My last article began to dig into the leveraging discussion and started to elaborate on this topic using an example. The example was from a recent paper from our research group at Berkeley and focused on an important aspect of vehicles and transportation – the gear train.
The efficiency of gear systems was described as deriving from a variety of factors including the surface roughness of the mating surfaces. Other studies have shown an even greater dependence on the surface roughness of the mating surfaces for hypoid gear pairs, which are found in automotive differentials. And because the vast majority of environmental impacts of an automobile occur during the use phase, the impact of increased manufacturing precision through better surface finish on the final drive reduction of an automotive manual transmission drivetrain makes this an ideal example of leveraging.
The gear manufacturing process chain is relatively complex with several options available to the manufacturer at each fabrication stage. It is assumed here that the main process chain would be unchanged and that only gear finishing would need to be altered to produce gears with higher surface finish.
It might be helpful to digress a bit to talk about this important manufacturing process that underlies the efficient operation of most machines and transportation. Gear finishing, essentially abrasive machining, is one of those seemingly small and innocuous steps in manufacturing that “gets no respect” (to quote Rodney Dangerfield). In the world of machining with hard tooling (meaning not using lasers or some other type flow process) cutting processes are categorized by the geometry of the tool used and according to whether or not the tool is stationary relative to the workpiece or if the tool rotates. There is a logical division of these processes that, at the highest level, distinguishes between cutting tools that have a “defined geometry” (meaning specific dimensions that determine the shape of the tool) and cutting tools that are not defined (meaning the shape is more random)—having an “undefined geometry.”
Grinding uses undefined geometries – that is, the “tool” or abrasive doing the cutting does not have defined edges at all. Abrasive processes (grinding, sanding, polishing, etc.) use abrasive particles that are natural materials like sand, aluminum oxide, and so on, or materials made to appear as natural shapes. In typical grinding operations several abrasive grains (usually referred to as “grits”) are held together by a bonding material, as they would be in a grinding wheel or for abrasive (sand) paper. The shape of the grains is not defined but “random” depending on how the grain of abrasive was crushed to get the desirable size. If you’ve every sanded wood or other material or used an emery board on your fingernails, you’ve been abrasively machining.
Importantly, as you observed when standing and noted that small grits gave you a better surface finish (meaning smoother or lower roughness), we control the desired process output by controlling the grain size and the way it moves through the material surface during grinding. Chip formation with an abrasive grain is illustrated in the figure below and shows the grit displacing/removing
workpiece material. The “v” is the velocity of the grit over the work and the arrow shows the relative movement between the grit and the work – the speed and direction. In grinding there would be hundreds of thousands of grits coming into contact with the work and each grit removing a small chip of material.
Thanks to many decades of research on grinding by engineers and academics (like Professor Steve Malkin of University of Massachusetts-Amherst) the relationship between grinding process parameters and material removal and, finally, surface finish is well characterized. We can summarize the gist of this rather simply as follows. We can describe a general empirical relationship that links the achieved average height surface roughness of a grinding process to the process specific volumetric
removal rate and the grinding wheel speed, the v in the above diagram, by assuming a direct correlation between the surface roughness and undeformed chip thickness.
Let me explain.
The undeformed chip thickness is the depth of cut of the grain into the workpiece. Seen in the figure above it would be the difference between the bottom of the grit in the work and the top of the work surface. Specific volumetric removal rate is the volume per unit time of material removed by the process – here dependent on the number of grains moving over the surface at the undeformed depth. Each grain removes a small volume and the grains pass the surface at a specific rate. Surface roughness is a measure of the variation of the surface of a workpiece at a very fine scale, usually microinches or micrometers. The smaller the variation the smoother the surface. So small is good in the world of surface roughness!
Still with me?
Then we can move on to the leveraging part. The figure below shows the link we are trying to quantify. This figure illustrates the discussion above about removal and surface effects but also shows where
the impact comes in. This figure is motivated by the work of another researcher at the University of Kentucky – Professor I. Jawahir. He studies the connection between process parameters, surface integrity and part function. The trade off between volumetric removal rate and surface roughness must be done understanding that if we adjust the grinding (or finishing) process to create a better surface finish it will cost us something. Here the cost is likely to be time (as finer finishing processes often take longer – remember how much time you need to sand with fine paper as apposed to rough sand paper to achieve a certain surface?). It will also cost us energy – we’ll see why next time.
The “leveraging” comes in with the expected fuel savings due to the better efficiency of the gear operation due to the better surface finish. We need to determine if the increased consumption of energy in finishing is paid back in the improvement in the operation of the gear train and accompanying reduction in fuel use.
We’ll “do the numbers” next time.
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.