DEGREE PROJECT

Design of a variable focal length optics for a SWIR Earth observation camera

Sergio David Díaz Martínez

Spacecraft Design, master’s level (120 credits) 2021

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

Design of a variable focal length optics for a SWIR Earth observation camera

MASTER THESIS

Sergio David D´ıazMart´ınez

Lule˚aUniversity of Technology MSc in Spacecraft Design Abstract This thesis consists of a preliminary design study of a variable focal length optics for a SWIR Earth observation camera which is planned to be placed inside a 6U Cubesat. After the success of DRAGO instrument consisting on a SWIR camera onboard a Cubesat, which has been recently launched (January 2021), the Institute of Astrophysics of the Canary Islands (IAC) began this project with the intention of adding zoom optics to SWIR space imaging systems. This improvement will add versatility and it will allow changes in the effective field of view of the camera, hence achieving a certain magnification to study in more depth any region of interest. The main objective of this project is to provide a design solution for the presented challenge, where a mechanism has to displace different groups of lenses following their motion profiles in order to get the desired zoom. During this process different design options were evaluated. The chosen one consist of a ball screw mechanism where the rotation of the screw translates into linear displacement of the groups of lenses. The thesis presents a selection of commercial components constituting the mechanism, as one of the objectives of the project was to build a prototype of the mechanism. A structural analysis of the structure is done by using ANSYS simulations to ensure the viability of the design.

i Lule˚aUniversity of Technology

Acknowledgements Firslty, I would like to express my deepest gratitude to my supervisor Jos´eAlonso Bur- gal, for giving me the opportunity to work in collaboration with IACTEC in this beautiful, challenging project even though we are submerged in this tough times of pandemic. My biggest thanks to my mentor, Alvaro´ P´erez Garc´ıafor giving me support during this project. I would also like to thank to Pablo Gonz´alezde Chaves Fern´andezwho helped me giving me feedback during the entire period. I thank the rest of the team of IACTEC that is part of this project for their warm welcome and their help during this months. Lastly, special thanks to my family who are always supporting me.

ii CONTENTS Lule˚aUniversity of Technology

Contents

List of Figures v

List of Tables vi

List of Abbreviations vii

1 Introduction 1 1.1 Purpose & Aim ...... 1 1.2 Thesis Outline ...... 1

2 Theory 3 2.1 Zoom lens ...... 3 2.2 Considerations of the IR region ...... 3 2.2.1 Materials ...... 4 2.2.2 Athermalization ...... 4 2.2.3 Narcissus ...... 4 2.2.4 Vignetting ...... 4 2.2.5 Cold Stop and Cold Shield ...... 4 2.3 State of the Art ...... 4 2.3.1 ”Mechanism Design and Simulation of Continuous Zoom Lens” [26] . .5 2.3.2 ”Development of MWIR continuous zoom with large zoom range” [23] .6 2.3.3 ”Design of compact IR zoom telescope” [5] ...... 7 2.3.4 ”Two-Position IR zoom lens with Low F-number and Large Format”[9]7 2.3.5 ”The Development of a Compact Far Infra-Red Zoom Telescope” [7] . .8 2.3.6 ”Compact mid-wavelength infrared zoom camera with 20:1 zoom range and automatic athermalization” [12] ...... 8

3 Preliminary Design 9 3.1 Mission Overview ...... 9 3.2 Optical Subsystem ...... 10 3.3 Design Considerations ...... 12 3.3.1 Zoom Cam Mechanism ...... 12 3.3.2 Ball Screw Mechanism ...... 15 3.3.3 Chosen Design ...... 15

4 Design Setup and Analysis 17 4.1 Opto-Mechanical Design Setup ...... 17 4.1.1 Front Window ...... 17 4.1.2 Light Focusing ...... 18 4.1.3 Support Bearings ...... 19 4.2 Zoom Mechanism Breakdown ...... 20 4.2.1 Ball Screws ...... 20 4.2.2 Stepper Motors ...... 22 4.2.3 Couplings ...... 23 4.2.4 Rods ...... 23 4.2.5 Bushings ...... 24 4.2.6 Lens Supports ...... 24

iii CONTENTS Lule˚aUniversity of Technology

4.2.7 Components List ...... 25 4.3 Mass Budget ...... 25 4.4 Tolerance Analysis ...... 25 4.4.1 Radial Runout ...... 26 4.4.2 Axial Runout ...... 27 4.4.3 Axial Positioning Accuracy ...... 27 4.4.4 Expected Positioning Errors ...... 28 4.5 Structural Analysis ...... 29 4.5.1 FEM Analysis Setup ...... 29 4.5.2 Modal Analysis ...... 30 4.5.3 Quasi-static loads ...... 32 4.5.4 Random Vibrations ...... 34 4.5.5 Sinusoidal Vibrations ...... 36

5 Conclusion and Future Work 39

References 39

A Payload Constraints 42

B Components 43 B.1 Ball Screw ...... 43 B.2 Stepper Motor ...... 43 B.3 Coupling ...... 43

C Torque and Power Estimation 44

D Drawings 45 D.1 Lens Support 1 ...... 45 D.2 Lens Support 2 ...... 46 D.3 Lens Support 3 ...... 47

E Mass Budget 48

F Sinusoidal Vibrations 49

iv LIST OF FIGURES Lule˚aUniversity of Technology

List of Figures 2 Schematics of both optically and mechanically compensated zoom lenses. [14] .3 3 Diagram of continuous zoom cam mechanism.[26] ...... 5 4 Rail guides and lead screw drive.[23] ...... 6 5 The basic mechanical construction of IR zoom telescope.[5] ...... 7 6 Compact zoom telescope concentric cylinder arrangement.[7] ...... 8 7 Zoom lenses at 3 different positions and its ray trace...... 11 8 Zoom Cam Mechanism...... 13 9 Zoom Cam Mechanism without the rotating cam tube...... 14 10 Slewing Bearing ...... 14 11 Ball Screw Zoom Mechanism ...... 15 12 Mechanical design of half of the 6U Cubesat containing the opto-mechanical system...... 17 13 Zoom Out position and its ray trace...... 18 14 Zoom In position and its ray trace...... 18 15 Detail of ligth ray trace converging into the image sensor...... 19 16 Support Bearing of Ball Screw...... 19 17 FEM Setup...... 29 18 FEM Mesh...... 30 19 Modal analysis: Modes 1 & 2...... 31 20 Modal analysis: Modes 3 & 4...... 31 21 Modal analysis: Modes 5 & 6...... 32 22 Total deformation (left) and Equivalent stress (right) with X acceleration. . . . 33 23 Total deformation (left) and Equivalent stress (right) with Y acceleration. . . . 33 24 Total deformation (left) and Equivalent stress (right) with Z acceleration. . . . 33 25 Displacement (left) and Equivalent stress (right) with X acceleration...... 35 26 Displacement (left) and Equivalent stress (right) with Y acceleration...... 35 27 Displacement (left) and Equivalent stress (right) with Z acceleration...... 35 28 Equivalent stress with X acceleration (8-110 Hz)...... 37 29 Equivalent stress with Y acceleration (8-110 Hz)...... 38 30 Equivalent stress with Z acceleration (8-110 Hz)...... 38 31 Moving Group 1 Lens Support Drawing...... 45 32 Moving Group 2 Lens Support Drawing...... 46 33 Moving Group 3 Lens Support Drawing...... 47 34 Equivalent stress with X acceleration 1-8 Hz (left); 110-125 Hz (right) . . . . 49 35 Equivalent stress with Y acceleration 1-8 Hz (left); 110-125 Hz (right) . . . . 49 36 Equivalent stress with Z acceleration 1-8 Hz (left); 110-125 Hz (right) . . . . 49

v LIST OF TABLES Lule˚aUniversity of Technology

List of Tables 2 Orbital parameters ...... 9 3 Required values of the system...... 10 4 Zoom System Specifications ...... 10 5 Sizes of refractive lenses ...... 11 6 Linear displacement of the three moving groups of lenses ...... 12 7 Ball Screw Dimensions ...... 21 8 Rod Dimensions ...... 23 9 Bushing Dimensions ...... 24 10 Commercial Components List for the Ball Screw Zoom Mechanism...... 25 11 Ball Screw Zoom Mechanism Mass ...... 25 12 Description of alignment tolerances for Moving Lens Groups ...... 26 13 Radial Runout Contributions for each group of lenses.[25] ...... 27 14 Axial Runout Contributions for each group of lenses.[3] ...... 27 15 Axial Positioning Error for each group of lenses.[25] ...... 28 16 Positioning errors of each lens group...... 28 17 Z positioning error due to thermal expansion...... 28 18 Z displacement total error due to temperature changes for each moving group. 29 19 Modal Analysis Settings...... 30 20 Modal analysis natural frequencies...... 31 21 Quasi-static loads selected for the simulation...... 32 22 Quasi-static loads analysis settings...... 32 23 Quasi-static loads analysis results...... 33 24 PSD acceleration values...... 34 25 Random vibration analysis results...... 34 26 Envelope of sinusoidal vibrations...... 36 27 Sinusoidal vibration test profile...... 36 28 Sinusoidal vibration analysis results...... 37 29 Payload Constraints ...... 42 30 Ball Screw Specifications. [25] ...... 43 31 Stepper Motor Technical Characteristics. [18] ...... 43 32 Coupling Specifications. [22] ...... 43 33 Mass Budget...... 48

vi List of Abbreviations

BS Ball Screw CVCM Collected Volatile Condensable Material DOF Degree of Freedom DRAGO Demonstrator for Remote Analysis of Ground Ob- servations EFL Effective Focal Length FEM Finite Element Modelling FOV Field of View GSD Ground Sampling Distance LEO Low Earth Orbit LWIR Long-Wavelength Infrared MG Moving Group MTF Modulation Transfer Function MWIR Mid-Wavelength Infrared PSD Power Spectral Density SM Stepper Motor SS Stainless Steel SWIR Short-Wavelength Infrared TML Total Mass Loss 1 INTRODUCTION Lule˚aUniversity of Technology

1 Introduction

Short Wavelength Infrared light is typically defined as light in the 0.9 to 1.7 µm wavelength range. SWIR is similar to visible light in that photons are reflected or absorbed by an object, unlike Mid Wavelength Infrared (MWIR) and Long Wavelength Infrared (LWIR) light, where it is emitted from the object itself. [16] Due to minimal atmospheric influence or noise in this part of the electromagnetic spectrum as well as an enhanced ability to differentiate among ground materials, SWIR measurements are useful for many applications. SWIR serves for locating moisture on the surface, seeing through smoke and haze, identifying materials and detecting heat in order to identify hotspots on the ground during a fire. Some of the advantages of the SWIR band are that it can provide imagery during day and night, atmospheric aerosols have minimal effect on this band, it can penetrate clouds and haze and detect heat via high-heat thermal emissions. A valuable versatility to SWIR space imaging systems can be added by zoom optics, providing a variable focal length and so allowing changes in the effective filed of view of the camera to study in depth a region of interest. The design of a zoom system involves numerous challenges and issues to consider, specially when working on the infrared spectral band and dealing with Earth observing satellites, which are surrounded by a harsh space environment.

1.1 Purpose & Aim The objective of this thesis is to present a preliminary design of a variable focal length optics suitable for the SWIR camera DRAGO*. This implies the design and integration of complex mechanisms to move a specific group of lenses that are going to work remotely in space. To achieve this, the following steps needed to be completed: 1. Unerstanding of optics and study of zoom mechanisms’ principles. 2. Literature review on current designs of zoom mechanisms working on the IR region. 3. Trade-off between different design choices. 4. Preliminary design development and analysis

*Among the objectives of the project there was one subjected to COVID-19 evolution. The restrictions did not allow me to work physically at the installations of the Institute. The scope was to build a prototype and perform functional test after having a preliminary design of the zoom lens.

1.2 Thesis Outline In order to ensure that the thesis is easy to read and understand, it has been organized as follows: Section 1 is a brief introduction to the SWIR wavelength range, where it is explained why it is interesting observing at this wavelength range and what differences it with respect to other wavelength’s ranges.

1 1 INTRODUCTION Lule˚aUniversity of Technology

Section 2 begins with an explanation of the working principles of a zoom lens. Then it moves to the description of some phenomena related to the IR region and it finishes with a state of the art of different zoom mechanisms working on the IR range that has been developed over the last years by the industry. The following Section 3 is where the case of study is presented. It first gives a description of the mission overview and then it explains the optical system of the project, with its respective lenses and motion profiles. The last part of this section corresponds to the design part, where some considerations regarding with the design that have to be taken into account are explained. Lastly two possible design solutions are given and the final choice is explained. The next one is the main section of the project, where the decisions made along the project are explained and justified. Section 4 is divided in five subsections. First, the opto-mechanical setup is presented and then a breakdown of the different components constituting the zoom mechanism is done. After this, a mass budget of the instrument is given followed by a tolerance and a structural analysis of the zoom mechanism in question. Lastly, there is a conclusion of the project and suggestions for future work.

2 2 THEORY Lule˚aUniversity of Technology

2 Theory

2.1 Zoom lens A variable focal length or zoom lens consists of a number of fixed and movable elements which alter the focal length of the lens according to relative positions. The two primary optical principles involved are usually referred to as optical compensation and mechanical compensation. In the optical compensation zoom lens (Fig 2a), the moving elements are linked together and move as a single unit through the zoom range. This arrangement simplifies the mechanical construction and helps to maintain good control of boresight and alignment. In the mechanical compensation zoom lens (Fig 2b), typically one movable component pro- vides the change in magnification or focal length and defocusing is eliminated by a shift of one of the other elements of the zoom system. The moving components travel through the zoom range in a nonlinear relationship with respect to one another. [1] [14]

(a) Two different optically compensated zoom (b) Mechanically compensated zoom lens lenses

Figure 2: Schematics of both optically and mechanically compensated zoom lenses. [14]

Although the optical compensation zoom lens provides a simpler mechanism, they also tend to be longer than the mechanical compensation one and the image is not exactly focused on a constant plane. Almost all infrared zoom lenses are mechanically compensated.

2.2 Considerations of the IR region Infra-red zoom lenses are rare because they require a high state of correction (in order to work near to the diffraction limit at high spatial frequencies) and because of the problems associated with materials at this wavelength.

3 2 THEORY Lule˚aUniversity of Technology

2.2.1 Materials Selection of IR materials is based primarily on transmission since this property varies sub- stantially with the material and wavelength. There is a large number of optical materials that transmit in the infrared region of the spectrum. However, when considering physical characteristics, workability and cost, this amount of materials is quite limited. The cost of materials for infrared lenses is very high when compared with that for visible systems.

2.2.2 Athermalization Athermalization is the process of stabilizing an instrument’s optical performance by designing the optics, mounts, and structures to compensate for temperature changes. There is a significant problem in the infrared region with the focus shift with temperature, therefore a lot of effort is put into the correction of this effect by different mechanical and optical methods, active and passive. [14] [27]

2.2.3 Narcissus Narcissus occurs when the detectors sense variations in the amount of background radiation reaching them via reflections from lens surfaces. Narcissus reduction techniques include improved multilayer antireflection coatings on the offending lens surfaces and optical designer- controlled methods.[8]

2.2.4 Vignetting In an infrared application, any vignetting is unacceptable because it will lead to a false indication of a temperature differential at the image plane.

2.2.5 Cold Stop and Cold Shield The cold stop is an aperture or baffle which prevents the detector from looking at any extra- neous stray radiation. If it is not the aperture stop of the system, it is a cold shield.

2.3 State of the Art A research on the different zoom systems developed over the last years has been done for a better understanding of the state of the art of zoom mechanisms in general and zoom mechanisms for the infrared wavelength in particular. The main purpose of this section is to provide information about what are the solutions proposed for the industry regarding with zoom systems working on the infrared band of the electromagnetic spectrum, as this region presents some specific problems as those mentioned in section 2.2. Here below there will be described some infrared zoom mechanisms developed by the industry until now that are considered to be relevant for the present project.

4 2 THEORY Lule˚aUniversity of Technology

2.3.1 ”Mechanism Design and Simulation of Continuous Zoom Lens” [26] This paper describes two kinds of cam mechanism that take care of the zoom and focusing function of a traffic monitoring system for a wide range of visual field monitoring. This mechanism is designed for an operating wavelength from 380 nm to 950 nm, with 30x zooming ratio employing a mechanical compensation four-component zoom.

Figure 3: Diagram of continuous zoom cam mechanism.[26]

A diagram of this zoom cam mechanism is shown in the figure 3 above. The zoom cam mechanism designed in this paper mainly includes zoom cam, guide screws, guide rings, high-precision linear guide shafts and high-precision linear bearings. The zooming process is as follows: when the zoom cam is rotated, the zoom lens group and the compensation lens group are synchronously moved to the corresponding positions under the action of guide pins and guide rings. With the guide of the high-precision guide shaft and the linear bearing, the rotational motion of zoom cam is converted into the linear motion of zoom lens group and compensation lens group in the direction of the optical axis, thereby achieving continuous zooming of the system.

5 2 THEORY Lule˚aUniversity of Technology

2.3.2 ”Development of MWIR continuous zoom with large zoom range” [23] This paper describes a thermal imaging zoom system for the mid wavelength infrared band, between 3-5 µm, with greater than 30x zoom range. One key feature included in the design was athermalization, an active thermal compensation approach was used to cover a broad thermal range.

Figure 4: Rail guides and lead screw drive.[23]

The housing of this design has upper and lower halves, each supporting one drive mechanism. The IR lenses are bonded in their cells with athermalizing bond gaps. Both movable lens groups use a similar carriage design, guided by two rails each, shown in figure 4. Each primary rail locates the carriage by a collinear pair of linear bearings. The secondary rail and single linear bearing prevents that the carriage subassembly rotates about the first rail. The carriages are each positioned along the optical axis by a lead screw and anti-backlash lead nut which is flangemounted to the carriage. In this design the lead screw is supported by a pair of preloaded duplex bearings at the driven end, while the other end is radially constrained by the lead nut.

6 2 THEORY Lule˚aUniversity of Technology

2.3.3 ”Design of compact IR zoom telescope” [5] This paper presents a compact IR zoom telescope mechanically compensated with magnifi- cation from 2 to 6 times at 8-12 µm wavelength.

Figure 5: The basic mechanical construction of IR zoom telescope.[5]

In the design shown in figure 5, zooming lens and compensating lens groups possessing three roller followers for each are controlled by the stationary control cylinder, on which there are three pairs of cam slots where six followers are attached. When the outer cylinder having six linear slots is rotated, it will force the followers, ie. the two lens mountings, to turn, resulting in smoothly turning and moving the two groups. The effect of air gap between the follower and the slot on backlash in the cam track is eliminated by special design of elastic construction of the roller follower. By the force from the elastic roller, the effective roller is always in contact with one tracking surface.

2.3.4 ”Two-Position IR zoom lens with Low F-number and Large Format”[9] This paper describes the optical, mechanical and servo designs for a motorized, two-FOV Infrared objective lens for use in the 8-12 µm spectral band. Three lenses are moved by a DC servo motor which drives a precision ball screw via a 9 to 1 gear train. An anti-backlash ball nut is mounted to the screw and the slide tube containing the lenses is fastened to the ball nut with a bracket. The lenses are moved axially to change the FOV and to focus. These lenses are housed in a cylindrical structure called slide tube. The slide tube slides inside a bore in the main housing.

7 2 THEORY Lule˚aUniversity of Technology

2.3.5 ”The Development of a Compact Far Infra-Red Zoom Telescope” [7] The work presented describes a 3:1 ultra compact thermal imaging zoom telescope.

Figure 6: Compact zoom telescope concentric cylinder arrangement.[7]

The unit shown in figure 6 consists of four concentric cylinders which are machined as matched sets. The system is inherently self centring because of this concentric cylinder arrangement and this means that no optical alignment is necessary. The inner two cylinders carry the zoom elements and the outer cylinder carries the front (focussing) lens. The fourth cylinder is fixed to the back plate of the lens. All four cylinders are keyed together to prevent relative rotation. The motions of the zoom elements are achieved by means of cam followers located in an accurately machined double cam cylinder, which is rotated by a d.c. servo motor and gearhead.

2.3.6 ”Compact mid-wavelength infrared zoom camera with 20:1 zoom range and automatic athermalization” [12] This paper discusses the development of a compact mid-wavelength infrared zoom camera with a zoom range of 20:1 with automatic athermalization. The main mechanical issue in the development was the realization of a high accuracy and compact mechanism that can also ensure the accuracy of dynamic axial positions of the moving groups. The approach for this was to utilize lead screws of 1 mm pitch, guide bars of 8 mm diameter and a stepper motor. One end of a lead screw is fixed in front of the mainframe with bearing, and the other is directly connected to the stepper motor without any aids of gears, resulting in a simple configuration.

8 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology

3 Preliminary Design

After the explanation of the theoretical background of the project and having a better idea of what are the most common zoom mechanism working in the IR region used by the industry, it is time to move to the next step where the zoom mechanism solutions are proposed based on the mission constraints and the optical subsystem requirements. The camera will be responsible of taking and processing the images, while the platform will be responsible of generating and storing power, pointing the instrument and communicating with the ground segment.

3.1 Mission Overview The proposed concept is a SWIR camera mounted on a 6U Cubesat orbiting in a LEO orbit, with an orbit height range between 500 km and 650 km. The orbital parameters selected for this mission are shown in table 2 below.

Parameter Value Orbit type Sun-Synchronous Orbital height 500-650 km Orbits per day 14.1-16.4 Orbit inclination 97.769°

Table 2: Orbital parameters

Once in the LEO orbit, the Cubesat will be submerged in an environment that is potentially damaging to materials and to optical systems, including electronic controls and components. Some phenomena that will influence the reliability and long life of the Cubesat mission that have to be taken into account for the opto-mechanical design of the camera are: • Atomic Oxigen • Ionizing radation • Micrometeoroids • Debris • Outgassing In order to ensure reliability and long life of the Cubesat, there are some prohibited materials listed on Appendix A that have to be avoided in the design. Regarding with the ”Cubesat Design Specification” [19], Cubesat materials shall satisfy low out-gassing criteria to prevent contamination of other spacecraft during integration, testing, and launch (TML <1 % and CVCM <0.1 %). The preferred structural materials are Aluminum Alloys (Appendix A). With respect to the functionality and performance of the zoom system that will be designed, table 3 below shows the required values of the following parameters:

9 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology

Parameter Value Comments GSD min 20-50 m Consider sensor 640x512 pixels, pixel size 15 µm GSD max 150-200 m Consider sensor 640x512 pixels, pixel size 15 µm Swath (GSD min) >12 km Could be increased with a sensor 1280 Swath (GSD max) >90 km Could be increased with a sensor 1280 Optics Overal Transmittance >75 % Including SWIR filters MTF @ Nyquist Freq. >40 % Including sensor performance

Table 3: Required values of the system.

3.2 Optical Subsystem The optical system is in charge of properly focusing the light in the SWIR band into the focal plane where the SWIR image sensor is placed. Its main functions are: • Image forming into the focal plane • Zooming function • Band discrimination to the required wavelength range • Stray-light rejection The zoom system is based upon the following specifications:

Characteristics Value Zoom Range 2X Wide Angle Configuration EFL 150 mm Telephoto Configuration EFL 300 mm Spectrum 1 - 1.6 µm

Table 4: Zoom System Specifications

In table 4 wide angle and telephoto configurations correspond to zoom out and zoom in positions, respectively. For the present project the optical design will be implemented by refractive elements (lenses) instead of reflective (mirrors) with the purpose of keeping the design as simple as possible. The optical system for which the zoom mechanism is going to be developed consists of 5 refractive lenses grouped in three different moving groups: two pairs of lenses moving together and a third moving group consisting on a single lens. Figure 7 below shows the range of motion of the lenses and its ray trace. In order to know how much space is needed for the placement of the optical system inside the Cubesat, the distance between the first and the fifth lenses has to be measured. Hence, the position of the first lens in the wide open position of the zoom is determined and then the position of the fifth lens when the zoom is fully retracted is also determined, thus having a total distance between those positions of 252 mm.

10 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology

Figure 7: Zoom lenses at 3 different positions and its ray trace.

Lens Diameter (mm) Width (mm) 1 80 19.17 2 80 15.79 3 72 21.75 4 72 33.26 5 50 13.65

Table 5: Sizes of refractive lenses

From figure 7 it can be seen that lenses 1 and 2 move together forming a doublet, thus having the moving group 1; lenses 3 and 4 form moving group 2; and finally lens 5 is moving group 3. Table 5 shows the sizes of the 5 lenses and table 6 shows the linear displacement of the moving groups of lenses between three different zoom positions. From the data shown, it can be seen that moving group 1 and moving group 3 have the same displacement and moving group 2 moves with a different ratio. Although it can be deduced from figure 7, it is important to make clear that lens 1 is the first lens of the optical system, which means that light comes to it directly from space, being lens 5 the last one of the optical system, where light ray trace converges into the SWIR image sensor.

11 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology

Displacement between Displacement between Total Displacement positions 1-2 (mm) positions 2-3 (mm) (mm) MG1 45.89 44.1 89.99 MG2 25.26 32.17 57.43 MG3 45.89 44.1 89.99

Table 6: Linear displacement of the three moving groups of lenses

3.3 Design Considerations During the development of a zoom mechanism there are several design options. Each design option has its pros and cons and its own limitations and they will affect differently in the camera’s weight, cost, performance and complexity. It is a matter of taking the corresponding decisions based on a prior study of the available options for developing a zoom mechanism that best suits the presented challenge. The aim of a zoom mechanism is to adjust the effective focal length, EFL, of an optical system. In this project, the EFL is adjusted by moving the 3 lens groups presented above in figure 7. In this optical system, groups 1 and 3 have the same motion profile while group 2 has a different one. The proposed design has to maintain strict alignment requirements for the moving lens groups over their range of motion and throughout operational environments without detriment from backlash or thermal distortions. The idea is that half of the 6U Cubesat is dedicated for the zoom mechanism itself as the optical system occupies close to 250 mm long just with the displacement of the lenses (section 3.2). Hence the rest of subsystems will be placed on the other half of the Cubesat. As the camera is going to be placed inside a Cubesat in a LEO orbit in space, some important challenges that the mechanical design has to confront are: • Weight • Structural alignment and gravity release • Alignment accuracy and temperature change • Launch survival and verification • Harsh environment survival • Cost Although there are many types of zoom mechanisms, two possible solutions have raised based on the requirements and constraints of the present case of study and also taking into account the solutions used in the industry that were exposed in the state of the art in section 2.3. After presenting both possible solutions and doing a brief analysis, one of them will be selected as the final solution.

3.3.1 Zoom Cam Mechanism The first option presented in this project consists of a zoom cam mechanism that includes a zoom cam, a slewing bearing, guide pins, linear bearing slide rails and sliding carriages.

12 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology

Figure 8: Zoom Cam Mechanism.

Based on the principle of the zoom cam mechanism, when the zoom cam is rotated, this rotational motion is converted into the linear motion of the zoom lenses in the direction of the optical axis. [26]. To achieve this, three non-linear curve grooves are machined on the circumference of the cam (see Figure 8). The optical curve of the optical system is converted into the zoom movement trajectory of the actual moving groups of lenses, which are driven by guide pins to move in the direction of the optical axis. The zoom mechanism shown in figures 8 and 9 moves the three groups of lenses simultane- ously as follows: A stepper motor rotates a pinion gear that meshes with a gear of a slewing bearing attached to the cam tube, then the cam tube rotates accordingly and the guide pins follow motion profiles prescribed by cam slots cut around the circumference of the cam tube, thus making each zoom group move axially along linear bearing slide rails.

13 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology

Figure 9: Zoom Cam Mechanism without the rotating cam tube.

There are two barrels placed concentrically: the one placed at the exterior part rotates accordingly to the rotation transmitted to the slewing bearing by the pinion gear of the motor and the barrel placed in the interior stays motionless. The latter is the one were the rails are fixed. This motion is achievable thanks to the slewing bearing shown in figure 10, whose exterior part rotates but its interior part maintains stationary.

Figure 10: Slewing Bearing

The exterior barrel (shown in figure 8) has the three curve grooves where the pins are guided

14 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology when the barrel rotates while the static interior barrel (shown in blue color in figure 9) has a straight groove to allow the free linear motion of the guide pins displaced by the rotating barrel.

3.3.2 Ball Screw Mechanism The second option presented consists of a ball screw zoom mechanism that includes two stepper motors, two ball screws, two couplers, two guide rods and linear bearings among other components. The zoom mechanism shown in figure 11 moves the three groups of lenses as follows: There are two stepper motors, each one coupled to a ball screw. One ball screw is in charge of moving the first moving group and the other ball screw moves the second moving group. Rotation of each ball screw results in translation of the moving group coupled to it along the axis of each ball screw, which is parallel to the optical axis. As the motion profile of moving group 1 and moving group 3 is identical, both groups have been coupled by two union plates (shown in green color in figure 11), as a consequence, the displacement of moving groups 1 and 3 is the same.

Figure 11: Ball Screw Zoom Mechanism

3.3.3 Chosen Design A brief analysis has been done in order to decide which of the two options between zoom cam mechanism and ball screw zoom mechanism would be more suitable for the desired zoom lens. At first sight, one of the main differences is that the ball screw solution requires the use of two stepper motors whereas in the case of the zoom cam mechanism, all moving groups

15 3 PRELIMINARY DESIGN Lule˚aUniversity of Technology can be displaced at once with just one motor. This factor plays in favour of the zoom cam mechanism as power consumption, internal thermal dissipation and reliability drive the design to the minimum number of motors. However, when using cam actuation for the moving group, this type of mechanism usually requires wet lubrication, which has to be avoided in consideration of potential of lubrication leakage and outgassing, as it could affect the optical surfaces. Also, a mechanical cam is not desirable for a spaceborne zoom lens, as it happens to have reliability problems with long term operation in hard vacuum. [10] Nevertheless, the biggest limitation of the mechanisms designed for the present optical system is its size. The zoom mechanism is thought to work inside a 6U Cubesat, i.e. 100 mm x 200 mm x 300 mm, considering that the largest lens has a 80 mm diameter, there is a very narrow margin to work with. In figures 8 and 9 where the zoom cam mechanism design is shown, it can be seen that each lens support is attached to the sliders on the rails, then the rails are fixed to the static lens barrel and then outside this barrel, the rotation barrel is placed. It is clear that the zoom cam mechanism design goes out of limits of size constraints, as there is just a 20 mm margin from the 80 mm diameter of the largest lens (lenses 1 and 2 shown in figure 7) and the smallest dimension of the Cubesat, 100 mm. This gives no choice for selecting another option rather than the ball screw one. From now on, the project will focus on the Ball Screw Zoom Mechanism design solution.

16 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

4 Design Setup and Analysis

In this section, the final design option chosen in section 3.3.3 will be described and analyzed in detail. The decisions made are explained thoroughly in order to justify the chosen choices.

(a) 3U Cubesat Front Part. (b) 3U Cubesat Rear Part with open walls.

Figure 12: Mechanical design of half of the 6U Cubesat containing the opto-mechanical system.

In figure 12 above, two representations of the part of the Cubesat containing the opto- mechanical system are shown. Figure 12a is a view of the front part of the Cubesat while figure 12b is a view of its rear part. In this second figure, the walls of the Cubesat have been removed to show that the zoom mechanism fits inside the dimension constraints given by the outside structure of the Cubesat. In figure 12 it is shown that the front part has a window, whose purpose is explained in section 4.1.1, the sensor assembly on the rear part is also shown . Figure 12 shows half of the 6U Cubesat, the other half of the satellite will contain the electronics and the rest of necessary equipment, as it was explained in section 3.3. As the aim of this thesis is focuses on the design of the variable focal length optics, this is the part that has been represented, omitting the other half of the Cubesat.

4.1 Opto-Mechanical Design Setup In this section, some important aspects to be considered for the proper functioning of the optics are explained.1

4.1.1 Front Window A window is used as a transparent interface between the internal components and the out- side environment. This window allows the desired radiation to pass through with minimal

1NOTE: In the following figures, the structure of the Cubesat is hidden to get a clearer vision of the zoom elements.

17 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology effect on intensity and image quality. Its main purpose is to avoid dirt, moisture and other contaminants to reach the internal components. [27] As the camera will be working on the SWIR spectral band, the window must not radiate due to its temperature in a manner that interferes with its function.

4.1.2 Light Focusing An essential feature of the opto-mechanical design is that light needs to be focused into the focal plane in which the SWIR image sensor is placed (section 3.2).

Figure 13: Zoom Out position and its ray trace.

Figure 14: Zoom In position and its ray trace.

Above, the mechanism is shown in its zoom out position (figure 13) and in its zoom in position (figure 14). The total displacement of this linear motion is 89.99 mm for moving groups 1 and 3 (the one on the left and the one on the right united by the green plate) whereas for moving group 2 (the one in the middle) the total displacement is 57.43 mm (see table 6 in

18 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology section 3.2) . It can be seen that with the optical system formed by refractive lenses designed by the optical engineer, the ray trace of light converges into the image sensor in both zoom positions. Figure 15 below shows better this feature.

Figure 15: Detail of ligth ray trace converging into the image sensor.

4.1.3 Support Bearings In the assembly of the ball screws, each one has a ball nut and end support bearings. The use of these support bearings has a significant influence on the rigidity and buckling load of the screw assemblies. The design proposed has fixed support bearings with angular contact ball bearings which counteract both axial and radial forces on the screw.

Figure 16: Support Bearing of Ball Screw.

19 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

In figure 16 above, the support bearing is shown. It is placed between the coupling (section 4.2.3) and the ball screw nut. In this figure it can also be seen the stepper motor (section 4.2.2) connected to the other side of the coupling.

4.2 Zoom Mechanism Breakdown With the purpose of explaining the functioning of the zoom mechanism, a breakdown over the different elements constituting the design has been done. Here it is explained the function of each design element, its characteristics and finally it is presented the commercial solution chosen for each component. The reason of adding this last part is because as it was mentioned in section 1.1, one of the objectives of this thesis was to build a prototype. Although it was not possible to build a prototype during the development of this thesis due to COVID-19, the selection of components has been done as it is expected that the Institute of Astrophysics continues working on this project later on. As the designed zoom mechanism principle is based on the rotatory motion of a ball screw, this is the first element that will be described in this section. The elements that will be discussed are: 1. Ball Screws 2. Stepper Motors 3. Couplings 4. Rods 5. Bushings 6. Lens Supports

4.2.1 Ball Screws The screw mechanism is in charge of producing linear motion by its own rotation in the assembly. It receives a rotatory torque from the stepper motor. In comparison, ball screws have lower friction than other types of screws, which allows them to have a higher mechanical efficiency. This is an important factor to take into consideration for the high level of performance desired in the zoom operation, where it is needed to approach an exact position for each moving group in order to provide the magnification range designed. Another important factor for choosing a ball screw is its manageable backlash. The level of backlash is important within a ball screw design as it has an impact on the repeatability, which is the capability to repeatedly, precisely and continuously reach the exact same position that it reached before under the same operating conditions. In ball screw systems, this effect can be mitigated. Ball screws have other characteristics that may have been less important when choosing a screw drive mechanism for the desired zoom as for example its high force capabilities and the fact that they are ideal for high duty cycle application that demand high thrust levels. Among the disadvantages of ball screw mechanisms, it has to be mentioned that they require lubrication, which presents problems for space application. The low pressure environment

20 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology contributes to rapid evaporation of the liquid grease lubricants, what could result in contam- ination of the optical surfaces. The use of special grease for space application is mandatory. Other drawbacks of ball screw mechanisms are the noise created due to the sound produced by the balls circulating through the nut and its susceptibility to damage due to shock loading, which special attention should be paid to it during the satellite launch. For the implementation of the ball screw mechanism into the zoom for the SWIR camera, it had to be considered that three groups of lenses needed to be moved. As it was explained before in section 3.3, two of these three moving groups have the same motion profile. Early in the design, one of the options considered was to use a single ball screw with variable pitch with the purpose of moving all groups of lenses employing just one stepper motor and one ball screw. This option was discarded later because of its manufacturing and design complexity in benefit of the present design where two stepper motors and two ball screws are used. Each ball screw is in charge of moving one group of lenses, the remaining group is not moved by the ball screw but by the moving group that has its same motion profile, to which it is attached via two union plates.

• Commercial Component For the selection of the ball screws, the following dimensions according to the design presented were considered:

Parameter Value (mm) Nominal Diameter 6 Total Length 250 Thread Length 220 Lead 1

Table 7: Ball Screw Dimensions

After searching for precision ball screw’s manufacturers that have products that meet the required dimensions (SKF, Steinmeyer, Bosch, etc.), the chosen one for this project is a ball screw manufactured by THK. In Appendix B.1 the specifications of the selected ball screw are shown. For the later calculation of the travel distance per step angle of the ball screw-stepper motor assembly (see section 4.2.2), first it is necessary to know the travel distance per turn of the ball screw. Travel distance per turn is calculated as follows:

L = z · ph (1) where • L: Travel distance (mm) • z: Number of thread starts • ph: Thread pitch (mm)

21 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Thus having: Travel distance per turn: L = 1 · 1 = 1mm

4.2.2 Stepper Motors The rotating motion of the ball screw is given by the stepper motor. Its shaft is coupled to the ball screw via a coupling (see section 4.2.3), thus transmitting the rotation. A stepper motor converts digital pulses into mechanical rotation. Each pulse rotates the shaft by one step, hence having a large number of digital pulses gives a smooth rotation of the shaft. The stepper motors advantages are its position control, high reliability and long life. [15] As it was previously discussed in section 3.3.3, in order to minimize power consumption and internal heat, it is desired to have the minimum number of motors. In the design proposed there are two stepper motors, one for each ball screw.

• Commercial Component The criteria followed for the selection of the stepper motors were: • Motor Size • Power Consumption • Temperature Management • Vacuum Resistant With regard to the size, the envelope of the body of the stepper motor should not exceed 22 mm x 22 mm x 40 mm. After searching for suitable stepper motors for the ball screw zoom mechanism, the stepper motor series for SPACE applications manufactured by the company Phytron was chosen. This company offers products that optimise weight, power consumption and thermal dissipation. At the same time these motors are designed for withstanding high shock and vibration loads, ambient temperatures from -40 °C to +120 °C and for radiation of up to 106J/kg. More information about the technical characteristics of this component is given in Appendix B.2. On the one hand, in the previous section the travel distance per turn of the ball screw was calculated. This value is necessary to calculate the travel distance per step angle that the ball screw-stepper motor assembly can provide. As the stepper motor selected has a 1.8°step angle, the assembly can provide a precision of: Travel distance per step angle = 1.8 · 1/360 = 0.005mm = 5µm On the other hand, an estimation of the minimum torque necessary to move each ball screw was done to verify that the selected stepper motor fulfills the requirement. For this, the minimum torque necessary was estimated for the case of working under earth gravity con- ditions. Appendix C shows the calculation for this estimation, having a minimum torque of 1.64 mNm and a power of 68.8 mW

22 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

4.2.3 Couplings For the design of the zoom mechanism, two options were considered for the attachment of the screw to the motor: Via a coupler or integrating the screw directly into the motor. On the one hand, the use of a coupler adds length to the system and can introduce windup, backlash and hysteresis, thus affecting positioning accuracy and repeatability. On the other hand, having a direct fit of the screw to a hollow shaft within the motor gives higher accuracy alignment. This method would require laser weld on the back of the motor. Although this explanation makes clear that for the performance of the zoom it would be better to attach the screw directly to the motor due to its higher accuracy alignment, it was not possible to find a commercial stepper motor with hollow shaft that fulfilled the criteria of selection presented in section 4.2.2. The range of possibilities for choosing stepper motors with hollow shaft is very limited, and it is even more difficult to find this hollow shaft type for the dimensions requested and with the purpose of using it for a space application. Consequently, the design of the zoom mechanism includes two couplings in charge of connect- ing in-line the stepper motors with the screws, thus transmitting the rotating motion given by the motor to the ball screw.

• Commercial Component The coupling has to connect the ball screw shaft with the stepper motor shaft, both of them having 6 mm. The chosen component is a one piece rigid coupling with precision honed bores to ensure they are collinear and do not introduce misalignment into the system. Additional information of the component is given in Appendix B.3.

4.2.4 Rods Rods are in charge of guiding linear displacement of the three lens moving groups in the optical axis direction. There are two rods in the design placed parallel to the axis of the ball screws and parallel to the optical axis at the same time. The three lens moving groups are linearly guided by the rods by means of their lens supports (see section 4.2.6).

• Commercial Component It is important that these rods have tight manufacturing tolerances and ensure axial rigidity to not influence in lens supports positioning. The desired dimensions for the rods are:

Dimension Value (mm) Diameter 5/6 Length 250

Table 8: Rod Dimensions

23 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

The chosen component is manufactured by PBC Linear (section 4.2.7).

4.2.5 Bushings Bushings are placed between lens supports and rods. Their duty is to reduce friction between the surfaces sliding against each other and thus improve efficiency and reduce vibration and noise.

• Commercial Component For the design proposed, bushings have the following dimensions:

Dimension Value (mm) Internal Diameter 5/6 External Diameter 12

Table 9: Bushing Dimensions

In section 4.2.7 there is more information of the commercial component chosen manufactured by PBC Linear.

4.2.6 Lens Supports Lens supports play an important role in the functioning of the whole system. These elements have to maintain the strict alignment requirements for the moving groups of lenses over their range of travel without detriment from backlash or thermal distortions. There are three different lens supports: • The first lens support is in charge of holding moving group 1, which is a doublet (see Section 3.2). This support is connected to its ball screw via a ball screw nut, what makes it move along the ball screw axis (parallel to the optical axis of the system) when the ball screw is rotated. This support has two bushings that connects it with the two rods in order to ensure that the linear displacement of the moving group of lenses is guided along the optical axis without deviating. • The second lens support holds moving group 2, also formed by two lenses. Its design its similar to the first lens support but having different width. This support is connected to the other ball screw as its linear displacement is different from moving groups 1 and 3. • The third lens support holds moving group 3, formed by a single lens. This support is not connected to any ball screw. As it was explained in section 3.2, this moving group has the same linear displacement as moving group 1, therefore two union plates between the first lens support and the third lens support are attached to them with the purpose of transmitting the linear movement given to moving group 1 by its ball screw. For these lens supports, no commercial product was available as their design is very specific. Appendix D.1, D.2 and D.3 show the drawings of the three lens supports. These drawings were done with CREO Parametric.

24 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

4.2.7 Components List Table 10 below collects the discussed selection of commercial components for the zoom mech- anism.

Component Manufacturer and Ref. Details Ball Screw THK: BNK MDK 0601-3 Diameter 6 mm, lead 1 mm. Stainless steel. Stepper Motor Phytron: Physpace 19-2 Bore (B1) 6 mm, Bore (B2) 6 mm. Rigid Coupling Ruland: MCLX-6-6-SS Coupling. Rod PBC Linear:NIM05SS-xxxx Diameter 5 mm. 440 Stainless steel. Bushing PBC Linear: EP5G Internal diameter 5 mm. External diameter 12 mm

Table 10: Commercial Components List for the Ball Screw Zoom Mechanism.

4.3 Mass Budget The initial estimation of the ball screw zoom mechanism mass together with the lenses is 2109.4 g. Table 11 below shows the sum of the different components contributions to the total mass of the mechanism.

Component Mass (g) Moving Group 1 552 Moving Group 2 618 Moving Group 3 161 Ball Screw Assembly 434 Guiding Assembly 142 Walls 193 Bolts 10.4 TOTAL 2109.4

Table 11: Ball Screw Zoom Mechanism Mass

Appendix E shows a more detailed mass budget table with the complete list of weights.

4.4 Tolerance Analysis A Tolerance Analysis has been performed with the purpose of seeing the contributions of the different elements in the positioning and inclinations of the optical elements. It is also important to perform such an analysis in order to facilitate later work of the optical designer when considering the sensitivities of the design. Tolerance analysis is a powerful tool that allows the designers to estimate the effect of indi- vidual tolerances on final design requirement of an assembly, where all machined parts have mechanical uncertainties on their dimensions due to the manufacturing process. In order to determine the performance and quality of the assembly, it is important to identify the mechanical components that directly affect to this positioning of the optical elements. [6] [11]

25 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

In an opto-mechanical system, each optical element and lens group is required to be positioned within prescribed tolerances. Table 12 below shows the description of the tolerances required for the listed degrees of freedom that usually are drivers for a mechanism design.

DOF Name Description The radial distance (in orthogonal directions, X and Y) between Decenter the nominal optical axis and the center of the element or group Tip/Tilt The angular tilt of the element or group about X and Y axes The axial distance (in Z direction) between an element Despace or group and its nominal axial position

Table 12: Description of alignment tolerances for Moving Lens Groups

The design consists of a zoom mechanism based on two ball screws, being this elements the main source of inaccuracies. As ball screws are rotating elements, it is necessary to analyze the Runout of the mechanism, where Runout is the inaccuracy in a rotating mechanism where rotation does not occur exactly in line with the main axis [4]. In sections 4.4.1 and 4.4.2 the two main forms of this inaccuracy are analyzed.

4.4.1 Radial Runout It is related directly to the optical axis alignment between the optical components on the plane orthogonal to the optical axis. It occurs when the axis of rotation is off-center from the main axis, but still paralell. The contributions to the Radial Runnout are the following 2: • Radial Runout of Ball Screws • Fits between Ball Screws and Ball Screw Nuts In the zoom mechanism design proposed there are two lead screws, hence the contributions of radial runout and fit have to be taken into account for each of them. According to the technical data document of the ball screw, it has a radial runout of 0.008 mm [25]. Regarding the fits between the rotating elements, one fit for each ball screw have to be considered. Fits are between the ball screw nuts and the ball screws, defined as H7g6 fits. The values of the fits contributions are calculated according to the International Tolerance (IT) Grades table reference ISO 286. Each moving group of lenses is considered independently for the analysis. For each moving group, the radial runout of their ball screw and H7g6 fit is the same. With the object of obtaining the total runout, a RMS sum of the different contributions has been used. All this contributions for each moving group have been embodied in the following table:

2NOTE: Rods restrict displacements in X and Y directions whereas ball screws restrict them in Z direction.

26 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Tolerance Comment Value (mm) Radial Runout Ball Screw 0.008 H7g6 Fit ( 6 mm) Between Ball Screw and Ball Screw Nut 0.024 TOTAL (RMS Sum) 0.025 Requirement TBD

Table 13: Radial Runout Contributions for each group of lenses.[25]

4.4.2 Axial Runout Axial Runout is when the axis of rotation is tilted to some degree from the main axis, meaning the axis of rotation is no longer paralell to the main axis. Axial Runout has been analyzed in a similar way than the Radial Runout, having the following contribution: • Axial Runout of Ball Screws • Paralelism tolerances of the rotating elements The approach to analyze this contribution is the same as the used in section 4.4.1, where the runout of each ball screw is considered individually for each moving group. The axial runout of each ball screw is 0.010 mm and the paralellism tolerance between each ball screw and ball screw nut is 0.008 mm [25]. Table 14 below shows the contributions to the axial runout for each moving group of lenses:

Tolerance Comment Value (mm) Axial Runout Ball Screw 0.010 Paralellism Ball Screw and Ball Screw Nut 0.008 TOTAL (RMS Sum) 0.013 Requirement TBD

Table 14: Axial Runout Contributions for each group of lenses.[3]

4.4.3 Axial Positioning Accuracy There exists an error in the accuracy of axial positioning that is influenced by the following factors: • Axial Rigidity of the Ball Screw • Axial Clearance between Ball Screw and Ball Screw Nut • Axial Runout Table 15 below shows these contributions to the axial positioning error for each moving group of lenses:

27 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Tolerance Comment Value (mm) Axial Rigidity Ball Screw (200-300 mm Length) 0.012 Axial Clearance Ball Screw and Ball Screw Nut 0.005 Axial Runout Ball Screw 0.013 TOTAL (RMS Sum) 0.018 Requirement TBD

Table 15: Axial Positioning Error for each group of lenses.[25]

4.4.4 Expected Positioning Errors Taking into account the previous considerations for the inaccuracies of the positioning of the optical elements, a calculation of the expected positioning error between the initial and final position for each lens group is presented here.3

Moving Group 1 Moving Group 2 Moving Group 3 Total Displacement 89.99 mm 57.43 mm 89.99 mm Decenter (X and Y) 0.027 mm 0.027 mm 0.027 mm Tilt 0.018 ° 0.020 ° 0.029 ° Despace (Z) 0.018 mm 0.018 mm 0.018 mm

Table 16: Positioning errors of each lens group.

There is one last effect that is the thermal displacement due to temperature changes. It means that the ball screw lengthens or shrinks with temperature changes, hence decreasing positioning accuracy 4. According to the technical data document of the ball screw, if the temperature of the ball screw increases 1°C it lengthens 12 µm per meter. Finally, the Z displacement of each group of lenses due to thermal expansion at -20°C and 60°C is calculated. Taking 20 °C as the initial temperature and the plane of the image sensor as reference for the displacements, the Z displacements would be:

MG1 MG2 MG3 Position (mm) Zi Zf Zi Zf Zi Zf At 20°C 34.70 124.69 112.85 170.28 167.60 257.59 At -20°C 34.68 124.63 112.80 170.20 167.52 257.47 At 60°C 34.72 124.75 112.90 170.36 167.68 257.72

Table 17: Z positioning error due to thermal expansion.

Thus, the total amount of Z error positioning due to thermal expansion from -20°C to 60°C for each lens group at each position would be:

3NOTE: For Decenter, the value was obtained as the RMS of the axial runout contribution and the total radial runout contribution; Tilt was calculated with the axial runout contribution and the radii of the lenses; Despace values correspond with axial positioning accuracy values. 4NOTE: The shrink/lengthen of the ball screws due to temperature changes will be taken into account by the control system of the stepper motors and thus each optical element will be repositioned to its nominal position (at 20°C) through the performance of each stepper motor.

28 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

MG1 MG2 MG3 Position Zi Zf Zi Zf Zi Zf Total Z error 33µm 120 µm 108 µm 163 µm 161 µm 247 µm

Table 18: Z displacement total error due to temperature changes for each moving group.

4.5 Structural Analysis A structural analysis is vital in order to assure a normal operation of the Cubesat during its working time in space. In a conceptual design it is important to determine the natural fre- quencies of the structure, the deformation and stress induced at the corresponding vibration modes to prevent structural failure. A way to predict the structure overall natural frequencies and the level of the structure response to low frequency vibration is by means of a finite element model for analysis of the structure. In this section the zoom mechanism structure is analyzed by FEM simulations using ANSYS Workbench 2020.

4.5.1 FEM Analysis Setup A FEM analysis has to replicate the real scenario where the structure is going to be integrated. For this reason, the model of the zoom mechanism has the faces of the rails fixed, as in the reality they will be in contact with the Test Pod where the Cubesat will be positioned. This boundary conditions simulate an infinite stiff solid where the elements located in the face chosen do not move in the direction specified. This is done with the purpose of ensuring that the correct vibration loads are applied to the structure. With respect to the lenses and the front window, they have been idealized using point masses, which are attached to the structure through their corresponding supports. Figure 17 below shows the FEM setup.

Figure 17: FEM Setup.

Once the model is prepared, it has to be meshed and contacts between components has to

29 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology be defined. Below it can be seen the meshed model (see figure 18).

Figure 18: FEM Mesh.

4.5.2 Modal Analysis The structure of the Cubesat must ensure that its fundamental longitudinal and lateral frequencies satisfy the minimum prescribed values set by the launcher. Natural frequencies are those at which the structure tends to vibrate if it is subjected to a disturbance. The design has to ensure that the structure provide adequate stiffness and that it is able to withstand potentially damaging vibrations that occur during operation, especially during the launch phase. With the purpose of getting the natural frequencies and mode shapes of the system, a modal analysis has to be carried out. In order to demonstrate that the current design meets the launcher requirement where the first natural frequency shall not be less than 90 Hz [20], a modal analysis has been performed. The analysis settings are:

Analysis settings Value Description Desired Modes 6 N/A Boundary Condition 1 Displacement X = 0 Applied in ±X faces of rails Boundary Condition 2 Displacement Y = 0 Applied in ±Y faces of rails Boundary Condition 3 Displacement Z = 0 Applied in ±Z faces of rails

Table 19: Modal Analysis Settings.

The natural frequencies of the zoom cam mechanism together with the structure are shown in table 20 below. As all frequencies are above 90 Hz, hence the previous mentioned requirement is fulfilled.

30 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Mode Frequency (Hz) 1 1938.5 2 1990.8 3 2569.4 4 3044.3 5 3182.0 6 3283.0

Table 20: Modal analysis natural frequencies.

The natural frequencies and mode shapes of the proposed structure are shown in figures 19-21 below.

Figure 19: Modal analysis: Modes 1 & 2.

Figure 20: Modal analysis: Modes 3 & 4.

31 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Figure 21: Modal analysis: Modes 5 & 6.

4.5.3 Quasi-static loads Quasi-static loads are typically specified as the combination of steady-state accelerations and low-frequency vibrations, which have no direct dynamic coupling with the space vehicle. Their effect on the satellite structure is to cause buckling and yield phenomena. As its frequency of change is too slow, quasi-static loads do not cause fatigue problems. [2] [13] The static response of the Cubesat structure is simulated while being exposed to a quasi- static acceleration of 18g in the X, Y and Z directions. This value comes from the most demanding load obtained from the analysed sources, 12g [2], multiplied by a safety factor of 1.5. Thus having:

Quasi-static Direction acceleration (g) ± X 18 ± Y 18 ± Z 18

Table 21: Quasi-static loads selected for the simulation.

Then, a Static Structural Analysis is performed with the following acceleration in each axis with the following settings:

Analysis settings Value Description Acceleration 176.58 m/s2 N/A Boundary Condition 1 Displacement X = 0 Applied in ±X faces of rails Boundary Condition 2 Displacement Y = 0 Applied in ±Y faces of rails Boundary Condition 3 Displacement Z = 0 Applied in ±Z faces of rails

Table 22: Quasi-static loads analysis settings.

The equivalent stresses and deformations suffered by the instrument are shown in table 23 and figures 22-24

32 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Quasi-static loads Analysis result Value Maximum equivalent stress (MP a) 5.2948 Acceleration in X Maximum deformation (mm) 0.0029 Maximum equivalent stress (MP a) 5.1981 Acceleration in Y Maximum deformation (mm) 0.0029 Maximum equivalent stress (MP a) 4.5377 Acceleration in Z Maximum deformation (mm) 0.0039

Table 23: Quasi-static loads analysis results.

Figure 22: Total deformation (left) and Equivalent stress (right) with X acceleration.

Figure 23: Total deformation (left) and Equivalent stress (right) with Y acceleration.

Figure 24: Total deformation (left) and Equivalent stress (right) with Z acceleration.

33 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

It can be seen that the instrument’s structure experiences a maximum stress of 5.295 MP a in X, 5.198 MP a in Y and 4.538 MP a in Z which are fairly safe in terms of yielding, compared to the 275 MP a yield value of the aluminum 6061-T6. It can also be seen in figures 22-24 that the structure responds with a maximum value of total deformation of 0.0029 mm in both X and Y directions and 0.0039 in Z direction, which is found very acceptable in terms of the static deformation interference of the different components of the instrument.

4.5.4 Random Vibrations This analysis investigates the structural response to acoustic noise due to engine vibration, noise and air friction at the beginning of the launching phase. These are considered as random vibrations and are typically in a frequency range between 20 and 2000 Hz. The response of the structure to acoustics is random vibration, which is characterised with a power spectral density curve (PSD). PSD is a statistical measure of the structure response to random dynamic loads, where PSD can be displacement, velocity, acceleration or force. In this case of study the PSD is acceleration and has units of (g2/Hz). Table 24 shows the requirement of acceleration PSD for random vibration [20].

Environment Frequency (Hz) 20 50 200 640 2000 Amplitude (g2Hz) 0.0070 0.0070 0.0350 0.0350 0.0100 Design Loads Frequency (Hz) 20 50 200 640 2000 Amplitude with SF(g2Hz) 0.0157 0.0157 0.0787 0.0787 0.0225

Table 24: PSD acceleration values.

The values shown above represent the expected envelope of random vibrations in the system. To this values a safety factor of 2.25 has been applied for the ANSYS analysis [21]. Finally, to carry out the random vibration analysis, the primary modes of the structure are needed, as a consequence, the boundary conditions are the same. Also, to avoid unrealistic deformations, a structural damping is applied to the entirety of the model, using a fairly typical 3% value. The analysis has been performed in the 3 axis as the fundamental modes may have different responses in each axis. Table 25 shows the obtained maximum equivalent stress and maximum deformation for each acceleration in X,Y and Z.

Random Vibration Analysis result Value Maximum equivalent stress (MP a) 21.924 Acceleration in X Maximum deformation (mm) 0.0138 Maximum equivalent stress (MP a) 21.342 Acceleration in Y Maximum deformation (mm) 0.0136 Maximum equivalent stress (MP a) 14.270 Acceleration in Z Maximum deformation (mm) 0.0137

Table 25: Random vibration analysis results.

34 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

The equivalent stresses suffered by the instrument are shown in figures 25-27 below. Results are scaled to get 3 sigma values (99.73 %).

Figure 25: Displacement (left) and Equivalent stress (right) with X acceleration.

Figure 26: Displacement (left) and Equivalent stress (right) with Y acceleration.

Figure 27: Displacement (left) and Equivalent stress (right) with Z acceleration.

35 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Once again, the maximum equivalent stress is lower than the material tensile yield strength. Random vibrations do not cause damage to the instrument designed as the stress and defor- mations are under the critical damage points of the materials.

4.5.5 Sinusoidal Vibrations During the launch phase, the launch vehicle structure’s response to aerodynamic buffeting and to the operation of the rocket engines origin sinusoidal vibrations. These vibration loads are induced to the units through their interface adapters [2]. They are normally in the frequency band between 5 and 100 Hz. This analysis enables to verify whether the structure of the Cubesat will succesfully overcome resonance, fatigue and other effects during launching phase. Typical sinusoidal vibration lev- els are in the range of 0.1 to 3.0 g’s at sweep rates of 2 to 8 Hz [24]. Data from modal analysis is needed to perform this analysis, hence, the boundary conditions are the same. Table 26 summarizes the envelope of sinusoidal vibration levels that the system shall withstand, where a Safety Factor of 1.25 has been applied [21].

Environment Frequency (Hz) 1 2 5 8 100 110 125 Sine-equivalent vibration (g) 0.4 1 2.5 3 3 3 0.25 Design Loads Frequency (Hz) 1 2 5 8 100 110 125 Sine-equivalent vibration with SF (g) 0.5 1.25 3.12 3.75 3.75 3.75 0.31

Table 26: Envelope of sinusoidal vibrations.

The analysis has been performed in the 3 axis. To reduce the number of analysis to be done in Ansys, the amplitudes of the frequencies between 1 and 8 Hz have been grouped. Table 27 shows the test profile used for the analysis.

Frequency (Hz) Amplitude (g) Amplitude (m/s2) 1-8 3.12 30.61 8-110 3.75 36.79 110-125 0.31 3.04

Table 27: Sinusoidal vibration test profile.

Table 28 and figures 28-305 show the obtained maximum equivalent stress for each acceleration in X,Y and Z.

5NOTE: Here it is shown the cases covering frequencies from 8-110 Hz for each axis, the rest of the cases are shown in Appendix F

36 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Sinusoidal Maximum equivalent Frequency (Hz) vibrations stress (MP a) 1-8 0.8064 X axis 8-110 0.9718 110-125 0.0804 1-8 0.7997 Y axis 8-110 0.9638 110-125 0.0797 1-8 0.5442 Z axis 8-110 0.6562 110-125 0.0543

Table 28: Sinusoidal vibration analysis results.

Figure 28: Equivalent stress with X acceleration (8-110 Hz)

37 4 DESIGN SETUP AND ANALYSIS Lule˚aUniversity of Technology

Figure 29: Equivalent stress with Y acceleration (8-110 Hz)

Figure 30: Equivalent stress with Z acceleration (8-110 Hz)

For this analysis, the obtained values of maximum equivalent stress can be considered negli- gible compared to the yield parameters of the structure, verifying that the instrument design is safe for this test. This analysis would also be relevant for fatigue analysis purposes, but these loads are only expected during a short period of time, the launch phase.

38 5 CONCLUSION AND FUTURE WORK Lule˚aUniversity of Technology

5 Conclusion and Future Work

This thesis presents a preliminary design of a variable focal length optics for a SWIR Earth observation camera. Initially, a literature review on different zoom systems working on the IR region was done. This study provided two possible designs solutions for the presented challenge: A zoom cam mechanism where the rotational motion of the zoom cam is converted into the linear motion of the lenses in the direction of the optical axis; a ball screw mechanism in which the ball screws rotation result in the translation of each lens group along the optical axis. A brief discussion led to the conclusion of taking the ball screw mechanism as the final design solution. The complete opto-mechanical setup was broken down and the commercial components con- stituting it were chosen in order to build a prototype that will be tested to ensure that the design performance complies with the expected after the results of the analysis and simula- tions done. The tolerance analysis performed in this thesis will provide valuable information to the optical designer, who will need the contributions of the different elements constituting the mechanism in the positioning and inclinations of the optical elements when considering the sensitivities of the design. This analysis also resulted to be important to determine the performance and quality of the assembly. Finally, the structural analysis where the model was tested by FEM simulations, concludes that the proposed design will support the expected launch loads without any major difficulty. Also, based on the results, it can be assured that the instrument will have a normal operation during its working time in space. Overall, with the study done during this thesis, it could be said that the zoom mechanism will fulfill its purpose of displacing the zoom lenses with a determined precision, within desired tolerances, when functioning in a harsh environment as space is and working in a delicate wavelength region as SWIR is. For the next steps of the project, it is important to continue by analysing the thermal be- haviour of the instrument taking into account the environmental conditions of a LEO. This can be done by FEM simulations as it has been done for the structural analysis. Another important step to work in is the building of a prototype of the instrument and perform functional tests, where all components will be assembled and the correct functioning of the zoom mechanism could be tested, as well as the positioning and alignment of the lenses. Lastly, once having the opto-mechanical design developed and analysed, the mechanical in- terfaces with the rest of the Cubesat will have to be considered and further analysis of the complete assembly of the 6U Cubesat including the power and electronic subsystems should be added to the work done in this thesis.

39 REFERENCES Lule˚aUniversity of Technology

References

[1] Alan Ashton. “Zoom Lens Systems”. In: Advances in Optical Production Technology II. Vol. 0163. International Society for Optics and Photonics. SPIE, 1979, pp. 92 –98. doi: 10.1117/12.956916. url: https://doi.org/10.1117/12.956916. [2] Peter Berlin. Satellite Platform Design. 6th Edition. Lule˚aUniversity of Technology, 2014. isbn: 9789163753305. [3] Bosch. BASA Technical Notes. https://www.boschrexroth.com/ics/cat/content/ assets/Online/do/LT_BASA_Technical_Notes_ES_20181009_113003.pdf. [4] Celera. What are radial and axial runout error? https://www.celeramotion.com/ applimotion/support/faqs/what-are-radial-and-axial-runout-error/. [5] Ruiyi Chen, Xiuli Zhou, and Xingde Zhang. “Design of compact IR zoom telescope”. In: Infrared Technology XVII. Ed. by Bjorn F. Andresen, Marija Scholl, and Irving J. Spiro. Vol. 1540. International Society for Optics and Photonics. SPIE, 1991, pp. 717 –723. doi: 10.1117/12.48769. url: https://doi.org/10.1117/12.48769. [6] B.R. Fischer. Mechanical Tolerance Stackup and Analysis, Second Edition. Mechanical Engineering - Taylor & Francis. Taylor & Francis, 2011. isbn: 9781439863251. url: https://books.google.es/books?id=Pw4x1wzBHmoC. [7] Allan Gardam. “The Development Of A Compact Far Infra-Red Zoom Telescope”. In: Optical Systems Engineering IV. Ed. by Paul R. Yoder Jr. Vol. 0518. International Society for Optics and Photonics. SPIE, 1985, pp. 66 –72. doi: 10.1117/12.945180. url: https://doi.org/10.1117/12.945180. [8] James W. Howard and Irving R. Abel. “Narcissus: reflections on retroreflections in thermal imaging systems”. In: Appl. Opt. 21.18 (Sept. 1982), pp. 3393–3397. doi: 10. 1364/AO.21.003393. url: http://ao.osa.org/abstract.cfm?URI=ao-21-18-3393. [9] James W. Howard et al. “Two-position IR zoom lens with low f-number and large format”. In: Design of Optical Instruments. Ed. by David M. Aikens et al. Vol. 1690. International Society for Optics and Photonics. SPIE, 1992, pp. 129 –136. doi: 10. 1117/12.137988. url: https://doi.org/10.1117/12.137988. [10] Anthony B. Hull et al. “Design of a space-qualified zoom lens for the space station mobile servicing system video camera”. In: Zoom Lenses. Ed. by Allen Mann. Vol. 2539. International Society for Optics and Photonics. SPIE, 1995, pp. 37 –63. doi: 10.1117/ 12.222840. url: https://doi.org/10.1117/12.222840. [11] Saeed Khodaygan and Mohammad Movahhedy. “Tolerance Analysis of Mechanical As- semblies Based on Fuzzy - Small Degrees of Freedom (F-SDOF) Model”. In: vol. 3. Jan. 2010. doi: 10.1115/IMECE2010-40889. [12] Hyun Kim, Chang Kim, and Seok-Min Hong. “Compact MWIR zoom camera with 20:1 zoom range and automatic athermalization”. In: Optical Engineering - OPT ENG 41 (July 2002), pp. 1661–1667. doi: 10.1117/1.1481048. [13] M. Macdonald and V. Badescu. The International Handbook of Space Technology. Jan. 2014, pp. 1–731. isbn: 978-3-642-41100-7. doi: 10.1007/978-3-642-41101-4. [14] A. Mann. Infrared optics and zoom lenses: Second edition. Jan. 2009, pp. 1–165. doi: 10.1117/3.829008. [15] S. Murugesan. “An Overview of Electric Motors for Space Applications”. In: IEEE Transactions on Industrial Electronics and Control Instrumentation IECI-28.4 (Nov. 1981), pp. 260–265. issn: 2375-0502. doi: 10.1109/TIECI.1981.351050.

40 REFERENCES Lule˚aUniversity of Technology

[16] Edmund Optics. What is SWIR? https : / / www . edmundoptics . es / knowledge - center/application-notes/imaging/what-is-swir/. [17] PBCLinear. Linear Bearings & Shafting. https://www.pbclinear.com/Products. [18] Phytron. Stepper Motor Series for SPACE applications, Standard and Customised So- lutions. https://www.phytron.eu/fileadmin/user_upload/produkte/motoren_ aktuatoren/pdf/ds-physpace-en.pdf. [19] The Cubesat Program. CubeSat Design Specification. Rev 13. https://blogs.esa. int/philab/files/2019/11/RD-02_CubeSat_Design_Specification_Rev._13_ The.pdf. [20] “QB50 System Requirements and Recommendations. Issue 7”. In: 2015. [21] Guillaume Roethlisberger. “Launch Environment”. In: 2008. [22] Ruland. MCLX-6-6-SS. https://www.ruland.com/md_productpdf/index/generate/ product/3148/sku/MCLX-6-6-SS/store/1/. [23] Mark C. Sanson et al. “Development of MWIR continuous zoom with large zoom range”. In: Infrared Technology and Applications XXXVII. Ed. by Bjørn F. Andresen, Gabor F. Fulop, and Paul R. Norton. Vol. 8012. International Society for Optics and Photonics. SPIE, 2011, pp. 780 –786. doi: 10.1117/12.886270. url: https://doi.org/10. 1117/12.886270. [24] Alan D. Scott. “An analysis of spacecraft dynamic testing at the vehicle level”. In: 1996. [25] THK. Ball Screws. https://www.rodacenter.cl/pdf/503LS_A15_BallScrew.pdf. [26] Jing Wang et al. “Mechanism design and simulation of continuous zoom lens”. In: Sixth International Conference on Optical and Photonic Engineering (icOPEN 2018). Ed. by Yingjie Yu, Chao Zuo, and Kemao Qian. Vol. 10827. International Society for Optics and Photonics. SPIE, 2018, pp. 602 –607. doi: 10.1117/12.2500243. url: https://doi.org/10.1117/12.2500243. [27] Paul R. Yoder. Opto-Mechanical Systems Design, Third Edition (Optical Engineering). USA: CRC Press, Inc., 2005. isbn: 1574446991.

41 A PAYLOAD CONSTRAINTS Lule˚aUniversity of Technology

A Payload Constraints

Payload Constraints Property 3U 6U Average Power (W ) 1 7 Power Peak Power (W ) 6 48 Volume (mm3) 100x100x300 100x200x300 Physical Mass (kg) 1.5 4 Cadmium parts Cadmium-plated parts Zinc plating Prohibited Materials Mercury Materials Pure tin or tin electroplate (except when (alloyed with lead, antimony or bismuth) TML <1 % Outgassing CVCM <0.1 % Preferred Structural Materials Aluminum 7075, 6061, 5005 and 5052 Pressure (mbar) Vacuum (<10−5) Min. Operational Temp (°C) 0 Environment Max. Operational Temp (°C) 40 Min. Survival Temp (°C) -10 Max. Survival Temp (°C) 50

Table 29: Payload Constraints

42 B COMPONENTS Lule˚aUniversity of Technology

B Components

B.1 Ball Screw

Ball Screw Specifications Lead 1 mm Thread minor diameter 5.3 mm Clearance symbol GT Axial clearance 0.005 mm or less Nut mass 0.017 kg Shaft mass 0.14 kg/m

Table 30: Ball Screw Specifications. [25]

B.2 Stepper Motor

Technical Characteristics Standard Number of steps/step angle 200/1.8° Physical step accuracy 3 to 5 % Lubrication Space grade compatible Housing Stainless steel Temperature sensor Type K Pre-Conditioning First outgassing by Phytron Radiation resistant up to a dose of 106J/kg Environment temperature (operating) -40...+120°C Environment temperature (non operating) -70...+140°C

Table 31: Stepper Motor Technical Characteristics. [18]

B.3 Coupling

Product Specifications Bore B1 6 mm Bore B2 6 mm Outer Diameter 18 mm Length 30 mm

Table 32: Coupling Specifications. [22]

43 C TORQUE AND POWER ESTIMATION Lule˚aUniversity of Technology

C Torque and Power Estimation

For estimating the necessary torque, the following formula has to be used: F · ph TSM = (2) 2π · η Where,

• TSM : Torque (Nm) that the stepper motor has to provide to generate a pushing force F(N) • ph: thread pitch • η: mehcanical coupling throwput. (0.9 for ball screw) Considering that the weight to move is 1 kg, the necessary force under earth gravity conditions would be: F = m · g = 1 · 9.8 = 9.8N (3) With a ball screw thread pitch of 1 mm:

−3 F · ph 9.8 · 1x10 −3 TSM = = = 1.64x10 Nm (4) 2π · η 2π · 0.9 For estimating the necessary power, the typical speed for continuous operation of the selected stepper motor (400 rpm) is used. Having:

−3 TSM · 2π · n 1.64x10 · 2π · 400 W = = = 6.88x10−2W (5) 60 60 Where, • W(W ) : Power

• TSM (Nm): Torque • n(rpm): Speed

44 D DRAWINGS Lule˚aUniversity of Technology 4.9 33.2 1 of CREO PARAMETRIC SHEET 22 4.9 2.1 1 DRAWING NO. 14.6 76 SUPPORT GROUP 1

SERGIO DIAZ 10.05 A4 SIZE A SCALE 3:4 ← AUTHOR TITLE ← A 32 10 R 84 80.5 104.7 A-A 12 Figure 31: Moving Group 1 Lens Support Drawing. SCALE 1:2 4.1 1.9 SECTION 25 28.8 2.8 121.7 D Drawings D.1 Lens Support 1

45 D DRAWINGS Lule˚aUniversity of Technology 34.9 1 of CREO PARAMETRIC SHEET 25 22 13 3.8 2 DRAWING NO. 2.1 32 SUPPORT GROUP 2 72 14.7 68 SERGIO DIAZ A4

15.4 SIZE 9.6 SCALE 3:4 AUTHOR TITLE B B ← ← 1 R 10 R 76 104.7 3.9 12 SCALE 1:2 Figure 32: Moving Group 2 Lens Support Drawing. 13 51 B-B 2.4 SECTION 121.7 D.2 Lens Support 2

46 D DRAWINGS Lule˚aUniversity of Technology 1 of CREO PARAMETRIC 121.7 SHEET 20 25 3 DRAWING NO. SUPPORT GROUP 3 GF 54 SERGIO DIAZ 30.5 49 A4 SIZE 3 R 32 3:4 SCALE AUTHOR TITLE ← ← C C 1 8 5 46 4xR 104.7 C-C SCALE 1:2 Figure 33: Moving Group 3 Lens Support Drawing. 12 2.8 13.1 6 SECTION 17 51.5 D.3 Lens Support 3

47 E MASS BUDGET Lule˚aUniversity of Technology CAD CAD CAD CAD CAD CAD THK THK Bosch Bosch Ruland Source Phytron TOTAL FULLER FULLER Schott AG Schott AG Schott AG Schott AG Schott AG PBC Linear PBC Linear g g g g g g g g g g g g g g g g g g g g g g 83 76 16 69 70 34 80 10 75 66 76 4.8 5.6 252 217 123 369 126 100 140 117 2109.4 Total Mass 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2 2 6 1 1 6 8 Quantity g g g g g g g g g g g g g g g g g g g g g 8 5 83 76 69 35 17 50 70 40 11 76 0.8 0.7 252 217 123 369 126 117 37.5 Unit Mass SK5 SK5 TIF6 SK16 BASF2 Material Al 6061 T6 Al 6061 T6 Al 6061 T6 Al 6061 T6 Al 6061 T6 Al 6061 T6 Table 33: Mass Budget. Stainless Steel Stainless Steel Stainless Steel Stainless Steel Stainless Steel Stainless Steel Stainless Steel Stainless Steel A2 Stainless Steel A2 Stainless Steel L1 L2 L3 L4 L5 Rod Bearing Bushing B.S. Nut Coupling Rear Wall Ball Screw Front Wall Union Plate Component Stepper Motor DIN 912 M3x8 Support Bearing DIN 912 M3.5x6 MG1 Lens Support MG2 Lens Support MG3 Lens Support Bolts Walls Group Moving Group 1 Moving Group 2 Moving Group 3 Guiding Assembly Ball Screw Assembly E Mass Budget

48 F SINUSOIDAL VIBRATIONS Lule˚aUniversity of Technology

F Sinusoidal Vibrations

In the report, the sinusoidal vibration cases covering 8-110 Hz frequencies were presented. Here, the rest of the frequencies analysed (1-8 Hz and 110-125 Hz) are shown:

Figure 34: Equivalent stress with X acceleration 1-8 Hz (left); 110-125 Hz (right)

Figure 35: Equivalent stress with Y acceleration 1-8 Hz (left); 110-125 Hz (right)

Figure 36: Equivalent stress with Z acceleration 1-8 Hz (left); 110-125 Hz (right)

49