1 Appendix D: Mechanical Design Detail
1.1 Spectrograph Cavity Structural Stiffness
The spectrograph is enclosed in a cavity between the massive cold work surface (CWS) plate of the cryostat on one side, and a lighter cover plate on the other. A short skirt around the boundary separates these two plates. The modules of the spectrograph take the form of posts that are clamped between the plates.
The CWS plate is stiffened on the On-Instrument Wavefront Sensor (OIWFS) side by the presence of the Optable. This component takes the form of a deep-celled housing. In combination with the CWS plate, it provides a ribbed box-section platform onto which the spectrograph mounts.
For the purpose of determining optical component mounting stability (§4.22.2.1), the dominant forms of deformation in this structure are sag across the whole platform, local sag of the CWS plate between the ribs of the Optable, and shear between the CWS plate and the spectrograph cover plate.
1.1.1 Platform Sag
The sag across the spectrograph platform has been roughly estimated by means of simple beam theory. If the supported weight is W = 2500 N, the effective platform length is l = 720 mm, the elastic modulus of the structure material (aluminum alloy) is E = 69000 MPa, and the effective inertia moment of the platform section is I = 600×10-6 mm4, then the maximum sag of the platform is
1.1.2 Local Sag
The local sag of the CWS plate has been roughly estimated by plate theory. If the plate density is r = 2.70×10-6 kg mm-3, its elastic modulus is E = 69000 MPa, its thickness is t = 40 mm, gravitational acceleration is g = 9.8 m sec-2, and the typical distance between stiffening ribs (forming roughly square cells) is a = 220 mm, then the maximum sag between ribs under gravitational loading is
where the constant of proportionality is dependent on the degree of the constraint at the ribs. For point attachment at the corner of each ribbed cell, it is ~ 0.16. For fully fused ribs, it is ~ 0.012. A reasonable value for this case is ~ 0.06, for which the maximum sag is ~ 30 nm.
1.1.3 Shear Angle
The lateral load on the cover plate shears the structural skirt of the spectrograph housing. This load comprises the weight of the cover plate itself (~ 90 N), half the weight of the skirt (~ 50 N) and about half the weight of the suspended optics modules (~ 110 N). The total shear load is ~ 250 N. The cross sectional area of the skirt is ~ 19000 mm2, of which about half is effective in resisting shear. The shear stress is therefore ~ 0.026 MPa. For a shear modulus of 26000 MPa (aluminum alloy), the shear angle is then ~ 1.0 μrad.
1.1.4 Finite Element Analysis
At the left of Figure 172 is a view showing the spectrograph cover plate and skirt fused together to form a single part. This single part has been meshed and is ready for Finite Element Analysis (FEA). In the view on the right side of Figure 172, the fused part has been rotated by 180° to face the cover towards the observer. The part is now uniformly supported all around the 8 mm thick flange of the skirt and is loaded with a vertical 250 N force at the center of the cover, equivalent to the total shear load. Resulting FEA contour lines show a vertical deflection of ~260 nm where the lines cross the boundaries between the skirt and cover. This equates to a mean slope of ~ 1.3 μrad that is in broad agreement with the value estimated above.
Figure 172: Vertical deflection FEA of the skirt plus cover.
1.2 Pick-Off Probe Stiffness
The cantilevered pick-off probe carries the small pick-off mirror at the center of the large OIWFS field, as shown in Figure 49. It is important that image displacement caused by gravitational deflection in the probe be small relative to the total instrument flexure allowance (0.1 pixels per 15° attitude change).
The major deflection causing image displacement is rotation of the probe mirror about the incident beam axis, which results from lateral bending of the probe vane. A conservative estimate of this can be made by assuming that the probe is parallel rather than tapered.
For the probe, the thickness is a = 10 mm, the length is c = 84 mm, the density is r = 2.70×10-6 kg mm-3, the tensile modulus is E = 69000 N mm-3, gravitational acceleration is g = 9.81 m s-2, and the distance from the pick-off mirror to the focal plane is d = 100 mm. The maximum displacement of the image at the focal plane caused by gravitational deflection is then
The maximum deflection that can occur over a 15° change in attitude is 0.26 times this, or 0.12 μm. This corresponds to 0.0037 pixels at the detector, which is negligible.
1.3 Focal Plane Mask Wheel Drive
The Focal Plane Mask Wheel is driven in a “stop anywhere” fashion by a geared stepper motor drive, as shown in Figure 50. The motor has 200 steps per revolution and drives through a three-stage gear system having a total reduction ratio of 323.4:1. This drive system uses a magnetic friction drag brake mounted directly on the mask wheel axis to firmly hold the wheel, and the apertures it carries, at their driven-to position.
The three-stage spur gear drive is simple, reliable, and moves the focal plane mask through 0.1″ in 21 steps. The scale at the Gemini telescope focus is about 63 μm/0.1″ so this drive will allow a 0.1″ occulting disk to be positioned to ~ 6.3 μm or about 0.01″. As ALTAIR will deliver ~ 0.1″ images to NIFS this drive should allow an occulting disk to be positioned over a bright object with ample accuracy.
The Focal Plane Mask Wheel and gear trains rotate on miniature ball bearings. These bearing systems are lightly loaded and run without lubrication. A wave washer preloads each bearing set at one end. There is no anti-backlash system in the gear train and the final setting to any position is always approached from a clockwise direction. There are no end stops in the drive so the wheel can be driven in either direction to take the shortest path to the next required mask. The gears are aluminum with Teflon impregnated anodize dry lubrication. The gear train ratio has been adjusted to give an even number of steps between each mask as this simplifies the EPICS software record. The magnetic drag brake disk requires little setting up as the disk is axially flexible and friction is largely set by magnetic forces and the coefficient of friction between the hard metal surfaces. The drag brake torque is about 100 N mm. The torque capacity of the large stepper motor is about 1000 times greater than the drag brake torque. This large torque would destroy the fine pitch gearing if the mask wheel bearings or intermediate bearings jamb. To protect the gearing, a slipping clutch is included in the gear train.
1.4 Filter Wheel Drive
The Filter Wheel is driven by a “stop anywhere” system similar to the Focal Plane Mask Wheel drive. The first and second gear trains, the slipping clutch, and the encoding system are copied from the Focal Plane Mask Wheel drive. The only important difference between the drives is the larger diameter of the Filter Wheel, which increases the gear ratio and the time to set to any particular filter. The drive provides more than enough resolution to re-set the filters to their previous positions and sets the selected filter in ample time.
For this system, the total gear reduction ratio is 508.2:1. For a motor speed of 4500 steps/s, the time required to move between adjacent filters is 2.8 s. One complete revolution of the wheel takes 22.6 s. The filter positioning sensitivity is 1.85 mm/step.
1.5 Grating Drive and Grating Mounts
The grating turret is driven in a “stop anywhere” fashion by a geared stepper motor drive. This drive is the most crucial to the success of the instrument and was the most challenging of the NIFS mechanisms to design. Consequently, the adopted design is described in full detail below. Figure 173 shows the layout for the grating drive.
Figure 173: Layout for the grating drive gear train. A six position grating turret (top) is driven through a three-stage spur gear drive by a cryogenic stepper motor (bottom). The grating turret is supported on a shaft attached to the CWS plate (left) and the spectrograph cover plate (right).
1.5.1 Design Requirements
The grating turret is required to 1) operate at a temperature of ~ 65 K, 2) have an image stability in the spatial direction of < 0.1 pixels at the detector for a 15° change in instrument orientation, 3) have a turret position repeatability in the dispersion direction of 0.1 pixels at the detector, 4) carry six gratings (or mirrors), and 5) have an optical center-line 90 mm above the CWS plate.
1.5.2 Design Description
The grating turret design consists of the following major sub-components and sub-assemblies (Figure 173):
· A steel shaft bolted directly to the CWS plate and supported at the top end by the spectrograph cover plate in order to achieve maximum stiffness relative to CWS plate and good thermal contact with the CWS plate.
· The grating turret sub-assembly consisting of an aluminum alloy body mounted on the shaft via a pair of soft pre-loaded ball bearings. The preload is applied via a pair of disk springs to accommodate differential thermal contraction between the steel shaft and aluminum housing. Lateral shift of the bearing virtual center, due to rotation of the outer race about a lateral axis, is prevented by using a pair of parallel disk springs. The bearings are stainless steel light series angular contact ball bearings, ABEC grade 9, or equivalent. It is intended that the bearings will be cleaned and run in a lubricant free condition in accordance with successful previous practice at RSAA. The bearings are very lightly loaded in comparison with their load ratings.
· Six grating sub-assemblies with replicated gratings bonded to aluminum alloy blanks, together with flexure mounting and adjustment provisions.
· A friction brake to provide turret positioning stability and eliminate gear train backlash. The brake is axially pre-loaded with a pair of disk springs and has both rubbing surfaces made from hard steel. A pair of disk springs is proposed with the aim of keeping both rubbing surfaces in full surface contact by preventing torsional deflection of the fixed pad ring. This should optimize the thermal conductance to the rotating mass.
· A pair of Hall effect sensors mounted in tandem for redundancy and fixed to the CWS plate via a bracket such that they are close to the rim of the turret lower flange. The sensors align with 6 samarium-cobalt magnets, attached to the turret lower flange, one corresponding to each of the grating positions. The magnets are set at slightly different depths to provide different flux densities and are bonded into separate housings rather than directly into the flange, to facilitate removal and replacement should this prove necessary.
· The Hall effect sensors are very small and fragile and are supported via their leads, which are clamped and bonded, to an aluminum plate in order to provide good heat sinking, so forming a small sub-assembly.
· A sheet metal cover to protect the grating optical surfaces, screwed to the CWS plate and including access holes to facilitate grating adjustment with the cover in place.
· Gearbox consisting of the stepper motor pinion plus two other shafts, each with an integrally machined steel pinion and attached aluminum alloy wheel. This, together with the turret gear wheel, achieves a total reduction ratio of 1008:1. The shafts are supported by precision, stainless steel, deep groove ball bearings. As for the turret bearings these are run with no lubricant.
· Two preload sub-assemblies to axially load the bearings and so eliminate radial clearance. The preload is applied via a pair of disk springs to accommodate differential thermal contraction between the steel shaft and aluminum housing. Lateral shift of the bearing virtual center, due to rotation of the outer race about a lateral axis, is prevented by utilizing a pair of parallel disk springs.
· Cryogenic stepper motor, Phytron VSS 52.200.2.5, as commonly used on NIRI and having 1.8° steps.
· A gear-case consisting of a main housing machined from solid aluminum alloy and a top plate. The main housing contains the lower bearings and is bolted to the CWS plate. The lower face of the housing includes a longitudinal boss, which engages in a slot in the CWS plate to provide for adjustment of the gearbox relative to the turret gear wheel so as to eliminate clearance. The top plate is screwed to the main housing and provides for mounting the stepper motor, the upper bearings, the bearing pre-load assemblies, and the Hall effect sensors. The gearbox assembly is screwed to the CWS plate.
· A simple clutch sub-assembly to prevent stripping of the gear teeth in the event that some bearing seizure should occur and the maximum torque developed by the stepper motor is not restricted. The clutch is placed on the first gearbox shaft rather than the second since this provides maximum protection and there is more room to accommodate it. The rubbing surfaces are hard steel and it is loaded via a wave washer. The device includes a pair of co-axial holes to facilitate angular alignment of the wheel relative to the pinion on the same shaft.
· The stepper motor pinion is fixed to the shaft with a clamping collar. A small samarium-cobalt magnet is bonded into the collar and, together with a pair of Hall effect sensors mounted in tandem on the housing, provides determination of the motor shaft position. The Hall effect sensor sub-assembly may be identical to the turret sensor. It is screwed to the top plate of the gearbox so that the stepper motor and sensor form an integral sub-assembly independent of the rest of the gearbox in order to facilitate alignment.
1.5.3 Gear Ratios and Torque Capacity
The grating turret drive gear ratios are listed in Table 83. The gears are all 0.5 module. The 1008:1 ratio gives a resolution of 0.997 pixels/step at the detector. A full rotation of the grating turret takes 44.8 s. The torque capacity of the motor corresponds to a tagential force of 4860 N on the turret gear. The capacity of the gear teeth is 520 N so a slipping clutch is required to protect the gear train.
Table 83: Grating Turret Drive Gear Ratios
|
Gear |
Pinion Diameter (mm) |
Wheel Diameter (mm) |
Gear Ratio |
|
Primary gear |
12 |
168 |
14:1 |
|
Secondary gear |
10 |
90 |
9:1 |
|
Tertiary gear |
10 |
80 |
8:1 |
|
TOTAL |
… |
… |
1008:1 |
1.5.4 Bearing Preload
In view of the large differential thermal contraction between the aluminum turret and its steel shaft, and between the aluminum gearbox housing and the steel gear shafts, soft preloading is provided for all bearings via pairs of flexure disks. In this system, one bearing on each shaft is rigidly mounted, while two axially separated diaphragm discs carry the other. This bearing can then be displaced axially against the spring action of the disks, but is otherwise constrained. A low preload can therefore be applied with a low spring constant, and the bearing can then be safely operated without lubrication.
1.5.4.1 Turret Bearing Preload
The main load on the turret bearings is due to the mass of the rotating components (~ 4 kg). A safety factor of 1.5 is assumed so that the design axial preload is ~ 59 N. For two aluminum preload disks with outside diameter (OD) of 128 mm, inside diameter (ID) of 74 mm, and thickness of 0.6 mm, the required preload deflection is 0.97 mm at 70 K or 1.14 mm at ambient.
1.5.4.2 Gearbox Bearing Preload
The main load on the last gearbox shaft bearings is the reaction to the gear load of 5.54 N. A safety factor of 5.3 is assumed so that the design axial preload is ~ 29.4 N. There is relatively little room to accommodate very flexible preload disks of practical thickness, so a small preload deflection of 0.21 mm (cold) or 0.16 mm (ambient) will be accepted. This is achieved with a pair of aluminum preload disks; 25 mm OD, 8mm ID, and 0.3mm thick.
1.5.4.3 Friction Drag Brake Preload
A friction coefficient of 0.25, a brake radius of 72 mm, and a required friction torque of 500 N mm have been assumed for the friction drag brake. Therefore an operating preload of 28 N is required. This is achieved with a pair of aluminum disks with 133 mm OD, 95 mm ID, 0.4 mm thick, and a preload deflection of 1.21 mm (cold) or 1.25 mm (ambient).
1.5.5 Bearing Friction
The SKF web site, Interactive Engineering Catalogue has a proforma for calculating bearing friction. The method requires a value for the lubricant viscosity. However, it is proposed to run the bearings without lubricant. Provided the viscosity is less than 1500 mm2 s-1, the friction torque is independent of the viscosity. Therefore the calculations assume the “oil spot” lubrication option with v = 1500 mm2 s-1. The friction torque usually consists of two components; hydrodynamic and elastic deformation. Since the hydrodynamic contribution is non-existent, the calculated friction torques should be conservative, provided that no micro-welding effects occur. The turret bearing has a total friction torque of 9.1 N mm. The total friction torque of the gearbox shafts referred to this axis is 22.9 N mm so the total bearing friction torque is 32.0 N mm. As is required, the bearing friction torque is low compared to the friction brake torque of 500 N mm.
1.5.6 Grating Angle Repeatability
1.5.6.1 Shaft Torsional Deflection
Analysis shows that torsion in the drive shafts produces an image displacement of 0.052 pixels at the detector. The corresponding setting error is 0.0052 pixels.
1.5.6.2 Shaft Bending
The last gearbox shaft will undergo some bending deflection due to the gear load. This will cause a lateral shift of the pinion tooth and a corresponding rotation of the turret. The corresponding image displacement on the detector is 0.062 pixels, and the setting error is 0.0062 pixels. The effect of the middle shaft will be negligible because of the lower bending load and the gear ratio.
1.5.6.3 Turret Bearing Deflection
The turret bearings will undergo local deflection at the ball contact points. This will cause some turret rotational error. From Harris, “Rolling Bearing Analysis”, pg. 246, the radial deflection of a bearing without preload is
where Fr is the radial load, Z is the number of balls in the bearing, D is the ball diameter, a is the contact angle, and the constant has the units mm4/3 N-2/3. Applying this equation here gives a conservative estimate of deflection because the bearing is actually preloaded.
For the turret shaft lower bearing, Fr = 6.14 N, Z = 13 balls, D = 0.5 inches, and a = 20°, so the radial bearing deflection will be 0.37 μm. The upper bearing deflection is insignificant because the turret gear is almost coplanar with the lower bearing (Figure 173). The turret gear has a radius of 84 mm (Table 83) so the radial deflection corresponds to an angular deflection of 4.38 μrad or 0.140 pixels at the detector. The corresponding setting error is 0.0140 pixels.
1.5.6.4 Last Shaft Bearing Deflection
Using the theory applied to the turret bearing, the deflection of the last shaft bearings produces an image displacement on the detector of 0.104 pixels. The corresponding setting error is then 0.0104 pixels.
1.5.6.5 Dymamic Overshoot
When the stepper motor stops, the turret will decelerate over a certain angle under the effect of the friction brake torque. This will act to reduce the total windup by the dynamic overshoot amount that is dependent on the motor speed prior to reaching the end of the final step. This in turn depends on the motor torque, which is a function of the motor current, the step control mode, and whether the motor is running in half or full step mode.
For the 500 N mm brake friction torque and half step mode, the estimated overshoot is 0.304 pixels. The setting error resulting from torque variation is 0.0304 pixels.
1.5.6.6 Net Effect
The total setting error of the grating angle is the sum of the foregoing contributions, or 0.066 pixels.
1.5.7 Grating Angle Stability
The main purpose of the friction drag brake is to eliminate backlash in the grating drive system and so effectively lock the grating position during exposures. In principle, this eliminates grating angle change except when the system is being driven. In practice, there will be residual movements as the attitude changes, but these will be small compared to the repeatability error determined in §13.5.6.
1.5.8 Grating Tilt Stability in Spatial Direction
Various loading effects cause tilt in the rotation axis of the grating turret, and associated image displacement in the spatial direction on the detector. These are dealt with as follows.
1.5.8.1 Wind-Up Torque
Just as variations in drag brake torque causes grating angle setting errors, it also leaves variable wind-up torque in the drive train that causes variable tilt in the rotation axis of the grating turret. The corresponding error in image position is estimated to be 0.0040 pixels.
1.5.8.2 Turret Shaft Deflection
The turret shaft will undergo some bending deflection due to the weight it carries. The direction and amount of associated image shift will depend on the attitude of the instrument. Over a maximum attitude change of 15°, however, the image shift is negligible.
1.5.8.3 Turret Bearing Deflection
The differential radial deflections between the upper and lower turret bearings will cause a tilt in the turret axis and corresponding shift of the spectrum on the detector. Over a maximum attitude change of 15°, the associated image shift is calculated to be 0.0076 pixels.
1.5.8.4 Grating Flexures
The gratings are mounted on flexures to facilitate adjustment. The reaction loads they generate must not cause significant distortion of the grating surface, and so their stiffness is limited. This requirement must be balanced against the need for stability as the instrument changes attitude. The adopted design restrains the surface distortion to less than 50 nm. It allows a corresponding maximum image displacement of 0.0740 pixels over a 15° attitude change.
1.5.8.5 Net Effect
The foregoing image displacements that are dependent on instrument attitude combine as an arithmetic sum. The effect of the wind-up torque is independent, and so is added in quadrature. The net image displacement is 0.082 pixels.
1.5.9 Ball Diameter Variation
The bearing balls will vary slightly in diameter. With precision bearings, they will be graded within a range of typically 0.5 μm. Under no load conditions, with large and small balls diametrically opposite each other, an eccentricity of 0.25 μm would result. If, due to sliding, the balls were to change their positions relative to the races for a given turret position, then a grating positioning variation corresponding to 0.38 pixels at the detector would result, with approximately equal contributions of 0.19 pixels from the turret bearings and the last gearbox shaft bearings. In practice, the bearings are lightly preloaded and it appears that the preload is sufficient to cause enough deformation at the ball contact points to share the load between large and small balls but with the large balls taking a greater share. The effect is to substantially reduce the eccentricity and hence the positioning error.
1.5.9.1 Turret Bearings
The preload bearing geometry parameters and a deflection constant from Harris (Fig. 6.5) are used in equations from Harris to determine the loaded contact angle and corresponding axial deflection. This is resolved into components normal to the ball contact surfaces. Half of the ball diameter difference is subtracted from the normal deflection of the large ball and half is added to the normal deflection of the small ball. The lateral components of the resulting normal deflections are then calculated and the net axis eccentricity determined. Assuming the worst case scenario where the upper and lower bearing eccentricities are diametrically opposite, the resulting tilt of the turret axis causes a shift of 0.016 pixels at the detector.
1.5.9.2 Last Gearbox Shaft Bearings
The calculation method is the same as for the turret except that the net bearing eccentricity causes an effective error in the pinion tooth position, and therefore the turret angular position. The calculated effect is 0.012 pixels at the detector.
1.5.10 Thermal Response
A rough estimate of the grating thermal response time has been made. It was assumed that the gratings are attached to the turret by flexures having reasonable thermal contact (200 W C-1 m-2) at the joints. The turret is painted black, except for the grating surfaces, and has maximum practical radiative coupling to the cover and to the shaft. There will be some conductive coupling through the bearing ball contact points but, since this is hard to quantify, it has not been included. It is probable that the primary means of heat transfer to the turret and gratings will be via the friction brake and a conservative conductance of 10 W C‑1 m‑2 has been assumed. The actual value is expected to depend on the contact area and corresponding contact pressure. A torsionally stiff, flat, annular brake pad pressing against a similar surface on the turret gear wheel over the full surface is considered likely to have better thermal contact than if the surfaces are not parallel and have only edge contact, albeit at higher pressure.
It was optimistically assumed that the background temperature and the shaft temperature are fixed at 65 K from the start. The results indicate that, with the assumed brake conductance, the gratings will approach 65 K in about 2 or 3 days. With only radiative coupling it will take around 10 to14 days. Figure 174 shows predicted temperature versus time for these best and worst cases.
Figure 174: Predicted best and worst case grating cool down times.
1.5.11 Grating Mount
Several mounting schemes were considered for mounting the gratings. The adopted method is described as follows.
The grating is mounted on three aluminum alloy flexures with screws provided to adjust tilt in the spatial direction and azimuth rotation of the face, as shown in §5.5.4.9.1. The two lower flexure strips lie in a plane perpendicular to the grating face, and the upper strip lies parallel to the face. A spring-loaded screw passes through the center lug on one side of the grating, and allows the grating to be tilted about the lower flexures. Similarly, a spring-loaded tangent screw acts on the upper-left corner of the grating to allow face rotation. For tilt adjustment, the adjustment sensitivity is 500 pixels of image movement per millimeter of screw travel.
Together, the three flexures and the tilt-screw fully constrain the grating, so additional freedom is required to allow the face rotation adjustment. Attaching the upper flexure to the grating lug by means of a spring-loaded friction joint provides this by allowing slip to occur at this joint during adjustment. A pivot is provided to define the rotation center for this. It takes the form of a dowel that is machined onto the end of the screw that attaches the lower right grating lug to the flexure. This engages with a hole in the carrier turret.
An angular adjustment range of ±0.3° is provided. Operation of the adjusting screws bends and twists the flexures. This applies a bending moment to the grating that must not cause significant distortion of the grating face. This requirement must be balanced against the need to provide adequate mounting stability. To achieve this compromise, the flexures are 18 mm high, 1.2 mm thick, and 10 mm long. The resulting performance is specified in §13.5.8.4. The natural frequency of the mounted gratings is calculated to be 745 Hz.
1.6 Flip Mirror Assembly
The purpose of the flip mirror assembly is to place a plane mirror in the collimated grating input beam in order to provide an undispersed image of the slit “staircase” at the detector. The mirror surface is placed as near as practical to the grating in order to minimise pupil displacement and so maintain good camera performance.
The Flip Mirror optical element is a diamond turned surface on a 6061-T6 aluminum alloy blade.
The mirror blade shaft is supported in a pair of preloaded, precision, deep groove bearings, in order to remove radial clearances and ensure that the image position is repeatable to within 0.5 μm at the detector.
A stepper motor drives the mirror shaft via a 4:1 reduction pair of gears and a torsion spring. With the motor power off the mirror is then spring-loaded against hard stops in both the inserted or retracted positions. The stop for the inserted position is adjustable to control the angular position of the mirror. By driving the motor 10° past the nominal (90°) positions in either direction, sufficient preload is developed to counteract the changing effects of gravity as the telescope is moved. The detent torque of the motor is adequate to support the spring loading with motor switched off.
To prevent over-winding the torsion spring, hard stops are provided which limit the driven gear rotation to 110°. A micro-switch is mounted on each of these stops to provide position feedback and to cut the power to the motor.
1.6.1 Bearing Preload
Bearing preload is applied by carrying one of the two bearings on a pair of aluminum alloy diaphragms, and tensioning it against the other bearing. The diaphragms are axially separated to provide stiffness in all but the axial direction. The low axial spring constant of the mount allows light preload to be applied to the bearings that is insensitive to axial positioning errors. This allows the bearings to be safely run without lubrication.
1.6.2 Housing
The housing is designed such that machining is relatively simple, being machined from a single piece of 6061-T6 aluminum alloy, with most of the machining being from the top surface in one set-up. The 9 mm bores which locate the gear shaft and the mirror shaft bearings can be drilled from opposite ends with adequate alignment precision.
1.7 Pupil and Field Mirror Array Mechanical Analysis
This section presents bending, FEA, and natural frequency analysis for the pupil and field mirror array blanks. Figure 175 shows the blank deflection under self-load. The deflection is just 381 nm. This flexure in the pupil mirror array will cause the “staircase” slit image to move by 405 nm at the field mirror array, and 277 nm (0.015 pixels) at the detector. This effect is small compared to the Gemini specification of 0.1 pixels per 15° change in orientation. The same flexure in the field mirror array will cause a negligible displacement of the pupil image on the grating.
Figure 175: Pupil and field mirror blank deflection under self-load.
Figure 176 shows the effects of worst case clamping forces on the mirror array blanks. In this case the array is supported on its outer edges and a clamping screw force of 100 N is applied to each clamping screw. These forces bend the array by about 0.086 mm. This would bow the “staircase” slit image on the detector by a little more than two pixels, but the condition would be stable and insignificant relative to the intrinsic spectral line curvature.
Figure 176: Pupil mirror array deflection under worst case clamping conditions.
It is important that the natural frequency of the mirror array blank be well away from cryocooler vibrations. The principal vibration frequencies from the cryocoolers are near 2 Hz and 4 Hz as this is the piston cycle frequency, although there will be higher harmonics. Analysis shows that the lowest natural frequency of the mirror array plates is 1630 Hz.
1.8 Lens Retention System
All the lenses used in NIFS are axially located by pressing them against shoulders in the aluminum housings. Custom made wave springs manufactured from stainless steel shim are used to apply a force equal to about ten times the lens weight to ensure secure seating. The lens parameters are defined in Figure 177.
Figure 177: Lens parameter symbols.
Using these, the weight of the lens is
The lens parameters for all five NIFS lenses are listed in Table 84.
Table 84: Lens parameter values.
|
Lens Identification |
Material |
r (kg mm-3) |
dl (mm) |
tl (mm) |
r1 (mm) |
r2 (mm) |
W (N) |
|
Collimator Corrector |
Calcium Fluoride |
3.18´10-6 |
80.6 |
12.023 |
228.434 |
216.411 |
1.9 |
|
Camera 1 |
Calcium Fluoride |
3.18´10-6 |
95 |
18.25 |
155.964 |
-252.091 |
2.7 |
|
Camera 2 |
Fused Silica |
2.20´10-6 |
95 |
9 |
-193.957 |
-1141.467 |
1.7 |
|
Camera 3 |
Zinc Selenide |
5.42´10-6 |
89 |
9 |
93.105 |
80.989 |
3.2 |
|
Camera 4 |
Calcium Fluoride |
3.18´10-6 |
96 |
23 |
96.020 |
-252.091 |
3.3 |
|
Camera 5 |
Fused Silica |
2.20´10-6 |
65 |
6 |
-84.539 |
193.955 |
0.8 |
The wave spring parameters are defined in Figure 178.
Figure 178: Spring parameter symbols.
Using this and simple beam theory, the axial spring force is
and the maximum tensile stress is
For given functional parameters, it is desirable that the free parameters be chosen to minimize the maximum tensile strain. To facilitate this, the maximum tensile strain can be expressed as
Choosing low values of F, d, and n, and high values of ds, b, and E reduces strain. Using this theory, suitable parameters are selected and derived for all the required springs, as listed in Table 85. A single spring is used to support camera lenses 1 and 2 because they are mounted as a pair. In all cases, the springs are designed to have a free height of 4 mm and a compressed height of 1 mm. Parameter values common to all cases are b = 5 mm, d = 3 mm, n = 3, and E = 206000 MPa. The ultimate tensile strength of the spring material (stainless steel shim) is ~ 1100 MPa.
Table 85: Wave Spring Parameter Values.
|
Spring Identification |
ds (mm) |
ts (mm) |
F (N) |
s (MPa) |
|
Collimator Corrector |
81 |
0.5 |
30 |
520 |
|
Camera Lenses 1 & 2 |
90 |
0.6 |
38 |
500 |
|
Camera Lens 3 |
84 |
0.6 |
47 |
580 |
|
Camera Lens 4 |
91 |
0.6 |
37 |
490 |
|
Camera Lens 5 |
60 |
0.3 |
16 |
560 |
1.9 Lens Mount Cooling Strain
All of the lenses used in NIFS are radially located by mounting them in close fitting housing bores. In all cases the thermal contraction of the aluminum alloy housing is greater than that of the lens at operating temperature. The housing and lens tolerances are arranged so that the minimum clearance is zero under these conditions.
During the cooling process the lens temperature will lag behind the housing temperature, and it is therefore possible that a transient interference condition can develop. This phenomenon has the potential to fracture lenses, and so it is investigated here to ensure that the problem is avoided. If need be, the lens clearance can be increased at the cost of some increase in misalignment and consequent aberration.
The analysis used is conservative. With the cooling rate of the cryostat known, the temperature lag of the lenses is determined using the assumption that they are cooled by radiation alone. The clearances between lenses and housings is then determined from these temperatures using the thermal strain relationships presented in Appendix C (§12.11).
Data obtained from the NIRI web site has been used to model the cooling rate of the cryostat. If the time (sec) since the start of cooling is t, then the temperature (K) of the cryostat cold work surface plate (and lens housings) is
This relationship is plotted in Figure 179 over the range of time for which it is applicable.
Figure 179: Cryostat temperature versus cooling time.
The corresponding rate of temperature change is
The lag in the lens temperature is dependent on the spatial character of the cavity containing it. If this volume is large compared to the lens, it behaves as a black body and the rate of heat transfer is independent of its emissivity (but not that of the lens). If the cavity is closely conforming to the lens, then both emissivities are involved, but if they are equal (as they will tend to be), the rate of heat transfer will be twice that applicable for a large cavity. The cavity is here assumed to be large because this is both roughly realistic and conservative.
The emissivity of the lenses is assumed to be unity because they transmit only over relatively narrow wavelength pass bands. Over the wide range of thermal wavelengths they will be fully absorptive.
Cooling of the first two camera lenses will be further slowed because they are mounted close to each other and the adjacent surfaces are effectively disabled as radiators. These two lenses are therefore considered as the worst-case examples made from calcium fluoride and fused silica. A third lens of the camera is also considered because, even though it radiates from both surfaces, it is the only one made from zinc selenide.
The temperature lag is also dependent on the specific heat capacity of the lens materials. In general it is known that this decreases considerably as temperature is reduces, but the ambient-temperature values are used here because low-temperature data are not readily available. This assumption also makes the analysis conservative.
If the lens mass is m2, the lens specific heat capacity is C2, the lens radiating surface area is A2, the lens emissivity is x2,, and the Stefan-Boltzmann constant is s (5.67051´10-14 W mm-2 K-4), then the lens temperature is
The lens parameter values used here are listed in Table 86.
Table 86: Lens Parameters.
|
Lens Identification |
Material |
C2 (J kg-1 K-1) |
m2 (kg) |
A2 (mm2) |
x2 |
|
Camera Lens 1 |
Calcium Fluoride |
854 |
0.27 |
7088 |
1 |
|
Camera Lens 2 |
Fused Silica |
741 |
0.17 |
7088 |
1 |
|
Camera Lens 3 |
Zinc Selenide |
339 |
0.32 |
12442 |
1 |
The lens temperature lag derived from the foregoing theory is plotted in Figure 180.
Figure 180: Lens temperature lag during cryostat cooling.
The lens clearances corresponding to the predicted temperature lags are plotted in Figure 181.
Figure 181: Lens clearance to diameter ratio during cryostat cooling.
If it is conservatively assumed that the housing is entirely rigid, the ratio Clearance/Diameter can be read directly as the compressive strain in the lens when the value is negative.
From this, it can be seen that lens 1 never interferes with its housing. This is to be expected, because the thermal contraction of fused silica is extremely low, and in fact changes sign during cooling. It is actually slightly larger at operating temperature than at ambient temperature.
Lens 2 radiates from both sides and has relatively low specific heat capacity. The maximum compression is therefore very slight (-2×10-5 at 70 K). By comparison, the rupture strain for this material (zinc selenide) is –80×10-5.
Lens 1 (calcium fluoride) is by far the most adversely affected. It suffers maximum compression of ‑20×10‑5. Nevertheless, this is still low relative to the rupture strain of -50´10-5. Increasing the clearance in the fit by 20 µm would eliminate compression. Given that the width of the tolerance zone is 50 µm, such an increase would not significantly affect the alignment accuracy of the lens.