Height Gauge Depth Arm

In the shop I have a 2 beam dial height gauge that I use a lot for measuring and general layout work.  As far as measuring equipment, it is my favourite tool to use, even though I would want a micrometer and a caliper before a height gauge.  Once you get one you’ll wonder how you got by without one.

Most height gauges come with a tool for measuring flat surfaces, and for scribing.  To get the most out of the gauge you need a depth arm – basically a pin in an arm, for measuring depths.  I needed one to measure up a motor face so I can get a 3 phase motor mounted on my lathe – one of those projects to complete a project sort of deals.  I decided to make one up instead of buying it:

I made most of the arm on the shaper and used a gift from Max over at the Joy of Precision to bore the hole for the pin.  The boring head Max made is the star of this show.  It is the perfect size for the mini mill.  It is one of the best designs for a small boring head I’ve seen, and used.  The adjusting dial is a tad small but once you get a feel for it adjusting it is easy.  It’s also great because you can bore small holes – saving you from buying a lot of reamers.

The pin was turned between centers and was within .0004″ over the length – something I was very happy with.  The deviation was in the centre of the pin.  The pin sprung between centres a bit when I was cutting – aside from using a traveling steady there isn’t much you can do here about that.  The beginning diameter and end diameter were essentially the same within .0001.  I probably didn’t need  that much precision but I wanted to dial in my tailstock anyway.  At the end of the pin you can screw in standard dial indicator ends using a #4-48 thread.

I made the screw out of brass because it looks nice, and doesn’t mar the pin.  I usually don’t turn that much brass so I was reminded how easy it is to work with.

Here is the drawing for the height gauge arm.  I will be sharing all the projects in Fusion at some point and I’ll post a link.

Height Gauge Arm (Revision 01)

If you are looking to get a height gauge, do yourself a favor and go a dial one instead of a digital one.  Even though the dial on mine is graduated to .001″, you can actually measure much closer in the home shop with it.  Notice I didn’t say in the shop – in a professional environment I get that you need hard numbers and ‘guessing’ at the measurement is very poor practice.  Verniers are also good but I find them slow – probably because I don’t have enough practice.

X2 Mini Mill Vibrations and Chatter

Author’s Note:  I would like to thank Dr. Timber Yuen.  The analysis I did below was directly learned in his Machine Dynamics course as part of my degree in Manufacturing.  Dr Yuen’s practical problem solving teaching is a refreshing and needed approach where many engineering students are ‘drowning’ in math and not able to solve real world problems.

myx2

The Sieg X2 Mini Mill is know for the wet noodle characteristics of the column.  In particular the tilting column variation of the X2 (the most common variation) has extreme chatter and vibration issues when trying to take anything more than very small depths of cut in steel.  The reputation is such that Little Machine Shop has removed the Sieg’s tilting option on its mills in order to improve rigidity.

The other day I was single point fly cutting some tall plates with the Sieg X2 (no, I didn’t strip the plastic gears … yet) and noticed the column vibration was very significant.

I decided I should investigate what was going on.  Information on additional column support on the X2 is very plentiful around the web and I could have simply manufactured some form of column brace based on the modifications others have done.  But I wanted to learn more about the vibration issue before I went directly to a solution.  I though, hey that mill column looks a lot like a simple spring – mass – damper system.  The spring, well that’s the column, the mass – that’s the spindle housing and motor, and the damping – well there shouldn’t be much.

Firstly, I wanted to figure out what the natural frequency the column vibration.  How do you do this?  Most times an accelerometer would be mounted to the column.  I didn’t have an  accelerometer handy.  Or did I?  I started to think about the smart phone I owned.  Most smart phones have accelerometers built in.  I downloaded some software that retrieved data from the accelerometer, attached my phone to the column (zip ties work – electrical tape works well but leaves sticky glue on your screen!) and proceeded to strike the column with a dead blow hammer on the spindle housing in the Y direction and plot the response.

x2cell

I plotted the response in Excel.  The output from the accelerometer was in m/s².  I used the phone’s Z axis output only.

x2vibresponsebefore

Now is probably a good time to comment a little about the sample rate from the accelerometer.  My cell phone is an inexpensive Alcatel Pixi.  The maximum sample rate from the accelerometer I could achieve is 100 Hz.  This is why the above chart looks choppy.  I would have preferred something higher – say 500 Hz, but the data is good enough to make some general observations.

From the graph I found the period of the vibration to be 0.03941 seconds.  The inverse of the period is the frequency, which is 25.374 Hz.  25.374 Hz is 1522 rpm.  From this point on some math is involved, you can view it in the spreadsheet posted below.  If you want me to detail the math used, send me an email.  The mass was approximated using the mass of the spindle head and 0.23 x the mass of the column.  Using the data the following are calculated:

Damping Factor 0.110491
Natural Frequency 25.53079 Hz
Natural Frequency 160.4147 rad/s
Weight 45 lbs
Mass 20.45455 kg
K (spring rate) 526354 N/m
C (damping) 12.65826 kg/s

The low amount of damping is expected.  The low K value had me scratching my head a bit so I decided to calculate what the K value should be based on a fixed cantilever beam.  I estimated the moment of inertia using a square tube.  Again, I’ll spare the detailed math.

Ixx (Moment of Inertia) 1.68 in^4
Ixx 699268.795 mm^4
Ixx 6.99269E-07 m^4
Length 17 in
Length 431.8 mm
Length 0.4318 m
Young’s Modulus 12000000 psi
Young’s Modulus 82737120000 N/m^2
Calculated K 2155846.764 N/m
Weight 45 lbs
Mass 20.45454545 kg
Calculated Natural Frequency 324.6489688 rad/s
51.66948815 Hz
3100.169289 rpm

Whoa!   That’s a lot higher than what we measured!  What does this mean?  Something must be adding to the ‘springiness’ of the system.  I concur with most around the web that the large titling interface isn’t very good.

X2rearnut

Now before we go into improving the stiffness of the system, we should ask ourselves why we are doing it.  When I was single point flycutting, I was fly cutting at an RPM of around 500 – 600 rpm.  This is about 10 Hz.  Our measured natural frequency of the system is 25 Hz.  This condition where we are applying a load and taking it off is type of rotating unbalance problem.  The frequency ratio, simply the operating frequency divided by the natural frequency, gives an indication how close you are to resonance, and helps you figure out what the machine response will be.  In this case the frequency ratio, or r, is 0.4.  What does this mean?  Well avoiding all the math, a quick chart for rotational unbalance, (from Dr. Yuen’s spreadsheets – thank you!) gives a more clear picture:

VibrationAmplitude

At 10 Hz or r = 0.4 and zeta = 0.1 we are approaching the sharp peak where r = 1.  That’s really bad!  And the force chart shows the same story:

RotatingUnbalance

Since I really can’t do anything about the damping in the system I want to try to increase the stiffness of the system and thus operate at a lower frequency ratio, r.  Since the calculated stiffness should be closer to 50 Hz, I decided to fabricate a plate and mount it on the column, as well as add additional support for the base.  If you want additional pictures or drawings of the bracket send me an email and I’ll try to get them to you.

x2bracket

The bracket allows the mill to be trammed in the X direction, but removes the titling ability.  I never really used it anyway.  When I made the bracket I scraped it as flat as I could.  After installing I trammed the mill in the X and Y axis to within .0005″ (hence the shims).  I remounted my cell phone to the mill and determined the new natural frequency.

x2vibresponseafter

As you can see the data is becoming more choppy.  This is due to the increased frequency and the 100 Hz limitation by my phone.  From the graph I found the period of the vibration to be 0.022 seconds with the inverse or frequency to be 45 Hz.  That’s better!  The rest of the math shakes down below.

Damping Factor 0.089214
Natural Frequency 45.5025 Hz
Natural Frequency 285.9006 rad/s
Weight 45 lbs
Mass 20.45455 kg
K (spring rate) 1671937 N/m
C (damping) 13.64477 kg/s

The damping factor stays about the same (small change is due to experimental error!).

What type of improvement will you see with this?  Take my fly cutting scenario.  The new frequency ratio is 10 Hz / 45 Hz = 0.2.  From the rotating unbalance chart above if you move from r = 0.4 (where we were) to r = 0.2 the displacement decreases by a factor of over 5!  That is a pretty large reduction in displacement.

In conclusion, as many know already, the standard titling arrangement with 36 mm nut is not the best setup.  Adding a bracket or additional support is required.  At least now I have a quantifiable reason why.

You can download the spreadsheet if you want to: X2VibrationAnalysis.