Volumetric Error Compensation

Question 1

possible error sources

Answer 1

1. from the machine
   - systematic errors
   - kinematic errors
   - squareness errors
   - reversal errors
   - thermal errors
   - random errors (vibrations)
2. from the outside (setup)

Question 2

kinematic errors

Answer 2

for each axis, there are 6 possible errors:
one for the linear position, two for the straightness, three rotational errors

• > in a 3 axis machine, a total of 18 errors

Question 3

squareness errors

Answer 3

there is a perpendicularity error between each couple of axis, for a total of three errors

Question 4

thermal errors

Answer 4

errors due to structural deformation for thermal effects

Question 5

reversal errors

Answer 5

errors due to accelerations during the motion, for the presence of interpolation

Question 6

volumetric error: possible models

Answer 6

• kinematic, squareness and thermal errors can modeled, measured and compensated
• considering the machine as a rigid body, thermal errors are neglected (21 errors)
• considering the machine a quasi-rigid body, both geometric errors and thermal errors are considered (more than 40 errors)

Question 7

how to compensate the known error

Answer 7

3 ways:
1. hardware correction: reworking or reassembling of the components to reduce the error; it is not possible to delete the error
2. open loop compensation: obtained valued can be compensated after the measurement; used for CMS
3. closed loop compensation
used for CNC machine tools

Question 8

how to store the errors

Answer 8

for software compensation (open or closed loop), the model of the volumetric error nee to be represented in memory

1. error grid:
   - the working envelope is discretized
   - for each node of the grid the three components of the error are memorized
   - compensation for intermediate points is done by linear interpoation
   - huge amount of data
   - only few CNC allows it
2. error table
   - each axis is discretized
   - kinematic error function at each point
   - interpolation for intermediate points
   - very diffused
   - it does not include correlation between axes
3. coefficient table
   - considering a model of 18 cubic functions
   - only the coefficients can be memorized
   - very effective
   - complicated and not used at the moment