Lab #3 - Slider-Crank LabLast Updated: March 4, 2009INTRODUCTIONIn this laboratory we will investigate the kinematics of some simple mechanisms used toconvert rotary motion into oscillating linear motion and vice-versa. The first of these is theslider-crank - a mechanism widely used in engines to convert the linear thrust of the pistonsinto the useful rotary motion of the drive-shaft. In this lab you will measure the linearacceleration of the piston of a lawn mower engine at various rotation rates of the drive shaft.The results exemplify a simple relation between speed and acceleration for kinematicallyrestricted motions, which you will discover. An adjustable slider-crank apparatus and acomputer simulation will show you some effects of changing the proportions of the slider-crank mechanism on piston velocity and acceleration. Other linkages and cam mechanismsmay also be used for linear-rotary motion conversion and some of these will be included inthe lab.Linear momentum balance allows us to relate the forces acting on a body to its acceleration(F = ma). Thus a knowledge of the acceleration a of a piston permits analysis of the totalforce F acting on it. Knowledge of these forces is crucial if one is to choose the right material,proportions, and operating conditions for a new design.PRELAB QUESTIONSRead through the laboratory instructions and then answer the following questions:1. What data will you collect from the lawn-mower engine and what will you simulate onthe computer?2. Which parameter(s) can be varied on the adjustable slider-crank? Which are fixed?3. Derive an equation relating the piston displacement x to the crankshaft speed, ω, time,t, connecting rod length, L, and crank radius R. (Hint: Use trigonometry).SLIDER-CRANK KINEMATICS & INTERNAL COMBUSTION ENGINESFigure 3.1 shows a sketch of the slider-crank mechanism. The point A is on the piston, lineAB (with length L) is the connecting rod, line BC (with length R) is the crank, and pointC is on the crankshaft. In an engine, a mixture of gasoline and air in the cylinder is ignitedin an exothermic (heat producing) reaction. As a result, the pressure in the cylinder rises,forcing the piston out. The force transmitted through the connecting ro d has a momentabout the center of the crankshaft, causing the shaft to rotate. An exhaust valve releases thegas pressure once the piston is extended. Inertia of machinery (often a flywheel) connectedto the crankshaft (as well as forcing from other pistons in multi-cylinder engines) forces the4748 Lab #3 - Slider-Crank Labpiston back up the cylinder. In a standard “four-cycle” engine the crankshaft makes anotherfull revolution before another ignition (to bring in fresh air and compress it before ignition).In this experiment the crankshaft is driven by an electric motor. The piston is driven by thiscrankshaft rotation at a more or less constant rate. The same motion results as when thecombustion process takes place. As the crankshaft rotates the piston moves in the positiveand negative x direction. The basic measurements in this lab are the position and velocityof the piston in the x direction (which happens to be vertical in the laboratory). Thesemeasurements can be compared to those calculated by hand (if you are energetic) or to theresults of a computer simulation. The simulation and the adjustable crank will allow you tosee some of the effects of varying the ratio of connecting rod length L to crank length R.Figure 3.1: A diagram of the slider-crank system.LABORATORY SET-UPA stripped-down lawn mower engine is driven by a variable-speed electric motor. Sensorsare installed on the engine’s piston to measure displacement and velocity. A data acquisi-tion program is used to measure, analyze, and record the piston data. Look at the engineand see how its various parts fit together. It may help to look at Figure 3.1 and at thevarious demonstration slider-cranks present in the dynamics laboratory. Identify the piston,connecting rod, and crankshaft (the connecting rod won’t be visible at your lab set-up, butyou can see it in the demonstration slider-cranks). The cylinder head has been removed,exposing the top of the piston and allowing sensors to be att ached.The speed and direction of the electric motor are controlled by a knob and switch on themotor controller. The numbers on the speed controller are arbitrary; do not write themdown as r.p.m. or radians per second (instead obtain angular velocity information fromthe data acquisition program). Does the direction of mot or rotation affect the slider-crankkinematics?The displacement and velocity data are measured using a LVDT and velocity transducer.Acceleration is calculated by the computer through numerical differentiation of the velocitydata. This process magnifies any noise in the data. The computer also measures and displaysTAM 203 Lab Manual 49the angular frequency by timing successive crossings of the zero line and converting to radiansper second. The displacement, velocity, and acceleration are all plotted in LabView alongwith their minimum and maximum values (see Figure 3.2). A simple simulation program letsyou compare your data to theoretical values and look at the effects of different slider-crankgeometries.Please follow safety precautions. The electric motor driving the lawn mower engineis powerful enough to cause serious injury if you get in its way. Keep long hair and looseclothing well away from the belt and pulleys at t he back of the engine. If you need to touchthe pulley, piston, or LVDT for some reason, check first that the electric motor power is offand that the speed control is set to zero. Make sure your lab partner knows what you aredoing.Using the LabView software1. To run the software, open up the Engrd203Lab account and then open the folder Crankon the desktop. Open the program Crank. As soon as the program is running, it willask you to move the piston to the top of its travel. Press Ready after you have donethis and wait until the next pop-up comes before moving the piston again. Thenonce prompted move the piston to the bottom of its travel and press Ready again andallow the computer a few seconds to calibrate. This calibration procedure allows thecomputer to convert the output of the LVDT (in volts) into displacement (in meters).Do this carefully. It may help to rock the pulley back and forth slightly as you try tohome in on the highest (or lowest) piston position. If you make a mistake, you canredo the