E., Mandya
  23. 23. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 seizure, failure of driven equipment, foreign material passing through the gear mesh, or a sudden misalignment. Since the failure is usually the result of some unpredictable occurrence, it is difficult or impossible to prevent. If possible overloads are anticipated, torque-limiting couplings may provide some protection. Random fracture (Fig 2.1) can occur in areas such as the top or the end of a tooth, rather than the usual root fillet section. These failures are typically caused by stress concentrations from such things as minute grinding cracks, foreign materials in the gear mesh, or improper heat-treating. Little can be done to prevent random fracture, except at the design and manufacturing stages. However, maintaining cleanliness of the lubricant can help prevent one cause 2.9.5 ASSOCIATED GEAR FAILURES Associated gear failures usually are caused by improper processing, environmental conditions, or possibly by accidents. To minimize many of these failures, any gear that is repaired and heat-treated should be checked by magnetic particle inspection before being put back into service to be sure no cracks have developed. Whenever repairs are made to any gearing, at the very least, a dye penetrant inspection should be performed to check for cracks. Quenching cracks (Fig 2.1) may appear across the top land of a tooth, in the fillet area, or randomly at the tooth ends, although they may not become visible until after they have been used for a short time. They are caused by improper quenching or uneven cooling during heat treatment, which causes excessive internal stresses. Prevention of quenching cracks calls for a thorough review of heat-treating procedures, as well as an inspection of the equipment used. Grinding cracks (Fig 2.1) usually show up as a definite pattern, either as a series of short cracks that are parallel to each other or with the appearance of chicken wire mesh. Usually, they are between 0.003 in. and 0.005 in. deep, with the parallel type being deeper than the chicken wire pattern. Causes include improper heat treatment or a metallurgical structure that is prone to cracking. To prevent this cracking, the M-Tech Thesis 23 P.E.S.C.E., Mandya
  24. 24. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 grinding procedure should be reviewed. Feeds and speeds may have to be reduced to lower the heat developed during grinding. The metallurgy of the gear material also should be examined to choose an alloy and heat treatment that will not tend to crack during grinding. Rim and web failures (Fig 2.1) tend to start between two teeth and propagate through the rim and into the web. These failures are common on highly loaded thin rim and web sections. Causes include stress risers from holes in the web as well as from web vibrations. Remedies include increasing rim or web thickness, depending on failure mode, and eliminating stress risers such as grinding marks, tool marks, and sharp fillets. Rim and web failures also may be caused by vibrations, which can be minimized by damping or by redesign to change the natural frequencies of the gear. Electric current damage (Fig 2.1) shows up as tiny pits occurring in a well-defined pattern that is distributed uniformly along the gear surfaces. They can be further identified by their smooth, molten appearance and lack of any fibrous appearance. This damage results from electric current passing through two lightly contacting surfaces, either from arc welding or from electric equipment such as motors or electrically actuated clutches. The remedy is to insulate the electrical equipment or relocate the grounding wires properly. Welders and maintenance workers should be made aware of proper grounding procedures. M-Tech Thesis 24 P.E.S.C.E., Mandya
  25. 25. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Moderate wear Abrasive wear Corrosive wear Scoring Pitting Destructive pitting Spalling Micropitting Micropitting magnified Case Crushing Rippling Ridging Quenching cracks Grinding cracks Rim and web failures Electric current damage Fig 2.1 Modes of gear failures M-Tech Thesis 25 P.E.S.C.E., Mandya
  26. 26. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.10 TOOTH LOAD VS TIME DISTRIBUTIO I GEAR MESHI G Fig: 2.2 Tooth load VS time distribution (a) for low speed, (b) for medium speed, (c) for high speed The Fig. 2.2 shows the tooth Vs load distribution during gear meshing [23]. During low speed the Dynamic load transmitted will be systematic and during medium the load varies and similarly the load varies violently during high speed. This effect is due to the reduction of time gap between two successive teeth. The gap can range from 2e-12 for high speed and 2e-6 to low speed. This gives load to transmit irrespective to its plot and gives more effective tooth load to excite. 2.11 BA D OF CO TACT GEAR MESHI G Gear fails by pitting and wear as well as by tooth breakage [22]. Frequently gear will wear to the point where they begin to run rough. Then the increased dynamic load plus the stress concentration affects of the worn tooth surface cause the teeth ultimately to fail by breakage. Figure shows the kinds of stresses that are present in the region of the contact. In the canter of the band there is a point of maximum compressive stress, directly underneath this point there is a maximum subsurface shear stress. The depth to the point of maximum shear stress is a little less than one-third the width of the band of contact. The gear toot M-Tech Thesis 26 P.E.S.C.E., Mandya
  27. 27. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 surfaces move across each other with a combination of rolling and sliding motion. The sliding motion plus the coefficient of friction tend to cause additional surface stresses and just behind the band of contact there is a narrow region of tensile stress. A bit of metal on the surface of a gear tooth goes through a cycle of compression and tension each time a mating gear tooth passes over it. Fig o: 2.3 Gear meshing band of contact. 2.12 GEAR POWER TRA SMISSIO SYSTEM According to AGMA standard Test charts the distribution of Gear Transmission Power will be uniform. During any defect the power fluctuate and the effect of defect will be suppressed by fluctuating of power. This means the transmission of power does not vary during running conditions in defective cases but fluctuate to overcome the defect. The transmission loss during any disturbance like pitting in Gear will lead to addition of fluctuate power to compromise the defect. [6] [7] The amount of additional power will be constant 2% to 10% of full power per each Gear pair that is 1-1 contact for destructive pitting. This addition is to overcome the defect and transmit the corresponding power to the system. M-Tech Thesis 27 P.E.S.C.E., Mandya
  28. 28. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 2.13 FORMATIO OF GEAR DESTRUCTIVE PITTI G The formation of Destructive pitting is as shown in the Fig 2.4. Here, a considerable amount of material may be removed uniformly from the gear tooth surfaces, and the pitch line may show signs of pitting at constant rate. Pitting failures depend on surface contact stress and the number of stress cycles. Initial pitting, with areas of small pits from 0.4 mm. to 0.4 mm in diameter, occurs in localized parts of the gear teeth that are over-stressed. Destructive pitting appears as much larger pits than initial pitting of 1.5mm in diameter, often in the dedendum section of the gear teeth. These larger craters usually are caused by more severe overload conditions that cannot be relieved by initial pitting. As stress cycles build up, pitting will continue until the tooth profile is destroyed. To correct the cause of destructive pitting, the load on the surface of the gear needs to be reduced below the material’s endurance limit, or the material hardness needs to be increased to raise the endurance limit to where pitting will not occur. Fig o: 2.4 Formation of pitting in Gear M-Tech Thesis 28 P.E.S.C.E., Mandya
  29. 29. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 CHAPTER 3 FI ITE ELEME T METHOD 3.1 I TRODUCTIO Finite Element Method is a numerical procedure for solving physical problems in the fields of mechanics, fluid dynamics, thermodynamics etc. Finite element method is particularly useful for solving problems that do not have satisfactory analytical procedures. The analytical procedures maybe difficult because of complicated geometry of the body that cannot be modeled numerically. The finite element method solves the problems by discretizing the body into small elements of known geometry, whose solution can be found easily. The method generates a set of algebraic equations that can be solved numerically. With the advent of fast processing computers, these procedures have become even simpler, faster and effective. [18] The finite element method is a numerical method, which can be implemented to solve many problems. The method was used for the accurate solution of complex engineering problem. It was first developed in 1956 for the analysis of aircraft structural problems. Thereafter within a decade, the potential of the method for the solution of different types of applied sciences and engineering problems were recognized. Over the years, the finite element technique has been so well established that today it is considered to be one of the best methods for solving a wide variety of practical problems efficiently. The FEM originated as a method of stress analysis. Today FEM is used to analyze problems of heat transfer, fluid flow lubrication, electric and magnetic fields and many others. Thus it has become a powerful tool for the numerical solution of a wide range of engineering problems with the advances in computer technologies and CAD systems, complex problems can be modelled with relative ease, several alternative configurations can be tried out on a computer before the first prototype is built. In this method of analysis, a complex region defining a continuum is discretized into simple geometric shapes called finite elements. The material properties and the governing relations are considered over these elements and expressed in terms of unknown values at element corner. An assembly process, M-Tech Thesis 29 P.E.S.C.E., Mandya
  30. 30. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 duly considering the loading and constraints, results in a set of equations gives us the approximate behavior of the continuum. 3.2 FI ITE ELEME T A ALYSIS Finite Element Analysis is a way to simulate loading conditions on a design and determine the design’s response to those conditions. The design is modeled using discrete building blocks called elements. Each element has exact equations that describe how it responds to a certain load. The “sum” of the response of all elements in the model gives the total response of the design. The elements have a finite number of unknowns, hence the name finite elements. [19] The finite element analysis is needed to reduce the amount of prototype testing. Computer simulation allows multiple “what-if” scenarios to be tested quickly and effectively. To simulate designs that is not suitable for prototype testing. Example: Surgical implants, such as an artificial knee. Finite element analysis results in Cost savings; Time savings reduce time to market and create more reliable, better-quality designs. 3.3 E GI EERI G APPLICATIO S OF FEM In particular the FEM can be systematically programmed to accommodate complex and difficult problems such as non-homogeneous materials, non-linear stress strain behaviour, and complicated boundary conditions. This FEM is applied to wide range of boundary value problems in engineering. In boundary value problems, a solution is sought in the region of the body, while on the boundaries or edges of the region, values of dependent variables or their derivatives are prescribed. There are three major types of boundary value problems. • Equilibrium or steady state problems. • Eigen value problems. • Propagation or transient problems. In an equilibrium problem, we need to find the steady state displacements or stress distribution if it is in solid mechanics problems, temperature or heat flux distribution if it is a heat transfer problem and pressure or velocity distribution if it is a fluid mechanics problem. M-Tech Thesis 30 P.E.S.C.E., Mandya
  31. 31. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 In Eigen value problems, time will not appear explicitly. They may be considered as extensions of equilibrium problems in which critical values of certain parameters are to be determined in addition to the corresponding steady state configurations. In this problems we have to find the natural frequencies or buckling loads and mode shapes if it is a solid mechanics or structural problem, stability of laminar flows if it is a fluid mechanics problem and resonance characteristics, if it is an electric circuit problem. The propagation or transient problems are time dependent problems. This type of problem arises, for example, whenever we are interested in finding the response of a body under time varying loads, in the area of solid mechanics and under sudden heating or cooling in the field of heat transfer. 3.4 STEPS I VOLVED I THE FI ITE ELEME T A ALYSIS In general, a finite element solution may be broken into the following three stages. This is a general guideline that can be used for setting up any finite element analysis. 1. Preprocessing: Defining the problem; The major steps in preprocessing are given below: Define key points/lines/areas/volumes Define element types and material/geometric properties Mesh lines/areas/volumes as required The amount of detail required will depend on the dimensionality of the analysis (i.e. 1D, 2D, axi-symmetric, 3D). 2. Solution: Assigning loads, constraints and solving; Here we specify the loads (point or pressure), constraints (translational and rotational) and finally solve the resulting set of equations. 3. Post processing: Further processing and viewing of the results; In this stage one may wish to see: Lists of nodal displacements Element forces and moments Deflection plots Stress contour diagrams M-Tech Thesis 31 P.E.S.C.E., Mandya
  32. 32. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 3.5 A SYS 7.1 A SYS is a general-purpose finite element modeling package for numerically solving a wide variety of mechanical problems. These problems include: static/dynamic structural analysis (both linear and non-linear), heat transfer and fluid problems, as well as acoustic and electro-magnetic problems. The A SYS 7.1 Family of Products continues A SYS, Inc.'s commitment to provide the highest quality engineering tools to help all of your design and analysis needs. This release of the products contains all of the capabilities from previous releases, plus many new features to enhance your productivity. [19] A SYS enables to perform the following tasks. Creating of computer models or structures, products, components, or systems. Apply operating loads or other design performance conditions. Study physical response, such as stress levels, temperature distributions. Optimize a design early in the development process to reduced production costs. Do prototype testing in environment where it otherwise would be undesirable or impossible. 3.6 A ALYSIS PATTER S Structural analysis is probably the most common application of the finite element method. The term structural (or structure) implies not only civil engineering structures such as bridges and buildings, but also naval, aeronautical, and mechanical structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools. The four types of structural analyses available in the A SYS family of products are explained below. The primary unknowns (nodal degrees of freedom) calculated in a structural analysis are displacements. Other quantities, such as strains, stresses, and reaction forces, are then derived from the nodal displacements. Static Analysis: Used to determine displacements, stresses, etc. under static loading conditions. Modal Analysis: Used to calculate the natural frequencies and mode shapes of a structure. Different mode extraction methods are available. M-Tech Thesis 32 P.E.S.C.E., Mandya
  33. 33. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Harmonic Analysis: Used to determine the response of a structure to harmonically timevarying loads. Transient Dynamic Analysis: Used to determine the response of a structure to arbitrarily time-varying loads. 3.7 ELEME T TYPES There are mainly three types of elements, which could be used in FEA based on the shape of the structure. They are O E, TWO and THREE dimension elements. An exhaustive element library is available with all FEM packages, which could be used to select the suitable type of element. [19] Depending on the application, one-dimensional elements can be classified as bar and beam elements. Bar elements is one, which can take only axial tension and compression loads. Beam elements are one, which can withstand bending loads along with axial tension and compression loads. Similarly, under two-dimensional elements, commonly used elements are membrane, plate and shear elements. Membrane elements can take only in-plane loads and plate elements can take in plane and also bending loads. The shear element can withstand pure shear loads. So, one has to be familiar with the element library of a particular FEA package and accordingly should choose the right kind of element depending on the application and shape of the structure. The elements used for modeling the lathe structure are elastic shell elements SHELL 63, structural mass element MASS 21, beam elements BEAM 188 and spring elements MATRIX 27. 3.8 ELEME T LIBRARY The A SYS element library consists of more than hundred different element types. An element type is identified by a name and a unique identifying number. The different elements used during the modeling of a lathe structure are elastic shell elements SHELL 63, structural mass element MASS 21, beam elements BEAM 188 and spring elements MATRIX 27. The description of the above elements is given below. [19] M-Tech Thesis 33 P.E.S.C.E., Mandya
  34. 34. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 3.8.1 SHELL 63 SHELL 63 has both bending and membrane capabilities. Both in-plane and normal loads are permitted. The element has six degrees of freedom at each node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The element is defined by four nodes, four thicknesses, elastic foundation stiffness, and the orthotropic material properties. The element x-axis may be rotated by an angle THETA (in degrees). A summary of the element input is given as follows Element ame : : odes SHELL 63 I, J, K, L Degrees of Freedom : UX, UY, UZ, ROTX, ROTY, ROTZ Real constants TK (I), TK (J), TK (K), TK (L), EFS, THETA o. : ame Description 1 TK(I) Shell thickness at node I 2 TK(J) Shell thickness at node J 3 TK(K) Shell thickness at node K 4 TK(L) Shell thickness at node L 5 EFS Elastic foundation stiffness 6 THETA Element X-axis rotation 3.8.2 MATRIX 27 MATRIX 27 represents an arbitrary element whose geometry is undefined but whose elastic kinematic response can be specified by stiffness, damping, or mass coefficients. The matrix is assumed to relate two nodes, each with six degrees of freedom per node: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes The element is defined by two nodes and the matrix coefficients. The stiffness, damping, or mass matrix constants are input as real constants. All matrices generated by this element are 12 by 12. The degrees of freedom are ordered as UX, UY, UZ, ROTX, ROTY, ROTZ for node I followed by the same for node J. If one node is not used, simply let all rows and columns relating to that node default to zero. The element input summary is as given below. M-Tech Thesis 34 P.E.S.C.E., Mandya
  35. 35. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM Element ame : MATRIX 27 : odes 2004 /2005 I, J Degrees of Freedom : UX, UY, UZ, ROTX, ROTY, ROTZ Real Constants Constants C 1 through C 78 defines the upper triangular : portion of the matrix. Constants C 79 through C 144 define the lower triangular portion of the matrix. 3.8.3 BEAM 188 BEAM 188 is suitable for analyzing slender to moderately stubby/thick beam structures. BEAM 188 is a linear (2-node) beam element in 3-D. BEAM 188 has six degrees of freedom at each node. BEAM 188 is defined by nodes I and J in the global coordinate system. ode K is always required to define the orientation of the element. The element input summary is as given below. Element ame : : odes BEAM 188 I, J, K Degrees of Freedom : UX, UY, UZ, ROTX, ROTY, ROTZ Material Properties EX, PRXY, DE S, GXY, GYZ, GXZ, DAMP : 3.8.4 MASS 21 MASS 21 is a point element having up to six degrees of freedom: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z-axes. The mass element is defined by a single node. The element input summary is as given below. Element ame odes : MASS 21 : I Degrees of Freedom : UX, UY, UZ, ROTX, ROTY, ROTZ Real Constants MASSX, MASSY, MASSZ, IXX, IYY, IZZ M-Tech Thesis : 35 P.E.S.C.E., Mandya
  36. 36. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 3.9 DEVELOPI G FEM MODEL OF A LATHE The development of the lathe structure is considered to be the complex method by using classical approaches. Hence a suitable approach has to be considered and the finite element modeling is the one that gives the representation of the geometrical model in terms of finite number of elements and nodes, which are the building blocks of the structure. The lathe model was divided into a number of elements, so that the behavior of the different elements can be studied under the action of loads transmitted from the adjacent elements. The finite element model of a Lathe was developed by using A SYS 7.1. The model was described as given below. A finite element model of a lathe structure is as shown in the Fig. 3.1. The lathe model was made up of elastic shell elements SHELL 63, structural mass element MASS 21, beam elements BEAM 188 and spring elements MATRIX 27. In a model, left leg, right leg, carriage, tool post, bed walls are modeled by elastic shell element SHELL 63, which has six degrees of freedom at each node. It has both bending and membrane capabilities. The spindle shafts front and rear bearing was modeled by using MATRIX 27, which was represented by stiffness and damping values. The spindle shaft was modeled by using BEAM 188 element. The material data along with their properties is listed in the Table 3.1 below. Table 3.2 gives the lists of parts and element names. The finite element of the lathe structure has totally 2050 elements and 1869 nodes. The various unbalance elements of the lathe structure considered for the analysis was shown in Fig. 3.2 and the headstock assembly of the lathe showing the unbalance elements was shown in Fig. 3.3. Table 3.1: Material Data used in Modeling Material Model O: Material ame Modulus of Poissons Density Elasticity Ratio Kgf/mm3 Kgf/mm2 1 Cast iron 2 M-Tech Thesis 9700 0.27 7.9e-9 Steel 21000 0.3 7.8e-10 36 P.E.S.C.E., Mandya
  37. 37. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Table 3.2: Details of the parts with their Element ame Sl. o. Part ame Element ame 1 Tail stock SHELL63 2 Head stock SHELL63 3 Right leg SHELL63 4 Bed walls SHELL63 5 Feed gear box SHELL63 6 Head stock SHELL63 7 Carriage SHELL63 8 Spindle bearing front horizontal MATRIX27 9 Spindle bearing front vertical MATRIX27 10 Spindle bearing rear horizontal MATRIX27 11 Spindle bearing rear horizontal MATRIX27 12 Spindle shaft BEAM188 Fig. 3.1: Finite Element Model of a lathe M-Tech Thesis 37 P.E.S.C.E., Mandya
  38. 38. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 3.2: Unbalance Components of a Lathe Fig. 3.3: Head Stock Assembly of a Lathe M-Tech Thesis 38 P.E.S.C.E., Mandya
  39. 39. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 3.10 A ALYSIS PROCEDURE The analysis of Lathe is done in three forms first the Modal Analysis second the Harmonic Analysis and lastly Transient Analysis with assumed Defect in Gear. The three types are mentioned below. 3.10.1 MODAL A ALYSIS After the modeling of lathe structure, first step is to carryout modal analysis. It is used to calculate the natural frequencies and mode shapes of a structure. The natural frequencies and mode shapes are important parameter in the design of a structure for dynamic loading condition; mode shapes can be defined as the amplitude of displacements of all the mass points during the vibration of the structure at natural frequencies. Modal analysis results obtained can be used for the dynamic analysis such as harmonic response analysis, transient response analysis or a spectrum analysis. Mode extraction is used for this purpose. Block Lanczos extraction method is employed. [19] The analysis was carried out in the absence of damping and load. The number of modes to compute is ten to know the behavior of the structure completely at the natural frequencies. 3.10.2 HARMO IC RESPO SE A ALYSIS Harmonic response analysis was used to determine the response of the structure to harmonically time varying loads. The idea is to calculate the structures response at several frequencies and to obtain a graph of vibration velocity with frequency. Due to the presence of the rotating members in the structure, there exist unbalance forces, which vary harmonically with time. These unbalance forces given by the various elements in the structure is calculated and applied on the structure at their location and the response is observed at their corresponding operating frequencies. The unbalance forces are calculated as follows. The weight of the various elements is obtained by multiplying area, length and density. Unbalance centrifugal force is given by m * r * ω2 Where -------------- 3.1 m = mass of the element r = Eccentricity mm M-Tech Thesis 39 P.E.S.C.E., Mandya
  40. 40. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 ω = Angular velocity rad/s According to Indian Standard, the balanced quality grade for machine tool spindle is G 6.3 mm/s. i.e., V = 6.3 mm/s [20] Speed of the spindle = 1200 rpm Frequency = /60 = 20 Hz Eccentricity r = V/ω ∴ ------------- 3.2 = 6.3 * 1000 40* π = 50.134 µ Bearing clearance = 8 µ (In spite of preloading) [21] Total Eccentricity = (50.134 + 8) µ = 58.134 µ = 0.05814 mm The unbalance forces from the different rotating members in the lathe structure were considered and calculated as follows: Chuck Unbalance Force Weight of the chuck = 10 kg Unbalance Force = m * r * ω2 = 10/9810 * 0.05814 * (40π) 2 = 9.31821 Spindle Unbalance Force Weight of the spindle = πr2L * Density = π [(352 – 202) + (32.52 – 202)] * 225 * 7.8 * 10– 6 = 8.166 kg Unbalance force = m * r * ω2 = 8.166 * 0.05814 * (40π) 2 9810 M-Tech Thesis 40 P.E.S.C.E., Mandya
  41. 41. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 = 7.494 Gear Shaft Unbalance Force Speed of the gear = 800 rpm = 800/60 = 16.67 Hz Maximum permissible deflection of the shaft = 2 * 10– 4 * length of the shaft [20] = 2 * 10– 4 * 450 = 0.09 mm = π* 202 * 450 * 7.8 * 10– 6 ∴Weight of the shaft = 43.26 Angular velocity ω = 2π /60 = 2 * π* 800 60 = 83.77 rad/s ∴Unbalance force = 4.41 * 0.09 * (83.77) 2 9810 = 2.7850 There were three gears present on the shaft. From the specification of the lathe structure the module of three gears are 2.75 mm, 2 mm and 2 mm respectively. The unbalance forces due to these gears are as follows. Radial clearance of the bearings = 15 µ Permissible deflection of the gears = 10 * Module [21] Mass of gear 1 = 19.62 M-Tech Thesis 41 P.E.S.C.E., Mandya
  42. 42. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM Permissible deflection 2004 /2005 = 10 * 2.75 = 27.5 µ Mass of gear 2 = 3.5 kg Deflection = 10 * 2 = 20 µ Mass of gear 2 = 29.43 Deflection = 10 * 2 = 20 µ ∴Total deflection of gear 1 = 27.5 + 15 = 42.5 µ = 0.0425 mm Total deflection of gear 2 = 20 + 15 = 35 µ = 0.035 mm Total deflection of gear 3 = 20 + 15 = 35 µ = 0.035 mm Unbalance force due to gear 1 = m * r * ω2 = 2/9810 * 0.425 * (83.77) 2 = 0.5964 Unbalance force due to gear 2 = m * r * ω2 = 3.5/9810 * 0.035 * (83.77) 2 = 0.8593 Unbalance force due to gear 3 = m * r * ω2 = 3.0/9810 * 0.035 * (83.77) 2 = 0.7357 Pulley Shaft Unbalance Force Speed of the pulley = 760 rpm Angular velocity ω = 2π /60 = 2 * π* 760 60 = 79.59 rad/s M-Tech Thesis 42 P.E.S.C.E., Mandya
  43. 43. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Due to Weight of the pulley: Outside diameter = 206 mm Inside diameter = 132.35 mm Length = 80 mm ∴Weight = π[(206/2) 2 – (132.35/2) 2] * 80 * 8 * 10– 6 = 122.82 Deflection of pulley = 0.478 mm ∴Unbalance force due to pulley = 12.52/9810 * 0.478 * (79.59) 2 = 37.92 Due to the Weight of the Pulley Shaft: Weight of the pulley shaft = π * 20 2 * 400 * 7.8 * 10– 6 = 3.92 kg Deflection of pulley shaft = 0.15 mm ∴ Unbalance force = 3.92/9810 * 0.15 * (79.59) 2 = 3.7278 Due to Gear on the Pulley: Gear is present at the center of the pulley shaft Deflection of the gear = 0.109 mm Mass of the gear = 29.43 Radial clearance of the bearing = 0.015 mm Total Deflection = 0.109 + 0.015 = 0.124 mm ∴Unbalance force due to gear on the pulley = 3/9810 * 0.124 * (79.59) 2 = 2.3544 In the rotating machineries, it was also observed that the gear meshing frequencies also contribute towards getting the response of the structure. These unbalance forces from the gears are occurred at their corresponding gear meshing frequencies. The unbalance force obtained is the tangential load Ft acting on the gear. Calculation of the unbalance forces Ft on the meshing gears present on different shafts are as follows. M-Tech Thesis 43 P.E.S.C.E., Mandya
  44. 44. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Unbalance gear-meshing force on Pulley Shaft Speed of the pulley = 760 rpm Gear meshing frequency = umber of teeth on the gear * speed of the shaft [21] = 42 * 760/60 = 532 Hz For non-cutting conditions Idle power = 0.3 KW from the wattmeter. Tangential load of meshing gear Where Ft = 2 Mt/d --------------- (3.3) Mt = 975000P/ = 975000 * 0.3/760 Mt = 3775.57 -mm Diameter of the gear d = 84mm ∴ Unbalance tangential force Ft = 89.8939 Similarly gear-meshing forces due to gear shaft and spindle shaft has been calculated. The summary of the unbalance forces and their corresponding frequencies were given in the Table 3.3. Table 3.3 Unbalance Forces and their Corresponding Frequencies Sl. o. Component 1 2 3 4 5 6 7 8 9 10 Chuck Spindle Gear shaft Gear 1 on the gear shaft Gear 2 on the gear shaft Gear 3 on the gear shaft Weight of the pulley Gear on the pulley Weight of the pulley shaft Meshing gears on the gear shafts 11 12 Meshing gear on the pulley shaft Meshing gear on the spindle shaft Unbalance force 9.182 7.494 2.785 0.596 0.859 0.735 37.92 2.354 3.727 67.19 43.47 89.89 28.98 Frequency of occurrence Hz 20 20 13.33 13.33 13.33 13.33 12.67 12.67 12.67 533.33 532 600 The unbalance forces calculated above were applied at their corresponding locations. Frequency range of 0-600 Hz was selected to know the response of these forces. The responses in the form of vibration velocity were taken at front and rear bearings along both the horizontal and vertical directions. M-Tech Thesis 44 P.E.S.C.E., Mandya
  45. 45. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 3.10.3 TRA SIE T RESPO SE A ALYSIS Transient response analysis was a technique used to determine the dynamic response of a structure under the action of any general time-dependent loads. The variation of loads can be represented in terms of vibration velocity with respect to time [22]. A defect assumed as Destructive pitting and the effect of this defect on the vibration level was studied. Transient dynamic analysis is carried out to determine the response of structure subjected to time varying loads. The variation of loads can be represented in terms of amplitude versus time. The pitting defect that is assumed is present in all teeth of the driven gear, which is meshing with the driver gear in main spindle of the machine tool. The unwanted disturbing forces are generated due to meshing of good gear with pitted Gear teeth. The nature of contact of two mating pair is shown in the below figure 3.4 using band of contact as the point of contact. This gives sufficient details about the effect and load distribution with respect to time. The figure 3.5 shows the corresponding load transmitted Vs time for the given pitting defect for any speed only the time varies according to the standard time calculations. Fig o: 3.4 Band of Contact during Pitting M-Tech Thesis 45 P.E.S.C.E., Mandya
  46. 46. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 3.5 Load Transmitted Vs Time Graph during Pitting Once both the gear starts to rotate, the concept of movement of band of contact is addendum to dedendum in driven gear and dedendum to addendum in driver gear. When meshing starts during pitting the band of contact starts from normal position to pitting leading to zero contact. When the contact starts again the force required to over come is high leading to fluctuation power utilization of driving motor. The figure 3.4 and 3.5 shows how band of contact is establish during pitting and transmission of load versus time is established. In figure 3.5 the graph shows normal ideal power running at 0.3 KW of main Ideal Power. This Power shoots up to 2% of Full power only when it starts to retard from its zero contact position. This effect is due to slight backlash effect or in other words jerking of driver gear to retard itself to its original position. The amount of fluctuation load is calculated as 2% of Full Power per pair of Gear Teeth in meshing. The time taken by the pinion for one revolution is 20 sec at 1200rpm. As each tooth of gear meshes with defected tooth of pinion, it produces a triangular pulse. Thus, for one revolution of driven gear 30 pulses were generated. M-Tech Thesis 46 P.E.S.C.E., Mandya
  47. 47. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 ormal ideal torque and Disturbing force calculations for 1200 rpm: Speed of the spindle, Idle Power, = 1200RPM P = 0.3 KW Ideal Torque=2385.69 -mm Ideal Load=2 * Ideal torque/D Diameter of the Driven Gear, D = 82.5mm Ideal load = 57.83 Due to defect 4% of Full power is taken as Additional Power Speed of the spindle, = 1200rpm Additional Power = 0.045 KW Additional Torque = 36.491 -mm Additional Load = 2* Additional Torque/D Diameter of the Driven Gear, D = 82.5mm Additional Load = 8.67 Disturbing Load = Ideal Load + Additional Load = 57.83 + 8.67 Disturbing Load = 66.50 Similarly the analysis has been carried for different spindle speeds and results are calculations and tabulated below. Sl. o 1 2 3 4 5 Table 3.4 list of disturbing force at different speed Spindle speed, Idle Load Disturbing Load Rpm 1200 57.83 66.50 775 89.53 102.95 500 138.75 159.57 315 220.25 253.33 140 495.75 567.56 These results are applied to the graph shown in figure below and the time steps or increments are noted and the effect is studied in transient analysis. M-Tech Thesis 47 P.E.S.C.E., Mandya
  48. 48. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 CHAPTER 4 EXPERIME TAL A ALYSIS 4.1 EXPERIME TAL SETUP Experiments were carried out on the enterprise 1330 precision lathe. This lathe has eight spindle speeds ranging from 54 to 1200 RPM. The specification of the lathe is given in Table 4.1. Fig. 4.1 shows the enterprise 1330 precision lathe. Table 4.1: Specification of Enterprise –1330 1 Center height 175 mm 2 Swing over Bed 350 mm 3 Swing over Cross slide 200 mm 4 Swing in Gap 520 mm 5 Width of gap in front of Face plate 130 mm 6 Spindle nose 4”-D1 Cam lock 7 Morse Taper in spindle sleeve MT 3 8 Spindle Bore 41 mm 9 Power of Motor (Main motor) 2.25 K.W. (3 H.P) 10 Range of spindle speed (8 os.) 54- 1200 RPM 11 Cross slide travel 210 mm 12 Compound slide travel 100 mm 13 Tai Tail -stock Quill travel 14 Capacity of Sq. Tool Post 20 x 20 mm Shank 15 Longitudinal feed range (36 os.) 0.045 – 0.676 mm/rev 16 Metric Thread range (11 os.) 0.5 – 6.0 mm 17 Inch Thread Range (36 os.) 4 – 60 T.P.I 18 Lead Screw Pitch (1” diameter) 4 T.P.I / 6 mm pitch M-Tech Thesis 48 140 mm P.E.S.C.E., Mandya
  49. 49. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 4.1 Enterprise 1330 Precision Lathe M-Tech Thesis 49 P.E.S.C.E., Mandya
  50. 50. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 4.2 MACHI E CO DITIO TESTER T 30 Machine Condition Tester is the instrument used to carry out the experiment. It has gained application in industries as a practical bearing-monitoring tool, providing relevant information on bearing condition. The Machine Condition Tester is based on high frequency acceleration signal referred as shock pulse. Machine Condition Tester is the instrument used to monitor rolling element bearings and detect wear and damage at an early age. Planned replacements will help to reduce downtime and prevent bearing failures. A ring surface of a bearing always has certain roughness even when they are new, which causes low acoustic emission. During the usage, cracks and pits appear due to which small particles of metal comes off and these are circulated within the bearing. As the fault area pass into caution zone, they cause small knocks, which are transmitted into bearing housing as a discontinuous knocks. More severe the crack, stronger will be the knock and pulses. These pulses will have high frequency range. Table 4.2 shows the specification of Machine Condition Tester T 30. Fig 4.3 shows the Machine Condition Tester T 30. Fig. 4.2: Machine Condition Tester T 30. Machine Condition Tester T 30 is available in three different versions: [21] BASIC LOGGER EXPERT M-Tech Thesis 50 P.E.S.C.E., Mandya
  51. 51. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 “Basic” measures vibration severity, shock pulses and temperature. It has no data logging functions. Measuring results are recorded manually. “Logger” measures the same quantities. In connection with the SPM software it gets its measuring instructions from a computer and uploads measuring results via cable to the computer. “Expert” has all the logger features. In addition, it uses the EVAM method for vibration spectrum analysis. Machine condition Tester combines the functions of a shock pulse meter, vibration meter, and tachometer. It requires few input data and allows an instant interpretation of machine condition by supplying, • Direct indication of machine vibration and bearing condition in terms of good reduced –bad • Digital display of shock values and vibration severity. With the Machine Condition Tester T 30, it is possible to monitor all significant aspects of mechanical machine condition during a single inspection round like the mechanical condition of the rolling element bearings and the general machine condition due to the effect of structural looseness and imbalance on machine vibration. The machine condition tester T 30 is based on two different methods for condition monitoring. Each method is tailored to supply the most accurate and useful information on the machine condition. Table 4.2: Specification of Machine Condition Tester T 30 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Measuring range, SPM Resolution, SPM Measuring range, VIB Resolution, VIB Accuracy, VIB Measuring range, TAC Measuring distance Resolution, TAC Accuracy, TAC Temperature range Power Size, T 30 Weight, T 30 Display M-Tech Thesis - 9 to 99 dBsv 1 dBsv 0.2 – 99.9 mm/sec RMS 0.1 mm/sec ± (0.1 mm/sec + 2% of reading) 10 to 19,999 rpm optical Max. 0.6 m (2 ft.) 1 rpm ± (1 rev. + 0.1 % of reading) 0o to 50o C 6 x 1.5 V LR6 cells 255 x 105 x 60 mm 0.85 kg Liquid crystal 51 P.E.S.C.E., Mandya
  52. 52. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 4.3 MEASURI G PARAMETERS Vibration ranks among the most destructive forces in the machine tools. Vibration influences the operation, performance and life expectancy of the machine tools. The vibratory signatures measured will be of a greater value in knowing the machine condition. Since lathe is a complex system, it is not possible to monitor all the parameters. The parameters selected for measurement are vibration velocity. Vibration velocity is the parameter to evaluate the severity of the vibration of the lathe measured in RMS value. In driving spindle, the most frequent failure is due to spindle bearings. 4.4 MEASUREME T LOCATIO The proper selection of the measurement location is important and care should be taken to select the measurement location and direction of measurement to ensure that the most effective data is obtained. The measurement locations generally selected are the bearing housing of a lathe because it is through these housing that the force of vibration of the rotating elements are transmitted. The measurements are made on the front and rear side of the bearing housing in the horizontal and vertical directions respectively. When the dominant mechanical defect in a machine is unbalance, vibration transducers which are mounted on each bearing housing in horizontal direction will be adequate to detect such imbalance. If the defect in the machine is misalignment, to insure its presence, measurements in both horizontal and vertical directions are needed. 4.5 EXPERIME TAL PROCEDURE 4.5.1 VIBRATIO VELOCITY MEASUREME T For measuring vibration velocity Machine Condition Tester T 30 was used. It measures vibration severity in the range of 0.2 to 99.9 mm/s. To measure the vibration one end of the vibration transducer was connected to the input marked VIB of T 30 instrument and the other end of the cable was connected to the vibration transducer and switch on the T 30 to the VIB mode. The same measuring points were selected for measuring the vibration. Machine class number is set to class I according to ISO 2372 recommendations since the power of the motor was 2.25 KW [16]. To measure the vibration velocity, transducer with the magnetic base was placed at the front and rear bearing housings along horizontal and vertical directions respectively. The readings were taken for different spindle speeds. After M-Tech Thesis P.E.S.C.E., Mandya 52
  53. 53. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 taking the readings, the data was transferred back to the computer for the further analysis. Table 4.5 shows the experimental values for different spindle speeds at the front and rear bearing Table 4.3: vibration velocity at different spindle speeds Sl. o. Spindle speed Vibration velocity at Front Vibration velocity at (rpm) Bearing mm/s Rear Bearing mm/s Horizontal Vertical Horizontal Vertical 1 140 0.21 0.10 0.12 0.10 2 315 0.24 0.13 0.16 0.11 3 500 0.29 0.17 0.19 0.16 4 775 0.35 0.19 0.20 0.18 5 1200 0.39 0.22 0.23 0.21 M-Tech Thesis 53 P.E.S.C.E., Mandya
  54. 54. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 CHAPTER 5 RESULTS A D DISCUSSIO 5.1 MODAL A ALYSIS Modal analysis was carried out to obtain the natural frequencies and its mode shapes. The natural frequencies and mode shapes were important parameters in the design of a structure for dynamic loading conditions. The first ten mode shapes were computed. The Fig. 5.1 shows the first mode shape of the lathe structure. When modal analysis is performed on a lathe, it reveals the possible resonant conditions and these resonant conditions with their frequencies of occurrence and their description are given in the Table 5.1. Mode shapes are defined by the amplitude of displacements of all the mass points during the vibration of the structure at natural frequencies. From the Fig. 5.1 it was observed that the rocking of the bed was occurring in the X- direction during the first mode shape of resonant frequency 57.199 Hz. Similarly the five different mode shapes were shown in the Fig. 5.2 to Fig. 5.5. Modal analysis was used as a starting point for a harmonic response analysis. The results obtained were used in the harmonic response analysis. Table 5.1: Mode Shapes and Its atural Frequencies Mode shapes atural frequencies in Hz Description 1 57.199 Rocking of the bed in X- direction 2 71.388 Bending of the carriage. 3 83.861 Bending of the right and left leg. 4 88.477 Twisting of the right leg 5 119.29 Twisting of the bed. 6 151.67 Torsion movement of the carriage. 7 152.96 Deformation in the right leg. 8 169.55 Torsion movement of the left leg 9 179.29 Deformation in the left leg. 10 199.62 Higher mode deformation in the left leg. M-Tech Thesis 54 P.E.S.C.E., Mandya
  55. 55. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.1: First Mode Shape of a Lathe Structure Fig. 5.2: Second Mode Shape of a Lathe Structure M-Tech Thesis 55 P.E.S.C.E., Mandya
  56. 56. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.3: Third Mode Shape of a Lathe Structure Fig. 5.4: Fourth Mode Shape of a Lathe Structure M-Tech Thesis 56 P.E.S.C.E., Mandya
  57. 57. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.5: Fifth Mode Shape of a Lathe Structure 5.2 HARMO IC RESPO SE A ALYSIS After the modal analysis, next step is to carry out harmonic response analysis. Harmonic response analysis was used to determine the response of the lathe structure to the unbalance forces. Fig 5.6 to Fig 5.17 shows the response of the structure in terms of vibration velocity in the frequency domain measured at the front and rear bearing housing along horizontal and vertical directions respectively. Fig.5.6 shows the vibration velocity at front bearing along horizontal and vertical direction. The effect of unbalance forces from the chuck and the spindle are as shown in the Fig.5.6 and gives the information about the vibration level during the operation. The value of vibration velocities by the chuck and the spindle at their operating frequency of 20 Hz were observed. Also, as it is seen from the Fig. 5.6 the resonance was occurring at the first natural frequency i.e. at 57.199 Hz. Fig.5.7 shows the vibration velocity at the rear bearing. Similarly Fig. 5.8 to Fig. 5.17 shows the vibration velocities from the different elements at front and rear bearing. M-Tech Thesis 57 P.E.S.C.E., Mandya
  58. 58. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.6: Vibration Velocity due to Chuck and Spindle at Front Bearing Fig. 5.7: Vibration Velocity due to Chuck and Spindle at Rear Bearing M-Tech Thesis 58 P.E.S.C.E., Mandya
  59. 59. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.8: Vibration Velocity due to Gears at Front Bearing Fig. 5.9: Vibration Velocity due to Gears at Rear Bearing M-Tech Thesis 59 P.E.S.C.E., Mandya
  60. 60. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.10: Vibration Velocity due to Pulleys at Front Bearing Fig. 5.11: Vibration Velocity due to Pulleys at Rear Bearing M-Tech Thesis 60 P.E.S.C.E., Mandya
  61. 61. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.12: Vibration Velocity due to Pulley Shaft at Front Bearing Fig. 5.13: Vibration Velocity due to Pulley Shaft at Rear Bearing M-Tech Thesis 61 P.E.S.C.E., Mandya
  62. 62. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.14: Vibration Velocity due to Gear Shaft at Front Bearing Fig. 5.15: Vibration Velocity due to Gear Shaft at Rear Bearing M-Tech Thesis 62 P.E.S.C.E., Mandya
  63. 63. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.16: Vibration Velocity due to Spindle Shaft at Front Bearing Fig. 5.17: Vibration Velocity due to Spindle Shaft at Rear Bearing M-Tech Thesis 63 P.E.S.C.E., Mandya
  64. 64. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Further, the vibration levels in the frequency domain are transformed to vibration levels in time domain. This is to obtain the RMS value of the vibration velocity of various signals, which are at different frequencies. For this Fast Fourier Transformation analysis technique was used to convert the vibration velocity from the frequency domain to time domain. Fig.5.18 to Fig.5.21 shows the vibration velocities due to different elements measured in the time domain. Fig. 5.18 shows the vibration velocity in time domain measured at front bearing along horizontal direction. It is the result of harmonic analysis in frequency domain converted to time domain. The figure depicts the effect of unbalance forces of individual elements on the machine tool. The combined effect of these unbalance forces is shown as RMS velocity having the value of 0.36477 mm/s. Fig. 5.19 shows the vibration velocity in time domain measured at front bearing along vertical direction. The RMS vibration velocity for the front bearing along vertical direction was 0.1957 mm/s. Similarly; the RMS vibration velocities in horizontal and vertical direction for rear bearing are 0.1791 mm/s and 0.239 mm/s respectively as shown in the Fig. 5.20 and Fig. 5.21. Fig. 5.18: Vibration Velocity in Time Domain at Front Bearing along Horizontal Direction M-Tech Thesis 64 P.E.S.C.E., Mandya
  65. 65. Vibration Analysis of Lathe Structrure Due to Gear Defect Using FEM 2004 /2005 Fig. 5.19: Vibration Velocity in Time Domain at Front Bearing along Vertical Direction Fig. 5.20: Vibration Velocity in Time Domain at Rear Bearing along Horizontal Direction M-Tech Thesis 65 P.E.S.C.E., Mandya

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