The Amateur’s Lathe

LH Sparey’s Amateur’s Lathe is on my  ‘must read’ list for not only anyone interested in home shop machining, but also anyone interested or studying mechanical or manufacturing engineering.  I think that the book is so good that it should be a mandatory part of a first year engineering course.

amateurslathe

Even though the publishing of this book is seriously showing its age (the drawings, typing and photographs could be updated in quality), the content is very very good.  Sparey approaches the information within the constraint of doing work on one piece of equipment: a small workshop lathe.  So many teach that the lathe is only for turning work, such as turning small shafts or bushings.

The reason I like the book so much is because it encourages you to think outside of the box.  It helps develop the skill of trying to complete a project using the tools at your disposal.  It teaches one of my favorite words: ingenuity.  “Ingenuity is the quality of being clever, original, and inventive, often in the process of applying ideas to solve problems or meet challenges. Ingenuity (Ingenium) is the root Latin word for engineering.”  Ingenuity is solving a problem within the constraints you are placed in.  And remember constraints produce good design.

Ingenuity is the skill we desperately need in engineering.  Engineers today are really good at math, but math is only one tool to solve a problem.  At some point we have to move from the theoretical to the practical.  I remember  one of my professors (a mathematician / engineer) jokingly told me that the solving the problem is the important part – you can find any idiot to do the math.  He was joking, and wasn’t downplaying the importance of mathematics, but rather highlighting the importance of solving the problem.

So if you are a mechanical or manufacturing engineer – read the book to get an interesting insight to what a small bench lathe can really do – while actually learning how to use a lathe.  If you are someone working in your shop the book has excellent insight and information to get those machining projects done you think you don’t have enough tools to do.

It’s on Amazon here.  Don’t let the bad reviews fool you – you have to read the book and think not just look at the pictures.

 

Under the Dome

This is Manufacturing Matters – my weekly opinion on manufacturing topics.

The pollution problems facing countries like China are not getting the publicity in the main stream media they deserve.  Below is an excellent documentary detailing the problems from a first hand account.  The documentary is long – over 1 hour, but I highly recommend you view it – I consider it a must watch.  At the very least those involved in making company purchasing decisions for goods coming out of China should review their suppliers.

 

Every tool was used

I’ve been very busy lately outside of the shop on coursework so I haven’t had a lot of time in the shop this week.  I’ve managed to get some time in the shop making 4 more brackets for my friend’s Audi S4 antics:

s4brackets

The brackets are made out of 1018 cold rolled steel.  What I really liked about this project is everyone of my powered machine tools (bandsaw, shaper, lathe, mill, belt sander, bench grinder!) was used.  The method went something like this:

  • Cut to size on the bandsaw
  • Face and machine to thickness on the shaper
  • Square up on the mill
  • Drill the holes and start tapping on the mill (finish up by hand)
  • Cut the large radius in the lathe using a face plate setup (I used a hacksaw first to remove most of the material!)
  • Cut the outside profile on the bandsaw
  • Add the profile radii on the belt sander
  • And of course, sharpening all the tools on the bench grinder and / or belt sander

It was the first job I really put my newly acquired 7″ Ammco Shaper to work.

ammcoshaper

The shaper worked great, and it was really nice to just let the little machine work away while I was drilling on the mill.  Would I trade my mill for a shaper?  No, probably not, but the little shaper is a pretty useful tool.  It did a very good job on finishing the 1018, which can be really gummy at times with poor chip control.  I used a 1/4 HSS turning tool with a small stepper over for roughing and finishing.  Roughing used a depth of cut of about .020″, which I though was fairly respectable given the 1/3 hp motor powering the little shaper.  I’ll be posting some more details on the HSS tool geometry I used soon.

My Favorite Tool

This is the first post of Manufacturing Matters – my weekly opinion on manufacturing topics.

It’s a bit of a running joke in my mechanical family that you can fix anything with a hammer.  We laugh, but seriously, could you live without a good hammer?  A hammer is an indispensable tool – I use them every day at work and in the shop. In fact I use multiple hammers in a day.

Here is my favorite hammer that I use in the shop while machining:thebasher

Its a zinc cast hammer made by Forest City Castings in Canada.  I use this hammer pretty much exclusively while doing setups, and I love it.  It’s also the first hammer that I’ve ever used that has instructions on the handle.

All kidding aside, the reason I like this hammer so much is because it is made in Canada at a price that you can afford, and is a quality product.  Disclaimer: I have ‘off shore’ tools in my shop and I don’t want to come across as being a hypocrite.  The ‘off shore’ tools in my shop are there because I couldn’t find tools made here that were reasonably affordable (new) or in reasonable used condition (used).  I would have gladly paid more money for my mini mill if I could get a made in North America one.  The reality is if you want a mini mill you don’t have much choice.

Some people say we just can’t compete with countries like China.  Companies like Apple routinely tell us that they couldn’t function without countries like China (read we need shareholder value on the back of inexpensive labour and lax environmental laws).  I beg to differ because every time I’m setting up in my mill or shaper I’m using my affordable, Canadian made, zinc cast hammer – which is arguably a commodity product.  It is made by a great company that is helping its community by providing good, honest jobs.  I’m reminded that yes we can effectively manufacturing  things here, and yes we can compete with countries like China while treating the worker and environment  with the respect and dignity they deserve.

So this hammer is inspiration for me to try and make a difference in the manufacturing world I work and live in.  It reminds me everyday that a good product at a reasonable price is possible to be sustainably made right where I live.

If you want one of these hammers, (I think they make them in aluminum and zinc) send me an email and I’ll try to get you one as I don’t think you can purchase them online.

justin@thecogwheel.net

 

 

Bench Grinder Balancing with a Smart Phone

Disclaimer:  Bench Grinders are dangerous.  If you improperly mount the grinding wheels they will explode and hurt or kill you.  If you mount damaged wheels they will explode and hurt or kill you.  Find someone to help you or educate yourself thoroughly on appropriate safety before attempting any work on a bench grinder.  Attaching weights to the bench grinder to balance it is not a straightforward task.  The weights could fly off when the machine is running and cause serious injury.  Do so at your own risk!

There with that out of the way, I found another use for my smart phone in the shop: dynamically balancing my bench grinder.

Here is my bench grinder.  It is a 8″ Ryobi from Home Depot.  It spins at 3600 rpm which is a little fast for HSS tool bits but it works and has plenty of power for what I do.  Of course I removed the wheels it originally came with and purchased 2 new  CGW Abrasives wheels from a reputable tool supply house in my area.

Ryobi_BenchGrinder

Before we move on to balancing, let me say that I re-machined the wheel mounting hardware that came with my bench grinder so it was flat.  I made new grinding wheel bushings for the wheels so they were mounted as true as I could get them.  I also trued up the wheels with a diamond tipped dressing tool similar to this one: http://www.mcmaster.com/#grinding-wheel-truing-tools/=132y8pr

My bench grinder still vibrated.  It wasn’t serious, and didn’t affect the grinding of high speed steel tools, but it bothered me.  It was an inexpensive bench grinder, and I could go out and by a more expensive one, but most of the new ones all come from China anyway, and I was getting sick and tired of searching for sale posts for a good used Baldor for a reasonable price.  So I decided to see if I could at least make things a bit better.  I also know that surface grinding wheels are balanced when they are mounted.

First you need to know the mass of the entire grinder.  I used a baby scale that we have around the home.  Of course I had to remove the grinder from my grinding table.

Ryobi_BenchGrinder_Mass

I then determined the resonant frequency of my grinder.  To do this you need to mount your smart phone to the bench grinder.  I used zip ties, again.  You can see some of my other ‘cell phone’ engineering on my other page where I analyzed my mini mill using my smart phone:  https://thecogwheel.net/2016/06/27/x2-mini-mill-vibrations-and-chatter/

Ryobi_BenchGrinder_withcell

Next step was to determine the  natural frequency of the system. With the grinder off, turn on your accelerometer app and tap the grinder with a dead blow hammer.  I exported the results and took a look at the response in Excel.  Here is what the chart:

BenchGrinder_NaturalFrequency

Now you can see the wave is a little choppy.  This is due to my smart phone’s accelerometer limitations.  You could do much better with a higher quality accelerometer programmed using a micro controller (a Arduino works well!) but that wasn’t the point of what I was trying to do.  I wanted to see if my smart phone would provide useful information because it is easy to use!

From the graph I found the period of the vibration to be 0.032891 seconds.  The inverse of the period is the frequency, which is 30.403 Hz.  Note this is the damped frequency, denoted Wd.  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.  Using the data the following was calculated:

Damping Factor 0.3890832
Natural Frequency 33.00449108 Hz
Natural Frequency 207.3733334 rad/s
Natural Frequency 1980.269465 rpm
Weight 39.996 lbs
Mass 18.18 kg
K (spring rate) 781807.2555 N/m
C (damping) 47.7799696 kg/s

As we can see, my bench grinder’s natural frequency is around 2000 rpm.  This means that it must accelerate through the natural frequency when it starts up.  I plotted the a startup of my bench grinder using my cell phone to confirm my results.  The very right of the chart shows the grinder running in steady state, or 3600 rpm.  You can see the response is stable and repetitive at the right hand of the graph.

BenchGrinder_StartupPlot

Not so good!  Now this is a rotational imbalance problem.  Essentially a unbalanced mass is causing the entire system to oscillate.  This oscillate is the worst at the resonant frequency, but the unbalanced mass also contributes to the oscillation during steady state operation, in our case 3600 rpm.  Can we calculate what this unbalanced mass is?  Of course we can!

First we need to calculate what the response displacement is.  To do this you need to find the maximum, vibration amplitude during steady state.  My grinder had a maximum acceleration amplitude of 10.42 m/s^2 during steady state operation.  To calculate what the displacement is you need to divide this number (subtracting gravity first!) by the rotational speed squared (converted to radians per second).  You do all this and  found my displacement to be 0.004292 mm.  Once we have this, we have all the information we need to calculate what the unbalanced mass times radius factor (mR)  that is causing this vibration.

We need to solve the following equation where X is the displacement, mR is the mass x radius due to the unbalanced mass, M is the mass of the entire system, r is the frequency ratio and zeta is the damping factor:

Displacement_EquationAgain 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.  Using the data the following was calculated:

Max Amplitude 10.42 m/s2
Gravity 9.81 m/s2
Absolute Difference 0.61 m/s2
Rotational Frequency 3600 rpm
Rotational Frequency 60 Hz
Rotational Frequency 376.9911184 rad/s
Frequency Ratio, R 1.817934409
Displacement, X 4.29208E-06 m
Displacement, X 0.004292078 mm
Unbalanced Mass x Radius, mR 6.38521E-05 kgm
Unbalanced Mass x Radius, mR 0.063852078 kgmm
Radius of Required Mass 20 mm
Required Mass 0.003192604 kg
Required Mass 3.192603888 grams

So there, we now know how much mass we need.  Since I didn’t have any way to use my cell phone to figure out where the unbalanced mass was occurring  (this would require a some sort of method to determine phase of the wave from, such as a proximity sensor trigger), I decided to stick on trial weights and move them methodically around the wheels and watch the response on my smart phone.  After several tries I found a spot that was close to where it should be and proceeded to stick on the weights.  I used little washers, and I placed them on each wheel.

I used the following mounting tape:

BenchGrinder_MountingTape

I mounted the weights on each wheel, covered them with high strength tape, and let it sit overnight (according to the tape’s instructions) to harden up.

BenchGrinder_MountedWeight

I put the covers all back on and started it up.  It ran much smoother, and my cell phone’s accelerometer showed significantly less vibration.  I couldn’t get the weights placed perfectly to get rid of all vibration, so some is still present.  But it is a lot better than it was.

BenchGrinder_CellOutput

 

I plotted the results of my grinder starting up and overlaid them over the results before I added the mass:

BenchGrinder_StartupPlotAfter

That looks a lot better!

In the future I am going to try to come up with a simple way to measure phase.  This might involve a computer instead of a cell phone, but for now I’m much happier with my bench grinder.   When it accelerates and decelerates it is much quieter and during operation you cannot tell it is running.  Hey, its not a Baldor, but it works like one now!

You can view the spreadsheet I used to do the calculations: BenchGrinderAnalysis.

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.