Dynamic Analysis Of A Reciprocating Compressor

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DYNAMIC ANALYSIS OF A RECIPROCATING COMPRESSORByClare Marie Sia An An12554Dissertation submitted in partial fulfilment of the requirements for theBachelor of Engineering (Hons)(Mechanical Engineering)MAY 2013Supervisor: AP Dr. Tadimalla V.V.L.N. RaoUniversiti Teknologi PETRONASBandar Seri Iskandar31750 TronohPerak Darul Ridzuan

DYNAMIC ANALYSIS OF A RECIPROCATING COMPRESSORByCLARE MARIE SIA AN ANA project dissertation submitted to theMechanical Engineering ProgrammeUniversiti Teknologi PETRONASin partial fulfilment of the requirement for theBACHELOR OF ENGINEERING (Hons)(MECHANICAL ENGINEERING)Approved by,(AP Dr .Tadimalla V.V.L.N. Rao)UNIVERSITI TEKNOLOGI PETRONASTRONOH, PERAKAugust 2013

CERTIFICATION OF ORIGINALITYThis is to certify that I am responsible for the work submitted in this project,that the original work is my own except as specified in the references andacknowledgements, and that the original work contained herein have not beenundertaken or done by unspecified sources or persons.CLARE MARIE SIA AN ANiii

ABSTRACTReciprocating compressors are widely used in the industry and plays animportant role in maximising productivity as it increases the pressure and reduces thevolume of a gas. Compressors are sensitive equipments and maintenance has to beperformed when the equipment fails. Reciprocating compressor has both rotary andreciprocating motion involved. Unbalance forces are bound to occur on the dynamiccomponents and this causes a lot of vibration in which might spoil the compressor.Analyzing these forces might help to overcome the unbalance forces and thus reducethe vibration and faultiness in the compressor.Using softwares that are made available, analyzing of these forces will bepossible with less hassle. CATIA is used to produce the model of the compressor andwith the completed model, it is then imported in ADAMS for simulating andanalyzing. Results are shown through graphs and discussions were made to analyzethe results.iv

CONTENTSCERTIFICATION OF ORIGINALITY . iiiABSTRACT . ivCONTENTS . vLIST OF FIGURES . viiLIST OF TABLES . viiLIST OF GRAPHS . viiiCHAPTER 1: INTRODUCTION . 11.1Background Study . 11.1.1Reciprocating Compressor . 11.2Problem Statement . 21.3Objectives . 21.4Scope of Study. 2CHAPTER 2: LITERATURE REVIEW . 32.1Slider-Crank Mechanism . 32.2Unbalance Forces . 42.3Rotating and Reciprocating Unbalance . 62.3.1Inertia Balance . 82.3.2Torque Reaction . 82.3.3Torsional Vibrations of Crankshaft . 92.4Balancing of Reciprocating Engines. 92.5Balancing of Single-Cylinder Cranktrain. 92.6Balancing of a Multi-Cylinder Cranktrain .10CHAPTER 3: METHODOLOGY .143.1Research .143.2Modelling and Simulation .143.3Data Analysis .15v

3.4Project Flow Chart .163.6Gantt Chart .17CHAPTER 4: RESULTS & DISCUSSIONS .184.1Modelling and Simulation .184.2Graph Analysis .214.2.1Element Force Analysis for Single Cylinder Configuration .214.2.2Element Force Analysis at Cylinder 1 .234.2.3Element Force Analysis at Cylinder 2 .244.2.4Element Force Analysis at Cylinder 3 .264.2.5Element Force Analysis at Cylinder 4 .274.2.6Vibration Analysis at Crankshaft .304.2.7Vibration Analysis at Piston 1 .314.2.8Vibration Analysis at Piston 2 .324.2.9Vibration Analysis at Piston 3 .334.2.10Vibration Analysis at Piston 4 .34CHAPTER 5: RECOMMENDATIONS .36CHAPTER 6: CONCLUSION .37CHAPTER 7: REFERENCES.38APPENDIX .39APPENDIX I .39vi

LIST OF FIGURESFigure 1 Friction Marks on the Piston . 2Figure 2 Friction Marks on the Cylinder . 2Figure 3 Slider-Crank Mechanism . 3Figure 4 Forces Acting in the Engine Frame. 4Figure 5 Partial Balancing of Unbalanced Primary Force in a Reciprocating Engine. 5Figure 6 Gas Pressure Load on a Single Cylinder Machine . 7Figure 7 Complete Balance of the Inertial Forces of the First Order .10Figure 8 General Arrangement of a 6 Cylinder Compressor .11Figure 9 ADAMS Analysis on Single Crank-Crosshead-Piston ConfigurationMechanism.18Figure 10 Completed Model in 3-dimensional View .19Figure 11 Completed Model in Multiple Views .19Figure 12 CATIA model Imported into ADAMS .20Figure 13 Crosshead Top and Bottom View .36LIST OF TABLESTable 1 Star Diagram of the 1st and 2nd Order for Three- to Six-Cylinder, In-LineEngines .12Table 2 Forces and Moments Applied to the Piston, Connecting Rod and Crankshafton an Engine .13Table 3 Resultant Mass Forces and Mass Couples for Reciprocating Engines .13vii

LIST OF GRAPHSGraph 1 Piston Force Analysis .21Graph 2 Crosshead Force Analysis .22Graph 3 Piston Force Analysis .23Graph 4 Crosshead (Force Analysis at Revolute Joint) .23Graph 5 Crosshead (Force Analysis at Translational Joint) .24Graph 6 Piston Force Analysis .24Graph 7 Crosshead (Force Analysis at Revolute Joint) .25Graph 8 Crosshead (Force Analysis at Translational Joint) .25Graph 9 Crosshead (Force Analysis at Revolute Joint) .26Graph 10 Piston Force Analysis .26Graph 11 Crosshead (Force Analysis at Translational Joint) .27Graph 12 Piston (Force Analysis) .27Graph 13 Crosshead (Force Analysis at Revolute Joint) .28Graph 14 Crosshead (Force Analysis at Translational Joint) .28Graph 15 Vibration Analysis of Crankshaft at the End of Cylinder 1 .30Graph 16 Vibration Analysis of Crankshaft at the End of Cylinder 4 .30Graph 17 Vibration Analysis at Piston 1 in X-direction.31Graph 18 Vibration Analysis at Piston 1 in Z-direction .31Graph 19 Vibration Analysis at Piston 2 in X-direction.32Graph 20 Vibration Analysis at Piston 2 in Z-direction .32Graph 21 Vibration Analysis at Piston 3 in X-direction.33Graph 22 Vibration Analysis at Piston 3 in Z-direction .33Graph 23 Vibration Analysis at Piston 4 in X-direction.34Graph 24 Vibration Analysis at Piston 4 in Z-direction .34viii

CHAPTER 1: INTRODUCTION1.1Background Study1.1.1 Reciprocating CompressorReciprocating compressors are classified under positive displacementcompressors. Volumes of gas are confined within a limited space andincreased to a higher pressure.Reciprocating compressors are the mostly used compressors in theclass of positive displacement compressors. The mechanism is simply by themeans of a pushing force of a piston in a cylinder. The piston moves up anddown inside the cylinder and this force the gas into a smaller space, and thusincreases the pressure. The basic reciprocating compression element is asingle cylinder compressing on one side of the piston. The use of both sideswill be the two basic single-acting elements operating in parallel in one set ofup-down action.Rotary motion from the motor or any other external driver to thecompressor is translated to linear motion by using the crankshaft, and thepiston rod. The end of the piston rod is secured by the crankpin to thecrankshaft, and the other by the piston, as the crankshaft turns, reciprocates ina linear motion. The suction and discharge valves are usually located at thetop and bottom of the cylinder and are simply, check valves that allows theone way flow of the gas. When the piston moves up, a partial vacuum in thelower end of the cylinder will occur; the pressure differential makes thevalves to open and allowing gas to flow into the cylinder. Whereas for thedownward stroke, pressure in the cylinder exceeds the pressure in thedischarge line will cause the valve will open and allow the gas to flow fromthe cylinder to the discharge. If this occurs on one side of the piston, it iscalled ‘single-acting’ compression whilst both side; it is called ‘doubleacting’ compression.The drawing of a reciprocating compressor and its components can bereferred to Appendix I1

1.2Problem StatementFollowing through the repair of the compressor during the industrialinternship period, it was brought to attention that the cylinder was of an ovalcross-section due to the rubbing of the piston against the cylinder wall.A specialist from the original equipment manufacturer was called in toconduct the repair, still the compressor experience the same problem after aperiod of time. Thus this led to conducting a dynamic analysis on thereciprocating compressor in which the balancing of the compressor will bestudied.Figure 1 Friction Marks on thePiston1.3Figure 2 Friction Marks on theCylinderObjectivesThe project is set out to achieve a few objectives which are listed as follows:1.4 To identify the unbalanced forces of the reciprocating compressor. To model and simulate out the reciprocating compressor’s dynamics. Suggest in any possible modifications and recommendations.Scope of StudyThe project will study in the range of the balancing and unbalancing of thereciprocating compressor Balancing of reciprocating compressor. Four cylinder, vertical reciprocating compressor. Analysis of the crankshaft, crosshead and piston.2

CHAPTER 2: LITERATURE REVIEW2.1Slider-Crank MechanismThe slider-crank mechanism is mainly used to translate the rotary motion to areciprocating motion or vice versa.Equation 1:𝒂𝒑 𝑨𝒄𝒄𝒆𝒍𝒆𝒓𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝑷𝒊𝒔𝒕𝒐𝒏 𝑟𝜔2 cos 𝜃 cos 2𝜃𝑛1; 𝑛 𝑟Equation 2:𝐹𝑖 Force required to accelerate the mass 'm' 𝑚𝑟𝜔2 cos 𝜃 cos 2𝜃𝑛 𝑚𝑟𝜔2 cos 𝜃 𝑚𝑟𝜔2cos 2𝜃𝑛In the second equation, 𝒎𝒓𝝎𝟐 𝐜𝐨𝐬 𝜽 is called the primary accelerating forcewhilst 𝒎𝒓𝝎𝟐𝐜𝐨𝐬 𝟐𝜽𝒏is known as the secondary accelerating force. The maximumvalue of primary accelerating force is 𝒎𝒓𝝎𝟐 . Maximum value for secondary𝟐accelerating force is 𝒎𝒓𝝎 𝒏. The primary force is big compared to thesecondary force and thus the secondary force can be safely neglected in slowspeed engines.Figure 3 Slider-Crank Mechanism3

Figure 3 shows the inertia force caused by the accelerating force. WhereasFigure 4 shows the inertia forces; at’0’ the force exerted by the crankshaft on the main bearings has two components, the horizontal and vertical marked by 𝐹21and𝑣 𝐹21respectively. 𝐹21is an horizontal force, which is an unbalanced shaking force.𝑣𝑣𝐹41and 𝐹21balance each other but form an unbalanced shaking couple. (Bongale)Figure 4 Forces Acting in the Engine Frame2.2Unbalance ForcesFrom the point of view in design, the unbalanced forces are produced byrotating and reciprocating masses. Reciprocating forces occur in all compressorsfrom acceleration and deceleration of the reciprocating weights. Rotating forcesresult from the centrifugal force produced from the unbalanced weights of thecrank-throw and part of the connecting rod. (Bloch, 2006)Since the shaking force and a shaking couple differ in magnitude anddirection during the engine cycle, therefore they cause very objectionablevibrations. In most of the mechanisms, the shaking force and a shaking couple canbe reduced by adding appropriate balancing mass, but it is usually not practical toeliminate them completely. This means that the reciprocating masses are onlypartially balanced. In reference of Figure 5, the primary force acts from ‘O’ to ‘P’along the line of stroke. Consequently, balancing of primary force is considered asequivalent to the balancing of mass ‘m’ rotating at the crank radius r. This isbalanced by having a mass B at a radius b, placed diametrically opposite to thecrank pin C. (Khumi, 2010)4

Figure 5 Partial Balancing of Unbalanced Primary Force in a Reciprocating EngineReferring again to Figure 4, the primary force will be completely balanced if Bb mr. However the centrifugal force by the revolving mass B, also has a verticalcomponent in which it is perpendicular to the line of stroke, of magnitude Bω2b sinθ and this force remains unbalanced. The maximum value of this force is equivalentto Bω2b when θ is at 90 and 270 , which is same as the maximum value of theprimary force mω2r.The primary unbalanced force acts along the line of stroke whereas in thesecond case, the unbalanced force acts along the perpendicular to the line of stroke.The maximum value of the force remains same in both the cases. Thus, the effect ofthis balancing changes the direction of the maximum unbalanced force from alongthe line of stroke to the perpendicular of line of stroke. A fraction ‘c’ will be used tocompromise for the reciprocating masses balanced, giving: cmr BbUnbalanced force along the line of stroke: 1 𝑐 𝑚𝜔2 𝑟 cos 𝜃Unbalanced force along the perpendicular to the line of stroke: 𝑚𝜔2 𝑟 (1 𝑐)2 cos 2 𝜃 𝑐 2 𝑠𝑖𝑛2 𝜃5

2.3Rotating and Reciprocating UnbalanceTorsional oscillation in the crankshaft and in the shafting of drivenmachinery is an important group of vibration phenomena of practicalimportance in reciprocating machines. A combination of periodicaccelerations of moving parts (piston, connecting rod, crank) and periodicvariations in cylinder steam or gas pressure seems to be the cause.For a single cylinder vertical reciprocating machine, the pistonexecutes an alternating motion, and in the process experiences alternatingvertical accelerations. To have a downwards motion on the piston, theremust exist a downward force acting on it and this force must have a reactionpushing upward against the stationary parts of the engine. Therefore, thealternating acceleration of the piston is coupled with an alternating force onthe cylinder frame, making a feel of vibration in the engine and its supports.Whereas in the lateral direction perpendicular to both the crankshaft and thepiston rod, moving parts are also being accelerated which are the crank pinand the part of the connecting rod. The forces that cause these accelerationsmust have equal and opposite reactions on the frame of the machine. Thislast effect is the horizontal unbalance. In the crankshaft main axis, no inertiaforces appear, since all moving parts remain in planes perpendicular to thecrankshaft.These various inertia forces can cause moments can cause moments.When two vertical cylinders are considered with a crank set 180 o apart,when one piston is accelerated downward the other piston is acceleratedupward, the two inertia forces from a couple tend to rock the machine abouta lateral axis. Consequently, the horizontal or lateral inertia forces of thetwo cracks are equal and opposite, forming a couple tending to rock themachine about a vertical axis. Rocking about the crankshaft axis can happeneven in a single cylinder machine. If the piston is accelerated downwards bya pull in the connecting rod, this pull exercises a torque about the crankshaftaxis. Since the piston acceleration is alternating, this inertia torque is alsoalternating. (Rangwala, 2006)6

If the whole machine mounted on weak springs is considered as themechanical system, the external torque is zero and with any increase inclockwise angular momentum of the moving parts must be neutralized by anincrease in counter-clockwise angular momentum of the stationery parts ofthe machine. Considering merely the dynamic parts of the machine as themechanical system, an increase in clockwise angular momentum of themoving parts must be caused by a clockwise torque on these parts, whichhas a counter-clockwise reaction torque is transmitted to the foundation andmay cause problems. However, if instead it is mounted on soft springs,reaction to the foundation cannot penetrate through these springs and thecounter torque is absorbed as an inertia torque of the frame and cylinderblock, and the machine block must vibrate. (Rangwala, 2006)Figure 6 Gas Pressure Load on a Single Cylinder Machine7

In reference to Figure 6, inertia forces are excluded by assuming themachine to be rotating at a slow and constant speed ω, or the moving partshave negligible mass. Apart from acting on the piston, the gas pressure alsopresses upward against the cylinder head. Pressure force on the piston istransmitted through the piston rod to the crosshead. If friction is neglected,it is held there in equilibrium by forces 2 and 3 in Figure 6. Of the forcesacting on the crosshead, force 3 is a compression in the connecting rod, and2 is a reaction pressure on the frame to the right, of magnitude Pv tan (ϕ).Force 3 of magnitude P/cos (ϕ) is transmitted through the connecting rod tothe crank pin. Force 5 is taken up by the main bearings at O and can beresolved into a vertical component 6 and a horizontal component 7. Triangle1, 2, 3 and 5, 6, 7 are alike so the magnitude of 6 is P and that of 7 is P tan(ϕ).No forces occur along the longitudinal crankshaft axis of a machine,while in the lateral and vertical directions, only inertia forces appear. On thevertical and lateral axes, only inertia torques were found, and in thelongitudinal direction both an inertia torque and a cylinder gas pressuretorque occur. If assumptions are made that the machine is built of anelastically non-deformable members, the problem is one of static balanceonly. The frame and other stationary parts generally fulfil this condition, butthe crankshaft can be twisted significantly, making torsional vibrationspossible. The subject may be divided into three categories:2.3.1Inertia BalanceRefers to the balancing of the machine against vertical andlateral forces, and against moments about the vertical andlateral axes.2.3.2 Torque ReactionUnder this heading the effects of torque due to inertia and gaspressure acting on the stationary parts about the longitudinalaxis are analyzed.8

2.3.3 Torsional Vibrations of CrankshaftConsequences of the longitudinal torque on the moving partsof the reciprocating machine are dealt with. (Rangwala, 2006)2.4Balancing of Reciprocating EnginesThus, from the equations of the unbalance forces, the balancing massrequired in balancing the rotating and reciprocating masses can be obtained by thefollowing equation:𝐵𝑏 𝑚1 𝑐𝑚 𝑟Where:𝑚1 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑟𝑜𝑡𝑎𝑡𝑖𝑛𝑔 𝑚𝑎𝑠𝑠𝑒𝑠, 𝑘𝑔𝑚 𝑀𝑎𝑔𝑛𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 �� 𝑚𝑎𝑠𝑠𝑒𝑠, 𝑘𝑔𝐵 𝑀𝑎𝑠𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑡𝑜 𝑏𝑎𝑙𝑎𝑛𝑐𝑒, 𝑘𝑔𝑏 𝑅𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝐵, 𝑚2.5Balancing of Single-Cylinder CranktrainActions that compensate for the outside effect of mass forces are thebalancing of reciprocating masses. Stress still remains in the engine as aresult of the mass forces. For a single cylinder cranktrain, a completecompensation of the mass forces is possible when two pairs of rotatingmasses are added. The compensating masses are arranged in a way that theresulting alternating harmonic forces act in the centre of the cylinder and areopposite to the masses forces F1 and F2. The arrangement of the balancingmasses can be shown in Figure 7.9

Figure 7 Complete Balance of the Inertial Forces of the First Order2.6Balancing of a Multi-Cylinder CranktrainThe mass force of a multi-cylinder cranktrain is the sum of the mass forcesof the individual cylinders. Since the reciprocating mass forces of the individualcylinders act in the individual cylinder centre lines, mass couples can result. Forin-line engines, a schematic calculation is used to determine the mass forces dueto a parallel cylinder arrangement. It is sufficient to consider the vectors of theindividual cylinders F 1k, F 2k (k is the number of cylinders that rotate in thesame direction). For each order, these vectors can be added directly to resultingrotating vectors F I or F 2. (Baharom, 2013)In a multi-cylinder, it is possible to balance some or all of the inertia forcesand torques by proper arrangement of the cranks. Figure 8 shows the generalarrangement of six cylinder compressor. To balance the force, the total inertiaforce in the x and y directions must be zero. (Singiresu S. Rao, 2011).10

Figure 8 General Arrangement of a 6 Cylinder CompressorMulti-cylinder engines have mutual counteractions between the variouscomponents in the crankshaft assembly which is one of the essential factors indetermining the selection of the crankshaft's configuration. The inertial forces will bebalanced when the common centre of gravity for all moving crankshaft-assemblycomponents lies at the crankshaft's midpoint. In other words, the crankshaft issymmetrical when viewed from the front. The crankshaft's symmetry level is definedusing geometrical representations of 1 st and 2nd order forces or the star diagrams. The2nd order star diagram for the four-cylinder in-line engine is asymmetrical, denotingthat this order is characterized by substantial free inertial forces. These forces can bebalanced using two countershafts rotating in opposite directions at double the rate ofthe crankshaft as also shown in Figure 7. (Robert Bosch Gmbh, 2002)11

Table 1 Forces and Moments Applied to the Piston, Connecting Rod and Crankshafton an Engine12

Table 2 Star diagram of the 1st and 2nd order for three- to six-cylinder, in-lineenginesTable 3 Resultant Mass Forces and Mass Couples for Reciprocating EnginesTable 3 show the analyzed resultant mass forces and mass couples of thereciprocating engines for different type of configurations. Through this table, it isshown that the best configuration that will eliminate both the free moments and freeforces will be a 6-cylinder in-line engine configuration.13

CHAPTER 3: METHODOLOGYThis project is separated into a few phases where different methods arecarried out. In the beginning, identifying the problem and objective of project wasperformed. Next the project background study was conducted. Then the project willproceed with the research phase where ample studies and literature review is beingdone. The project would then be continued with modelling stage using relevantsoftware. The methodology involved for all project phases is explained at the fewmethodology breaks down below:3.1ResearchPreliminary research was done to explore the topic further. Sufficientreading was done on relevant books from the Information Resource Centre as wellas conference proceedings and journals that are available in the internet. Theresearch will be carried out throughout the study to better understand the project.As dynamic analysis has a very wide scope, it will be narrowed down to theunbalance forces of the reciprocating compressor.Literature reviews on research papers, journals and articles previously doneby researchers were conducted. The centre of the literature reviews includesbalancing of reciprocating compressors and engines, vibration analysis of thereciprocating compressor and unbalanced forces in single and multi cylinderengines. Nevertheless, it is not limited to the few focuses stated as it changes maydevelop through the project as it goes on. Literature review would be doneconstantly throughout the project to gather more information or as data validationprocess.3.2Modelling and SimulationADAMS software is used directly to simulate the forces in X, Y and Zdirection for a single crank-crosshead-piston assembly. Links in ADAMS were setup and joined in order to simulate. The dimensions were not to scale with theactual reciprocating compressor mentioned in the problem statement. Weight wasalso added into the simulation to obtain a more accurate simulation and result.14

Modelling out the primary internal components of the reciprocatingcompressor using software called CATIA. Firstly, the crankshaft was modelledout, since the dimensions, tolerances and other relevant measurements of thecompressor is kept confidential to the original engineering manufacturer (OEM),the compressor modelled is similar to the compressor mentioned in the problemstatement in terms of component arrangement and not to scale or to the exactdimension. Modelling in CATIA consist of drawing out using the softwareplatform and then extrusion to produce a 3D model. When each component iscompleted, the components are added in together through the CATIA assemblyplatform. After the modelling is completed, the centre of gravity markers for eachcomponent connection is taken down. The next step is to save each component inthe assembly drawing as ‘igs’ format so it can be imported into ADAMS to besimulated. Through the ADAMS software, the whole operation can be simulatedand the forces in X,Y and Z direction can be analyzed for the three maincomponents which is the crankshaft, crosshead and the piston. Vibration analysiscan be obtained after simulating and through plotting of the graphs.3.3Data AnalysisAfter simulating is done, the software, ADAMS, will be able to plot outgraphs of forces in X,Y and Z direction for the primary components of thecompressor. Another set of graphs will be plotted for vibration analysis; this graphis obtained through the difference in forces during static simulation and dynamicoperation. By obtaining this, analyzing the compressor will be possible and moreaccurate.15

3.4Project Flow nof theModelYESValidationNOYESDissertationSTOP16NO

3.6Gantt ChartSemester 1Activities12345678Semester 291

reciprocating compressor in which the balancing of the compressor will be studied. 1.3 Objectives The project is set out to achieve a few objectives which are listed as follows: To identify the unbalanced forces of the reciprocating compressor. To model and simulate out the reciprocating compressor's dynamics.

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