# 01-18: Course introduction #

## Overview #

This class focuses on three main components – manufacturing processes, dimensional tolerances, and design communication – and how they interact with one another.

The class is made up of 9 modules:

- Fundamentals
- Subtractive manufacturing processes
- Additive manufacturing processes
- Forming processes
- Joining processes
- Graphical visualization techniques
- Metrology: measuring manufactured objects
- Geometric dimensioning and tolerancing
- The future of manufacturing

## Why manufacturing? #

- In 2018, U.S. manufacturing accounted for 11.6% of the U.S. economy, 18.2% of global manufacturing output, and 8.2% of the U.S. workforce – source
- Manufacturing output is growing, and is returning to the U.S.; output increased >30% between end of 2008 and 2014
- 67% of U.S. R&D is funded by industry
- Even when production is offshore, design is often done here anyway
- Automation is increasing, yet there is a shortage of skilled (human) talent
- Even if you don’t want to go into manufacturing industry, research and academia still require manufacturing knowledge
- Even if the process if outsourced, design is still done in the US. To design well, you have to have a base-level understanding of manufacturing

Manufacturing output and employment are rising

Many companies have regionalized their supply chains since the pandemic

## Processes #

In this class we will consider multiple families of processes:

- This is a rapidly moving field that is always adapting
- This class should give you a top level overview so you can evaluate novel methods

## Materials #

In this class we will consider multiple families of materials:

- Materials choices influence performance
- For example, consider the progress of the plane:
- In 1903 the right brothers low-density wood with steel wire and silk
- In 1935 the Douglas DC3 used aluminum alloy (since it became feasible to produce and manipulate)
- Now the 2010
Boeing 787 Dreamliner is made up of 50 wt% composites 20 wt% aluminum 15 wt% titanium 20% lower fuel consumption per passenger mile
- Composite materials are two(+) materials combined together to get best of both worlds, in aviation typically stiff/strong carbon fibers embed in tough/fatigue-resistant polymers.

- Materials choices influence market size
- There isn’t always a best material; different materials fit different markets/needs
- Opposite side of the coin: There may be multiple valid material choices for a particular function

## Tolerance #

- Tolerancing is a formal way of specifying limits on the amount of dimensional variability allowable in manufactured parts
- We need a range because measurements will never be 100% precise; we need to define an acceptable range
- Some sources of variation
- Human operator changes and/or errors
- Tool wear
- Environmental changes (temperature, humidity leads to tiny expansions / contractions)
- Input material variability
- Measurement error

- Affordable mass-production
*relies on interchangeability of parts*- When mating parts of given designs, it should not matter which specific parts

- Therefore part dimensions must be consistent
- But no manufacturing process is perfectly consistent

- If you don’t understand the process of manufacturing and the capabilities of tools, then you will won’t know how to create manufacturable designs

- Tighter tolerances (closer tolerance limits) are generally more expensive to achieve
- The solid green line shows an ideal process
- The dotted green line shows the impact of an error shifting the distribution, shifting the tails to approach the tolerance upper / lower bound
- The red line shows a unsuitable process (even if it’s calibrated accurately, the poor precision causes high variance that it’s not really feasible; however, if outside of the limits an additive (or less common subtractive) could be used to )

### How E29 integrates manufacturing and tolerancing #

- Tighter tolerances are more expensive
- The physics of a process determine how tight a tolerance is achievable and how much it costs
- Therefore we need to understand how manufacturing processes work in order to:
- Select a suitable process for the application
- Specify reasonable tolerances
- Geometric Dimensioning and Tolerancing: a graphical language for specifying tolerances robustly

## Design Communication #

- Important to effectively describe your ideas and designs graphically
- Persuade – we need to be able to show are perspective
- Instruct – we need an agreed an unambiguous way to communicate
- Document – we need to convey how to construct our final design
- Seek feedback – we need to ensure everyone is on the same page

- Drawings can be 2D or 3D representations
- Interpreting 2D drawings made by others
- Creating 2D “working drawings” with unambiguous instructions

- Design communication is not only graphical
- Oral, written
- Manufacturing relies on teams
- Teaming activities

# 01-20: Fundamentals of Tolerancing #

- See why we study tolerancing from yesterday’s notes

## Basic tolerance formats #

- Unilateral
- e.g. Inches: .$.500^{+0.005}_{-0.000}$, Metric: .$35^{+0.05}_0$ (notice sigfig notation)

- Bilateral
- Most common; start with nominal then you have some tolerance bounds above and below
- Equal or unequal deviations from nominal dimension
- Same number of decimal places for upper and lower limits
- e.g. Inches: .$.500 \pm .005$ or .$.500^{+0.005}_{-.010}$, Metric: .$35 \pm 0.05$ or .$35^{+0.05} _{-0.10}$

- Limit
- Given only bounds, not the nominal value
- e.g. Inches: .$.250, .248$, Metric: .$35.05, 35.00$

## Tolerance buildup #

- In the real world we have error, so the way we define dimensions have an impact
- Best dimensions to label depend on function
- That is, dimensioning should be done intentionally such that
*critical*distances result in minimal error, - e.g.suppose distance between .$X$ and .$Y$ is critical

- That is, dimensioning should be done intentionally such that

- Chain is bad since the potential (and often times real world) maximum error is large

- The errors compound since dimensions are in reference to other dimensions that
~~may~~will contain error.- The more dimensions chained, the greater the possible error
- Baseline is better – every feature references a single base.

- However the worst case is still significant
- .$X$ may be off by .$\pm .05$ and .$Y$ may be off .$\mp 05$, compounding to .$\pm 0.10$!
- Direct is ideal

- Depends on which dimensions are critical (that is, .$X, Y$)

## Normal cumulative distribution function #

- Tighter tolerances (closer tolerance limits) are generally more expensive to achieve
- The physics of
**the process used determines the curve’s characteristics**- .$\sigma$ is the stdiv (width) of this density

- .$\mu = x_0$ is the target (average) value we give
- This probability density characterizes how this function is distributed and the chance a given range of values occur
- The area under the curve in a given range is the probability the value falls within that range
- Single values, i.e .$x_0$, have a 0% probability. We can only calculate ranges because this is a
**density function**.

Probability density, e.g. given by Gaussian/Normal probability density function: $$p(x) = \frac{1}{\sigma \sqrt{2\pi}}e^{-\frac{(x-x_0)^2}{2\sigma^2}}$$

- Why do we care about statistics?
- We want to look at a process, look at tolerances, and figure out whether it’s worth to manufacture using this process
- If you know the distribution of a process, you can work out the probability a given part satisfies spec limits.

- There is no easy, exact analytical way to integrate the normal probability density function.
- The probability that a randomly chosen member of a normally distributed population has a value .$\leq x$ is
$$\int_{-\infty}^x p(x)\ dx = P(x) = Z\bigg(\frac{x-\mu}{\sigma}\bigg) = \frac{1}{2}\bigg[1 + \text{erf}\bigg(\frac{x-\mu}{\sigma\sqrt{2}}\bigg)\bigg]$$
- .$\text{erf()}$ is the error function
- .$Z$ is the normal cumulative distribution function; values of .$Z$ are tabulated in a Z table

- The probability that a randomly chosen member of a normally distributed population has a value .$\leq x$ is
$$\int_{-\infty}^x p(x)\ dx = P(x) = Z\bigg(\frac{x-\mu}{\sigma}\bigg) = \frac{1}{2}\bigg[1 + \text{erf}\bigg(\frac{x-\mu}{\sigma\sqrt{2}}\bigg)\bigg]$$

## Example probability of part lying between within spec limits

## Process capability and tolerancing #

- Sigma, .$\sigma$, is the standard deviation of dimensions actually produced by a process
- Six sigma processes
Six Sigma (6σ) is a set of techniques and tools for process improvement. […] A six sigma process is one in which 99.99966% of all opportunities to produce some feature of a part are statistically expected to be free of defects.

- Specification limits are .$12\sigma$ apart. Here, 2 parts per billion lie outside specification limits if process is ‘in control’ (i.e. if mean output of process is centered between specification limits)
- Arose because the cost of manufacturing, specifically the process that creates an error, has a cost. This cost can grow very large, very quickly, when mass-manufacturing.
- You’re best off spending money improving the process so the distribution gets tighter
- The alternative is either (1) accepting errors (resulting in faulty products) or (2) testing all components to ensure they are ‘good’ and tossing out the bad ones

- Process capability: .$C_p = \frac{\text{USL - LSL}}{6\sigma}$

## Classes of Fit #

- Tolerances should be…
- Not too tight: tight tolerances are expensive
- Not too loose: otherwise function is compromised

Clearance fit:designed with space left between two components

- e.g. a shaft with a bearing need to have some give / free space
Interference (push) fit:designed to be touching

- You may want interference because you want the friction between the components; you want the two pieces to not move/rotate/etc
- How? Elastic or even plastic deformation
- e.g. two pieces may need to fit tightly with friction as to prevent vibrations
- Expansion fit:

- If there are large forces/torques acting on these two components so you want them
very tight- e.g. you may temporarily expand one component (e.x. with heat) to fit on/around the other, then it will shrink down
- Shrink fit:

- Same as expansion, but using some cooling process (e.x. liquid nitrogen)
- Why do this over heat?

- It’s typically more expensive to cool down
- The material may deform / weaken – e.g. steel will be degraded if heated up
Transition fit:complete interchangeability is compromised to allow looser tolerance on individual components.

- If fit type is not critical.
- But even then, why not choose one or the other? Because you don’t want a large gap and the materials/parts cannot withstand the force needed to assemble them with an interference fit.
- The pieces are just for alignment – think Ikea assembly pegs; they’re just to align components.
- It’s easier to manufacture these parts

## Snap fits #

- Involves temporary elastic deflection which enables parts to interlock, e.g. involving bending of one component
- Done often with molded parts
- Tends to involve Cantilever (e.g. casings), Annular (e.g. pen lids, take-out soup container lids)
- Designed to be assembled once, and typically not disassembled (multiple times) – irreversible.
- Relatively simple: you don’t need screws/glues/etc. – useful for rapid prototyping since you don’t have to consider fasteners
- Takes advantage of the fact that the material has some elasticity

- You need to stay within the elasticity limits of the material
- Most 3D plastics have ’enough’ give
- You (generally) want to design such that the stress is from bending, not stretching
- More, additional, extra, readings

### Terminology Definitions #

Don’t stress about memorizing these !

Maximum material conditionThe greatest allowable amount of material left on the part (max size for a shaft; min size for a hole)(MMC):Minimum/least material conditionThe least allowable amount of material left on the part (min size for a shaft; max size for a hole)(LMC):

- Important with MMC since they tell us how much they’re able to ‘slosh around’
Basic size:Exact theoretical size from which limits are derived

- Different form nominal since basic refers to the standard table which gives respective upper and lower bounds (MMC and LMCs)
- Hole basis: Basic size is minimum size of hole
- Shaft basis: Basic size is maximum size of shaft – used when many components need to fit on to one shaft.
- Basic size could be chosen to be in-between hole and shaft basis
Tolerance:Allowable variation of one particular dimensionFundamental deviation:Difference between basic size and the closer of the MMC and LMCAllowance:Difference between maximum material conditions of the two components

## Types of fit #

- These types are created by ANSI: American National Standards Institute
- Exact values are tabulated in many source

- RC: Running and sliding clearance fits
- Nine categories:
- RC1: Close sliding: assemble without perceptible “play” (e.g. watches)
- Less than a 1/1000".
- Basically impossible for air, let alone liquids, through.

- RC2: Sliding fits: seize with small temperature changes (e.g. )
- RC3: Precision running: not suitable for appreciable temperature differences
- RC4: Close running: moderate surface speeds and pressures
- RC5/6: Medium running: higher speed/pressure
- RC7: Free running: where accuracy not essential and/or temperature variations large
- RC8/9: Loose running

- RC1: Close sliding: assemble without perceptible “play” (e.g. watches)
- Go for lower if you want minimal vibration/gaps – no perceivable play.
- Has drawbacks:
- The less clearance, the easier it is to seize up – especially if two components are touching and made up of different materials (different expansion/contraction rates).
- Susceptible to dust, you would have to seal the machine or use it in clean conditions.

- If you go less precise, you don’t need to go slow, cheaper operator costs, cheaper tooling
## RC Chart

## RC Table

- Nine categories:
- LC: Locational clearance fits
- Normally stationary, but freely assembled/disassembled
- Used when you need clearance to dis able and clean
## LC Chart

- LT: Location transition fits
- Accuracy of location important
- Small amount of clearance or interference OK
- e.g. ikea furniture pegs

- LN: Locational interference
- When you need friction
- Accuracy of location is critical

- FN: Force fits
- When you need to hold a load (typically uses temporary heating)
- Designed to transmit frictional loads from one part to another

## Example: Which type of fit?

## Processes, tolerances, and surface quality #

- How do we relate physical processes and tools to these values?

FromMF Ashby, Materials Selection in Mechanical Design

### Roughness #

- How do we define roughness? You may use tool that uses a tiny needle to ‘scan’ the surface, measuring deflections as you go

FromMF Ashby, Materials Selection in Mechanical Design

**RMS roughness:**root mean square of deviations over the measured surface length- i.e.: .$R^2 = L^{-1} \int_0^L y^2\ dx$
- Usually, tolerance, .$T$, lies between 5R and 1000R

- Generally, if you go high rotation speed and slow translational speed you get less rough surfaces
## RMS Roughness Example