3D CMM

Trends in parts to be measured:

• rotationally symmetric parts with freeform shapes

• prismatic parts with small bores

• flat metal sheet parts with limited shape stability

• 2D parts with bores and cutouts

Probe types:

• touch-trigger probes

• optical (non-contact) probes

Conventional 3D CMM:

• measured 3D complex shapes

• trends: smaller dimensions, tighter tolerances

• reduced mesauring uncertainty

• four main error sources: geometric, thermal, abbe error and finite stiffness

Specifications in design of the new 3D CMM:

• low measuring volume

• lowe measuring uncertainty

• incremental position-measurement system

• platform for different probe types

Approches for 3D CMM elimination of errors:

• minimize finites stiffness and thermal errors by mechanical design

• reduciton of geometric errors by machine concept

• software compensation of ersidual geometric errors

Describe concept 1

= polar coordinate based measuring coecpet using two rotating discs with friction drives and encoders

• tight requierements on parallelism of the rotation axes

• bearing are in one plane to avoid tilting

• preloaded hollow rollers acting as a nest of spring

→ rejected because how accurately would the rotations be

Describe concept 2

= 6 actuated rods connecting to a fixed base to a moving platform that carries the probe/table

• elastic hinges introduce elasticity, avoid hysteresis

• pros: flexible movement (full 6 DOF control), limited number of errors

• cons: large size, tight temperature stability requierements

Describe the Abbe principe

= straightness error causes a measurement error that is linearly proportional to the offset h between the probe and the scale

→ always place the measuring scale in line with the actual point of measurements

Describe concept 3

= machine concept with intermediate bodies

• while moving in the x and y direction, the measuring systems stay pointed to the probe

• guiding beam B_I does not cause measuring error due to the application of the Abbe principle

• scale beam B_A does not cause measuring error due to the application of the Bryan principle

Describe the Bryan principle

= a straightness error that is measured at the offset h that causes a measurement error that is linearly proportional to the offset between the scale and the probe

What is the final kinematic design of the 3D CMM?

= a 3 body system (platform, intermediate body A (constrains x and Rz), intermediate body B (constrains y))

• measuring systems stay pointed at the probe

• bearing far apart for improving stability

• vertical guide (pinole) is integrated into the platform, driven almost in the COG

Describe what are the geometric errors for a single moving body and how do they apply for the 3D CMM?

For a single moving body:

the error vector contains T=translational error, R=rotational error and P=position erro

• straightness error == TOTAL ERROR VECTOR

For the 3D CMM:

there are 30 possible errors= 18 rotational, 3 straightness and 9 translational errors.

By applying the Abbe and Bryan principles, those error reduce from 30 to 13 = 2 rotational, 8 translational (2 intermediate body A, 2 intermediate body B, 1 flatness of the table, 1 of the z direction, 2 of the vertical beam) and 3 straightness errors

What are the two concepts tackled for the machine frame of the 3D CMM? Explain in detail.

Geometry and material/

For the geometry, a closed box plate constructions were used in the pyramid shape for optimal material utilization, force transmission through plate plane was accounted for (light and stiff moving parts), monolothic parts were used (prevents hysteresis, improves stiffness and thermal conductivity), parts are glued togethers.

For the material, aluminium was used for its excellent thermal behaviour. It is very respondent to heat; however, it reaches a thermal equilibrium very fast. To add, it has low density, therefore, light moving parts with thicker plates.

Explain how the passive compensation of thermal expansion works.

By using thermal centers, Zerodur scales (a glass-cermaic with near zero thermal expansion used for the actual position scales) and temperature measurement of the product

= method used to cancel out uniform themral explansion using symmetric thermal chains

• additionally, room temperature requirement needs to be satisfied due to uncertainties in thermal expansion and non-uniform temperature distribution

Explain why are direct drives a good choice to move the slides.

There is no gearbox, no mechanical transmission, no belts.

It is a simple design and maintenance free, high dynamic characteristic, small position errors, no friction, no backlash, small power dissipation, no cogging or transversal attracion, additional damping via controller software, weight compensation of vertical slide

Describe the positioning control loop.

Describe the air bearing in the 3D CMM.

+frictionless, high guiding accurcay, clean operation, long stroke motion capability

-need preload and self-alignment

Kinematic design principle: minimum constraint design =

= use the exact number of constraint points needed

overconstraint causes stress

undersonstraints causes play

Describe the difference.

Form-closed bearings: mismatch thermal expansion, rigidly constrained, generating internal stress since both sides are stiff

Force-closed bearings: more tolerant of dissimilar thermal expansion and lower overall stiffness

Describe what is the elastic cardan.

= flexture based mounting that allows the air bearing to self-align with the guiding surface without any hysteresis

• two orthogonal hinges, located in the same horizontal plane

• no hysteresis

• compact

• horizontal strips prevent sideways deflections

How is vibration isolation done?

During preparation and during measurement. Explain in detail why it happens.

Through a machine table carried by pneumatic springs to isolate from ground vibrations.

During measurement preparations, the load changes and causes a tilt, resulting in a deformation component under gravitational force and extra driving force, therefore, a quasi statis machine levelling system was implemented, which becomes stable after 20s.

During measurement, an active electromagnetic system prevents tilting due to mass travelin and changng load distribution, tilting the machine. It is done by differential tilt measurement (sensor 1-2) and feedback by controller and amplifier to the voice coil actuator.

Resulting in low power dissipation, vibrations are isolated, force is enlarged bua a cantilever (1/10).

How does horizontal vibration isolation works?

By using flexures (rods) for no play and no hysteresis. They are NOT at COG.

horizontal motion → rotation → vertical motion → damped by vertical dampers

What is calculated in the error budget of the 3D CMM?

1. finite stiffness - right design principles to geomtery and assempy

2. thermo mechanical errors - extensive use of aluminium, mechanical thermal lenght-compensation

3. geometric errors - through straightness errors, Abbe and Bryan principles, machine concept, calibration

How is calibaration done by NMi VSL standards?

Via a interferometer (calibrating geometric errors)

Via a polyglo mirror (to determine perpendicular beams)

Via sensitivity and diameter of a reference ball (probe calibration)