This is the last in the Less Is More series.
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. T
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.
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, ?, 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 E?/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
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.
David Dornfeld is the Will C. Hall Family Chair in Engineering in Mechanical Engineering at University of California Berkeley. He leads the Laboratory for Manufacturing and Sustainability (LMAS), and he writes the Green Manufacturing blog.“