Python - Data Optimization using Newton-Raphson method

Transient behaviour of a simple pendulum   Objective To write a program in python to simulate the transient behaviour of a simple pendulum and to create an animation of it's motion using the ODE for the motion of a pendulum.   Procedure Formulae: g = gravity in m/s^2 L = length of the pendulum in m m = mass of…

Data Optimization using Newton-Raphson method   Objective  To determine the minimum cushion pressure needed to break a given thickness of ice using an air cushion vehicle, Muller (“Ice Breaking with an Air Cushion Vehicle”) and to calculate the best relaxation factor.   Formulae p = the cushion…

Simulation of a 2R Robotic Arm   Objective To write a program in MATLAB to simulate the forward kinematics of a 2R Robotic Arm and to obtain the necessary output images and stitche them together for an animation.   Procedure The robotic arm consists of two links both of which have constrained motion between 0…

Genetic Algorithm using MATLAB   Objective To write a program on MATLAB to determine the global maxima and minima of a stalagmite function using genetic algorithm.   Procedure In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural…

Planetary Gear   Objective To run the motion analysis on a planetary gear system, complete with the sun gear, ring gear planetary gear and the carrier for the planetary gears   Procedure 3D models of the various components in a planetary gear system such as sun gear, planetary gear, ring gear and the carrier…

Simulation on a Piston Assembly   Objective To model all the parts(Piston,Wrist pin,Crank,Connecting Rod) and then assemble them in SolidWorks and to carry out motion analysis test on the motion of the setup in accordance with the various parameters given  Sl.No Wrist Pin Offset ` Crank Speed (Rpm) 1 "0" mm 2000…

Internal Geneva Mechanism    Objective  To create CAD models of the driver and driven wheel of an internal Geneva mechanism in solidworks and run motion analysis to obtain plots for the contact force and angular displacement.   Procedure  Model the driver and the driven wheel in solidworks according…

Modelling and simulation of a flow through a flowbench     Objective   To model a flowbench in solidworks and run a flow simulation to study the mass flow rate,velocity and pressure according to the various valve lift parameters of the flowbench valve.   Procedure The Flowbench is modelled in approximated…

FLOW OVER A CYLINDER   Objective: Simulate the flow of air over a cylinder of the given dimensions and to calculate the baseline case Reynolds number and then increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation.   Formulae used : `Re = rho*u*D/mu` D = cylinder…

NACA Airfoil   Objective Model the flow of air over a NACA0017 airfoil for the angle of attacks 0,2,4,6,8,10 compare the lift and drag forces along the ordinate and abscissae   Procedure  NACA0017 co-ordinates were chosen from the airfoil database and the curve is generated in solid works Following which…

Internal Pipe Flow Simulation    Objective  To run computational fluid dynamics on a pipe of given dimensions and to study the Normalized Velocity profiles with Reynolds Numbers 100 ,1000 and 10,000 at 85% , 90% and 95% of the pipe length.   Procedure Reynolds Number: ρ is the density of the…

1. What does popt and pcov mean? popt contains the arbitary values of constants passed through the function of the predicted curve fit. pcov is a 2D array which is the estimated covariance of popt   2. What does np.array(temperature) do? np.array is used to conver the list of temperature from data into an array to…

Constraint Minimization Function `f(x,y) = 5-(x-2)^2-2(y-1)^2` Contraint `x +4y=3`   `frac{deltaf}{deltax} = -2(x-2)` `frac{deltaf}{deltay} = -4(y-1)`   `g(x,y) = f(x,y) + lambda(x+4y-3)` `g(x,y) = 5 -(x-2)^2-2(y-1)^2 + lambda(x+4y-3)` `frac{deltag}{deltax} = -2x+4+lambda =0` ----Eq.` `frac{deltag}{deltay} =…

Air Standard Cycle   Objective To write a program using python to check the engine kinematics of an engine operating on the otto cycle and to make the PV diagram plot and display/print the total thermal efficiency of the engine.   Procedure An Otto cycle is an idealized thermodynamic cycle that…

Kinematics of a 2R Robotic Arm   Objective To write a program in python to simulate the forward kinematics of a 2R Robotic Arm and to obtain the necessary output images and stitche them together for an animation.   Procedure   We import the matplotlib.pyplot and the math modules for the program to display…

FLOW OVER A BICYCLE Objective To write a program on python to calculate the drag force and to plot Velocity vs Drag force Drag Co-efficient vs Drag force For various values of velocity and drag coefficient while keeping the frontal area constant   Drag Force Formulae:   Procedure Any vehicle moving through a…

Comparison of Bending in Beams   Objective To compare the bending due to loading on three different types of beams with a orce of 1500N and to compare the results in their stress , strain , displacement plots.   Procedure Material Chosen - Alloy Steel  Material Properties  Elastic Modulus - 2.1 e+11…

Analysis on a Plate with a hole   Objective To conduct a basic FEA analysis on 2 metal plates of given dimension and to study and compare the Stress, Strain and Displacement along the entity.   Procedure: Material chosen – Alloy Steel Material Properties: Elastic Modulus – 1 e+11 N/m^2 Poisson’s…

Analysis of a rotating shaft   Objective To conduct a frequency analysis using FEA simulation in solidworks on a shaft with a disc mounted and to determine the corresponding resonant frequencies and the associated mode shapes with each spectrum.   Procedure Material chosen – Alloy Steel Material Properties:…

Analysis of Buckling Phenomena   Objective To perform buckling analysis on an isolated cyclonic separator stand and to study the effects of adding a metallic stiffener along the variable distance aong the axis of tope plane of the stand and to compare the buckling fator for a suitable conclusion.   Procedure…

Flow over a bicycle using MATLAB Objective To write a script in MATLAB to take in various drag coefficient and velocity values and to compute the drag force along with geneating plot for Velocity Vs Drag force and ; Drag coefficient Vs Drag force.  Procedure Formulae `DF = c_d.*v.^2*(rho*A*0.5)` A = frontal area `rho`…

Curve Fitting using MATLAB Objective To write a script on MATLAB to perform linear and cubic curve fit for the given data series of variance of Cp with temperature to compute the errors in predicted values and to see the trendline for each outcome.   Procedure Load command is used to copy the data file to MATLAB directory. …