Re: Force on the ball/lead screw
Reply with QuoteHi,
To measure rigidity, at least using terminology and techniques applicable to CNC machines, requires that you apply a force, usually at the nose of the spindle relativeHow does one test rigidity? If that is the factor that determines what motors/electronics then there must be a way of gauging how stiff = what motors...?
to the table. You would apply say a 10kg force, or 100N, and measure the deflection. You would probably do this is in the X direction, Y direction and Z direction.
This is a subset of the general process of measuring the 'stress tensor'. A tensor is a matrix of numbers representing the compliance of the controlled point at any given location
within the machining envelope of the machine. Note that 'compliance' is the exact opposite or reciprocal of stiffness or rigidity. Compliance has the units of Force per unit Distance.
The stress tensor is a 3 x 3 matrix. The leading diagonal of the matrix is the three measurements I have described above, namely the compliance in the three axis directions. The remaining
six numbers of the tensor represent the rotational deflection when a torque is applied, say torque on the X axis causes a rotational deflection along the Y axis.
Generally speaking if a torque in the X direction causes a deflection in the Y direction then the reverse applies, a torque in the Y direction cause an equal deflection in the X direction.
Thus of the six numbers that we seek to populate the stress tensor there will be three pairs of identical numbers. The arrangement of those numbers in the matrix is called
'symmetrical' and has a very important property that allows a huge simplification in the mathematics to find Eigenvalues and Eigenvectors of the matrix which in turn can be used
to determine the motion of the system described by the stress tensor.
All this talk of tensors, Eigen functions and stuff like that make my A-hole pucker and I come out in a cold sweat....and that's 40 years after first learning about them....rue the day!
Fortunately computers have come to our salvation and this sort of thing is handled by Finite Element Anlaysis programs these days, and a huge boon to the engineering community
it has been. I would commend you look at the FEA module of Fusion , free download to hobbyists, to see the power that it brings to a designer.
More importantly than the complexities of stress tensors etc is that there is a very useful and simple grain of truth to the process that will inform you as to the basic properties of the machine.
In CNC machines its common to see 'stiffness' quoted as 150 N/um. Observing the units the number quoted is the compliance rather than stiffness....but none the less conveys useful meaning
to any engineer, ie if you push 15kg force (weight of 1 1/2 slabs of beer) then the machine will deflect 1um (half an ants dick). Note that it's not common to specify the deflection of an axis when a force is applied
along a different axis, ie the 'cross terms' of the stress tensor as they tend to cloud the essential and simple understanding.
Now the question is what numbers should you be looking at.
For instance a moderate size commercial VMC , say $100,00 to $200,000, may well have stiffness of 150N/um.
A huge fixed gantry machining centre, say 3,000,000 , may well have a stiffness of 750N/um
That's all very well for large and expensive machines, but what can we expect or hobbyist level machines?. As an example you may bee familiar with the RongFu or Precision Matthews
type drill mills. They tend to be cast iron dovetail beds with a steel column, typically a 2hp spindle, and maybe $2000USD. Having used them they are very useful, nothing like
the rigidity of a bigger mill, but rigid enough that when used with care can do a good job in aluminum and steel. They have a stiffness of around 20N/um. This would be a good goal
for you to aim at if you want a metal capable hobbyist machine.
Peteeng has a very long running thread about a composite mill design trying to achieve stiffness of 20N/um in all axes in a benchtop footprint and weighing 500kg. Its well worth a read....
although its a long thread!
Really its not about ' a certain stiffness = a certain size motor', but rather 'how stiff does my machine need to be to make these parts from that material?'. Thereafter the question changes to 'what
is a good motor/ballscrew combination to maximize the use of the machine of this given stiffness?'.
The best way to answer those questions is get out into the workshop and start making parts on the machine you have. That experience will tell you what the limitations are....and inform your
choice of your upgrade path or new machine.
Craig
Originally Posted by joeavaerage
Peter
