CHAPTER 5 PREDICTIVE MODELING STUDIES TO DETERMINE THE CONVEYING VELOCITY OF PARTS ON VIBRATORY FEEDER


 Alicia Cook
 2 years ago
 Views:
Transcription
1 93 CHAPTER 5 PREDICTIVE MODELING STUDIES TO DETERMINE THE CONVEYING VELOCITY OF PARTS ON VIBRATORY FEEDER 5.1 INTRODUCTION The development of an active trap based feeder for handling brakeliners was discussed in Chapter 4. The appropriate gate and feeder input parameters such as track angle, trap angle, excitation frequency (f) and amplitude of vibration (A) for maximum smooth conveying velocity were determined experimentally. In this chapter, predictive models to determine the conveying velocity of parts based on the gate and trap parameters was developed. In industries, there is a need for such models to set the input parameters based on the desired conveying velocity to maintain a continuous flow of parts. A theoretical model, regression model and Artificial Neural Network (ANN) model were developed to predict the conveying velocity of the part on the trap. The limitations of theoretical model and comparison of regression and ANN models with experimental results are discussed. The development of theoretical model is explained in the next section. 5.2 DEVELOPMENT OF THEORETICAL MODEL The analysis of part motion on a vibratory feeder was done by Lim (1997), Keraita (2008) and Ramalingam and Samuel (2009) and discussed in section 2.4. Lim (1997), in his analysis, assumed that the forcing element in case of a vibratory feeder would provide Simple Harmonic Motion (SHM). The same assumption was made here in developing the theoretical model as well. An introduction to representation of the SHM for mathematical modeling is found in book by Rao (2000). The SHM of the trough used in a vibratory feeder was
2 94 discussed by Ramalingam and Samuel (2009). Similarly, a typical harmonic motion of the trap on the feeder was developed and is shown in the Figure 5.1. The vibration force was provided to the horizontal feeder at an angle e the line of action of vibrational force was along PQ in Figure 5.1. f Figure 5.1 SHM horizontal to the Since the motion was SHM, the length of OP, OQ and OR represent the amplitude of vibration. The amplitude of vibration is denoted as A and frequency of vibration as f (as discussed in Chapter 4). As the plane of vibration is along the line PQ, the line of motion of the feeder also lies along the line PQ. Considering the initial position of the feeder to be at the point Q and after time period, it was displaced to point S along the line of motion PQ. This displacement of the feeder is given by SQ, which is represented as d f (Figure 5.1), inclined at an angle with the horizontal. The horizontal and the
3 95 vertical components of the displacement d f are denoted as X df and Y df respectively as shown in Figure 5.1. The harmonic motion could be represented by vector of magnitude A rotating at constant angular with the plane of vibration PQ (Rao 2000), as shown in Figure 5.1. The angular velocity, = 2 f and hence, where, f excitation frequency, Hz t time, s Considering ORS as highlighted in Figure 5.2, From Equation (5.1), (5.1) (5.2) (5.3) f Figure 5.2 ORS highlighted Considering the encircled section in Figure 5.3, SQ = d f = OQOS Since, OQ=A and OS= A cos2 ft (5.4)
4 96 Figure 5.3 Line OSQ highlighted The horizontal and the vertical components of feeder displacement (encircled in Figure 5.4) are derived as follows: (5.5) From Equation (5.4), Figure 5.4 STQ highlighted (5.6) (5.7) (5.8) The horizontal velocity component ( of the feeder (i.e conveying velocity) is determined by differentiating the Equation (5.6) (5.9) The maximum velocity of feeder in horizontal direction is obtained when sin 2 ft = 1, in Equation (5.9)
5 97 (5.10) The maximum velocity of the feeder obtained matches with the equation derived by Ramalingam and Samuel (2009). It is found that the direction of vibration force ( ) does not affect the conveying velocity of the feeder. The acceleration of the feeder ( obtained by double differentiating Equation (5.4), ) in the direction of oscillation is (5.11) The acceleration obtained matches with the equation derived by Ramalingam and Samuel (2009). It is found that the acceleration is not affected by the direction of vibration force ( ). From Equation (5.9), it could be observed that the horizontal velocity and trap angle (as discussed in section 4.4) could not be included in the 2D representation of SHM of feeder. So, regression analysis was done to have a model to predict the conveying velocity based on f and A, which is discussed in the next section. 5.3 DEVELOPMENT OF REGRESSION MODEL Regression is a procedure, which selects, from a class of functions, the one which best fits a given set of empirical data. The application of regression analysis is elaborated in section 2.4. The popularity of regression is due to its applicability to different types of problems, easiness in interpretation, robustness to violations of the underlying assumptions and widespread availability (Mason and Perreault 1991). When two or more quantitative variables are used to predict the quantitative response variable, then it is termed as multiple regression. The conveying velocity of the part
6 98 on the trap was the dependent variable whereas the track angle, trap angle excitation frequency (f) and amplitude of vibration (A) were the input variables. The velocity of orientations 3, 4, 7 and 8 were only considered because of reasons discussed in section The conveying velocity of orientation 3, 4, 7 and 8 on the trap were denoted as V3, V4, V7 and V8 respectively. The experimental results as discussed in section were used to develop the regression model. The model using Minitab software is as follows: R 2 = 82.4% (5.12) R 2 = 83.1% (5.13) R 2 = 81.3% (5.14) R 2 = 84.2% (5.15) where, R 2  percent of total variation that could be explained by the regression equation. is track angle (degree) is trap angle (degree) f is excitation frequency (Hz) A is amplitude of vibration (% of input voltage).
7 99 The development of ANN model is discussed in the next section and the comparison of regression and ANN model results with the experimental values is discussed in section DEVELOPMENT OF ANN MODEL The significance of ANN and its application in predicting the response variables is discussed in section 2.4. Neural networks donot get stuck in local minima and could be trained faster to converge (Eskandari et al 2004). The parameters of ANN proposed by Yusoff and Aziz (2004) were used for developing the ANN model to predict the conveying velocity of the part in orientations 3, 4, 7 and 8 and are listed in Table 5.1. The learning rate of 0.01 and momentum 0.95 were used to enable faster simulation. The weights and bias were initialized randomly. The simulations were stopped after it reached 1000 maximum epoch or when square error reached a value of between the actual and predicted value. The program was developed using Matlab software. The network was trained using the experimental results discussed in the section Table 5.1 Parameters for developing ANN model Structure Feed Forward Algorithm Back propagation Type of Training Trainlm Network structure 15,h and l Transferfunction TANSIG Number of iterations 1000(max epoch) Performance function MSE = Data division Random Learning rate 0.01 Momentum 0.95
8 100 The input combinations of track angle, trap angle, excitation frequency (f) and amplitude of vibration (A) were fed as input data in the Matlab software. The corresponding output value (conveying velocity of orientations 3, 4, 7 and 8) were fed as target to develop the network model using the parameters listed in Table 5.1 and the ANN architecture is shown in Figure 5.5. Input layer Hidden layer Output layer Trap angle Track angle Conveying velocity Excitation frequency Amplitude of vibration Figure 5.5 ANN architecture To determine the number of neurons in the hidden layer (Figure 5.5), trial and error method was followed (Ricca et al 2012). ed the correlation between outputs and targets. f 1 meant a closer relationship (Ricca et al 2012). The number of neurons had to be selected such 1.The training, validation and test data samples for determining the number of neurons in the hidden layer is listed in Table 5.2.
9 101 Table 5.2 Test and validation data S.No Description % of samples No.of samples 1 Training 70 % Validation 15 % 38 3 Testing 15 % 38 The training samples were provided to the developed network during training phase and based on the error, the network was adjusted. The validation samples were provided to measure network generalization and to stop the training when the generalization fails to improve. The testing samples were provided to have an independent measure of performance of network during and after training. The hidden neurons were initially varied from 10 in increments of 10 (i.e, 10, 20, The by varying the hidden neurons is shown in Figure overall R value No.of neurons Figure 5.6
10 102 From Figure 5.6, it could be inferred that hidden neuron size of 50 had (shown in dashed line) and hence 50 was chosen as the appropriate number of hidden neuron. On increasing the neurons in hidden layer and hence the test was stopped at neuron size of 70. Using this, the ANN network was again created and trained. An ANN model capable of predicting the conveying velocity based on input parameters was thus ready. The comparison of conveying velocity values predicted by regression and ANN models were compared with the experimental results in the next section. 5.5 COMPARISON OF EXPERIMENTAL RESULTS WITH REGRESSION AND ANN MODEL RESULTS To validate the developed regression and ANN models, twelve random sets of input values as listed in Table 5.3 were considered. Table 5.3 Set of input values considered for validation Experiment set no. Track angle, (degree) Trap angle, (degree) Excitation frequency, f (Hz) Amplitude, A (% of input voltage)
11 103 Table 5.4 to Table 5.7 list the conveying velocity of parts in orientations 3, 4, 7 and 8 predicted by regression and ANN models along with the percentage deviation (%) with the experimental values. The average deviation of results predicted by regression and ANN models for orientation 3 is 16.56% and 2.5% respectively (Table 5.4). Similarly, the average deviation of results predicted by regression and ANN models for orientation 4 is 14.01% and 2.8 % respectively (Table 5.5). 24.8% and 3.72% were the average deviation of results predicted by regression and ANN models respectively for orientation 7 (Table 5.6). Similarly, 10.42% and 3.34% were the average deviation of results predicted by regression and ANN models respectively for orientation 8 (Table 5.7). These models will be of great use in industries to match the conveying velocity of parts with the subsequent processes to maintain an uninterrupted flow. Exp Set. No Table 5.4 Comparison of conveying velocity of orientation 3 Conveying Velocity, V3 (mm/s) Deviation % Experiment Regression ANN Regression ANN Average
12 104 Orientation 3 60 Conveying velocity, mm/s CONVEYING VELOCITY V3 EXPERIMENT CONVEYING VELOCITY V3 REGRESSION CONVEYING VELOCITY V3 ANN Experimental set no. Figure 5.7 Comparison of experimental conveying velocity of orientation 3 with results predicted by regression and ANN models Exp Set. No Table 5.5 Comparison of conveying velocity of orientation 4 Conveying Velocity, V4 (mm/s) Deviation % Experiment Regression ANN Regression ANN Average
13 105 Orientation 4 60 Conveying velocity, mm/s CONVEYING VELOCITY V4 EXPERIMENT CONVEYING VELOCITY V4 REGRESSION CONVEYING VELOCITY V4 ANN Experimental set no Figure 5.8 Comparison of experimental conveying velocity of orientation 4 with results predicted by regression and ANN models Exp Set. No Table 5.6 Comparison of conveying velocity of orientation 7 Conveying Velocity, V7 (mm/s) Deviation % Experiment Regression ANN Regression ANN Average
14 106 Orientation 7 70 Conveying velocity, mm/s Experimental set no CONVEYING VELOCITY V7 EXPERIMENT CONVEYING VELOCITY V7 REGRESSION CONVEYING VELOCITY V7 ANN Figure 5.9 Comparison of experimental conveying velocity of orientation 7 with results predicted by regression and ANN models Exp Set. No Table 5.7 Comparison of conveying velocity of orientation 8 Conveying Velocity, V8 (mm/s) Deviation % Experiment Regression ANN Regression ANN Average
15 107 Orientation 8 60 Conveying velocity, mm/s Experimental set no CONVEYING VELOCITY V8 EXPERIMENT CONVEYING VELOCITY V8 REGRESSION CONVEYING VELOCITY V8 ANN Figure 5.10 Comparison of experimental conveying velocity of orientation 8 with results predicted by regression and ANN models From the results, it could be inferred that ANN model was able to predict the results much closer to the experimental values than the regression model. This is in agreement with Abounoori and Bagherpour (2007), who also concluded that ANN could predict results much better than regression models. Since, ANN could make rules without any implicit formula, they were able to predict the results much accurately than the regression equations (Ahangar et al 2010). Further, ANN are robust to noise in the training data and execute faster than regression. Though the regression models could not predict the results much accurately as that of ANN models, they follow the same pattern as that of the experimental results which is evident from Figure 5.7 to Figure 5.10.However, the limitation is that, a model in the form of an equation (as that of regression model) is not available in ANN model.
16 CONCLUDING REMARKS In this chapter, a theoretical model, regression model and ANN model were developed to predict the conveying velocity of part. The theoretical model could not accommodate the effect of track angle, trap angle and orientation of the part, since it was developed based on 2D free body diagram of the feeder. The predictive models to determine the conveying velocity of part orientations 3,4,7 and 8 amplitude (A) were developed using regression and ANN. The results predicted by the models were compared with the experimental results. The average deviation of regression results with the experimental results for the part orientations 3, 4, 7 and 8 were found to be 16.56%, 14.01%, 24.8% and 10.42% respectively. The average deviation of ANN results with the experimental results for the part orientations 3, 4, 7 and 8 were found to be 2.5%, 2.8%, 3.72% and 3.34% respectively. From the results, it could be inferred that ANN model was able to predict the results much closer to the experimental values than the regression model. ANN could make rules without any implicit formula and hence were able to predict the results much accurately than the regression equations. These models will be of great use in industries to match the conveying velocity of parts with the subsequent processes to maintain a continuous flow. Though the regression models could not predict the results much accurately as that of ANN models, they follow the same pattern as that of the experimental results.
Analecta Vol. 8, No. 2 ISSN 20647964
EXPERIMENTAL APPLICATIONS OF ARTIFICIAL NEURAL NETWORKS IN ENGINEERING PROCESSING SYSTEM S. Dadvandipour Institute of Information Engineering, University of Miskolc, Egyetemváros, 3515, Miskolc, Hungary,
More informationINTRODUCTION TO NEURAL NETWORKS
INTRODUCTION TO NEURAL NETWORKS Pictures are taken from http://www.cs.cmu.edu/~tom/mlbookchapterslides.html http://research.microsoft.com/~cmbishop/prml/index.htm By Nobel Khandaker Neural Networks An
More informationANN Based Fault Classifier and Fault Locator for Double Circuit Transmission Line
International Journal of Computer Sciences and Engineering Open Access Research Paper Volume4, Special Issue2, April 2016 EISSN: 23472693 ANN Based Fault Classifier and Fault Locator for Double Circuit
More informationSimple Harmonic Motion
Simple Harmonic Motion 1 Object To determine the period of motion of objects that are executing simple harmonic motion and to check the theoretical prediction of such periods. 2 Apparatus Assorted weights
More informationNTC Project: S01PH10 (formerly I01P10) 1 Forecasting Women s Apparel Sales Using Mathematical Modeling
1 Forecasting Women s Apparel Sales Using Mathematical Modeling Celia Frank* 1, Balaji Vemulapalli 1, Les M. Sztandera 2, Amar Raheja 3 1 School of Textiles and Materials Technology 2 Computer Information
More informationAPPLIED MATHEMATICS ADVANCED LEVEL
APPLIED MATHEMATICS ADVANCED LEVEL INTRODUCTION This syllabus serves to examine candidates knowledge and skills in introductory mathematical and statistical methods, and their applications. For applications
More informationLecture 6. Artificial Neural Networks
Lecture 6 Artificial Neural Networks 1 1 Artificial Neural Networks In this note we provide an overview of the key concepts that have led to the emergence of Artificial Neural Networks as a major paradigm
More informationAP1 Oscillations. 1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false?
1. Which of the following statements about a springblock oscillator in simple harmonic motion about its equilibrium point is false? (A) The displacement is directly related to the acceleration. (B) The
More informationAP Physics C. Oscillations/SHM Review Packet
AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete
More information1.10 Using Figure 1.6, verify that equation (1.10) satisfies the initial velocity condition. t + ") # x (t) = A! n. t + ") # v(0) = A!
1.1 Using Figure 1.6, verify that equation (1.1) satisfies the initial velocity condition. Solution: Following the lead given in Example 1.1., write down the general expression of the velocity by differentiating
More informationCOMBINED NEURAL NETWORKS FOR TIME SERIES ANALYSIS
COMBINED NEURAL NETWORKS FOR TIME SERIES ANALYSIS Iris Ginzburg and David Horn School of Physics and Astronomy Raymond and Beverly Sackler Faculty of Exact Science TelAviv University TelA viv 96678,
More informationdegrees of freedom and are able to adapt to the task they are supposed to do [Gupta].
1.3 Neural Networks 19 Neural Networks are large structured systems of equations. These systems have many degrees of freedom and are able to adapt to the task they are supposed to do [Gupta]. Two very
More informationSimple Harmonic Motion Experiment. 1 f
Simple Harmonic Motion Experiment In this experiment, a motion sensor is used to measure the position of an oscillating mass as a function of time. The frequency of oscillations will be obtained by measuring
More informationSolving Simultaneous Equations and Matrices
Solving Simultaneous Equations and Matrices The following represents a systematic investigation for the steps used to solve two simultaneous linear equations in two unknowns. The motivation for considering
More informationPower Electronics. Prof. K. Gopakumar. Centre for Electronics Design and Technology. Indian Institute of Science, Bangalore.
Power Electronics Prof. K. Gopakumar Centre for Electronics Design and Technology Indian Institute of Science, Bangalore Lecture  1 Electric Drive Today, we will start with the topic on industrial drive
More informationPractice Test SHM with Answers
Practice Test SHM with Answers MPC 1) If we double the frequency of a system undergoing simple harmonic motion, which of the following statements about that system are true? (There could be more than one
More informationCHAPTER 3 MODAL ANALYSIS OF A PRINTED CIRCUIT BOARD
45 CHAPTER 3 MODAL ANALYSIS OF A PRINTED CIRCUIT BOARD 3.1 INTRODUCTION This chapter describes the methodology for performing the modal analysis of a printed circuit board used in a hand held electronic
More informationManufacturing Equipment Modeling
QUESTION 1 For a linear axis actuated by an electric motor complete the following: a. Derive a differential equation for the linear axis velocity assuming viscous friction acts on the DC motor shaft, leadscrew,
More informationIntroduction to Machine Learning and Data Mining. Prof. Dr. Igor Trajkovski trajkovski@nyus.edu.mk
Introduction to Machine Learning and Data Mining Prof. Dr. Igor Trakovski trakovski@nyus.edu.mk Neural Networks 2 Neural Networks Analogy to biological neural systems, the most robust learning systems
More informationNewton s Second Law. ΣF = m a. (1) In this equation, ΣF is the sum of the forces acting on an object, m is the mass of
Newton s Second Law Objective The Newton s Second Law experiment provides the student a hands on demonstration of forces in motion. A formulated analysis of forces acting on a dynamics cart will be developed
More informationLesson 11. Luis Anchordoqui. Physics 168. Tuesday, December 8, 15
Lesson 11 Physics 168 1 Oscillations and Waves 2 Simple harmonic motion If an object vibrates or oscillates back and forth over same path each cycle taking same amount of time motion is called periodic
More informationDesigning a neural network for forecasting financial time series
Designing a neural network for forecasting financial time series 29 février 2008 What a Neural Network is? Each neurone k is characterized by a transfer function f k : output k = f k ( i w ik x k ) From
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationboth double. A. T and v max B. T remains the same and v max doubles. both remain the same. C. T and v max
Q13.1 An object on the end of a spring is oscillating in simple harmonic motion. If the amplitude of oscillation is doubled, how does this affect the oscillation period T and the object s maximum speed
More informationArtificial Neural Network and NonLinear Regression: A Comparative Study
International Journal of Scientific and Research Publications, Volume 2, Issue 12, December 2012 1 Artificial Neural Network and NonLinear Regression: A Comparative Study Shraddha Srivastava 1, *, K.C.
More informationStanding Waves Physics Lab I
Standing Waves Physics Lab I Objective In this series of experiments, the resonance conditions for standing waves on a string will be tested experimentally. Equipment List PASCO SF9324 Variable Frequency
More informationCarbon Dioxide and an Argon + Nitrogen Mixture. Measurement of C p /C v for Argon, Nitrogen, Stephen Lucas 05/11/10
Carbon Dioxide and an Argon + Nitrogen Mixture Measurement of C p /C v for Argon, Nitrogen, Stephen Lucas 05/11/10 Measurement of C p /C v for Argon, Nitrogen, Carbon Dioxide and an Argon + Nitrogen Mixture
More informationHOOKE S LAW AND SIMPLE HARMONIC MOTION
HOOKE S LAW AND SIMPLE HARMONIC MOTION Alexander Sapozhnikov, Brooklyn College CUNY, New York, alexs@brooklyn.cuny.edu Objectives Study Hooke s Law and measure the spring constant. Study Simple Harmonic
More informationANALYTICAL METHODS FOR ENGINEERS
UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME  TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations
More informationOnline Tuning of Artificial Neural Networks for Induction Motor Control
Online Tuning of Artificial Neural Networks for Induction Motor Control A THESIS Submitted by RAMA KRISHNA MAYIRI (M060156EE) In partial fulfillment of the requirements for the award of the Degree of MASTER
More informationChapter 13, example problems: x (cm) 10.0
Chapter 13, example problems: (13.04) Reading Fig. 1330 (reproduced on the right): (a) Frequency f = 1/ T = 1/ (16s) = 0.0625 Hz. (since the figure shows that T/2 is 8 s.) (b) The amplitude is 10 cm.
More informationEE 402 RECITATION #13 REPORT
MIDDLE EAST TECHNICAL UNIVERSITY EE 402 RECITATION #13 REPORT LEADLAG COMPENSATOR DESIGN F. Kağan İPEK Utku KIRAN Ç. Berkan Şahin 5/16/2013 Contents INTRODUCTION... 3 MODELLING... 3 OBTAINING PTF of OPEN
More informationOPTIMIZATION OF VENTILATION SYSTEMS IN OFFICE ENVIRONMENT, PART II: RESULTS AND DISCUSSIONS
OPTIMIZATION OF VENTILATION SYSTEMS IN OFFICE ENVIRONMENT, PART II: RESULTS AND DISCUSSIONS Liang Zhou, and Fariborz Haghighat Department of Building, Civil and Environmental Engineering Concordia University,
More informationAP1 Waves. (A) frequency (B) wavelength (C) speed (D) intensity. Answer: (A) and (D) frequency and intensity.
1. A fire truck is moving at a fairly high speed, with its siren emitting sound at a specific pitch. As the fire truck recedes from you which of the following characteristics of the sound wave from the
More informationINTERFERENCE OF SOUND WAVES
1/2016 Sound 1/8 INTERFERENCE OF SOUND WAVES PURPOSE: To measure the wavelength, frequency, and propagation speed of ultrasonic sound waves and to observe interference phenomena with ultrasonic sound waves.
More informationPrecise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility
Precise Modelling of a Gantry Crane System Including Friction, 3D Angular Swing and Hoisting Cable Flexibility Renuka V. S. & Abraham T Mathew Electrical Engineering Department, NIT Calicut Email : renuka_mee@nitc.ac.in,
More informationA New Approach For Estimating Software Effort Using RBFN Network
IJCSNS International Journal of Computer Science and Network Security, VOL.8 No.7, July 008 37 A New Approach For Estimating Software Using RBFN Network Ch. Satyananda Reddy, P. Sankara Rao, KVSVN Raju,
More informationChapter 15, example problems:
Chapter, example problems: (.0) Ultrasound imaging. (Frequenc > 0,000 Hz) v = 00 m/s. λ 00 m/s /.0 mm =.0 0 6 Hz. (Smaller wave length implies larger frequenc, since their product,
More informationSome Comments on the Derivative of a Vector with applications to angular momentum and curvature. E. L. Lady (October 18, 2000)
Some Comments on the Derivative of a Vector with applications to angular momentum and curvature E. L. Lady (October 18, 2000) Finding the formula in polar coordinates for the angular momentum of a moving
More informationPHYS 1014M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PHYS 1014M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
More informationSOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS  VELOCITY AND ACCELERATION DIAGRAMS
SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS  VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering
More informationDetermination of Acceleration due to Gravity
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
More informationOptimum Design of Worm Gears with Multiple Computer Aided Techniques
Copyright c 2008 ICCES ICCES, vol.6, no.4, pp.221227 Optimum Design of Worm Gears with Multiple Computer Aided Techniques Daizhong Su 1 and Wenjie Peng 2 Summary Finite element analysis (FEA) has proved
More informationProof of the conservation of momentum and kinetic energy
Experiment 04 Proof of the conservation of momentum and kinetic energy By Christian Redeker 27.10.2007 Contents 1.) Hypothesis...3 2.) Diagram...7 3.) Method...7 3.1) Apparatus...7 3.2) Procedure...7 4.)
More informationInternational Journal of Computer Trends and Technology (IJCTT) volume 4 Issue 8 August 2013
A ShortTerm Traffic Prediction On A Distributed Network Using Multiple Regression Equation Ms.Sharmi.S 1 Research Scholar, MS University,Thirunelvelli Dr.M.Punithavalli Director, SREC,Coimbatore. Abstract:
More informationPhysics 111 Homework Solutions Week #9  Tuesday
Physics 111 Homework Solutions Week #9  Tuesday Friday, February 25, 2011 Chapter 22 Questions  None MultipleChoice 223 A 224 C 225 B 226 B 227 B 229 D Problems 227 In this double slit experiment we
More informationChapter 24 Physical Pendulum
Chapter 4 Physical Pendulum 4.1 Introduction... 1 4.1.1 Simple Pendulum: Torque Approach... 1 4. Physical Pendulum... 4.3 Worked Examples... 4 Example 4.1 Oscillating Rod... 4 Example 4.3 Torsional Oscillator...
More informationCambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level
Cambridge International Examinations Cambridge International Advanced Subsidiary and Advanced Level *0123456789* PHYSICS 9702/02 Paper 2 AS Level Structured Questions For Examination from 2016 SPECIMEN
More informationSample Questions for the AP Physics 1 Exam
Sample Questions for the AP Physics 1 Exam Sample Questions for the AP Physics 1 Exam Multiplechoice Questions Note: To simplify calculations, you may use g 5 10 m/s 2 in all problems. Directions: Each
More informationForecasting of Economic Quantities using Fuzzy Autoregressive Model and Fuzzy Neural Network
Forecasting of Economic Quantities using Fuzzy Autoregressive Model and Fuzzy Neural Network Dušan Marček 1 Abstract Most models for the time series of stock prices have centered on autoregressive (AR)
More informationTime Domain and Frequency Domain Techniques For Multi Shaker Time Waveform Replication
Time Domain and Frequency Domain Techniques For Multi Shaker Time Waveform Replication Thomas Reilly Data Physics Corporation 1741 Technology Drive, Suite 260 San Jose, CA 95110 (408) 2168440 This paper
More informationPolarization of Light
Polarization of Light References Halliday/Resnick/Walker Fundamentals of Physics, Chapter 33, 7 th ed. Wiley 005 PASCO EX997A and EX999 guide sheets (written by Ann Hanks) weight Exercises and weights
More informationChapter 2 The Research on Fault Diagnosis of Building Electrical System Based on RBF Neural Network
Chapter 2 The Research on Fault Diagnosis of Building Electrical System Based on RBF Neural Network Qian Wu, Yahui Wang, Long Zhang and Li Shen Abstract Building electrical system fault diagnosis is the
More informationLeast Squares Estimation
Least Squares Estimation SARA A VAN DE GEER Volume 2, pp 1041 1045 in Encyclopedia of Statistics in Behavioral Science ISBN13: 9780470860809 ISBN10: 0470860804 Editors Brian S Everitt & David
More informationPower Prediction Analysis using Artificial Neural Network in MS Excel
Power Prediction Analysis using Artificial Neural Network in MS Excel NURHASHINMAH MAHAMAD, MUHAMAD KAMAL B. MOHAMMED AMIN Electronic System Engineering Department Malaysia Japan International Institute
More informationBank Customers (Credit) Rating System Based On Expert System and ANN
Bank Customers (Credit) Rating System Based On Expert System and ANN Project Review Yingzhen Li Abstract The precise rating of customers has a decisive impact on loan business. We constructed the BP network,
More informationTIME SERIES FORECASTING WITH NEURAL NETWORK: A CASE STUDY OF STOCK PRICES OF INTERCONTINENTAL BANK NIGERIA
www.arpapress.com/volumes/vol9issue3/ijrras_9_3_16.pdf TIME SERIES FORECASTING WITH NEURAL NETWORK: A CASE STUDY OF STOCK PRICES OF INTERCONTINENTAL BANK NIGERIA 1 Akintola K.G., 2 Alese B.K. & 2 Thompson
More informationEDUMECH Mechatronic Instructional Systems. Ball on Beam System
EDUMECH Mechatronic Instructional Systems Ball on Beam System Product of Shandor Motion Systems Written by Robert Hirsch Ph.D. 9989 All Rights Reserved. 999 Shandor Motion Systems, Ball on Beam Instructional
More informationTrigonometry Hard Problems
Solve the problem. This problem is very difficult to understand. Let s see if we can make sense of it. Note that there are multiple interpretations of the problem and that they are all unsatisfactory.
More informationPhysics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE
1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object
More informationMathematics Extension 1
Girraween High School 05 Year Trial Higher School Certificate Mathematics Extension General Instructions Reading tjmc  5 mjnutcs Working time hours Write using black or blue pen Black pen is preferred
More informationAn Introduction to Neural Networks
An Introduction to Vincent Cheung Kevin Cannons Signal & Data Compression Laboratory Electrical & Computer Engineering University of Manitoba Winnipeg, Manitoba, Canada Advisor: Dr. W. Kinsner May 27,
More informationApplication of Neural Network in User Authentication for Smart Home System
Application of Neural Network in User Authentication for Smart Home System A. Joseph, D.B.L. Bong, D.A.A. Mat Abstract Security has been an important issue and concern in the smart home systems. Smart
More informationMechanics lecture 7 Moment of a force, torque, equilibrium of a body
G.1 EE1.el3 (EEE1023): Electronics III Mechanics lecture 7 Moment of a force, torque, equilibrium of a body Dr Philip Jackson http://www.ee.surrey.ac.uk/teaching/courses/ee1.el3/ G.2 Moments, torque and
More informationANNMD  Artificial Neural Network Model Developer. Jure Smrekar
ANNMD  Artificial Neural Network Model Developer Jure Smrekar June 2010 University of Stavanger N4036 Stavanger NORWAY wwwuisno 2010 Jure Smrekar ISBN: 9788276444162 Abstract This booklet presents
More informationCentripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.
Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.
More informationResponse to Harmonic Excitation Part 2: Damped Systems
Response to Harmonic Excitation Part 2: Damped Systems Part 1 covered the response of a single degree of freedom system to harmonic excitation without considering the effects of damping. However, almost
More informationCandidate Number. General Certificate of Education Advanced Level Examination June 2010
entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 1 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Friday 18
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationActive Vibration Isolation of an Unbalanced Machine Spindle
UCRLCONF206108 Active Vibration Isolation of an Unbalanced Machine Spindle D. J. Hopkins, P. Geraghty August 18, 2004 American Society of Precision Engineering Annual Conference Orlando, FL, United States
More informationR f. V i. ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response
ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response Objective: Design a practical differentiator circuit using common OP AMP circuits. Test the frequency response
More information300 MW Variable Speed Drives for PumpStorage Plant Application Goldisthal
May 24 MW Variable Speed Drives for Aurélie Bocquel APCG / 4BOC4 (MWGoldisthal 1524).PPT MW Variable Speed Drives for Content Major benefits of the cycloconverter driven doublyfed induction machines
More informationDually Fed Permanent Magnet Synchronous Generator Condition Monitoring Using Stator Current
Summary Dually Fed Permanent Magnet Synchronous Generator Condition Monitoring Using Stator Current Joachim Härsjö, Massimo Bongiorno and Ola Carlson Chalmers University of Technology Energi och Miljö,
More information1.3. DOT PRODUCT 19. 6. If θ is the angle (between 0 and π) between two nonzero vectors u and v,
1.3. DOT PRODUCT 19 1.3 Dot Product 1.3.1 Definitions and Properties The dot product is the first way to multiply two vectors. The definition we will give below may appear arbitrary. But it is not. It
More informationBCM 6200  Protein crystallography  I. Crystal symmetry Xray diffraction Protein crystallization Xray sources SAXS
BCM 6200  Protein crystallography  I Crystal symmetry Xray diffraction Protein crystallization Xray sources SAXS Elastic Xray Scattering From classical electrodynamics, the electric field of the electromagnetic
More informationComparison of Kmeans and Backpropagation Data Mining Algorithms
Comparison of Kmeans and Backpropagation Data Mining Algorithms Nitu Mathuriya, Dr. Ashish Bansal Abstract Data mining has got more and more mature as a field of basic research in computer science and
More informationcos Newington College HSC Mathematics Ext 1 Trial Examination 2011 QUESTION ONE (12 Marks) (b) Find the exact value of if. 2 . 3
1 QUESTION ONE (12 Marks) Marks (a) Find tan x e 1 2 cos dx x (b) Find the exact value of if. 2 (c) Solve 5 3 2x 1. 3 (d) If are the roots of the equation 2 find the value of. (e) Use the substitution
More informationPerformance Evaluation On Human Resource Management Of China S Commercial Banks Based On Improved Bp Neural Networks
Performance Evaluation On Human Resource Management Of China S *1 Honglei Zhang, 2 Wenshan Yuan, 1 Hua Jiang 1 School of Economics and Management, Hebei University of Engineering, Handan 056038, P. R.
More informationFRICTION, WORK, AND THE INCLINED PLANE
FRICTION, WORK, AND THE INCLINED PLANE Objective: To measure the coefficient of static and inetic friction between a bloc and an inclined plane and to examine the relationship between the plane s angle
More informationComponent Ordering in Independent Component Analysis Based on Data Power
Component Ordering in Independent Component Analysis Based on Data Power Anne Hendrikse Raymond Veldhuis University of Twente University of Twente Fac. EEMCS, Signals and Systems Group Fac. EEMCS, Signals
More information* Biot Savart s Law Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B. PPT No.
* Biot Savart s Law Statement, Proof Applications of Biot Savart s Law * Magnetic Field Intensity H * Divergence of B * Curl of B PPT No. 17 Biot Savart s Law A straight infinitely long wire is carrying
More informationIMU Components An IMU is typically composed of the following components:
APN064 IMU Errors and Their Effects Rev A Introduction An Inertial Navigation System (INS) uses the output from an Inertial Measurement Unit (IMU), and combines the information on acceleration and rotation
More informationData Mining mit der JMSL Numerical Library for Java Applications
Data Mining mit der JMSL Numerical Library for Java Applications Stefan Sineux 8. Java Forum Stuttgart 07.07.2005 Agenda Visual Numerics JMSL TM Numerical Library Neuronale Netze (Hintergrund) Demos Neuronale
More informationPhysics 40 Lab 1: Tests of Newton s Second Law
Physics 40 Lab 1: Tests of Newton s Second Law January 28 th, 2008, Section 2 Lynda Williams Lab Partners: Madonna, Hilary Clinton & Angie Jolie Abstract Our primary objective was to test the validity
More informationRESONANCE PASSAGE OF CYCLIC SYMMETRIC STRUCTURES
11 th International Conference on Vibration Problems Z. Dimitrovová et.al. (eds.) Lisbon, Portugal, 9 12 September 213 RESONANCE PASSAGE OF CYCLIC SYMMETRIC STRUCTURES Marius Bonhage* 1, Lars Panningv.Scheidt
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 28] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationAnalysis of Multilayer Neural Networks with Direct and CrossForward Connection
Analysis of Multilayer Neural Networks with Direct and CrossForward Connection Stanis law P laczek and Bijaya Adhikari Vistula University, Warsaw, Poland stanislaw.placzek@wp.pl,bijaya.adhikari1991@gmail.com
More informationThree phase circuits
Three phase circuits THREE PHASE CIRCUITS THREEPHASE ADVANTAGES 1. The horsepower rating of threephase motors and the kva rating of threephase transformers are 150% greater than singlephase motors
More informationUsing artificial intelligence for data reduction in mechanical engineering
Using artificial intelligence for data reduction in mechanical engineering L. Mdlazi 1, C.J. Stander 1, P.S. Heyns 1, T. Marwala 2 1 Dynamic Systems Group Department of Mechanical and Aeronautical Engineering,
More information226 Chapter 15: OSCILLATIONS
Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion
More informationCHAPTER 13 SIMPLE LINEAR REGRESSION. Opening Example. Simple Regression. Linear Regression
Opening Example CHAPTER 13 SIMPLE LINEAR REGREION SIMPLE LINEAR REGREION! Simple Regression! Linear Regression Simple Regression Definition A regression model is a mathematical equation that descries the
More informationVibrations can have an adverse effect on the accuracy of the end effector of a
EGR 315 Design Project  1  Executive Summary Vibrations can have an adverse effect on the accuracy of the end effector of a multiplelink robot. The ability of the machine to move to precise points scattered
More informationPeriodic wave in spatial domain  length scale is wavelength Given symbol l y
1.4 Periodic Waves Often have situations where wave repeats at regular intervals Electromagnetic wave in optical fibre Sound from a guitar string. These regularly repeating waves are known as periodic
More informationPrediction Model for Crude Oil Price Using Artificial Neural Networks
Applied Mathematical Sciences, Vol. 8, 2014, no. 80, 39533965 HIKARI Ltd, www.mhikari.com http://dx.doi.org/10.12988/ams.2014.43193 Prediction Model for Crude Oil Price Using Artificial Neural Networks
More informationStructural Dynamics, Dynamic Force and Dynamic System
Structural Dynamics, Dynamic Force and Dynamic System Structural Dynamics Conventional structural analysis is based on the concept of statics, which can be derived from Newton s 1 st law of motion. This
More information6.2.8 Neural networks for data mining
6.2.8 Neural networks for data mining Walter Kosters 1 In many application areas neural networks are known to be valuable tools. This also holds for data mining. In this chapter we discuss the use of neural
More informationPlate waves in phononic crystals slabs
Acoustics 8 Paris Plate waves in phononic crystals slabs J.J. Chen and B. Bonello CNRS and Paris VI University, INSP  14 rue de Lourmel, 7515 Paris, France chen99nju@gmail.com 41 Acoustics 8 Paris We
More informationDynamics of Iain M. Banks Orbitals. Richard Kennaway. 12 October 2005
Dynamics of Iain M. Banks Orbitals Richard Kennaway 12 October 2005 Note This is a draft in progress, and as such may contain errors. Please do not cite this without permission. 1 The problem An Orbital
More information1 of 10 11/23/2009 6:37 PM
hapter 14 Homework Due: 9:00am on Thursday November 19 2009 Note: To understand how points are awarded read your instructor's Grading Policy. [Return to Standard Assignment View] Good Vibes: Introduction
More informationSimple Harmonic Motion(SHM) Period and Frequency. Period and Frequency. Cosines and Sines
Simple Harmonic Motion(SHM) Vibration (oscillation) Equilibrium position position of the natural length of a spring Amplitude maximum displacement Period and Frequency Period (T) Time for one complete
More information