Cup-wheel grinding from The GrindingDoc
2 September 2011
Dr. Jeffrey A. Badger, The Grinding Doc, takes a look at the intricacies of cup grinding.
A lot has been written over the years about the various types of grinding: surface grinding (heaps), cylindrical grinding (loads), double-disc grinding (oodles); centerless grinding (gobs, more than any one person can absorb in a lifetime). But one area of grinding has received scant attention: cup-wheel grinding.
And that’s a shame because its seemingly simple geometry is not simple at all: it changes throughout the life of the wheel. Or, at the very least, it changes between truings and dressings.
Cup wheels are used in a variety of applications. Most of my experience comes from diamond cup-wheel grinding of saw blades made of either tungsten-carbide or cermet. So let’s take a look at what’s going on in this peculiar type of grinding (see Figure 1 – below).
After truing the wheel, grinding occurs on the face of the wheel as shown in (a). The contact area is small so the forces on this face are extremely large, and the wheel takes a beating during the “break-in period”. A taper develops quickly (b) and grinding moves from the face of the wheel to the bottom of the wheel. Here the forces on the wheel are lower, and wheel wear is typically (but not always!) lower as the forces are distributed over a larger area.
Why does the wheel take a beating? It has to do with the contact area. Let’s say you have a rim width of 3 mm (0.12”) and a workpiece width of 5 mm (0.2”) and you take a depth of cut of 0.050 mm (0.002”). During the face-grinding break-in period, the contact area is Area = depth of cut X part width = 5 mm X 0.050 mm = 0.25 mm2. After break-in the contact area moves to the bottom of the wheel, increasing to Area = rim width X part width = 3 mm X 5 mm = 15 mm2. That’s 60 times more area to cope with the same material-removal, meaning 60 times the number of grits doing the same work.
So you may think, “Well, that’s good because now I have more area to do the grinding.” And you’d be mostly right. But only mostly. Here’s what’s happening:
If your rim is too wide, then the contact area on the bottom of the wheel is too large and your grit penetration depth is small. In other words, the grits don’t penetrate deeply into the workpiece material, they just tickle the surface – over and over again – meanings lots of rubbing and heat generation. Heat on a resin-bonded diamond wheel is bad: first, it softens the resin, making it easier to rip the grit out of the bond material; second, if the temperatures get above around 700°C, the diamond will turn to graphite.
Figure 2 shows the specific energy (grinding power divided by material removal rate, or how much energy is released when you grind one cubic mm of material) vs. the penetration depth using data taken from an excellent paper by Zelwer & Malkin (Grinding of WC-Co cemented carbides, Transaction of the ASME Journal of Engineering for Industry, Volume 102, 1980, pages 133-139) using a standard equation for grit penetration depth, hm in surface grinding:
where C is the cutting-point density, r is the shape factor, vw is the workpiece velocity, vs is the wheel velocity, ae is the depth of cut, and de is the equivalent diameter. There is much disagreement on how best to calculate C and r. Here we use C=2/dn, where dn is the grit diameter, and r=10.
When we’re grinding on the face, we’re on the far right side of the curve, the value of hm is very high and the specific energy is low. Here our wheel-face is taking a beating simply because we’re demanding so much from each individual grit.
When we move to the bottom of the wheel, our penetration depth decreases drastically, and we fall well to the left of the curve, sometimes as low as hm<0.1 µm. This is dangerous too as now we’re just rubbing and smearing and generating lots of heat.
What’s the best place to be? There’s no magic number, but we want to be somewhere in the ballpark of 1 µm. At 0.2 µm we’ll have trouble because we’re too timid; at 3 µm we’ll have trouble because we’re too aggressive.
So what’s the solution? In the break-in period, you want to reduce your penetration depth to save your wheel and keep temperatures down. You can do this with lower feedrates and higher wheel speeds. In the bottom-grinding period, you want to increase your penetration depth to prevent excessive rubbing. You can do this with lower wheel speeds and a smaller rim width. You can also do it with a larger federate and a deeper cut. But be careful here, as this also increases heat generation.
So considering all that, here are some things to think about:
1) If you take different depths of cut – say 0.050 mm (0.002”) on one pass, then 0.025 mm (0.001”) in the next pass, the taper will develop based on the largest depth of cut. So here the taper will be 0.050 mm (0.002”) high, and when you take the 0.025 mm (0.001”) depth of cut, you’ll be using only half of the available wheel face. This is shown in (c). Then you’ll wear only on that face of the wheel and when you take the 0.050 mm (0.002”) depth again, you’ll be grinding partially on the face again. In other words, your taper will be inconsistent and messed up, and you’ll pay the price with a rougher surface finish, more wheel wear and more frequent truings.
2) Consider whether you’re infeeding only on the forward pass or on both the forward and back passes. If you’re infeeding on both, you’ll develop a taper on both sides as shown in (d). Now you’re contact area consists of only half of the rim width, meaning more wheel wear.
Can you measure the taper? Sure. Just take a chunk of material and plunge the wheel axially (not radially) straight down into it. Then take that and look at the profile under a low-magnification microscope. You won’t see a perfect taper as shown in the diagrams, but you’ll see something close to it.
3) Consider how is the taper affecting surface finish. When the taper fully develops, your final part dimension is being formed by a line-contact at the end of the taper instead of an area-contact. This will mean a larger rougher surface finish. This brings me to point (4):
4) Can we dress that flat into the wheel to begin with? Let’s say you don’t rely on the break-in period to form your wheel, but rather you form it yourself. Now you can say, “I want to use 2.5 mm of my rim for rough-grinding and 0.5 mm of my rim for finish-grinding.” This is shown in (e). Here the forces on the wheel during rough-grinding are even throughout and you have a flat area to really polish off surface finish. Most truing stations will let you angle the wheel. Let’s say you want to take a consistent (never larger) depth of cut of 0.100 mm and use 2.5 mm of your rim for roughing (and 0.5 mm for finishing). Then a truing angle of angle=atangent(0.1/2.5)=2.3º.
5) Am I grinding too timidly and generating lots of heat? Since the forces are so large during the break-in period when grinding on the small-area face, grinders will slow down their feedrate to avoid chipping and burning. However, once the taper breaks in, this slow feedrate hurts them, as now the forces on the bottom of the rim are too small! (Remember how the area increased by a factor of 60?) That means that the grit penetration depth is too small. Tungsten-carbide is a combination of hard tungsten-carbide particles held in a soft cobalt matrix. When the grit penetration depth is too small, the grits don’t easily form a chip – the tungsten-carbide particles just get pushed around within the cobalt, leading to lots of rubbing and heat generation. This heat causes “diamond burn”, or graphitization of the diamond, and “bond burn”, or softening or burning away of the resin. This means excessive temperatures and excessive wheel wear.
Those are five key points when doing cup-wheel grinding. Take a look at your grinding process and see how they fit in. If you make changes, implement them one at a time and see how they work out. Also, get a copy of The Grinder’s Toolbox, available from TheGrindingDoc website. This will tell you your grit-penetration depth and if you’re close to the one-micron mark.
Dr. Badger, a.k.a. “The Grinding Doc” is an expert in grinding. He is giving his three-day High Intensity Grinding Course this October 19-21 in Columbus, Ohio, hosted by Diamond Innovations. Contact www.TheGrindingDoc.com, JB@TheGrindingDoc.com.