[jharvey407]

I am in the process of improving my CNC machine. This will increase the weight of the gantry. I would like to know how much weight the linear motion system will support safely. Since I lack the engineering expertise to do the calculations myself I am looking here for help.

I have attached some drawings. I believe the weakest component in the system is the 1/4-20 bolts used to attach the V-bearings. The bolts are marine grade, so they are not AN rated. The bearings themselves are rated for 615 lbs each.

Can someone help me?

[6061-t6]

why not buy 2 REAL linear rails for that axis? check igus® | igus USA site

[jharvey407]

why not buy 2 REAL linear rails for that axis? check igus® | igus USA site

Because the machine is already built and works well. There is no reason to make major design changes, I am simply looking to determine the load capacity of the linear motion system.

Can you help?

James

[6061-t6]

i cant, i apologize. You could make weight bags and a way to hold them on your carrier then using a dial indicator measure when you start to get substantial flex in your gantry. i think that would be the biggest concern out of the gate.

[jharvey407]

i cant, i apologize. You could make weight bags and a way to hold them on your carrier then using a dial indicator measure when you start to get substantial flex in your gantry. i think that would be the biggest concern out of the gate.

It shouldn't be that complicated. I'm sure that there is a simple calculation that can be done to determine at what weight the bolts would start to flex. There may actually be a table somewhere that gives the data.

[ger21]

If the top bearings are using concentric bushings, you can replace them with a grade 8 3/8" bolt, or a 3/8" shoulder bolt. I doubt you'll need to worry about flexing.
I would guess that even if you just used 1/4" grade 8 bolts, you shouldn't see any flex. You probably won't have more than 250-300lbs spread across 4 bearings, right?

[jharvey407]

If the top bearings are using concentric bushings, you can replace them with a grade 8 3/8" bolt, or a 3/8" shoulder bolt. I doubt you'll need to worry about flexing.
I would guess that even if you just used 1/4" grade 8 bolts, you shouldn't see any flex. You probably won't have more than 250-300lbs spread across 4 bearings, right?

Gerry,

I've thought about using 3/8" bolts instead of the bushings if necessary. I don't know exactly how much the gantry weighs right now. I am about to due the calculations so that I can figure out how much it will weigh if I add a spindle and fill the two large voids in the extrusion with EG. I am also considering rebuilding the Y axis carriage and Z axis using some EG components.

I have attached a drawing of the gantry, I estimate its current weight at about 150 lbs, but won't know for sure until I do the calculations.

Thanks for the input.
James

[dmalicky]

It's actually a pretty complex problem. The simple answer is that since PBC designed the v-bearing and VB2 bushing together, the system should be capable of 615 lbs for each bearing, so assuming a small preload, 1000 lb for the y-car (not accounting for cutting and dynamic loads).

That's the load for reliability. There may be substantial flex before that. There are 3 stages of flex (assuming the bolt is tightened to a moderate tension):
1. Removal of slop in the system. A preload should do this.
2. A ~linear portion of flex, due to compression in the bearing, bending of the bushing, and bending of the plate. The bolt actually doesn't change much: its purpose is just to keep the bearing and bushing firmly planted against plate. All the bending load is taken through the bushing--not the bolt. Normal operation should stay in this stage.
3. An increased rate of flex, when the load is high enough that the bushing starts to separate from the plate on the bushing's bottom edge. (Now the bolt would increase in tension.) If PBC engineered and tested the system thoroughly, 615 lbs won't be enough to get to this stage, but we need the bolt tension required for that.

From your system pic, the bushing OD is a little larger than the lateral distance from the plate to the center of the V (the overhanging moment arm, I'll call it w). This indicates PBC thought about the problem. The actual solution is really complex (contact mechanics). But we can easily approximate complete separation along the bushing's bottom face:
Load * w = BoltTension * OD/2.
BoltTension = Load * 2 * w / OD = ~ 615 * 2 * 0.85 = ~1000 lb
I'd guess 2000 lb would give minimal separation.

Bolt torque-tension is another complex relationship, but this pdf gives a rough guide:
http://www.fastenal.com/content/feds...0Gr8%20Gr9.pdf
So, a 1/4" grade 8 bolt is good for up to 2864 lbs tension, if it can be torqued appropriately. 2000 should be reasonable. All this indicates PBC (or BWC) did engineer the system. If currently using stainless bolts (similar to A307-A in the pdf, 859 lb max tension), upgrading to Grade 8 would be very smart.

Note that even though the system should stay in stage 2, the elastic flex could still be pretty large. To calc that stiffness (lb/in), we'd either need a complex FEA model or a simple experiment, like 6061 suggested.

Switching to 3/8" bolts has pros and cons. The pro of the PBC design is the bushing OD is > 3/8", so the bearing has a larger 'foundation'. Also the bushings have a precision fit to the bearing ID. But the bushing also pushes the system out for a larger "w"--more clearance but more bending. Using a 3/8" bolt with a small washer to space out the bearing just enough for clearance, w could be reduced by about half, for more stiffness. As Gerry suggested, a shoulder bolt with reamed holes would be best.

[jharvey407]

dmalicky,

Thanks for the reply. The calculations are a bit more complex than I imagined but everything makes sense. I guess I don't have to worry too much about the weight of a 200-300 lb gantry, the linear motion system seems strong enough.

James

It's actually a pretty complex problem. The simple answer is that since PBC designed the v-bearing and VB2 bushing together, the system should be capable of 615 lbs for each bearing, so assuming a small preload, 1000 lb for the y-car (not accounting for cutting and dynamic loads).

That's the load for reliability. There may be substantial flex before that. There are 3 stages of flex (assuming the bolt is tightened to a moderate tension):
1. Removal of slop in the system. A preload should do this.
2. A ~linear portion of flex, due to compression in the bearing, bending of the bushing, and bending of the plate. The bolt actually doesn't change much: its purpose is just to keep the bearing and bushing firmly planted against plate. All the bending load is taken through the bushing--not the bolt. Normal operation should stay in this stage.
3. An increased rate of flex, when the load is high enough that the bushing starts to separate from the plate on the bushing's bottom edge. (Now the bolt would increase in tension.) If PBC engineered and tested the system thoroughly, 615 lbs won't be enough to get to this stage, but we need the bolt tension required for that.

From your system pic, the bushing OD is a little larger than the lateral distance from the plate to the center of the V (the overhanging moment arm, I'll call it w). This indicates PBC thought about the problem. The actual solution is really complex (contact mechanics). But we can easily approximate complete separation along the bushing's bottom face:
Load * w = BoltTension * OD/2.
BoltTension = Load * 2 * w / OD = ~ 615 * 2 * 0.85 = ~1000 lb
I'd guess 2000 lb would give minimal separation.

Bolt torque-tension is another complex relationship, but this pdf gives a rough guide:
http://www.fastenal.com/content/feds...0Gr8%20Gr9.pdf
So, a 1/4" grade 8 bolt is good for up to 2864 lbs tension, if it can be torqued appropriately. 2000 should be reasonable. All this indicates PBC (or BWC) did engineer the system. If currently using stainless bolts (similar to A307-A in the pdf, 859 lb max tension), upgrading to Grade 8 would be very smart.

Note that even though the system should stay in stage 2, the elastic flex could still be pretty large. To calc that stiffness (lb/in), we'd either need a complex FEA model or a simple experiment, like 6061 suggested.

Switching to 3/8" bolts has pros and cons. The pro of the PBC design is the bushing OD is > 3/8", so the bearing has a larger 'foundation'. Also the bushings have a precision fit to the bearing ID. But the bushing also pushes the system out for a larger "w"--more clearance but more bending. Using a 3/8" bolt with a small washer to space out the bearing just enough for clearance, w could be reduced by about half, for more stiffness. As Gerry suggested, a shoulder bolt with reamed holes would be best.

[dmalicky]

James, Glad it's helpful. David