EPT 221 PARAMETRIC DESIGN

Objectives of Lecture Describe the parametric design phase. Describe and apply the steps involve in the parametric design phase. Describe and apply methods to evaluate alternative designs.

Configuration Design Configuration Design Configuration Design Special Purpose Parts: Features Arrangements Relative dimensions Attribute list (variables) Standard Parts: Type Attribute list (variables) Abstract embodiment Physical principles Material Geometry Architecture

Information Flow

Systematic Parametric Design

Systematic Steps in Parametric Design 5 major steps: Step 1: Formulate the parametric design problem. —Performance Parameters/ Solution Evaluation Parameter —Design Variables (DVs) —Problem Definition Parameters (PDPs) —Preliminary Plan for Solving the Problem Step 2: Generate alternative designs. Step 3: Analyze/ predict the performance of the alternatives. —Analytical Methods —Experimental Methods Step 4: Evaluate the performance of each alternative. Step 5: Refine/ optimize

Example: The design problem: A ½ -hp electric motor, running at 1,800 rpm, will be used to drive a grinding wheel operating at 6,000 rpm. A flat belt-and-pulley drive system configuration has been selected, as shown. The design team has also determined that: —the drive motor will have a 2 inch-diameter pulley mounted to its ½-inch output shaft, —candidate designs should be able to utilize the full horsepower available, —the customer desires a compact system design, —the drive pulley will slip first, before the driven pulley, —the purchasing department has located a vendor that can provide a flat belt that can withstand a maximum 35-pound tensile load, —the coefficient of friction between the belt and pulley is 0.3, —other design engineers in our group will design the mountings, bearings, and protective equipment, therefore —parametric design efforts should focus on distance between centres and driven- pulley diameter.

Principal Function: To transform the power of the motor from a high speed to a low speed. The belt-and-pulley system would fail to perform its principal function if the belt slipped or if the belt broke due excessive tension

Formulating the parameters: Determine the type of parameter:  Solution Evaluation Parameters (SEPs)  Design Variables (DVs)  Problem Definition Parameters (PDPs) Identify specifics of each parameter:  Name (parameter/ variable)  Symbols  Units  Limits

Solution Evaluation Parameters (SEPs) Related to function Why belt torque and tension? 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. So, need to calculate the maximum belt tension F 1 to make sure it does not exceed 35 (lbs) limit. T b is the torque that the motor can supply. Why centre of distance? Because the customer would be more satisfied with a compact design.

Design Variables (DVs) Related to form Centre distance effects the size of the design. Driven pulley diameter effects the torque and tension.

Problem Definition Parameters (PDPs) Values that are known, given

Parameter Values Something extra

Plan for solving the Design Problem Analyze engineering characteristics: 1.Grinding wheel pulley speed, n 2, 2.Angle of wrap as a function of the centre distance, c, 3.Belt torque, T b, 4.Maximum belt tension, F 1, 5.Slack-side belt tension, F 2, and 6.Initial tension (before torque is applied), F i. Check for constraints violation:  Belt delivers full motor torque to the grinding-wheel pulley.  Belt tension does not exceed the belt strength limit. For the belt-and- pulley example

Generating and Analyzing Develop analytical means to predict the behaviour of the system  Model the behaviour of the system using relations from physics and mathematics  Develop a system of equations to analyze the performance of each candidate design (by substituting different values for the design variables)

System of equations for the belt-and-pulley analysis Objective 1: to compare between T m, i.e. the maximum torque delivered by the motor with T b, i.e. the belt torque. If T b < T m, the belt will slip. Objective 2: to find the driven-pulley diameter and the distance between the pulley centres (i.e. to satisfy the compact design customer requirement)

Free-body diagram of motor pulley

Can use spreadsheet to reduce effort in computing the expected performance of the system. Spreadsheet for Analysing Belt-Pulley Performance Why? Because during calculation you will have a variety of design variable values. So, you need to make sure that the values obtained satisfy the requirements of the design (i.e. the principle function and customer requirements).

Redesigning: finding feasible values Generating and analyzing are carried out to find feasible values, i.e. those design variables that satisfy the constraints given. But are feasible values the best values? Trade-offs: one attribute improves as the other degrades. Caused by the interdependency of variables (i.e coupling) e.g.: as the centre distance increases, the belt tension is reduced and as a result the Factor of safety becomes higher (this is good!) BUT By increasing the centre distance, the size of the system increases (this is not good!) So, which is more important??? EVALUATE!!!

Evaluating: Weighted Rating Method Step 1: Establish a set of evaluation criteria. Evaluation criteria are often developed from the list of solution evaluation parameters, of from engineering characteristics. e.g. belt-pulley example 2 most important engineering characteristics: belt tension and centre distance  Solution evaluation parameters. The team decided to consider belt tension as ‘very important’  weight = 0.6 and centre distance as ‘ important’  weight = 0.4.

Step 2: Rate the feasible designs for each criterion. Rating should be done according to customer satisfaction. Customer satisfaction curve  a means to assess customer satisfaction. Customer satisfaction w.r.t belt tension Customer satisfaction w.r.t centre distance

Step 3: Weight the ratings according to importance. Multiply the satisfaction rating by the importance weight. Step 4: Sum the weighted ratings to calculate an overall weighted rating. Weighted Satisfaction Based on Different Centre Distances c

Satisfaction curve for belt-pulley system Value of c between 9 and 14. so which is the best?

Systematic Parametric Design

Design for Robustness Term used to describe a number of methods aimed at reducing the sensitivity of product performance and variations. Variations includes: manufacturing, wear, operating environment Alternative design can be generated and analyzed for their sensitivity to variations. Two methods used: 1. Probabilistic optimal design 2. Taguchi method – design of experiments

Computer-Aided Engineering CAE refers to computer software and hardware systems used in the analysis of engineering designs to validate functional performance. 4 main categories: Dynamic analysis –The kinematics and kinetics of bodies i.e. the motion and the forces and moment that cause motion. –Analyses: Positions, velocities, accelerations Contacts and collisions Joint forces, shaking forces Relative motions. Finite element analysis –A method that essentially divides a part into smaller discrete elements to analyze the functional performance of a part. –Analyses: Stresses and strains throughout a part Factors of safety Buckling of parts in compression Temperature gradients and resulting heat transfer Fluid pressures and flows Natural frequencies of vibration Displacement of nodes General purpose –Refers to computer applications covering word processing, spreadsheets, mathematics, oral presentations, and project management. Other –QFD, DFMA, MATLAB (systems simulation), etc