Design for low sensitivity


Maxwell quoted in 1890 that “In designing an experiment, the agents and phenomena to be studied are marked off from all others and regarded as the field of investigation. All others must be so arranged that the effects of disturbing agents on the phenomena to be investigated are as small as possible.”. The major disturbing agents are mechanical vibrations, temperature changes, humidity, acoustic noise, and electric and magnetic fields. Three design strategies for precision machines are distinguished to become resistant to environmental disturbances: 1) uncouple the machine from the environment, 2) design the machine so that environmental disturbances are minimized, and finally, 3) control the environment. This section will assess the former two, particularly focusing on short term (non-thermal) effects.

The first principle is referred to as isolated metrology loop. Often, manufacturing machines are set up as C-arches, connecting tool and workpiece at the point of interest. The C-arch stiffness is determined by the structural loop, and the C-arch position information by the metrology loop. Typically, these loops (largely) overlap in 3D space, potentially causing measurement errors in the metrology loop. In high tech systems, loops are preferably separated and assigned to different physical parts of the system in order to minimize uncertainty.

For precision machine design, it is recommended to incorporate symmetry to the maximum extent possible in properties of machine elements (e.g. mass- and force distribution or stiffness), the entire instrument and properties of the environment. In designing, manufacturing, assembling and operating a precision instrument, any departure from symmetry has to be weighed against the resulting compensation to overcome problems produced by the asymmetry. To overcome the effect of asymmetry about the horizontal plane, caused by gravitational forces, machines can be equipped with a vertical axis, e.g. the LODTM. Three dimensional symmetry is superbly achieved by a tetrahedral structure, e.g. the Tetraform by Lindsey of NPL.

A third key principle for generating low sensitivity in precision machine design, is to design for minimum offset. Abbe stated in this respect that “The measuring instrument is always to be constructed that the distance being measured is a straight line extension of the graduations on the scale that serves as a reference.”. About one century later, Bryan refined this principle by adding: “If this is not possible, either the slide ways that transfer the displacement must be free of angular motion, or angular motion data must be used to calculate the consequences of the Abbe offset.”.

In the development of servo-controlled positioning devices, it is essential to consider the place where the actuator force is loading the guide way to supply the (resulting) force generated by, among others, inertia, tool- or measuring forces, and friction. Drives should be placed to operate through the axis of reaction. Stated more generically, drives must be placed such that the system moves in the desired way even in the absence of a guiding system. If this is not possible, the deviation from the axes of reaction, called drive offset, includes moments on the machine guide ways. The effect of resulting rotations on the controllability is minimized, if both the drive- and measurement axis are at the same side of the center of rotation.

A final principle mentioned here is the concept of vibration isolation, either from random seismic disturbances, or from internal or external deterministic vibration sources. Passive vibration isolation implies the application of a large mass on low stiffness springs (second order system), to which is additional  damping is applied to provide attenuation at the resonance frequency. Multiple isolation stages can have higher natural frequency and give more attenuation above the critical frequency due to a steeper slope, such as applied in gravitation wave observatories and lithography systems. In case mass or volume are limited, a (small) reference mass can be used in combination with an active feedback loop.


Design principles