Less is more, part 7

Maximum flexibility with minimum impact

This will be the last in the less is more series and is "tech heavy" again.

In the last posting we described the concept of an error budget as used in design of precision machines and then proposed to apply a parallel concept as a "sustainability budget" for including the environmental/resource impacts in the design process. We hoped with this to design a machine that met both the requirements for machine performance as well as a more sustainable (or at least greener) machine.

We ended with a description of the construction of a sustainability budget following the three basic steps:

Step 1: determine an energy, material and resources (consumables, etc.) model of the machine and its principal components in the form of a series of relationships defining the energy consumption, materials use as a function of machine design or operation. (This might be referred to as energy or materials mapping.)

Step 2:  analyze systematically each type of energy and material use in the system and determine the relative performance-energy/material impact (for example, from Ashby charts).

Step 3: combine the energy/materials impacts to yield upper and lower bound estimates of the total energy/material impact of the machine.

We noted that it was important that the embedded energy and materials must be counted.

So, now an example of constructing a sustainability budget.

The critical part of building these budgets (error or sustainability) is accumulating the data needed to populate the budget. Material data sources are very helpful in determining the basic material-performance characteristics (like modulus of elasticity, thermal properties, density) that are of use in machine design as we have seen. But, these need to be “connected” to embedded energy and operating energy consumption for use in a sustainability budget. Although there are many materials texts available, one excellent source of such “connections” is the text book “Materials: Engineering, Science, Processing and Design” by Ashby, Shercliff and Cebon, Elsevier, 2010.

Ashby uses an approach (or strategy) for materials selection which is comprised of four steps:
- translation of design requirements in terms of function, objectives, etc.
- screening to select most usable materials meeting the requirements
- ranking with respect to some set of criteria, and
- documentation on background and history of the material in this or related uses

This strategy attempts to get the best match between the characteristics of materials (or processes if the four steps are used for process selection) and those required by the design (functionality and constraints). We would add, as one of the screening elements, the need to assess environmental compatibility, energy use and embedded energy, global warming gas emission impacts, etc.  Embedded energy is that energy that has gone into the mining, conversion, processing, and transportation of the material up to the point it enters our control or manufacturing facility for use in our product.

This would work as follows. The machine designer first determines the specifications required for the precision device as usual as inputs to the left side of figure below (from Dornfeld Precision Engineering, Springer, 2010). A parallel discussion could be had for a process design or system of devices of processes but to simplify the discussion we stay with one device here - a precision machine.

Figure  Design to sustainability selection chart, thermal stability example

The designer determines that a  critical requirement is that the device should be insensitive to variations in temperature where it operates and, since the device is heavily constrained (meaning the device cannot change size due to temperature variations without experiencing bending - picture a simple beam that is being heated and it is held at each end in a vise. When it heats up it will expand along the length and, if heated enough, eventually bend up or down) the variable set of interest includes the modulus of elasticity, E, the coefficient of thermal expansion, α, and the conduction coefficient, k. This defines how much the material can be deformed with out permanent "plastic" deformation or damage (that is, spring constant), how much the material expands per degree of temperature rise and how readily the material conducts heat.

For this situation, it is known that the combination of Eα/k (or elasticity times thermal expansion divided by the conductivity) should be as low as possible to minimize thermal distortion and that will define a set of suitable materials. We can find a wide range of materials with differing expansion and conduction coefficients. Depending on which of these materials we choose, we can determine the energy or sustainability impact by noting the embedded energy (for example) as a function of the weight or volume of the material (or materials) chosen and the amount needed for the design. For example, the figure below, from Ashby shows the relationship between embedded energy for a range of materials and the embodied energy/m3, or production energy per unit volume. We see that more “exotic” materials, often

Figure  Production energy per volume for a range of materials, from Ashby 

used for thermal stability have higher embedded energy due to production requirements. This gets us through Step 2 of the sustainability budget creation.

However, it must be noted that there are usually other issues that need to be considered besides embedded energy (such as societal impacts if the material is toxic or hazardous or comes from a region where damage is done in mining or extraction) for a complete assessment of sustainability. Also, it is clear that we could create a set of charts as in the design figure shown first above for other constraints in machine design (chatter or vibration for example, in a milling machine, where the key parameter might include stiffness of the component and the tradeoff could be between cross-sectional area/geometry and stiffness; alternate material choices could be conventional carbon steel, a composite material with high stiffness to weight ratio, or a ceramic (which would also have beneficial thermal properties).

Step 3 of the sustainability budget construction requires combining the energy/materials impacts to yield upper and lower bound estimates of the total energy/material impact of the machine. Summing these for a series of machines in a system would give us a system budget. The most challenging part of this step is determining the “sensitivity” of sustainability to device specifications.

We need to make the same type of analysis relative to the sensitive directions that we are designing our device to protect for error sources and the materials in their configurations we are  using to accomplish that. Ideally, following our procedure in the design figure above, we could determine a range of material properties that can be varied to affect the design requirement of concern, for example thermal stability in the above example, but which would have no or minimal effect on embedded energy. This would be a sort of sensitivity analysis to energy or environmental impact similar to that seen in machine stiffness evaluation.

That is, a design/material which allows us to meet design requirements with the maximum of flexibility while having minimal impact on environmental damage would allow the application of the conventional error budget without much additional constraint. It would, in effect, decouple the design and material choice from the sustainability impact for a defined range of conditions.

Let’s look at an example. In the Ashby figure above we can see that, at an embodied energy of  about 105 Mj/m3  a wide range of materials exist spanning cast irons and some carbon steels to metal foams. Depending on the density of metal foams their modulus of elasticity can be as far from or as close to their parent material. This is not the case for carbon steels and cast irons. Similarly, thermal properties will vary tremendously between metal foams and cast iron, as will damping characteristics (important in machine tool structures). But, from an embodied energy perspective they are all quite similar. So there is an insensitivity we can take advantage of.

Tradeoffs in energy/materials sustainability (depending on what part of the life cycle it is used in) also need to be considered. Some “static” structures such as heavy machine tool bases which support but do not move with the machine axes can be made of heavier materials as their impact on energy of the machine during the “use” phase will not be large. Components making up the moving portions of the machine will logically expend more energy during their life with than stationary components as with each motion, energy will be expended in moving the component proportional to mass (among other things.)

This was a rather straightforward example discussed above. More detailed examples are suitable for a graduate course discussion but one can get the idea.

The key "takeaway" here is the concept of a selecting a design/material which allows us to meet the design requirements with the maximum of flexibility while having minimal impact on environmental damage. Maximum flexibility with minimum impact! This would, in effect, decouple the design and material choice from the sustainability impact for a defined range of conditions.

Next time we are going to dig into leveraging a bit further with some examples.

Finally, a couple of "plugs" for conferences you may be interested in. We are hosting, at Berkeley, the 19th CIRP Conference on Life Cycle Engineering - "Leveraging technology for a sustainable world" - website is http://lce2012.berkeley.edu/home.html. There is also a "regional meeting" in achieving low CO2 industrial plants - California France Forum on Energy Efficient Technologies - website is http://caffeet.org/. Look forward to meeting some of you at one or both of these!

Less is more, part 6

Budgeting for sustainability

This will be the second to last in the series and, probably, these will be the most complicated since we are talking about some subtle aspects in the design of machines. But, interesting never-the-less!

In the last posting we looked at Ashby's approach to linking material properties to environmental impacts/resource requirements. This time we'll like to apply this to the an example - the design of a precision machine tool. The material here is adapted from Chapter 12 of my book Precision Manufacturing (Springer, 2010; it's on Amazon if you are interested!). We'll set up the discussion in this posting and complete the story in the next, and final, one.

First, we need a formalism for addressing sustainable design of precision machines. This follows from the formalism used for basic machine design. This is referred to as the "sustainability budget." Let me explain.

In the design of machines, specially precision ones (that is, machines that can operate reliably and repeatably positioning workpieces or tooling to great accuracy and with very high resolution - for example, repeatably positioning something within a couple of microns (or nanometers).) This is often accomplished using a technique called "error mapping" and developing an "error budget." These are methods for accounting for the magnitude and eventual impact of the numerous potential sources of error in a machine’s performance – relative to dimensional accuracy, form error, or surface finish.

One does this by determining the likelihood of errors due, for example, to thermal distortion (remember, things expand when heated and contract when cooled so if a machine component is subjected to either of these due to operation or environment) the component will change shape and that will affect the accuracy of the machine. Seems small but, over long machine components, it adds up. Or, for high accuracy, small temperature changes can have a big effect. Steel, for example, has a coefficient of thermal expansion of 11.7 microns/meter/degree C. So, a steel component 10 cm (or about 4 inches; one tenth of a meter) long that experiences a temperature rise of 5 degrees C during operation will "grow" almost 6 microns due to the thermal expansion. That's a lot in the precision manufacturing community! Larger structures can grow more. And, 5 degrees C is easy to experience in most conventional manufacturing facilities.

We can put the machine in a conditioned environment where the temperature is maintained constant but that cost money and, importantly, uses a lot of energy. Or we can put circulating oil systems on machines with temperature controlled oil to maintain a constant temperature but that adds to the machine's energy footprint also. And, since the circulating system usually runs even when the machine is not producing work, this makes the idle state of the machine almost as bad as the production state.

There are materials with almost zero coefficients of thermal expansion - but they are costly in terms of money and energy to create. So, we'd like to design the machine to have as little sensitivity to thermal distortion while using materials that have lower environmental impact.

One of the concepts in precision machine design relates to identifying, first, the  “sensitive direction” in the machine. This is the direction in which an error impacts the part quality: dimension, form, roughness. For example, if you are trying to create a surface with a certain dimension by machining, then you want to control the position of the cutting tool relative to that surface with great accuracy. Any error in the position of the tool relative to the surface will result in an error. So, for this operation, the axis of tool motion towards and away from the surface during machining would be the sensitive direction.

The way we can keep track of all the contributions to the errors in the machine can be referrer to as an "error budget." This budget allowed us to include all sources of error and an estimate of their relative magnitudes and then determine which of these sources actually impacted a sensitive direction resulting in a part error. The term budget is chosen exactly to represent what, like a budget for household expenditures, is available to be distributed over all the requirements for operation. Just as in a household budget where some of the monthly funds must cover groceries, insurance, transportation, etc., in an error budget, we allocate the elements making up the total error in such a way that, when we are done with designing the machine, the cumulative error, in the sensitive direction, do not exceed our requirements.

So, errors in the machine due to thermal effects, loads due to moving workpieces or forces generated in machining (which cause another type of distortion, elastic distortion, due to the elasticity of the material the component is made of), gravity loads, or vibrational excitation due to rotating spindles or tooling, are estimated. From these estimates it is determined by modeling the machine structure kinematically, in what way these errors affect the machine tool operation and accuracy and, then, to what extent they affect the sensitive direction.

Now, an important concept in this method is that an error that exists but does not affect the sensitive direction is not of concern. Meaning, something could be going on in the machine but as long as it does not affect the location of the tool relative to the workpiece in the example we've been discussing, we don't need to worry about it.

This would be like going to a restaurant which serves a fixed price buffet. You could eat a lot, or a little, and, from the point of view of your budget, it wouldn't matter. With graduate students, that means you can eat a lot!

So, in the case of an error source not impacting the sensitive direction, we have a lot more design freedom with no apparent penalty in terms of performance.

So by now you are asking what the heck this has to do with the subject of the blog!

Consider if we would add constraints on the environmental performance of a machine while insisting that the other quality metrics are met as well as the manufacturing performance (throughput, lead time, cost/piece to operate, etc.) This could be included in our budget analysis but, in this case, we’d call it a "sustainability budget". A sustainability budget would operate similarly to an error budget except we would be looking for the impact, from environmental metric point of view, of the design and operation of the precision machine, process or system.

Then, using the idea of sensitive directions (and the complementary concept of non-sensitive directions – that is, those directions for which any error from a specific source has no effect) we can imagine an analysis which measures the impact of  materials, designs, or operating conditions on the overall environmental behavior. Then we look for instances of materials, design features or operating conditions that give the largest range of variability, from the point of view of design, with the least environmental impact. That is, those instances for which little  or no sensitivity is displayed.

Following a methodology based on this would allow us to design the machine, or system of machines, in such a way that the basic performance, precision and accuracy, would meet the core error budget constraints but, in addition, we could do so in a way that was more sustainable.

Great idea but how do we do this?! Let's get started.

In the design of a precision machine the first requirement is to derive an error budget. Now it gets a bit complicated. Creating an error budget relies on two sets of rules — connectivity and combinational. Connectivity rules define the behavior of machine components and interfaces in the presence of errors. That is, how does the error in one component affect the position (for example) of another component. This is sort of like trying to level a table in a restaurant by sticking little bags of sugar under one of the legs. Sometimes you are lucky and it works the first time. Other times changing one leg makes another lose contact with the floor and the table still wobbles. That's is a simple example but that is connectivity.

Then, the combinational rules define how the errors are to be combined to determine the impact on the accuracy of the workpiece. That means, how all these connected components, experiencing the various sources of error, combine to affect the sensitive direction. Not surprisingly, this is done with mathematics.

The procedure is comprised of the following three steps:

Step 1 — make the model of connectivity. This is called the error map. We do this by determining a kinematic model of the machine and its principal components in the form of a series of matrices,

Step 2 — analyze systematically each type of error in the system and use the mold to determine the relative tool-work errors. This is determining a relationship defining how the errors affect the sensitive direction, and finally

Step 3 — combine the errors to yield maximum and minimum estimates of the total error of the machine. Sort of like specifying tolerances on a part length - the error of importance will likely be within this range.

If we revise this approach for a sustainability budget, we’d follow the same three basic steps but with some different objectives. For example, we would add some elements to the three steps, or, actually, develop a parallel set of “models” and analysis.

Parallel to Step 1 would be:

- determine an energy, material and resources (consumables, etc.) model of the machine and its principal components in the form of a series of relationships defining the energy consumption, materials use as a function of machine design or operation. (This might be referred to as energy or materials mapping.)

Parallel to Step 2 would be:

- analyze systematically each type of energy and material use in the system and determine the relative performance-energy/material impact (for example, from Ashby charts).

Parallel to Step 3 would be:

-  combine the energy/materials impacts to yield upper and lower bound estimates of the total energy/material impact of the machine.

Importantly, in this parallel analysis, the embedded energy and materials must be counted. That is, we cannot only look at the energy to move an axis of the machine (for example in a precision machine tool) but we’d need to consider also the energy associated with the earlier material processing and conversion, any subcomponents or subsystems, etc. Also, some measure of global warming gas generation and any other environmental impact effects must be included.

We are, essentially, estimating the footprint of this device we are designing. This makes the analysis rather complex and, unfortunately, not as analytical as the construction of the conventional error budget first described.

But, it makes sense. And, next time, we'll add details and apply this to an example.