# Introduction to Positioning Equipment

This tutorial introduces opto-mechanical component design basics and will familiarize the reader with the issues that need consideration in the selection of the most commonly used tabletop Opto-Mechanics. It emphasizes practical issues, not mathematical derivations.

### Performance Parameters

There are many different measures of performance one must consider when choosing a particular positioning component. Understanding the definitions of the various parameters and how they affect performance will simplify the selection process.

### Materials and Stability

The majority of all opto-mechanical components are made from aluminum, brass, or stainless steel. Therefore, the properties of these materials will be directly compared in the following discussion. Materials are sometimes selected by emphasizing a single property, such as thermal expansion. This is unwise as it is not likely to result in a good choice for general use. Therefore all relevant material properties should be considered.

### Stiffness

Stiffness is a measure of the amount of stress (force/area) required to cause a given amount of strain (normalized deformation). Stress and strain are proportional and related by the equation σ = Eε, where σ and ε are stress and strain respectively and E is Young’s Modulus, which is material dependent. A material is stiffer for larger values of E and more compliant for smaller values. For example, stainless steel is approximately three times stiffer than that of aluminum (see table). Aluminum, on the other hand, is 1.3 times more compliant than brass. Specific stiffness (Young’s Modulus divided by the material density) is important when settling time or vibration immunity is an issue. Components with the same shape and specific stiffness will have the same fundamental resonant frequencies. Higher specific stiffness results in higher resonant frequencies, faster settling times, and a reduction in vibration disturbances.

### Thermal Expansion

Temperature changes cause size and shape changes in a mounting component. The amount of size and shape change is dependent on the size of the component, the amount of temperature change, and the material used. The equation relating dimensional change to temperature change is ΔL = αLΔT where α is the material dependent coefficient of thermal expansion. The thermal expansion of stainless steel is roughly half that of aluminum. This can be important when the mounting component is being used in an application requiring interferometric stability. Note that aluminum is the best choice when temperature change across the component is non-uniform. This situation arises when mounting a power source, such as a laser diode. Because the diode is hotter than the surrounding environment, it dissipates heat through the mount setting up a temperature gradient along the component. The thermal conductivity of aluminum is ten times greater than that of stainless steel so heat can be dissipated more readily, thus reducing the magnitude of the thermal gradients and distortion. The distortion caused by non-uniform temperature changes is proportional to the coefficient of thermal expansion divided by the coefficient of thermal conductivity. Thus, aluminum distorts on the order of three times less than stainless steel in a non-uniform temperature environment. Brass - though nearly as thermally expansive as aluminum, has a coefficient of thermal conduction nearly a factor of two worse and thus is not as good as aluminum in this situation.

If the ambient operating temperature of the component is much different from room temperature, then close attention should be paid to components made with more than one material. In a linear stage, for example, if the stage is aluminum while the bearings are stainless steel, the aluminum and steel will expand at different rates when the temperature changes and the stage’s bearings may lose preload or the stage may warp due to stresses that build up at the aluminum-steel interface.

Material Properties Aluminum Stainless Steel Brass
Stiffness, k (MPSI) 10.5 28 14
Density, ρ (lb/in.3) 0.097 0.277 0.307
Specific Stiffness, k/ρ (M in.) 108 101 45.6
Coefficient of Thermal Expansion, α (µ in./in./°F) 12.4 5.6 11.4
Coefficient of Thermal Conduction, c (BTU/hr-ft-°F) 104 15.6 67
Relative Thermal Distortion (α/c) 0.12 0.36 0.17

### Material Instability

Material instability is the change of physical dimension with time — so called cold flow or creep. For aluminum, brass, and stainless steel, the period of time required to see this creep may be on the order of months or years.

Usually, the mechanical design of the component contributes much more to the instability than does the choice of material. For example, the lubrication on the micrometer’s threads can begin to migrate over time causing a slight shift in the micrometer. Alternately, if a translation stage’s bearings have not been sufficiently hardened, the stage can shift after not moving for extended periods as the bearings deflect locally at their points of contact.

### Summary of Materials Evaluation

Each of the materials used in positioning components have their own unique set of advantages and disadvantages. Unfortunately, a universal material that meets all requirements does not exist. We summarize here the characteristics of the materials outlined in the chart.

Aluminum: Aluminum is a lightweight material, resistant to cold flow or creep, with good stiffness-to-weight ratio. It has a relatively high coefficient of thermal expansion, but it also has a high thermal conductivity, making it a good choice in applications where there will be thermal gradients or where rapid acclimatization to temperature changes is required. Aluminum is fast machining, cost effective, and widely used in component structures. Aluminum is non-rusting and generally corrosion-resistant in a laboratory environment, even when the surface is unprotected. It has an excellent finish when anodized. However, anodized surfaces are highly porous, making them unsuitable for use in high vacuum. Vacuum applications require the use of unfinished aluminum surfaces.

Stainless Steel: Steel has a high modulus of elasticity, giving it very good stiffness (nearly three times that of aluminum), and good material stability. It also has about half the thermal expansion of aluminum, making it an excellent choice in typical laboratory environments where there are uniform changes in temperature. Machining of steel is much slower than aluminum, making steel components considerably more expensive. Corrosion of steel is a serious problem. Stainless steel alloys avoid the corrosion problems of other steels. Stainless steel is well suited to high vacuum applications, but the design of the component must also incorporate other factors. (Please the Vacuum Compatibility section below)

Brass: Brass is a heavy material, denser than steel, fast machining, but with a less desirable stiffness-to-weight ratio than either aluminum or steel. The thermal expansion of brass is similar to that of aluminum, but its thermal conductivity is nearly a factor of two worse. It is, however, a good wear material. The main use of brass is in wear reduction; it is often used as a dissimilar metal to avoid self-welding effects with steel or stainless steel screws or shafts. Brass is used in some high-precision applications requiring extremely high resistance to creep and can be diamond turned for extremely smooth surfaces.

### Exterior Finish

Anodized aluminum provides excellent corrosion resistance and a good finish. Black is the color most often used on optical mounts. The anodized surface is highly porous. For this reason, only non-anodized aluminum is used in high vacuum applications. However, this porosity results in a matte surface that does not specularly reflect light, adding to its value in optical mounts. Anodizing hardens the surface; improving scratch and wear resistance.

Steel parts are generally plated or painted. Platings are often chrome, nickel, rhodium, or cadmium. A black oxide finish is often used on screws and mounting hardware to prevent rust. Painted components should be avoided. Paint will eventually flake off, contaminating the optics or the moving parts of the positioner.

Stainless steel alloys avoid the rust problems of other steels. They are very clean materials that do not require special surface protection. A glass-bead blasted surface will have a dull finish that does not specularly reflect.
For optical use, brass is usually dyed black. In other cases, it may be plated with chrome or nickel for surface durability.

### Vacuum Compatibility

Many products within this catalog can be vacuum prepared. Please look for the “Vacuum Compatible” statement on the specific product page. “Vacuum Compatible” products are prepared for 10-6 Torr. If you require products specially prepared for 10-3 Torr, or greater than 10-6 Torr environments, please contact our technical staff for a quotation. For those products not designated as vacuum compatible, we may still be able to prepare for vacuum environments. However, these would require special quoting. Please contact our technical staff to discuss your needs.

### Vacuum Preparation

Preparation for vacuum environments depends on the vacuum you wish to maintain. The word “vacuum” does not adequately specify the conditions for a specific application. Acceptable levels of outgassing, mass loss and volatile condensable materials can vary with the application, pumping capacity, temperature, etc. It is, therefore, essential that the specific requirements be reviewed and understood prior to placing any component in a vacuum environment.

10-3 Torr environments: In general terms, a vacuum of 10-3 Torr requires minimal change to many of our products with the exception of possible lubricants. In this environment, it is not uncommon to use anodized parts and limited use of plastics should not pose any problems.

10-6 Torr environments: Components used in a vacuum of 10-6 Torr are specially prepared for this environment. Many of the materials used in standard components will outgas in a high vacuum, resulting in a “virtual” leak, which limits the ability to maintain a high vacuum. Highly porous anodized aluminum surfaces can trap large amounts of air molecules, resulting in significant outgassing. For those components, within this catalog, specified as “Vacuum Compatible” we perform the following in preparation:

Products with anodized aluminum are created without anodize. As such, we only use non-anodized aluminum, stainless steel or equivalent materials. Plastic knobs and handles are either removed or replaced (at additional cost) with high vacuum materials such as steel or Delrin. In some cases, you may choose to maintain the plastic knob due to incremental costs associated with producing an alternative design. In spite of plastics permeability it is common to use plastics in vacuum systems because of their insulating properties and price. Holes not tapped through are vented; or special vented hardware is used. Hardware and lubricants are changed to special vacuum compatible materials. Finished units are completely cleaned and sealed in appropriate packaging material.

Additional vacuum preparation steps, or preparation for vacuums of greater than 10-6, require special handling, including baking the product in a vacuum. If you have requirements at this level, please contact our technical staff to discuss the options available and, if appropriate, pricing.