Analysis of a Dynamic System - Gearbox Modelling - Case Study Example

Student’s Name Instructor’s Name Course Name: Date: 25th November, 2012. Abstract For any gearbox to be successful in compatibility with the vehicle or machine where it is used, the design and modelling should take into account that a gearbox can withstand various during it use. The faults that are experienced that need to be modelled include erosion, broken shafts, broken teeth and broken box. The gear box has been modelled on the assumption that ether of the above mentioned can be fault and the gearbox works to the satisfaction of the user. A gearbox has been modelled using Adams software focusing on teeth and the faults expected on it. The purpose was to make sure the gearbox was able to perform their duties while it had broken teeth. Simulation was done by mounting accelerometer which will detect signals that will emanate from the gearbox. At the beginning, a gearbox with a fault tooth was used and then another gearbox without defects was used. The signals were recorded and the force variation was measured and recorded in Adam’s software. The resulting meshing teeth was calculated and various simulations done on friction, force and stiffness coefficients. Simulation was done by mixing noise and supporting forces to determine its working conditions. The results showed that frequencies were different but resulting for were same that detected a gearbox with a broken tooth. Introduction Gearboxes are very important in vehicles and other machines that are in use in factories. If these gearboxes are faulty, many activities will not successively take place. A gearbox can experience faultiness when it has a broken box due to carrying heavy loaded, subjected to heat, having a broken teeth, being eroded because of lack of oiling, having broken shafts and other form of faultiness. This means faultiness should be detected earlier to avoid complete failure which may lead to accidents or damage or machine failure. To detect gearbox failure, accelerometer is used and it measures the differences in frequency of the gearbox during usage. It is important to consider having the knowledge concerning the simulation using Adams regarding the fault detection all the way to the diagnosis in gearbox. Following this process, fault detection occurs with similar models while considering the relationship that does exist between signals like the parameter estimation, observers, component analysis and parity equations. Furthermore, there are several examples that can be considered when it comes to fault detecting as well as the diagnosis of the gearbox. As a way of facilitating the detection regarding the mechanical defects that are experienced in the mechanical vibrators are normally converted to strong electrical signals through the use of a sensor which is the pre-conditioned therefore converting them to digital signals. Considering the preconditioning, the signals are normally comprised of processes like of anti-alias filtering as well a pre-amplifying. Regarding the anti-alias filter, the processes operate on a frequency of about 5 kHz while the highest limit of the sensors is normally approximately 10 kHz. However, there are other sampling rates that generally can be applied like the 14 AD converter ranging between 15 to 20 kHz (Norfield, 301). Ultimately, the collected information is then recorded into a known memory for future reference and can also be used for other calculations. As a matter of fact, there are present inventions that have been utilized when it comes to collection of vibration of data hence calculating particular sets of parameters regarding vibration analysis. This paper is using Adam’s software to simulate the operations of a gearbox by looking at the broken teeth gearbox and a perfect gearbox with the aim of explaining the causes of abnormal reaction force that emanates from the operations of the gearbox. A model has been designed to explain the impact of lack of teeth or broken tooth and be able to predict the force and movements of the gearbox during the testing. Various methods of determining the reaction force has been employed because each gearbox has different signals that emanate even when it is not faulty. If there is a fault in the gearbox, the frequency will continue to be different when the gearbox is rotating, therefore, it is important to simulate the signals vibrating from the gearbox under different conditions so that we can come up with a well documented gearbox which is free from fault. Adam’s software will help us in detecting and diagnosing a fault in a gearbox. The gearbox movements will be monitored and frequency taken in order to observe the impact of the missing or broken tooth with aim of knowing the relative conditions during periods when the gearbox has a broken tooth. This will help in coming up with standards which will guide in planning preventive and maintenance of the gearbox. The frequencies of the gearbox does not occur uniform when there is a fault in the system when there is a problem or imbalance in the gearbox it will produce frequencies which does not emit radial vibrations. Dynamic Model This model will require accuracy in computing the variables of the gearbox since the gearbox will not be rigid. The following is the specification of the gearbox that will be modelled using Adam’s software. Gearbox Technical Specification Gear ID Tooth Number Normal Modulus Speed Ratio Helical Angle Wheel Centre Distance Gear Widths Pressure Angle Y1 12 10 mm 6.8947 150 490 mm 120 mm 300 Y2 21 100 mm Y3 15 12 mm 6.132 100 700 mm 180 mm Y4 28 220 mm Y5 12 15 mm 4.467 100 650 mm 250 mm Y6 26 250 mm Total Speed Ratio I 136.56 Rated Motor Power kW 100 x 2 Rated Motor Velocity Rpm 645 Motor Overloaded Capacity 3.0 Max. Output Torque of the Gearbox kNm 425 x 2=850 In the equation x0-x represents deformation during the collision while x≥x0 represents a contact force when there is no collision. Collision occurs when x>x0. The dumping co-efficient is represented by C while D represents penetration debt. This equation has an S which is written as follows: S = where , , In this case change in d = and is deformation of the body that is contact with the broken tooth. Stiffness is presented by K and is calculated by using the following follows; The materials for the pinions and gears of the gearbox are alloy steel and cast steel respectively, and the values for the Poisson ratio and the Young’s Modulus are listed below. Through calculation, the stiffness values for the three gear pairs in the drive line of the gearbox. Gear Material Properties Item Gear ID Material Young’s Modulus Poisson Ratio Pinion Alloy Steel 0.29 Gear Cast Steel Stiffness for the Gear Pair Gear Pair Stiffness Friction Coefficient Values Static Friction Coefficient () Static Transition Velocity () Dynamic Friction Coefficient () Friction Transition Velocity () 0.1 1 mm/s 0.08 10 mm/s In order for simulation to be successful, the driving and breaking torque is applied on the upper structure of the rotating will of the gearbox. This is the model that is developed for Adam’s software. This model has been transformed and transferred to Adam’s multi-body model for simulation. In the model, the wheels are supported by bearings and will be recorded by the number they will make. The gearbox has a number of wheels which are fixed as well as shafts where torque will be applied in order for it to work well. The initial conditions during simulation were torque force of 4kN with a speed of 20 mm/s. The resistance for the simulation was set at 30kNmm. Broken tooth in the gearbox Measurements The measurements of a functioning gearbox will be done using sensors which will be installed in the gearbox and located in the paths of a rotating shaft. They will have optical sensors for the purpose of withstanding temperatures associated with the rotating shaft. These optical sensors will be computerized so that the signals are send to the computer to measure against predetermined values as shown above. This will help in determining the unevenness of the gearbox. The frequency or waves will be measured in terms of time so that proper data will be recorded. The combination of such values is generally used during the calculation of the general output values therefore characterizing a certain mechanical condition regarding the gearbox. As such, the initial values do match up to the overall state of the gearbox while the ensuing value normally corresponds to a state of the specified bearings. Considering the second value, it may be used in similar manner like detecting other mechanical problems that are characterized during impacts. They do contain the data that is supposed to be used during the analysis that does follow. In addition, they also contain particularly direct indication regarding the gearbox that is being monitored. More importantly, the major source of frequencies is the rotating shafts of the gearbox. This is due to the fact that as the gearbox does wear out more when with a broken tooth, the relative frequencies produced do also tend rise significantly. However, the supposed frequency is normally monitored as a way of determining the relative conditions regarding other gearbox so as to plan well certain preventive and maintenance procedures Results Simulation was done for duration of 0.6 seconds where the time interval was 0.003 seconds. The resistance force which was applied on the shaft of the gearbox was 200N. The initial velocity that was used acted on the output shaft producing a maximum torque on the shaft. The graphs below shows the results of the simulation carried out using Adams software The following is the force measured from the gearbox which had no default. It shows the meshing frequencies as well as stiffness for the gear during that period. The graph below shows the simulated gearbox which had one tooth broken and it was malfunctioning. The contact force is seen not to be stable as in the case above, the modulation in the graph is due to the malfunction of the tooth. The graph below shows the gearbox which had its teeth removed, therefore it was malfunctioning. The frequencies are not similar because of the malfunction of the teeth. The graph below shows the simulated gearbox which had one tooth broken and it was malfunctioning. The contact force is seen not to be stable as in the case above, the modulation in the graph is due to the malfunction of the tooth. The result shows the simulation that was carried on the left side where there was a broken tooth. This is because the configuration of the gearbox drive is symmetric. The results it can be noted that it is Y5 that had a broken tooth that why its vibrations were different from the other. However, the supposed vibration is normally monitored as a way of determining the relative conditions regarding other motors so as to plan well certain preventive and maintenance procedures. The supposed vibration of the motor does occur over a moderately broad frequency band as opposed to the low when compared to the higher frequencies. There are different problems that may occur in a rotating motor especially when loaded. The problems that do occur arise from the distinct vibration types. For instance, there are rotor imbalances that do produce a particular significant rise when it comes to the spectrum that does emit the radial vibrators. When the bearing problems do occur, they normally create such an increase particularly when it deals with the high frequencies. This is due to the fact that the high frequencies normally make the motors to rotate approximately twelve times more therefore the speed is much faster. There is a major concern especially when the proactive maintenance method is undertaken to detect the rolling element of bearings. In addition, there is vibration that is related and conn3cted with the worn bearings which is usually created from the numerous impacts of the numerous metal parts. There have been accurate analyses meant to figure out very well the internal structure of a bearing so as to provide frequencies that is the appropriate one for each motor. This is meant to reduce the various problems that do arise from the rotating machine especially if they have been in use for a long time. During the calculation of the various frequencies used in the bearings, the calculations do require one to know some basic information that is typically known. For example, the typical information includes the race diameter: inner and outer size, particular number of balls and their sizes. However, there are some manufacturers that do change particular internal designs so as to complicate the specifications. Consequently, the specified bearings sizes are not changed. What the manufactures guarantee is that the typical information concerning parameters: size, speed or load deployed: is not easily known. As such, the vibration analysis to monitor the rotating speed of the machines is dependant on such factors. Consequently, there is still a need to develop a particular universal monitoring device that does utilize a particular common as well as a statistical based algorithm which is not limited to a particular type of rotating machine (Adams, 123). The machine must be able to generally use the properties regarding the vibration analysis especially when during the concept of proactive maintenance when it comes to rotating machines. Discussion It is obvious that a fault gearbox can be a source of major system failure if it is not measured and adequately analysed and monitored. It is posted for this discussion that where extreme reliability is needed in the measurement and monitoring of the vibrations, then the permanent online monitoring system is most desired. Although this may be limited to a single component, it is notable for the ability to give sufficient information about the vibration that can be useful in determining the cause and source of a vibration in a machine. And as noted in the case of an engine in which reciprocating forces are applied, it is obvious that to train the dataset so as to enhance the extra body vibrations in the system will require a permanent online monitoring system to overlay such signals. The process of synthesizing the frequency domain from the separate single signals undergoes three main essential loops which are also concentric in nature. The outermost loop is the one that runs through the Log2N stages while the middle loop is the one which moves through each of the individual frequency spectra that are in the stage currently being worked on. The final loop which is also the innermost is what now uses the butterfly diagram mentioned earlier in the calculation of the points that are in each frequency spectra. The three loops are the three main stages that constitute the transformation of a given data from the time domain data into the frequency domain data and vice versa. In the case of the Adams software it transforms the time domain signals into the frequency domain signal. For instance, a single N point time domain signals in a Adams software will be transformed into two N/2+1 point frequency domain signals. It is these two signals that constitute the frequency domain that are made up of a real part and an imaginary part and thus making the resultant Adams software signal a complex function. The real and imaginary parts respectively hold the amplitudes of the cosine wave and the sine wave. On the other hand, in the case of the complex Adams software two N point time domain signals are transformed into two N point frequency domain signals which are constituted by a real and an imaginary part. In order to better understand this transformation, a simple example can be illustrated. Suppose one wants to use the complex Adams software to calculate the real Adams software using only one N point signal, they will begin by moving this N point signal into the real part of the time domain in the complex Adams software. The samples which are in the imaginary part will then be set to zero. The Adams software results calculated after the transformation will consist of both the real and the imaginary parts which will also be made up of N points (Adams, 123). After this short understanding of what constitute a Adams software and how one can transform the Adams software from a complex to a real form and vice versa, it is also important to understand how it works and also how it helps in the achievement of the aforementioned permutations and transformation. A typical complex notation in an Adams software computation is also made up of the time and frequency domains which contain a single signal in each of these domains that is constituted by N complex numbers. It is thus important to note that since each complex variable consists of two numbers, the multiplication of these variables must involve the combination of the four individual components in order to form a single product that is also made up of two components just like the initial variables. Conclusion In the production, design, modelling and simulation of a gearbox various procedures and testing are done to ensure that the gearbox produced is going to function at the minimum without any effect. The simulation has shown that Adam’s software can use the model to predict a broken tooth in the gearbox. The dynamics performance was the vehicle amounted to a gear with a perfect gearbox and another with a fault was revealed. Dynamics simulation will help in fault diagnosis regarding gearbox and the manufacturers and the users are keen enough to include certain diagnostics features located in the software meant to improve reliability and scalability. Apart from the location of precise harmonic mechanism particularly in the supposed line which is known signature analysis. There are other signals like the speed, specified torque, unnecessary and necessary noise as well as vibration generally is explored regarding their frequencies and their contents. In addition, there are other different techniques like the thermal measurements as well as chemical analysis which are also deployed as a way if establishing the nature of particular elements and the degree of the gearbox. Works Cited Adams, Maurice. Rotating Machinery Vibration: From Analysis to Troubleshooting. London: CRC Press, 2000. Print Forshoffer, William. Forsthoffer's Best Practice Handbook for Rotating Machinery. Elsevier Science & Technology, Manchester: 2011. Print. Forsthoffer, William. Forsthoffer's Rotating Equipment Handbooks: Principles of rotating equipment. Manchester: Elsevier, 2006. Print. Kong, Dewen, Jim, Meagher and Xi Wu. Dynamics Simulation and Malfunction Diagnosis of Heavy Machinery Using MSC ADAMS. Apr. 2009. 25 Nov. 2012 Kong, Dewen, Jim, Meagher and Xi Wu. Nonlinear Contact Analysis of Gear Teeth for Malfunction Diagnostics. Apr. 2009. 25 Nov. 2012 Norfield, Derek. Practical balancing of rotating machinery. Elsevier, London: 2006. Print. Overton, Caroline, Colin Davis, Lindsay McMillan and Robert Shaw. Rotating machinery: practical solutions to unbalance and misalignment. The Fairmont Press, Inc., London: 2004. Print. Robichaud, Michael. Reference Standards for Vibration Monitoring and Analysis. Saint John, NB Canada. n.d. Appendix Dynamic Model >> a gearbox ! 1=tooth, 2=brokentooth, 3=control ! Data set_id a elprop ! Node Node Coordinates ! ID x y z a 3 -0.3 0 0.0 ! gearbox to shaft connection a 4 -0.3 0 -1.6 ! with broken tooth a 5 -0.4 0 0.0 ! normal teeth a 6 -0.4 0 -1.6 ! thrust bearing location ! Element Node1 Node2 Center of gravity offset ! ID ID ID X Y Z a 1 22 2 0 0 0 a 2 2 1 0 0 0 a 3 22 3 0 0 0 a 4 3 5 0 0 0 a 5 5 6 0 0 0 ! Primitive rotation 1 rotation 2 rotation 3 ! Name axis angle(deg) axis angle(deg) axis angle(deg) a rshaft 2 -90 0 0 0 0 !rpm=1800 !gr = 87.965 !rpm_rotor = 1800/87.965 =20.4627 ==> omega = 2.1428 S ROTORPARAM ! Rotor Rotational Speed (rad/sec) a 2.1428 ! Row Elem. Child Gear Child Shaft Orientation Angles ! ID ID Node ID Ratio Phi Theta Psi a 1 1 7 1 0 0 0 a 2 1 8 87.965 0 0 0 S IDEALTEETH ! Elem. Node1 Node2 Axis of Connect to fixed system ! ID ID ID Bearing Subsys Prim_Str Node_ID a 2 5 6 X GEARBOX 6 !E S RIGIDBAR ! Element Node1 Node2 Center of gravity offset ! ID ID ID X Y Z !!a 3 1 5 0 0 0 ! lss 1 !!a 4 6 7 0 0 0 ! lss 2 a 5 9 10 0 0 0 ! hss 1 N ! ID Mass Ixx Ixy Ixz Iyy Iyz Izz a 3 100 2.0e11 0 0 0 0 0 ! lss inertia 2.0e9 !a 3 100 2.0e11 0 0 0 0 0 ! lss inertia a 5 10 1.0e3 0 0 0 0 0 ! hss inertia !---- a 4 3.2 TEETH.TAB a 14 ! ID ID ID (TR/RX/RY/RZ) (L/N) coefficient a 6 8 9 RX L 3.62E+6 !dt stiffness ? S DMPELE ! Element Node1 Node2 Trans./Rot. Type Linear Damping ! ID ID ID (TR/RX/RY/RZ) (L/N) coefficient a 7 8 9 RX L 0000 ! dt damper 2000 S RBMELE ! Generate rigid body mass element. ! ELID, node ID, prop ID A 10 1 2 SCREEN MECHLOAD ! Elem Node Steady Load Direction Coord. Frame Periodic ! ID ID Amplitude (FX|FY|FZ|MX|MY|MZ) (EL|PS) Input ID a 31 1 0 MX EL 0 S CONTROLCONNECT ! Control Swashplate Swashplate Element Type Element ! ID or Direct Phase(deg) (HIN/AUX/ENG ...) or ACP ID a 1 DIRECT 0.0 MLD 31 ! element_prop_id a elprop S RBMPRP ! Prop Elem. Center Mass Offset --- Mass Moment of Inertia Matrix --- ! ID Mass X Y Z Ixx, Ixy Ixz Iyy Iyz Izz A 1 1.e-7 0 0 0 0 0 0 0 0 0 A 2 50 0 0 0 1000 0 0 9000 0 10000 S NLBSHAPE ! NLB Shape Function Orders ! Shape fn ID Axial Bending Torsion A 1 1 0 1 S MATPROPER ! Input material properties (E, G) ! material id, Young's Modulus, shear Modulus a 11 1.0 Read More