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BELT-AND-PULLEY EXAMPLE A ½-hp electric motor, running at 1,800 rpm, will be used to drive a grinding wheel operating at 600 rpm. A flat belt-and-pulley drive system configuration has been selected r = radius of pulley d = diameter of pulley φ= angle of wrap n = pulley speed BELT-AND-PULLEY EXAMPLE Drive motor will have a 2-inch-diameter pulley mounted to its 1/2-inch output shaft Candidate designs should be able to utilize the full horsepower available Customer desires a compact system design Drive pulley will slip first, before the driven pulley Purchasing department has located a vendor that can provide a flat belt that can withstand a maximum 30-pound tensile load Coefficient of friction between the belt and pulley is 0.3 Other design engineers in your group will design the mountings, bearings, and protective equipment Parametric design efforts should focus on distance between centers and driven-pulley diameter BELT-AND-PULLEY Assignment Determine: – Solution Evaluation Parameters (SEP) – Design Variables – Problem Definition Parameters Develop a plan for solving the design problem – In developing the plan discuss and give the formulas that would be needed Solution Evaluation Parameters Principal function of the pulley: – transform the power of the motor from a high speed to low speed. smaller motor torque is converted to a larger torque, (conservation of energy law) Principal function failure - if the belt slipped or if the belt broke owing to excessive tension Customer would be more satisfied with a compact design. Since we know that the tension forces in the belt are limited by the amount of friction between the belt on the driver pulley, up to the point of impending slip, we could determine the torque that the belt can deliver to the pulley, Tb and compare it with the maximum torque, Tm that the motor can supply. Calculate the maximum belt tension, Fb to make sure that it does not exceed the 35 (lbs.) limit Solution Evaluation Parameters Design Variables Value of the center distance, c, – affects the compactness of the design – is to be determined by the designer – ???Center distance is increased, more of the belt wraps around the pulley increasing the ability of the belt to grip the pulley and thereby satisfy the torque requirements of the motor Problem Definition Parameters "givens" that define design problem conditions – friction coefficient, belt strength, motor power, and motor pulley diameter Plan for Solving the Design Problem Using analytical relations from physics and mathematics we can use a hand calculator or build a spreadsheet to analyze a variety of engineering characteristics, including: 1. grinding wheel pulley speed, n2 2. angle of wrap as a function of the center distance, c 3. belt torque, Tb' 4. maximum belt tension, F1 5. slack-side belt tension, F2 6. initial tension (before torque is applied), Fi Then we will check that the constraints are not violated. Specifically, we will make sure that the belt will deliver the full motor torque to the grinding-wheel pulley and that the belt tension does not exceed the belt strength limit. Generating and Analyzing Model the behavior of the system using relations from physics and mathematics and develop a system of equations to analyze Motor will deliver power W(hp), to a pulley rotating at n rpm when producing a torque T m lb.. ft. according to equation Belt is not permitted to slip on the pulleys, the pulley speeds are related to the ratio of the pulley diameters. Determine the angle of wrap φ1 using basic geometric relations Generating and Analyzing Belt – Coefficient of friction f – In contact with the pulley for an angle of wrap φ – maximum belt tension F1 on the taut side of the pulley – F1 related to the belt tension F2 on the slack side of the pulley: Static equilibrium, free-body diagram of motor pulley, – sum the moments about the bearing B obtain the torque Tb, delivered by the belt to the driver pulley of radius r1 Generating and Analyzing Tm - Maximum torque delivered by the motor Tb ≥ 17.52 (lb. ∙ in.) n2 - driven-pulley speed > as a function of the design variable, diameter d2 – grinding-wheel speed has been specified as 600 rpm Generating an Initial Value of the Design Variable c Customer more satisfied with a compact design → distance between the pulley centers c to be small. – The closest that the two pulleys can be is when their radii are almost touching, theoretically speaking φ1 - Angle of wrap on the driving pulley F1 - tensile force that satisfies the motor torque constraint Generating an Initial Value of the Design Variable c F1 - to satisfy the torque constraint, a 37.5-lb. tension will be necessary → exceeds the belt strength constraint of 35 lbs. – center distance of 4 in. is an infeasible value Redesigning Finding Feasible Values Safety factor, n Best values Trade-offs Evaluating Choose best design candidate from feasible designs – Select one criteria – Select multiple criteria Compactness vs. safety Weighted-rating method Step 1: Establish a set of evaluation criteria. Step 2: Rate the feasible designs for each criterion. Step 3: Weight the ratings according to importance. Step 4: Sum the weighted ratings to calculate an overall weighted rating. Step 1. Evaluation Criteria, Importance Weights, Satisfaction Evaluation criteria often developed from solution evaluation parameters or from engineering characteristics ("voice of the customer" ) Identify the customer's: 1. Functional requirements for the product 2. Key engineering characteristics (that measure how well the functions are performed) 3. Importance of each functional requirement Step 1. Evaluation Criteria, Importance Weights, Satisfaction Belt-and-pulley example – As long as motor horsepower fully utilized → two most important engineering characteristics belt tension (no slip) and center distance (compactness) – solution evaluation parameters Customer considers belt tension as "very important" and center distance as "important" – Assume that we interpret "very important" with a weight of 0.6 and "important" with a weight of 0.4 Step 2. Rate Feasible Designs for Each Criterion Rating scale 1-5 Customer Satisfaction curves – Link each criterion or SEP to a value of satisfaction – Graphs – curve fit – Rating scale 0-1 Satisfaction Curves Belt-Pulley Designs Two-point formula Substitute satisfaction S for y, and solution evaluation parameter for x – Smax = 1 – Smin = 0 Decreasing Curve Increasing Curve Step 3: Weight Rating by Importance Multiply satisfaction rating by the importance weight Step 4: Calculate Overall Weighted Rating Sum of the importance weighted satisfaction levels to obtain Q, overall satisfaction For a center distance of 6 in. Overall Weighted Ratings Belt-and-Pulley Sum of the importance weighted satisfaction levels to obtain Q, overall satisfaction Planning and Scheduling Planning – Identify & order key activities – Top 10 – 20 critical activities Break down into sub-activities – Break down into sub-sub-activities Scheduling – Create a time frame for the plan Timelines - Schedules Bar chart - Gantt Chart – No connectivity between tasks Network logic diagram - Critical Pathway – Dependent project activities (tasks) are connected with arrows and time durations Gantt Chart Network Logic Diagram Critical-Path Method Elements 1. An activity - time-consuming effort that is required to perform part of a project. An activity is shown on an arrow diagram by a line with an arrowhead pointing in the direction of progress in completion of the project. 2. An event - the end of one activity and the beginning of another. An event is a point of accomplishment and/or decision. A circle is used to designate an event. Critical-Path Method Logic restrictions 1. An activity cannot be started until its tail event is reached. 2. An event cannot be reached until all activities leading to it are complete. 3. An event dependent on another event preceding it, even though the two events are not linked by an activity, has a dummy activity denoted by Longest Time Through Network Methodology - Parameters 1. Earliest start time (ES): The earliest time an activity can begin when all preceding activities are completed as rapidly as possible. 2. Latest start time (LS): The latest time an activity can be initiated without delaying the minimum completion time for the project. 3. Earliest finish time (EF): EF = ES +D, where D is the duration of each activity. 4. (Latest finish time LF): LF = LS +D 5. Total float (TF): The slack between the earliest and latest start times. TF = LS-ES. An activity on the critical path total float. Time durations - same time units & most likely estimate of time Calculation of ES Calculation of LS Calculation of EF, LF, TF Critical path is defined by the activities with zero total float Modified Bar Chart

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posted: | 6/28/2011 |

language: | English |

pages: | 33 |

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