1. FME461 Engineering Design II
Dr.Hussein Jama
Office 414
Lecture: Mon 8am -10am
Tutorial Tue 3pm - 5pm
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2. Statistical Considerations
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3. Introduction Engineering design considerations
This lecture is based on Shigley Ch 20
Random Variables
20 – 2 Mean, variance & Std Deviation
20 – 3 Probability distributions
Normal
Weibull
Probability of error
20 – 5 Linear Regression
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4. Engineering Design
is an iterative process that has as its primary objective the synthesis of machines in which the critical problems are based upon material sciences and engineering mechanics sciences.
This synthesis involves the creative conception of mechanisms, and optimization with respect to performance, reliability and cost.
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5. Engineering design
Machine design does not encompass the entire field of mechanical engineering. Design where the critical problems involve the thermal/fluid sciences fall under the broader category of “mechanical engineering design.”
The primary objective of machine design is synthesis, or creation, not analysis. Analysis is a tool that serves as a means toward an end.
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6. Design Process
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7. Design steps
Often the first step in which a designer becomes involved, and may not involve intense iteration. In this phase, we deal with the entire machine:
Define function
Identify constraints involving cost, size, etc.
Develop alternative conceptions of mechanism/process combinations that can satisfy the constraints
Perform supporting analyses (thermodynamic, heat transfer, fluid mechanics, kinematics, force, stress, life, cost, compatibility with special constraints)
Select the best mechanism
Document the design
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8. Design steps- prelim
Concept 1 Two longitudinal members, one trans-verse split-end cross member, small transverse member in transmission tunnel, rear transverse member similar to original, gauge reduction.
Concept 6 Two integrated, split transverse cross members, rear transverse member similar to original, reduced sheet thickness in cross members.
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9. Intermediate step
Generally occurs after preliminary design, but the two phases may overlap. Intermediate design always involves iterations. In this phase, we deal with individual components of the machine:
Identify components
Define component functions
Identify constraints involving cost, size, etc.
Develop tentative conceptions of the components mechanism/process combinations using good form synthesis principles
Perform supporting analyses (including analyses at each critical point in each component), FMEA, C& E
Select the best component designs
Document component designs; prepare a layout drawing
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10. Detail Design Phase
Subsequent to intermediate phase. In this phase, we deal with individual components of the machine and the machine as a whole:
Select manufacturing and assembly processes
Specify dimensions and tolerances
Prepare component detail drawings
Prepare assembly drawings
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11. Ass 2 - requirements General consideration of similar machines
Availability
Cost
Designs
Weakness/strengths
Design , details in the appendix
Analysis
Drawings
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12. Statistics – engineering design
Engineering statistics is the study of how best to…
Collect engineering data
Summarize or describe engineering data
Draw formal inferences and practical conclusions on the basis of engineering data all the while recognizing the reality of variation
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13. Use of statistics in engineering
Design of experiments (DOE)
use statistical techniques to test and construct model of engineering components and systems.
Quality control and process control
use statistics as a tool to manage conformance to specifications of manufacturing processes and their products.
Time and method engineering
use statistics to study repetitive operations in manufacturing in order to set standards and find optimum (in some sense) manufacturing procedures.
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14. Collection of quantitative data (Measurement)
If you can’t measure, you can’t do statistics… or engineering for that matter!
Issues:
Validity
Precision
Accuracy
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15. Statistics
FME471
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16. Precision and Accuracy
Accurate, Not Precise
Not Accurate Not Precise
Precise, Not Accurate
Accurate and Precise
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17. NO! Statistical thinking
Statistical methods are used to help us describe and understand variability.
By variability, we mean that successive observations of a system or phenomenon do not produce exactly the same result.
Are these gears produced exactly the same size?
NO!
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18. Sources of variability
Environment
Method
Man
Material
Machine
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19. Example
An engineer is developing a rubber compound for use in O-rings.
The engineer uses the standard rubber compound to produce eight O-rings in a development laboratory and measures the tensile strength of each specimen.
The tensile strengths (MPa) of the eight O-rings are
103,104,102, 105, 102, 106, 101, and 100.
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20. Variability There is variability in the tensile strength measurements.
The variability may even arise from the measurement errors
Tensile Strength can be modeled as a random variable.
Tests on the initial specimens show that the average tensile strength is 102 MPa.
The engineer thinks that this may be too low for the intended applications.
He decides to consider a modified formulation of rubber in which a Teflon additive is included.
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21. Random sampling
Assume that X is a measurable quantity related to a product (tensile strength of rubber). We model X as a random variable
Occur frequently in engineering applications
Random sampling
Obtain samples from a population
All outcomes must be equally likely to be sampled
Replacement necessary for small populations
Meaningful statistics can be obtained from samples
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22. Point estimation
The probability density function f(x) of the random variable X is assumed to be known.
Generally it is taken as Gaussian distribution basing on the central limit theorem.
Our purpose is to estimate certain parameters of f(x), (mean, variance) from observation of the samples.
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23. Sample mean M is a point estimator of m S is a point estimator of s
Sample variance:
M is a point estimator of m
S is a point estimator of s
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24. Normal Distribution
Mean and standard deviation to describe the sample or population
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25. Example
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26. Solution
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27. Weibull distribution
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28. Example 2
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