Determining Gib dimensions from the way-gap, way-hole, gib-saddle-gap

[B2]

Determining Gib dimensions from the way-gap, way-hole, gib-saddle-gap

Some time ago I was trying to figure out how to fix a poorly made factory gib. When I took the gib out it was cupped, bowed, and poorly machined. In addition its backside face was scarred due to the way clamp screws. It had been scrapped! It is cast iron, I think. I think some of this may have been when it was initially made and some of it may have been when it was installed improperly and cut off too short. Needless to say, it was not ideal. When I tried to measure it's thickness as function of length I found it varied even across the width. It was cupped across the width as well as bowed along the length and this made thickness measurements difficult. The corners were not well defined. Anyway, after some time I set about trying to measure the inside of the hole where the gib slides into. Due to the parts weight and the attachment to the lead screw I did not want to take the machine and ways apart. It is not easy to measure things at the ends as the clamping screw locations interfere at the ends. It certainly is not easy to measure the gab thickness down inside the way and yet it is the gap thickness as a function of distance (z) which is the most important parameter to have. See sketch.

From the attached sketch can you tell me if the dimension Hs is suppose to be a constant as a function of distance into the drawing of the gib or the gib-way-gap? Clearly, the other dimensions labeled, such as T(z) thickness is a function of the distance, z, into the sketch. I labeled Hs as being the height spacing of the way of the saddle. Hence, the subscript "s." Clearly the gib does not have to be this tall, Hs, but in the gig-way-gap (hole) the distance Hs seems to me to have to be a constant. Shown on this figure is the way cut angle, theta. For my China made mill this is 55 degrees.



From this figure, I have derived an expression for the thickness, T(z), as only a function of Hs, Theta, and D(z) which is measurable. (Hopefully I got the math correct! ) I am writting this up to post later, but for now the quadratic root expression is (where the - sign yields non-physical results):

Hence, by measuring D(z), theta and Hs one can obtain the function of Gib-way-slot thickenss, T(z) vs z. In concept one could also just try to measure T(z) directly, but it is somewhat difficult to ensure that a gauge would be square to the surfaces when far into the way hole. However, measuring D(z) is somewhat easier as it is between corners and so a pointed gauge self settles into these corners. Of course one must compensate for any fill-in at the corners that was not cut away by a dovetail cutter. I have measured this and have obtained the T(z) values using the equation, but have nothing to compare them to as the original gib measurements are untrustworthy. Assuming the equation is correct, it is easy to see that having the exact value of the Hs and D(z) are important as a few thousands change in gib thickness is all that is allowed. If the ways are indeed straight then the T(z) function is of the form T(z) = T(z=0) - m*z, where z=0 is at the large end of the gib and m is the slope or taper of the Gib and the Gib-way-slot walls.

So I am seeking conformation to my initial question/assumption. Hs is a constant as a function of z?

 

[dabear3428]

Determining Gib dimensions from the way-gap, way-hole, gib-saddle-gap

Some time ago I was trying to figure out how to fix a poorly made factory gib. When I took the gib out it was cupped, bowed, and poorly machined. In addition its backside face was scarred due to the way clamp screws. It had been scrapped! It is cast iron, I think. I think some of this may have been when it was initially made and some of it may have been when it was installed improperly and cut off too short. Needless to say, it was not ideal. When I tried to measure it's thickness as function of length I found it varied even across the width. It was cupped across the width as well as bowed along the length and this made thickness measurements difficult. The corners were not well defined. Anyway, after some time I set about trying to measure the inside of the hole where the gib slides into. Due to the parts weight and the attachment to the lead screw I did not want to take the machine and ways apart. It is not easy to measure things at the ends as the clamping screw locations interfere at the ends. It certainly is not easy to measure the gab thickness down inside the way and yet it is the gap thickness as a function of distance (z) which is the most important parameter to have. See sketch.

From the attached sketch can you tell me if the dimension Hs is suppose to be a constant as a function of distance into the drawing of the gib or the gib-way-gap? Clearly, the other dimensions labeled, such as T(z) thickness is a function of the distance, z, into the sketch. I labeled Hs as being the height spacing of the way of the saddle. Hence, the subscript "s." Clearly the gib does not have to be this tall, Hs, but in the gig-way-gap (hole) the distance Hs seems to me to have to be a constant. Shown on this figure is the way cut angle, theta. For my China made mill this is 55 degrees.

View attachment 514418View attachment 514423

From this figure, I have derived an expression for the thickness, T(z), as only a function of Hs, Theta, and D(z) which is measurable. (Hopefully I got the math correct! ) I am writting this up to post later, but for now the quadratic root expression is (where the - sign yields non-physical results):
View attachment 514419
Hence, by measuring D(z), theta and Hs one can obtain the function of Gib-way-slot thickenss, T(z) vs z. In concept one could also just try to measure T(z) directly, but it is somewhat difficult to ensure that a gauge would be square to the surfaces when far into the way hole. However, measuring D(z) is somewhat easier as it is between corners and so a pointed gauge self settles into these corners. Of course one must compensate for any fill-in at the corners that was not cut away by a dovetail cutter. I have measured this and have obtained the T(z) values using the equation, but have nothing to compare them to as the original gib measurements are untrustworthy. Assuming the equation is correct, it is easy to see that having the exact value of the Hs and D(z) are important as a few thousands change in gib thickness is all that is allowed. If the ways are indeed straight then the T(z) function is of the form T(z) = T(z=0) - m*z, where z=0 is at the large end of the gib and m is the slope or taper of the Gib and the Gib-way-slot walls.

So I am seeking conformation to my initial question/assumption. Hs is a constant as a function of z?

Hs should be constant, Dz will vary, but would it not be easier to use gage pins in the saddle way to measure the width of the dovetail way at each end and then calculate the taper of the gib?
get the taper right make the gib longer than required and then trim to fit. or am i missing something?

 

[cooper1203]

dunno if you have seen this but he is quite a good teacher.

can you not set up an indicator on the side of the carriage with no gib and see how much it moves to get a rough idea of thickness. Failing that if you tell us what the machine is maybe someone will have one and can tell you the dimensions of theirs

 

[B2]

Hs should be constant, Dz will vary, but would it not be easier to use gage pins in the saddle way to measure the width of the dovetail way at each end and then calculate the taper of the gib?
get the taper right make the gib longer than required and then trim to fit. or am i missing something?

Thanks. As evidenced by my effort to generate the equation I had convinced myself that Hs is a constant. However, I just wanted to confirm this. No I do not think you are missing much, but maybe I had/have a special case.

It was hard to measure, but I do not think Hs = constant was the case for the factory gib that I pulled and tried to measure. There is nothing that says the gib has to have a constant Hs value. Hs really applies to the saddle surfaces of the way hole. The Gib can be smaller in this direction and still function. D(z) varied with the length as it should, but the edges are so rough that I could not get good data from it. Also, because of this the bottom locking screw actually missed the end of the gib and chewed it off crookedly. This also makes me think that the Hs of the gib used was not constant.

The best I can tell it has turned out that the Thickness, T(z), at the large opening is about 0.4" and at the small opening about 0.3" which yields an over all taper of about 0.0085inch/inch. The saddle length (or gib-way-hole length) is about 12.375 inches (large gib-way-hole to small gib-way-hole distance) . This taper is an angle of less than 0.5 degrees.

Yes, inserting gage pins would be a good approach and was my first thought. But there are issues. For example, their are cut outs for the locking screws' heads at the ends of the gib-way-hole which any internal measurement method must deal with. The way surfaces in these areas of the way hole are also somewhat beat up. This means that the gage pin measurement needs to be some distance from the z=0 start of the hole depth (almost 2 inches) to get clean measurements. Also, this works at the big end, but because the tapper is getting larger as you go in from the small end one would not get a particularly good fit at the small end. At this small end, you cannot insert the gage unless it is smaller than the spacing you want to measure. Compounding this is both the beat up nature of the edge of this hole (the locking screw cut out, paint, etc.). Again this area does not lend confidence. In my case the way at this end is pretty beat up because the original gib was improperly cut and so was clamped sideways into the way via the locking screw. Alternatively one could insert the gage pin from the big end of the hole all the way to the small end of the hole. This can be done but due to the gib hole length (12.375") requires a special homemade gage pin construction. (By the way, I only own a hand full of pin gages. But, I suppose I could make my own special cylinder disks on the end of a stick style gages.)

For the z-axis gib of my PM940M-CNC machine, which was a very limited edition machine, the length of the gib is about 12.375" so the gage pin would need to be nearly 12 inch long. Or some sort of attachment made to connect to it and lower it from the top hole end down to the bottom. Plus a depth measurement is needed, but this not a serious issue. More realistic is to take a rod and turn it down everywhere except at the measurement end ... or to tap a hole into a gage pin like cylinder shape and attach a long plunge rod/handle to it. This would then allow a round gage to clear to near the small end of the hole.

Then there is the issue of tightness. You do not wish to push the gage pin in hard as the mating surfaces between the gage pin and the gib-way-hole, due to the taper, only occurs at the end edge of the gage pin. If you push hard the gage pin edge may dig into the way surface a bit. It does not take much.

Unlike the video that @cooper1203 just attached I cannot easily take my ways apart. It would be a major task. The saddle carries the entire head of the z-axis on the mill (motor, gearing, spindle, etc) which I estimate to weight in about 250 to 275 pounds. I moved the head to a vertical position, where I had, at-least, some confidence in and using the old gib I tightened things up while wiggling the head to cause it to seat. I then blocked the head in this vertical position and removed the weight from the lead screw by inserting a block between the head and the x-y table. I then took a giant C-clamp and a woodworking bar clamp that I had and clamped the saddle from two directions, towards and across the column) to ensure that the saddle seated flat both against the opposing way dovetail and against the sliding rail surface at the gib side. After clamping solidly I removed the gib by tapping it out. I actually did this three separate times along with the measurements mentioned below before I was confident that I had the ways well seated. Along with the measurements mentioned below this took several hours.

Rather than inserting a gage pin, I resorted to another approach. I cut a very long piece of 0.010" Al sheet metal shim into a strip which tapered in width from one end to the other. Then using a vice jaws, with a pattern on it similar to a knurl pattern, I impressed a texture into the Al to make it stiff and flat. From the top, the large hole entrance, I gently inserted it along z so that its width fit into the way hole in the direction of D. It went down until the corners of the end of the shim was trapped by the gib-way-hole corners, the diagonal D(z). I marked the depth at the top of the shim strip where it entered the hole. I pulled it out and measured the shim corner spacing where the D points hit. The mark to the shim corner gave me a z value. So I had z1 and D(z1). But just as with the gage pins I was concerned that only a couple of measurements might yield false results. So I made a number of measurements (~20) at different locations in z. I did this by repeatedly cutting off a piece of the Al metal shim so that the width was progressively narrower and could then be insert farther into the gib hole. By getting several points I could build some confidence in the data. You can see that in order to get a bunch of data points of T(z) directly using pin gages would require making them for each length of measure. A lot more work than just cutting my tapered shim off to enable another depth vs width measurement. Anyway, I may still try some of this direct gap thickness measurement sometime.

Below is the measured data that I got for the Gib Hole Diagonal, D(z). The blue dots represent the measured data. I did a least square fit to that data to then extend the curve on out to the ends of the hole and to develop the linear equation shown. Note that there are missing data points at the two way-hole ends. Also, there is more scatter in the data near the ends. I also had to compensate for the corners of the Gib-way-hole not being completely sharp. The fit equation allows me to extend the results to the way hole ends (D(z) Trend). This data is plotted below. Using this and the equation I first posted I calculated the Gib thickness via the equation that I put in the first posting. The calculated thickness result is shown in the second plot. The data referred to as Trend are the least square fits to the Measured D(z) or Calculated T(z).



There are a couple of realizations. With a thickness taper of only 0.00855 inches/inch small errors in measurements can yield a gib that only hits in one portion of the gib-way-hole. For example, if the taper (slope of the gib) were made larger, say 0.0095 then the gib would hit at the large end and never touch over most of the rest of the gib. At the small end the gap would be 12.375 * (0.0095-0.00855) ~ 0.012". If the gib were made with too small a taper, say 0.0075 then it would hit only at the small end. Either way would result in the saddle being able to twist or torque during operation.

In these plots the Hs that I used is actually a bit larger (a few percent) than what I had measured. I am not surprised as one of the surfaces in that Hs measurement is cast and unfinished so could be different from the ideal. However, it does change the gib slope a bit. I think the idea of using a pin gage to obtain a direct thickness measurement at a couple of points would confirm the value of Hs.

Failing that if you tell us what the machine is maybe someone will have one and can tell you the dimensions of theirs

Yes, I did ask a fellow HM and PM940M user (@ptrotter ) to measure his gib thickness while he had his machine apart and was making it CNC capable. He purchase his machine sometime after I did but it was not the CNC variety. I am not for sure that it was made from the same China manufacturer or exactly the same manufacturer's specs. His gib data was pretty close to what I had found before I did all of these calculations, but different enough in the slope that I was not sure about using it as a reference. His Gib slope was only about 0.0005 inch/inch DIFFERENT from mine. Not bad, but he had only taken a few data points. This would mean that over the 12.375 inch length the gib thickness gap would only be off by 0.0005*12.375 ~ 0.006" . For the twisting movement axes the distance would have been 0.006/sin(55 degree) = .0073" However, I also found it interesting that the thickness at the large gib end was different by about 0.027". Again, not bad but one might think that an assembly line would make two parts closer in size than this. Anyway, the over all thickness is not very important. As @dabear3428 pointed out you make the gib longer than it should be, using the correct slope, and then just drop it in and cut off the excess. This works if Hs = constant. But if our thickness is off by 0.027" and the slope is around 0.0085 inch/inch it means that the gib would have to be at lease 3 inchs longer to start with and probably on both ends. So maybe the Gib really needd to be longer (> ~18 inches) with a longer range of thicknesses. Drop it in the hole make it tight and then cut off both ends to fit leaving a little extra for future wear.

Also, I have been thinking, maybe the gib should be made from something significatlly softer (brass?) than the hardend way or the current cast iron gib. Then put a bunch of somewhat deep scraping marks in it so that there are a lot of points sticking up. Then fit it tight and let the wear of the peaks take it to a final taper!? How long would it take to wear 0.006" off from the scrapped peaks. On the other hand the mill head is so heavy that with its hanging on the column/lead screww tends it tends to torque on the column ways. The top of the saddle tends to pull outward on the ways and the saddle tends to ride on the rail flat at the bottom. So, there is a lot more force compressing the gib at the top and virtually none compressing it at the bottom of the saddle. I am not for sure how all of that comes into play!

Dave

PS. Sorry this is so long! I just wanted to confirm the Hs concept. Anyway, I have sorta explained things and provided a couple of plots so maybe I do not need to write up my work any more? On the other hand maybe I should show algebra for the equation derivation and show more details of the measurement data? Also maybe it would be helpful to someone else. For now my mill is running, but with the old gib after having shimed it several thousandths. I also had to build a specially shaped washer for the gib lock at the small end. It reaches all the way into the gib hole so as to secure the gib position. I just never have liked it. I have not had the gib out for a while so I do not know if it is wearing uniformly.

 

[dabear3428]

"The Gib can be smaller in this direction and still function."
better if it does not and is as large as is consistent with the way.
when i said us gage pins let me elaborate,
1. take the mill apart.
2. insert 2 regular leingth gage pin that are small enough to fit in the way as close to 1 end on the way as you can get good readings of the distance across the way.
3. take the same gage pins and insert them in the other end of the way and repeat the measurement.
4. measure the distance between measurements.
5. find the delta in the measurements on each end of the way.
6. divide the delta by the distance to get your taper in delta/leingth which is your taper.
7. put the mill back together and make a gib blank that is longer and spans the Tz range that you expect.
8. put the gib blank back in the mill and fit it to find the leingth that you need (also scrape it to as perfect fit as you need/can stand).
9. cut the blank to leingth and machine all of the ends to match your hardware.

the gage pins do not need to be the same size you just need 2 that are small enough to work because you just need the delta.

as to taking the head off the mill either use a engine hoist (you can rent 1) or put some wood blocks on the table and crank it down until it rests on the table and unbolt it from the slide and then the weight should be manageable.
you are assuming that the ways are perfect and uniform when the gib was mis-machined? better expect to have to blue it on a surface plate (if you want it perfect) and fit the gib to your way.