Mechanical Design Control System Design Rafael Quintanilla Escalante March 22, 2005
Lecture Contents Design Process * Miscellaneous Components ** Gears and Belts Flexible Couplings Bearings Fixing Components to Shafts Stress and Strain Analysis Design Studies TIM (Infrared Mexican Telescope) * Based on the notes of Douglas Wright on Mechanical Analysis of Machine Elements, Department of Mechanical and Materials Engineering, University of Western Australia. ** Based on last year s lecture on Mechanical Design given by Ben Potsaid to the CSD class, ECSE, RPI.
What is Design? Goal Plan Thinking process Invention Interpretation of Design: Design is the application of creativity to plan the optimum solution of a given problem and the communication of that plan to others.
The Rudimentary Design Process STATE THE PROBLEM broad, complete GENERATE IDEAS methods AVAILABLE KNOWLEDGE BANK OF SOLUTION CANDIDATES uncritical quantity not quality RENDER PRACTICABLE SPECIFY CONTRAINTS & CRITERIA EVALUATE CANDIDATES OPTIMUM SOLUTION communicate
Problem Statement Understand the problem communicate Designer s responsibility to initiate communication and clear up any misunderstanding. Avoid artificial constraints Real boundary Fictitious restrictions Solution Space Your limitation knowledge Example: Team 4 - track a target in various lighting conditions. Broaden the problem Example: Financial Problems!! How to reduce car s fuel consumption? Improve driving habits Tune engine Switch off engine at red lights more broadly How to reduce car s running costs? Fuel consumption Ignore maintenance
Problem Statement (Cont.) more broadly How to travel between home and work at minimum cost? more broadly How to get money? walk bike bus Go to work Lottery car Get another job Complete the problem Identify everyone and everything likely to be affected by any solution. Examples: Inaccurate launching system causes iterative refinement not been able to compensate errors. Team 1 spills water on the car of Team3 You must ask the right questions BEFORE NEXT STAGE OF DESIGN, PROBLEM STATEMENT MUST BE AS BROAD AND COMPLETE AS POSSIBLE
Generation of Ideas Avoid ALL criticism while creating Inventiveness depends upon: Inherited qualities: Leonardo DaVinci Attitude: Be positive. Knowledge: Understanding of similar problems and area of study. Effort: Edison, inventor of the light bulb, said: Invention is 1% inspiration and 99% perspiration Ideation is carried out before considering constraints and criteria (crazy candidates trigger or are transformed into practical solutions) Generate as many ideas as possible; quality doesn t matter at this stage. However, recognize when stop inventing. Rate of idea generation Cumulative number of ideas generated QUIT TIME? time
Specify Constraints and Criteria Identify ALL the constraints and criteria Constraints: Bounds that every candidate solution must satisfy to be valid. Examples: Pour water from a bottle into a cup without spilling. The motor current should be lower than 300mA. Criteria: Measurements used to judge different candidate solutions. The degree by which candidate i satisfies the criterion j may be expressed by the utility, uij, often a real number between 0 and 100%. Examples: Pour water from a bottle into a cup minimizing spilling. The motor circuit should be cooled down. Solution space can be increased by converting constraints into equivalent criteria A common criterion which is often neglected is the need for simplicity
Render Practical candidate solution from bank Solve secondary problems, modify Candidate CAN satisfies ALL constraints? NO Candidate CANNOT satisfies ALL constraints? NO YES YES practical solution to evaluation activity impractical solution to trash A problem is trivial if it has been previously solved satisfactorily. NEW SOLUTION NEW SOLUTION NEW SOLUTION PROBLEM SECONDARY PROBLEM TERTIARY PROBLEM TRIVIAL SOLUTION TRIVIAL SOLUTION TRIVIAL SOLUTION DONE! DONE! DONE!
Render Practical (Cont.) Need to consider the manufacture and operation of the candidate solution in detail. Manufacture: Knowledge or Direct experimentation. Operation: Direct experimentation if possible (certain components or subsystems), or Mathematical model Inter-dependence of kinematics and forces occurs in all devices. Beware the dangers of a kinematic analysis without looking also at the forces involve. Candidates must be rendered practical before evaluation
Evaluation Compare practical solution candidates based on the problem criteria 1) Relative importance of criteria Weight w j : relative importance of the jth criterion Example: w mass is 25% for the vacuum cleaner and 75% for the military aircraft 2) Satisfaction of the criteria - utility Utility u ij : degree to which the ith candidate satisfies the jth criterion. ( 0 u ij 1 or 100%) 3) Overall utility U i : degree to which the ith candidate satisfies the whole problem. U i = n j= 1 w u j ij ; n = number of criteria Optimum candidate is the one with highest overall utility
Fixing Components to Shafts Setscrews: Low torque transmission High stress generation Low cost UNRELIABLE Examples:
Fixing Components to Shafts Pins: Low torque transmission High stress generation Low cost Examples: Straight round pin Tapered round pin Circular or roll pin
Fixing Components to Shafts Keys: Medium torque transmission High stress generation Medium cost Examples: square key flat key round key
Fixing Components to Shafts Spline: High torque transmission Low stress generation High cost Examples: spline
Fixing Components to Shafts Camp : High torque transmission Low stress generation Medium cost Examples:
Fixing Components to Shafts
Mechanical Design Fixing Components to Shafts Method Torque Stress Cost Setscrew Low High Low unreliable Clamp High Low Med Pin Low High Low Key Med High Med Spline High Low High
Gears and Belts Instantaneously, gears and pulleys act like levers
Gears and Belts (Cont.) At steady state velocity or ignoring inertia r1 Fr 1 1 τ 1 N = = = r F r τ τ FBD (F and M balance) = 2 2 2 2 Nτ 1 2 Thermodynamic (conservation of energy) Power = τθ τ 1θ 1 = τ 2θ 2 θ 2 τ1 N = = θ τ Conservative System 1 (Power in = Power out) 2 Kinematic (velocity analysis) r 1 θ 2 N = = r 2 θ1 θ = N θ 2 1
Gearheads - Spur Inexpensive Efficient Low torque Some backlash Motor and Gearhead often combined
Identical stages can be stacked together Gearheads - Planetary Large reduction in a small and lightweight assembly Large torque capacity Considerable backlash
Gearheads - Harmonic Flexspline has 2 fewer teeth than circular spline One tooth advances every rotation Huge reduction in small and lightweight assembly Almost no backlash Aerospace and robotics applications
Gearheads Comparison Type Torque Efficienc y Backlas h Cost Spur Low High Low Low Planetar y Harmoni c High Low High Med Med Med Low High
Bearings Outer race Inner race Bearings are usually press fit to the shaft or housing. Correct bearing hole diameter is critical. Heat expansion can be used to assist assembly. Bearings allow for slight misalignment
Flexible Couplings Parallel offset misalignment Angular misalignment Coupling is used to transmit torque between two shafts. Coupling is rigid in torsion and flexible in bending. Without flexible coupling, there would be excessive loads on the shafts and bearings. Without flexible coupling, bearings would fail prematurely and performance would suffer.
Stress and Strain Dynamic forces are exerted on the mechanical components. F = m x τ = J θ Dynamic forces cause deflections (strain) and internal forces (stresses) in the structural components. A Strain ( ε ) : ε = L L o Stress ( σ ) : σ = F A
Stress and Strain Yield Stress (elongation) In the linear region, material acts like a spring ( F = kx ). Stresses in the components should never exceed the Yield Stress to prevent permanent deformation. Why we do not design to the yield strength?
Design Study - TIM
Conclusions Mechanical Design and Control System Design cannot be done separately when high performance is required. Apply the Rudimentary Design Process. Don t forget about first principles and the basics.