MF2077 Machine Design Advanced Course II

School of Industrial Engineering and Management

Linas Capas, Teodor Hidén, Joseph Montuoro, Matilda Svensson, Maryam Tarik Hamad

Final report

Test Rig for a Load Sharing Unit in a Ball Screw Transmission

KTH Royal Institute of Technology, Stockholm, Autumn 2019

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Abstract The project goal was to reassemble and test an existing load sharing unit, working on 3 ball nuts and a ball screw. The load sharing unit should be tested for “load sharing”, and the ball nuts on ball screw should be tested for efficiency. To be able to perform these tests, a test rig is needed, where different amount of force could be applied repeatedly. All this in a short period of time, only 16 weeks. This project was originally started in 2016 and was then put on hold until 2019. The test rig that was originally planned to be used had been scrapped and recycled in the time on hold. The load sharing unit was completely taken apart and reassembled. The piping was redone and it was no longer leaking oil. Possibility of properly bleeding the system was added. The test rig was designed with the scope of keeping as many of the existing parts as possible. To apply the force to the system (power in) the most feasible solution was used, a rope - pulley and weight drop system. The weight that was dropped could be increased or decreased. The test rig and ball screw was also fitted with a brake to control the speed that the load sharing unit was traveling at for different weights. In order to measure the load sharing between the ball nuts and the efficiency of the linear ball screw transmission, multiple load cells, a force sensor, a torque sensor and one encoder were used. The load cells showed the load that each ballnut had to take. The force sensor could together with the encoder show the power in, and the torque sensor could together with the encoder show the power out. The difference in power in and out gave the efficiency. The complete measuring system could not be finalized due to time constraints. The efficiency was never managed to be tested and the non-complete load sharing test gave results that were hard to analyze. Two of the six load cells stopped working and could not be used in the data acquisition. Future work with testing of the load sharing and efficiency should be done.

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Foreword We would like to thank Pontus Karlsson with colleagues at Cascade Drives for a educational cooperation, discussion and support. We also want to thank Stefan Björklund and Kjell Andersson for the discussions that have been ongoing during the whole project. We also thank the KTH staff that has been helping us with answering questions, testing and building. We especially want to thank Tomas Östberg that has been manufacturing parts for the test rig and has been helpful in all ways and Mikael Hellgren who has helped us with the electronic components and setups. A big thanks to KTH Prototype Center for letting us borrow your soldering station, tin and your Picoscope. Thanks / Joe, Linas, Maryam, Matilda and Teodor

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Table of Contents

1. Introduction 10 1.1 Background 10

2. Literature Review 12 2.1 Load Sharing Unit 12

2.1.1 Ball nut 12 2.1.2 Hydraulics 14 2.1.3 Ball Screw 15

2.2 Test Rig 16 2.2.1 Force Applying System 17 2.2.2 Frame 19 2.2.3 Measuring system 20

3. Methodology 22 3.1 Project Management Methods 22 3.2 Product Development Methods 22

3.2.1 Concept Evaluation 22 3.2.2 CAD 23

3.3 Test plan 23 3.3.1 Test Procedure 24 3.3.2 Hypothesis 24 3.3.3 Safety and Uncertainties 25

4. Design Results 26 4.1 Load Sharing Unit 26

4.1.1 Hydraulics 26 4.1.2 Ball Screw 26 4.1.3 Mounting 27

4.2 Test Rig 27 4.2.1 Steel Frame 28 4.2.2 Power Input and Output 28 4.2.1 Measuring system 29

5. Test Results 34 5.1 Tests 34

5.1.1 Load sharing 35 5.1.2 Efficiency 39 5.1.3 Uncertainties 39

6. Discussion 40

7. Future work 42

References 43

Appendix A: Project charter 44

Appendix B: Links to components of choice 47

Appendix C - Work Breakdown Structure Chart 52

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Appendix D - GANTT chart 53

Appendix E - Torque Sensor 54

Appendix F - Doughnut Load Cells Data Sheet 56

Appendix G - Arduino Data Sheet 59

Appendix H - S-Shaped Force Sensor Data Sheet 63

Appendix I - Encoder Data Sheet 64

Appendix J - Ball Screw Data Sheet 75

Appendix K - Matlab Code 76

Appendix L - Arduino Code 78

Appendix M - Matlab Code for Test Data 81

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List of Abbreviations

Arduino Open-source microcontroller used for data acquisition

CAD Computer Aided Design

KTH Kungliga Tekniska Högskolan (Royal Institute of Technology)

LSU Load Sharing Unit

WBS Work Breakdown Structure

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1. Introduction This chapter provides an overall background to the project and highlights the purpose and the requirements as well as the delimitations of the project.

1.1 Background In 2016 a student project started with the aim of investigating load sharing in a linear ball screw transmission with the use of a load sharing unit (LSU). CorPower was the stakeholder and aimed for using this type of transmission for wave power purposes. Using load sharing higher load capacity can be reached. In this unit, six hydraulic cylinders enable the load sharing by spreading the load over the three ball nuts. Figure 1 illustrates how they are assembled. There was no time for the project to conduct tests on how the load sharing was performing or how efficient the transmission was in 2016.

Figure 1: Overview of the assembly of the load sharing unit. [1]

In 2019 the project was given to our group with a new stakeholder, Cascade Drives, an affiliate company of CorPower and a new scope. Since the previous project hadn’t done any tests the aim of the new project was to test the load sharing of the unit and measure the efficiency of the transmission. Everything that was left from previous projects, including the load sharing unit, had been lying in a box at the department of machine design at KTH and some of the parts that were supposed to exist according to their report did not. Considering that the test rig that the previous project had intended to use for testing had been scrapped by CorPower which meant that the project had to be extended to cover the design, manufacturing and assembling of a test rig.

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1.2 Problem Definition and Purpose The project is part of the course Machine Design Advanced Course part II, MF2077, where the focus is to do detailed design, manufacture and assemble a product. The main goals of the project are to test if the load is shared between the three ball nuts of the load sharing unit (LSU) and find the efficiency transmission. To reach these goals the project also has to find and repair the oil leakage of the load sharing unit as well as mount it correctly on the ball screw. Since the planned test rig was scrapped, one of the scopes the project had to cover design, manufacturing and assembly of a test rig where the load sharing and the efficiency could be tested. 1.3 Delimitations One delimitation of this project is the time since the project is only due to span during the course MF2077, meaning from August 26 to December 12. Because of the time constraints it was imperative to make the design of the test rig as simple and feasible as possible.

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2. Literature Review This chapter provides the information search made before getting started and how the project was divided into subsystems in order to finish the project on time. The project was divided into two subsystems: load sharing unit and test rig. The main source of information was the final report of the previous group.

2.1 Load Sharing Unit The load sharing unit (LSU) consists of three ball nuts connected with hydraulic cylinders that are used to evenly distribute the load among the ball nuts (see Figure 2). The cylinders are double acting to allow the system to handle bidirectional movement. A major reason that multiple ball nuts are used to share the load evenly is the low load capacity of the ball screw transmission. [1]

Figure 2. Overview of the load sharing unit with the hydraulics. [1]

The ball nuts are attached to a plate which is then connected to an attachment plate to the test rig. In the ball screw assembly the screw and nuts need to have matching helical grooves. [2]

2.1.1 Ball nut In a ball nut ball bearing balls roll between the helical grooves of the ball screw which converts rotational motion into linear motion thanks to recirculating ball bearing balls. As the screw rotates or nut travel linearly the balls are deflected by a deflector into a ball return system in a continuous path. [2] Ball return system There are two different ball return systems: external and internal ball return system. For the external ball return system the return tubes are located outside the ball nut body while for the internal the balls return inside the nut based on tangential deflection (see Figure 3). [2]

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Figure 3. Section view of an external ball return system (left) and internal ball return system (right) [2]

Due to the having different return systems the two ball nuts have different pros and cons. For the external ball nut the two main pros are that they are both cost effective and are easy to install maintain and repair. However, they are noisy, cause jams and there is high risk of lubrication leakage. For the internal ball nuts the pros are that they don’t result in leakage of lubrication, are compact, are good for high load and speed applications and they have a high efficiency and reliability. But this type of ball return system also comes with cons: they are also noisy, they are expensive and are hard to manufacture for high volumes. [2]

Internal load distribution Within each ball nut there is internal load distribution which is characterized by the relative compression of the rolling elements. This distribution varies along the length of the nut due to errors in manufacturing, the elastic properties of the material of the balls as well as the load added. When neglecting the manufacturing errors in pitch and size of the rolling elements contact stress depends on two factors: the stiffness of the components in contact (in our case the nut and the screw) and if the stress of these components is compression or tension. If the ball nut has a matching stiffness as the ball screw the optimal load distribution is achieved. However, this is not possible since the nut most oftenly has a greater torsional stiffness. [1] To understand how the internal distribution is dependent on the characteristics of the stress of each component two scenarios are considered in the models made by X. Mei et al. and M. Izawa et al. (see Figure 4) [3]. The first scenario is that the ball nut and the screw are exposed to the same type of stress (tensile-tensile, T-T) while the second is that they are exposed to different types of stress (tensile-compressive, T-C).

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Figure 4. Load distribution curve of balls under T-C and T-T stress scenarios. The proposed model is by X. Mei

et al while the half pitch model is by M. Izawa et al. [3] With these models it is possible to see how the distribution is not constant along the length of the nut.

2.1.2 Hydraulics Without the hydraulic cylinders the load will not be distributed evenly in the load sharing unit due to internal tolerances, backlash and elasticity of the ball screw. This would lead to the nuts breaking down one after the other. Figure 5 shows a schematic view of the hydraulic connections to the ball nuts. [1]

Figure 5. Hydraulic scheme for the load sharing unit. [1]

The scheme in Figure 5 show two identical but separate hydraulic pressure canals where the red canals are active when the pistons are being pushed and the black canals are active for the reversed movement. To enable a distribution of the hydraulic pressure between the cylinders through canalas the hydraulic housing the cylinders have a threaded body. A sleeve is mounted on the hydraulic housing to create hydraulic oil canals from the slots in the housing and O-rings are used to seal the gap between the housing and the sleeve.

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The hydraulic cylinders of the load sharing unit are going to be re-used and new hydraulic fittings need to be ordered for the bleeding system and for repairs because the previous group had used aluminum tubing, which is not rated for hydraulic use. Additionally many of the fittings were installed incorrectly without proper seals and at incorrect torques. This caused leakage, which would become highly problematic under pressure. A bleeding system was also needed to remove air pockets from the hydraulic system which could interfere with load sharing.

2.1.3 Ball Screw A ball screw drive is an assembly that can convert linear motion into rotational motion or vice versa. Efficiency The efficiency of a ball screw drive is typically greater than 90%, thanks to the rolling interface. This is important in applications where high speeds are used to avoid large heat development. Efficiency is an important factor when choosing what type of transmission to use in an energy generating device since it has a direct influence on the cost of the energy. [1] There are two type of efficiency: direct and indirect. The direct efficiency is applied to scenarios where a torque is applied to the screw and converted to a linear force on the ball nut while the indirect efficiency is for back-driving scenarios. The theoretical direct efficiency of a ball screw can be calculated according to the following equation from SKF [4]:

(1)

where d0 is the nominal diameter, Ph is the pitch and μ is the coefficient of friction of the linear guides. The indirect efficiency is calculated through equation 2:

(2)

Buckling When the ball screw is experiencing compressive loads it is prone to buckling. To make sure that the screw doesn’t buckle it is important to investigate what buckling strength, Fc, it has. [1] This can be calculated through:

(3)

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where d2 is the root diameter, l is the unsupported length and f3 is the mounting correction factor and is chosen according to what end support condition the screw will have (see table 1). [4] Table 1: Mounting correction factor for buckling strength. [4]

Critical speed Critical speed is an important characteristic for ball screws and is defined as the lowest rotational speed at which a shaft is in resonance. [1] This critical speed can be calculated through the following equation given by SKF:

. (4)

The critical speed depends on the mounting which is illustrated by table 2. Table 2: Mounting correction factor for critical speed. [4]

2.2 Test Rig To make the design process easier the test rig was divided into three subsystems; force applying system, frame and measuring system. The requirements of the test rig from the previous project are presented in table 3.

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Table 3. Requirements of the test rig from the previous project. [1]

Axial force on the screw 1 kN

Torque on ball screw 5 Nm

Ball nut translational velocity 1 m/s

Hydraulic pressure in system 20 bar

Number of ball nuts 3 nuts

Threaded length of ball nut 1.5 m

These requirements must be true for the new test rig as well and need to be considered during design.

2.2.1 Force Applying System To analyze the load sharing and calculate to efficiency a load needs to be applied to the load sharing unit. The ball screw mechanism will then convert the added linear motion and force to a rotational motion and torque as can be seen in Figure 6.

Figure 6. Ball screw mechanism [1]

To apply the load were multiple different methods considered: hydraulic actuator, pneumatic actuator, electric solenoid actuator, electric driven secondary ball screw and weight drop. Hydraulic linear actuators Hydraulic actuators function by moving hydraulic fluid inside the cylinder and then creating a pressure differential, therefore moving the piston. Due to the incompressibility of hydraulic fluid, these are precise and act with high force as most hydraulics reach several hundred bar. There are two main different types of hydraulic actuators or hydraulic cylinders. They have either one or two different inlets/outlets/connectors. A single connector cylinder is called a single acting cylinder. A typical two connector piston, a double acting cylinder, is shown in Figure 7. [5]

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Figure 7. A typical hydraulic two connector cylinder [6].

Pneumatic linear actuator Pneumatic actuators work similar to hydraulic actuators in they function by creating a pressure differential, therefore causing the piston to move. Due to the compressibility of air, they are not as precise. They also move at much higher rates due to the low shear resistance of air. [7] Electric linear actuator Electric linear actuators take rotational motion from the motor and turn it into linear motion. This is most commonly done by using a lead screw with a nut on it to constrain the piston to only having one degree of freedom. These can vary greatly due to different motors or screw angles, but often come with high accuracy, and high power. [7] Electric Driven Secondary Ball Screw The method the previous group had suggested consisted of a secondary ball screw (purple in Figure 8) driven by an electric servo motor (shown as green). As the driven ball screw is actuated by the motor the screw starts to rotate which creates a linear motion on the ball nuts and the load sharing unit via the carriage (also shown as purple). The linear motion of the ball nut module will translate into a rotational motion on the main ball screw. [1]

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Figure 8. Driven ball screw with motor and carriage [1].

The advantage of using this method was that the rig consisting of the secondary ball screw and the motor existed during that time however, that is no longer the case meaning that this solution would be costly and time consuming. Weight Drop For the last concept a load (red in Figure 9) is attached to a rope and pulley system (shown as orange and black). The end of the rope is connected to the load sharing unit so when the load is dropped the load sharing unit will be pulled horizontally which leads to the rotational motion on the ball screw.

Figure 9. A simplified model of a weight drop system

The advantages of this solution are that pulley system can have any gear ratio of choice and the load can be manually changed. Furthermore, it is a simple and cheap approach. However, unlike the other force applying systems this method cannot give cyclic nor bidirectional testing.

2.2.2 Frame Since the operation principle of the load sharing is that the ball screw has to be back-driven, i.e. a force is applied to the load sharing unit and causing the ball screw to rotate, linear

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guides had to be used to effectively and precisely move the load sharing unit. An existing welded metal structure with smooth shafts and linear ball bearing carriages was found in the premises of KTH, the structure was used as a design base point for the whole test rig. The structure had the perfect length for the ball screw and the load sharing unit to be mounted. The structure was intended to be mounted with 5 M5 bolts on each of the ends. That eventually lead to designing and manufacturing custom frame structure that acts as a support for the linear guides and mounting interface for complementary components such as torque sensor, brake, bearing housings, encoder. Having in mind the environmental aspects and impacts, the whole project was performed by purchasing and ordering as little of custom materials and products as possible. The first aspect of the design was checking what materials were in stock at KTH warehouses and if they could serve the purpose. All the parts were cut and machined by either staff of KTH or a member of the team. No manufacturing and assembling was outsourced and no custom material stock had to be ordered during the duration of the project.

2.2.3 Measuring system Load Sharing The concept for the load sharing was already existing when the project was taken over. Six doughnut shaped load cells, two per ball nut, each connected to a hydraulic cylinder measured how the load was varying. These load cells are 247W-100-08 100 kg compression load cells from Vetek and existed in the load sharing unit assembly. Data sheets for the compression load cells are found in Appendix F. The previous project had the intention to pretension them to 50 kg to be able to measure tension as well as compression. Efficiency Efficiency is the energy output divided by the energy input. To find the efficiency of the load sharing unit and the ball screw transmission it’s necessary to know the force applied on the system, the linear velocity of the load sharing unit, output torque and rotational acceleration of the ball screw. By measuring the input force and the angular velocity it is possible to calculate the input power using

, where .F in · vlinear = P in vlinear = ωrotational itch· p (5)

Measuring the output torque and the angular velocity of the ball screw the output power can be calculated accordingly

.T out · ωrotational = P out (6)

Finally to get the efficiency the power output is divided by power input as equation 7 show:

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.η = P in

P out (7)

To get all the information needed for the efficiency calculation a torque sensor, a force sensor and an encoder will be needed. Data logging To display the signals from the load cells the previous project had decided to use an analogue transmitter. The transmitter intended to be used was a Vetek DGT4 which only has four channels [1]. To solve the issue with having six sensor and only four channels the idea was to hook up three sensors at the time to the transmitter [8]. This wasn’t the only issue with the previous data acquisition concept. The DGT4 transmitter didn’t have the ability to store the data which meant that the data had to be written down manually which isn’t a robust measuring system. A more robust system is crucial if more sensors are to be used. There are different ways to acquire and store data from sensors. One such way is to use a PicoScope which is a PC Oscilloscope and a smaller version than the traditional benchtop oscilloscope. It can be used as an advanced oscilloscope, function analyzer, protocol decoder, spectrum analyzer or waveform generator. Some PicoScopes can measure both analogue and digital signals. Those mixed signal oscilloscopes can add up to a 16 channel logic analyzer. [9] The PicoScope has a software which enables graph plotting of the signals. Another way is to use a data logger. A data logger can if connected correctly set up a database where the data is not only recorded and registered but also stored. This device can also analyze, sort and process the stored data due to its high capacity memory. There are different data loggers for different purposes and different number of available channels. Some are used for measuring room temperature and CO2 content of the air while others can be used to measure different types of signals or have up to 48 analogue signal inputs.[10] A third way is to use an Arduino which is an electronics open-source platform with an easy-to-use hardware and software. The Arduino board can read an input and turn it into an output which is possible to control by sending instructions to the microcontroller on the board. This platform can be used by both beginners and more advanced [11]. It is also easy to find extension or additional programmes such as code to input data to excel due to the open-source feature of Arduino. For analysing the data, its either done in by using an existing program from PicoTech or by inserting the data to Matlab for plotting.

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3. Methodology This chapter explains what methods the project used in order to get successful.

3.1 Project Management Methods For projects to be successful are project management tools needed. The methods used in this project was project charter, project planning with GANTT-chart and work breakdown structure (WBS). Project Charter A project charter is a document which states what the project is going to be about, who are working in the project and for how long the project shall be ongoing. It should also address the budget of the project. The project charter should be an agreement between the project manager of the project and the stakeholder. When the project charter is finished it should be signed by both the project manager and the stakeholders.[12] The project charter can be found in Appendix A. Work Breakdown Structure The WBS is considered to be one of the key tools for project success and its diagram breaks down the work that needs to be done in the project. In a WBS, the work should be divided into the different deliverables of the project and all the work needed for each deliverable to be fulfilled. [12] The WBS can be found in Appendix C. GANTT - Chart When the WBS is made and you have set times for the project it is possible to start to assemble a GANTT-chart with the different work stages. This is a great tool to see how the project timing is and what is realistic in terms of planning. The GANTT-chart can be found in Appendix D.

3.2 Product Development Methods The product development have been of Top - Bottom structure. We had a goal, a test rig that could test the existing load sharing unit for efficiency and load sharing.

3.2.1 Concept Evaluation For choosing the final concept for the force applying system an evaluation matrix was made. The concepts looked upon can be found in chapter 2.2.1 and the criteria with weights investigated were based upon the purpose of the project. Each concept was given a score between 1-5 for every criteria. This led to the concept evaluation matrix found in Figure 10.

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Figure 10. Concept evaluation matrix

Due to the time limitations, the feasibility of the concept had the highest priority. Therefore, even though other concepts would fulfill the purpose in a more efficient manner or scored almost the same, the weight drop approach of applying force was chosen.

3.2.2 CAD An assembly of the finished load sharing unit already existed. The CAD model itself is not in the aim of the project but it is important to use this type of tool to visualise and to verify the concept. A first design of the test rig was made to visualise the concept before deciding on the final concept. Both the first conceptual CAD and the detailed design was made using Solidworks. All parts: the load sharing unit, the test rig and the pulley system are put into CAD in such a way that no interference occurs.

3.3 Test plan The goal is to measure the efficiency of the ball screw vs. ball nut transmission and to make sure that the load sharing unit is doing its job of sharing the load between the 3 ball nuts. A reference test of efficiency were only one ball nut is connected to the ball screw is also wanted. The input force should be able to vary so the efficiency for different load cases could be evaluated. Test 1. Initial Testing The first step is to set up the whole test rig and load sharing unit, connect it to the force applying pulley and rope system and see if everything moves smoothly. It is also important that the braking components work and all sensors give “reasonable” numbers.

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Test 2. Increase and Decrease in Load - Load Sharing When everything is working well, the load will increase and decrease, eg. the pulling force will vary. The load sensor outputs will be monitored at all times to make sure that they match the load variation and work as intended. This will give results about the load sharing. Test 3. Increase and Decrease in Load - Efficiency To test the efficiency different loads will be used. The variation in power input will be monitored by an S-shaped force sensor together with the power output (torque and speed change). Efficiency for the different loads will be tracked and compared. Test 4. One ball screw test When all tests, including load sharing, have been performed the load sharing unit will be rebuilt in such way that only one ball nut takes all the load. This new assembly will then be tested for multiple load cases and the efficiency will be tracked. The difference for each load case will then be compared to the load test for the full 3 ball nut assembly.

3.3.1 Test Procedure ● First step is to make sure that everything that shall be moving during the test can

move “freely”. ● Second step is to connect the Arduino to the computer, see so connection is working

fully and start the data logging. ● Third step is to create the moving that gives changes in load cell force, force sensor

force from the rope, torque increase and speed change. This can either be done: ○ Driving the ball screw through turning the brake disk and pushing the load

sharing unit towards its end position, creating compression of the load cells. ○ Driving the ball screw through turning the brake disk and pushing the load

sharing unit towards the other end of the test rig. This motion will lift the weight connected to the rope off the ground and load the system with potential energy. The load cells feels tension in this case.

○ Releasing the weight when it’s in it top position, creating back driving of the ball screw. The load cells will be under tension.

The last two alternatives can be combined. Then the weight is kept at high position thanks to applying force to the disk brake, and the weight is dropped when the braking force is released. After the test is performed the logged data is saved in a text file for importing to Matlab for analysis.

3.3.2 Hypothesis The hope is of course that the load sharing is working; the load between the stiff structure and the ball nuts vary accordingly to each other.

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The hypothesis is that the difference in effectiveness between three ball nuts that equally share the load compared to one ball nut taking all the load will be very small. This is due to the estimated linear friction coefficient. Three ball nuts with ⅓ of the friction will equal the single ball nut with full friction. But what's more interesting is the life time of the components. The life time can be estimated to be at least linear between force and wear, meaning that the three ball nut assembly will last three times as long as the single ball nut. This can not be tested in a feasible way with the current test rig.

3.3.3 Safety and Uncertainties It’s important to be able to perform the tests with minimized uncertainties to maximize the repeatability and correctness of the tests. The testing must also be made completely safe to avoid damage on people or the equipment. To ensure a safe procedure the test will be performed with the lowest possible load in the beginning, to make sure that everything works as intended. Then the load can slowly be increased. There will always be one, only one, responsible person at each test occasion. This person is responsible for making sure that no one gets hurt before preparing the quick release and pulling the trigger rope.

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4. Design Results In this chapter all design results are presented of a finished load sharing unit and a final test rig. The project was successfully maintained under a budget of 25.000kr and most of the intended deliverables were delivered except for the efficiency testing and results.

4.1 Load Sharing Unit As mentioned in Chapter 2, the load sharing unit was leaking hydraulic fluid and was not fully assembled. This subchapter will discuss what was done to finalize the load sharing unit.

4.1.1 Hydraulics Due to the expected high forces, the aluminum tubing was upgraded to steel hydraulic tubing and all the seals and cutting ring fittings were replaced. Teflon tape was used as an additional measure to prevent leakage. Pressure gauges were added to monitor internal forces. For the bleeding system, one way valves were attached to the bottom of the load sharing unit and flow control valves were placed at the top to allow for the load sharing unit to be filled with hydraulic fluid using a hand operated pump.

4.1.2 Ball Screw The theoretical direct efficiency, ɳ, of the ball screw was calculated according to equation 1 to 99% but since the concept used when doing the experiments were backdriving, the indirect efficiency, ɳ’, is the important efficiency to calculate. This was calculated to 98% with equation 2. To calculate the buckling strength and the critical speed it is important to understand what end support condition the screw has (see table 1 and 2). Without the load sharing unit the screw is supported by a fixed support bearing on one side and a simple support bearing on one side (fixed - radial support). This would also mean that we have an unsupported length of 1.5 m, the length of the ball screw between the bearings. This would give us a buckling strength of 16 kN (safety factor 3, equation 3) and a critical speed of 1800 rpm (safety factor 1.25, equation 4). However, when the load sharing unit is mounted on the ball screw the ball nuts also count as fixed supports. This means that the ball screw would have two different sections, one with an fixed - radial support end condition and one fixed - fixed end condition. Depending on where the load sharing unit is mounted the buckling strength and the critical speed would vary for both sections on the ball screw. It can be concluded that since the unsupported length will be smaller and the correction factor will stay the same for one section and increase for the other section, both the buckling strength and the critical speed will increase.

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4.1.3 Mounting To ensure that everything will line up the whole assembly is mounted on the ball screw simultaneously. The main design change from the original design performed was the way the load sharing unit mounted on the linear guide, see Figure 11 for a visual description of it was mounted. The middle aluminium frame pieces could be machined to suit the new design and the two end plates had to be made from scratch, found in Figure 12.

Figure 11. The load sharing unit mounted on the test rig,

Figure 12. The load sharing unit with the new mounting plates on the ball screw.

The pieces were easily manufactured due to simple waterjet cutting operations and then some light machining. The machined surface also got holes drilled and tapped to make the mounting on the slide possible.

4.2 Test Rig The finished design of the test rig will be presented in this chapter.

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4.2.1 Steel Frame

A welded metal guide rail structure was found in the premises of KTH which was used as a foundation for the frame and to control the movement of the load sharing unit. As mentioned in the section 2.2.2., two additional welded steel structures were designed that were bolted to the existing structure with linear guides. The structure of the frame was designed for using 40x40x2 mm square steel tubing. The main reason of choosing this type of structure was because that exact steel tubing could have been easily acquired from the warehouses of KTH and easily cut to length and welded by the staff of KTH. Interfaces for complementary parts were also though thoroughly and as a result, steel tubing sleeves were welded in the bolt holes for mounting support bearing blocks and attaching the linear guide structure to the end frames, to prevent considerable deformation of the frame members, resulting in misalignment issues. Figure 13 show the steel frame of the test rig.

Figure 13. The steel frame of the test rig.

Both of the welded steel frames had a threaded plates welded on the bottom of the vertical tube for connecting the adjustable feet to ensure full contact with the ground. One of the welded steel structure has a flat surface on top that allows an adjustable jack to be mounted between the test rig and the ceiling. This made the test rig completely fixed and stopped it from lifting when the rope was pulled and the load sharing unit was moving forward.

4.2.2 Power Input and Output The power input to the test rig concept was chosen to be a very cheap and feasible solution. Instead of using hydraulics or electronics that need multiple parts and coding for controllers, a rope and pulley system was chosen to use as the power input system. This allowed quick development, low budget costs and quick assembly time. A weight will fall from a certain height, geared through the pulley system, and pull the load sharing unit along the linear guide rails. Changing the amount of weights is an easy way to increase or decrease the load. This concept centered around the transformation from potential energy into kinetic energy. The pulley system is made to gear the forces from the weights two times. A gantry crane will be used to lift the weight. At the top the weights are held in place with a quick release with a high safety rating. To the left Figure in Figure 14 the test rig is loaded and the right show when the weights have been dropped.

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Figure 14. CAD-design of the pulley system.

Since the ball screw has a critical speed of 1800 rpm and the load sharing unit shouldn’t risk ramming into the frame, a disc brake of a gokart was installed after the torque sensor so that it was possible to break the speed of the load sharing unit.

4.2.1 Measuring system For the measuring system both the data collection method and the sensors had to be decided and the results are presented below. Data Collection It was a tough decision to decide which data gathering system to use but the final choice landed on using an Arduino MEGA 2560 microcontroller, data sheet can be found in Appendix G. The need of having at least nine input channels to be able to read all sensors simultaneously narrowed the span of possible controllers and transmitters. Arduino is also a commonly used, not too expensive, open source microcontroller which gives the possibility to easily find working code. Although it might have been easier using a Picoscope or a data logger but these options weren’t found early enough to make a thorough investigation into before a final decision needed to be made. All sensors was connected to the Arduino according to Figure 15. When performing tests the serial monitor from the Arduino software was used to log all the data. When a test was performed the data points where copied into a text file to be imported to Matlab where the analysis could be performed. The code for the Arduino is found in Appendix L and the code for importing the data to Matlab is found in Appendix M.

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Figure 15. Concept of the measuring system.

Torque Sensor Instead of buying a torque sensor, an already existing one at KTH was borrowed, thus minimizing the total cost of the project. The torque sensor is a Hunan WTQ-66 with two types of output signals - velocity and torque. Figure 16 show the specifications of the torque sensor.

Figure 16. The data specification label of the torque sensor.

The torque sensor operates on +/- 15 VDC and both output signals for torque and velocity are frequency signals. So, the torque signal is 10 kHz with +/- 5 kHz depending on torque and direction of rotation. This means that 10 kHz is zero torque, 15 kHz is 100 Nm in one direction, and 5 kHz is 100 Nm in the other direction. On the contrary for velocity, the signal starts at 0 Hz and increases with speed. Both signals have a too high voltage rating for the Arduino to handle. Therefore, the signals need to go through a voltage divider made of resistors before they can be imputed to the Arduino. A voltage divider changes the signals

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from 10+ V down to roughly 4 V, which are allowed by the Arduino. The frequency is square waves with an amplitude of less than 5V, which is in the range of what the analogue inputs on the Arduino need. Figure 17 describe how the torque sensor is mounted on the test rig. The data sheet for the torque sensor can be found in the Appendix E and other information have been achieved through interviews with Mikael Hellgren, research engineer at KTH.

Figure 17. The torque sensor mounted on the test rig.

Load Cells Two types of load cells are used in this project. One S-shaped 1 tonne compression and tension load cell for measuring the input force and six doughnut shaped compression load cells, two for each ball nut on the load sharing unit for measuring the load sharing. An S-shaped load cell was found at KTH, see Figure 18 and its specifications suited our needs. All data sheets for the compression load cells can be found in Appendix F and the data sheet for the S-shaped load cell can be found in Appendix H. The signal from all load cells have to pass through an amplifier before being inputted to the Arduino. This is so that the signal output will match the readable parameter specifications that the Arduino have. In order to ensure that the load cells showed trustable values they were calibrated manually at first with a 2 kg known weight. However, it was later realised that a larger weight more similar to the maximum weight of the load cells should have been used. This issue was solved by using the analogue transmitter from the previous project and each individual data sheet. The four channel transmitter had the option to use a theoretical calibration where the user can insert the given calibration factor from the manufacturer. The load cells were then tensioned to 50 kg and reattached to the arduino to have the calibration factor in the code adjusted until they read as zero.

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Encoder To measure rotational velocity it was decided that an encoder should be used. An encoder which suited the needs of the project was found at KTH. It was a Wachendorff WDGI 58H, see the right sensor in Figure 18, and the data sheet can be found in Appendix I.

Figure 18. The S-shaped force sensor to the left and the encoder to the right.

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5. Test Results In this chapter the results from the test are presented.

5.1 Tests The main goal of the testing was to test if the principle of the load sharing worked as intended and to find out the efficiency of the transmission. The tests were performed with different amounts of weights pulling the rope to varying the load. The monitored variables were:

● Force in (between rope and load sharing unit), one load cell ● Load sharing in the load sharing unit, six load cells ● Rotational torque, one torque sensor ● Rotational speed, one encoder

Thanks to the known lead on the ball screw the linear speed could be calculated from the rotational speed. The problem with decoding the signal from the torque sensor about torque and speed resulted in that only the load cells forces be analyzed. The S-shaped force sensor showed values for the rope very similar to know real values when monitored. This could be ensured thanks to a known mass hanging on the rope and the known gear ratio. Plots of the force sensor value are not included in the general results and the forces neither are plotted on the load sharing plot. This is due to the extreme difference in amplitude (100+kg vs. 2kg) compared to the load sharing load cells values, see Figure 19.

Figure 19. The rope force of roughly 100 kg is similar to the load of ~50 kg and the gearing of 2:1. The big

increase in force is after the weight drop - when the weight is released and brake is engaged before the weight hits the ground, leaving the weight to hang in the air.

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5.1.1 Load sharing The load sharing should be monitored from the six load cells, with one load cell per hydraulic cylinder. A problem here was that two of the six load cells, which had damaged cabling already when the project was started, stopped working before the tests could be performed. This means that only the load sharing for the load cells number three to six could be monitored, and the load sharing for load cells one and two, both connected to ball nut one, could not be monitored. Multiplet tests were done, and the load sharing did not show great results. The results are differing between compression and tension, which in theory should not be the case. To deeper analyze this should more testing needs to be done. Figure 20, 21 and 22 show the results from the compression test and Figure 23, 24 and 25 show the results from the tension test. The compression tests are done while driving the ball screw and pushing the load sharing unit towards the end of the frame. The constraint here and gearing of the ball screw makes it possible to reach high forces.

Figure 20. Load sharing in compression, better and more even results than the tension tests.

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Figure 21. Load sharing in compression, better and more even results than the tension tests.

Figure 22. Load sharing in compression, better and more even results than the tension tests.

It is clear how the force in all of the load cells follows the same pattern and shows the same behaviour. The amplitude difference can depend on error in calibration or difference in load, so no hypothesis can be confirmed or denied. When looking at the tension tests, completely different behaviour is seen. These tests are done while lifting the weight by driving the ball screw and then dropping the weight and backdriving the ball screw.

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Figure 23. Load sharing in tension, just during the backdriving weight drop procedure.

Figure 24. Load sharing in tension, during the backdriving. The weight is already loaded, then is the weight

hold through the brake, and after 150s is it released.

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Figure 25. Load sharing in tension, during the driving and loading of the weight, holding the weight, and finally

releasing the weight and causing backdriving.

The results are inconsistent, shows different forces and different load cell show different extreme values for each test. No sure and good results have been able to be concluded. Not until the very end did the design mistake of the load sharing unit and the mounting of the load cells came clear. The tension tests are not working, due to that the bolt holding the hydraulic cylinder, load cell and load sharing unit mount together needs to be stretched. The hydraulic cylinder is fixed, and so is the ball nut mount due to the constraints of the ball screw. This means that when the hydraulic piston is extended due to pressure change from the other ball nuts, the load cell is compressed. But when the hydraulic piston is pulled inwards,the preload of the load cell is not released more that the screw holding everything together can stretch. See Figure 26 for a graphical illustration.

Figure 26. Graphic illustration of what is meant with compression and tension.

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5.1.2 Efficiency A big issue was faced when trying to do the efficiency tests. The torque sensor could not be set up with correct wiring until the very end of the project. There was also no time to make a working code for the Arduino to manage to interpret the output of the torque sensor. However, a Picoscope was borrowed from KTH Prototype Center to see what the signals looked like. Figures 27 and 28 show the torque and velocity signal from the torque sensor.

Figure 27. This is frequency for torque, the change in frequency for different torque was hard to get in the

picture.

Figure 28. This is frequency for speed, and how it changes for different speeds.

5.1.3 Uncertainties ● One of the ball nuts was already opened when the project was taken over. This means

that there is a risk that some of the balls have been falling out of the nut case. This is something that would affect the efficiency of the ball screw gearbox in a negative way.

● Lubrication of the ball screw, linear ball bearings. ● Wipers in ball nuts that keep contamination from outside away add friction due to

pressure on the ball screw. ● Ball screw end bearings. ● Potential misalignment of all components.

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6. Discussion Project Management The project had a slow start due to missing information and lack of communication between teachers, stakeholders and students. Parts from the previous group had gone lost, and some parts had to be redone. Nor did we as students have a good place to start the work. The most of the work in the project was performed in school. This to make the process as transparent as possible between all group members, even when the main responsible for each area was divided among us. The work of finding suitable components that had to be bought took unexpectedly long time. This partly due to the fact that we had the full responsibility for our self and just needed to go to the stakeholder to get it approved before ordering. Better communication with stakeholders in an earlier stage here would have been beneficial so we could have gotten some more constraints, like: Swedish supplier and as few suppliers as possible. Load Sharing Unit We adapted to the existing design and parts. Some minor changes had to be done but this was tried to be minimized due to time effectiveness. It would have been beneficial to have the load sharing unit made not so compact, so assembling could have been easier. This would not have an effect on the test results, but would make this first stage testing easier. The original design of the load sharing unit had not taken the fixed dimensions of the ball screw into account. The fixed lead on the ball screw, ball nuts and the 6 mounting holes in each ball nut mean that the distance between the ball nuts can not be floating. If the distance is not an even divider between lead, turns and mounting holes will the ball nut assembly be over constraint with high internal forces. The mounting direction of the load sharing unit makes the load cells measure in tension. Thanks to the preload should this theoretically not be a problem, but when the load sharing unit is driven in “wrong” direction can better load sharing results be achieved compared to when it’s driven by the force applying system. Changing the compression load cells to tension load cells could be another way to solve the issue even though it’s a more expensive way. Test Rig We wanted a test rig that could both push and pull the load sharing unit. This would have lead to a more realistic testing and more correct results.

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The test rig was made simple but robust, to withstand the single directional test that would be performed. Good quality components like SKF bearings, etc. were used to ensure the lifetime and minimize the unwanted friction. Measuring System Two of the six load cells were damaged when the project started. They were working in the beginning but at the end of the project when the actual testing should take place they didn’t give any value. If this is due to the damaged wiring or due to over tightening at some point during the project process can’t be said. The wiring diagram for the torque sensor was missing and when the cabling was investigated it was found that it had damaged cabling as well. This caused lots of trouble and was very time consuming. Thanks to reverse engineering with the old cabling (which was unmarked and not 100% correct), new data sheets from the manufacturer in China and help from Mikael Hellgren could the complete wiring be done. The working solution came so late that no working code to perform the tests could be written and results achieved. Tests and Results We monitored all the data through an Arduino. It was possible to monitor all load cells, force sensor, encoder and torque sensor simultaneously even though it was never necessary. This was needed for us to make possible to ensure proper load sharing and to calculate the power going in and out from the system. To find the suitable components for monitoring was a time consuming problem. Very few components could handle the input from six load cells, one force sensor, one torque sensor and one encoder. This needs nine total inputs, and we need to monitor them simultaneously to ensure that the data gathered is useful. Overall Project The overall organization around the hand over of the project was not very well performed. We did miss a lot of instructions and it took time to understand the project. A lot of time was lost due to finding new components and new suppliers when the concepts or products weren’t approved by the stakeholder.

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7. Future work First of all, two new load cells for the load sharing unit need to be bought so that complete load sharing can be tested. A code for the Arduino that can handle the frequency input from the torque sensor about torque and speed should be written. Then actual efficiency testing can be conducted. Next step in the development and testing would be to perform cyclic testing. Bi-directional cycles going back and forward to ensure that the friction stays low and no heat is created. This might be possible to perform at different loads and speeds to find the optimal combination for this type of application. At the moment, the load cells were tested in tension only. When being preloaded, this should not affect the results (theoretically it should be the same results). This might not be the case, and this might be the reason for the low values achieved in each load cell when testing. Turning the load sharing unit around so that compression test can be run might give different results. The best solution is of course to have bi-directional testing going in cycles.

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References [1] A. Bölke et.al. “Design of a Prototype for load sharing unit in a Ball Screw Transmission”, Institute of Machine Design at KTH, 2016 [2] Barnes Industries, Inc., 2019. [Online]. Available at: http://www.barnesballscrew.com/how-a-ball-screw-works/ [accessed 10 Dec 2019] [3] X. Mei, M. Tsutsumi, T. Tao, N. Sun, "Study on the Load Distribution of the Ball Screw with Errors". Department of Mechanical Engineering at Xi’an Jiaotong University, Xi’an 710049 China, 2001. [4] SKF, "Precision rolled ball screws," SKF, 2013. [Online]. Available at: https://www.skf.com/binary/21-149715/Precision-rolled-ball-screws---6971_1-EN.pdf [accessed 16 Dec 2019]. [5] Go Hydraulics, 2019. [Online]. Available at: https://gohydraulics.ca/what-are-single-acting-and-double-acting-hydraulic-cylinders/ [accessed 16 Dec 2019] [6] CPI, Inc., 2015. [Online]. Available at: https://gohydraulics.ca/what-are-single-acting-and-double-acting-hydraulic-cylinders/ [accessed 16 Dec 2019] [7] MachineDesign, 2016. [Online]. Available at: https://www.machinedesign.com/mechanical-motion-systems/linear-motion/article/21832047/whats-the-difference-between-pneumatic-hydraulic-and-electrical-actuators [accessed 16 Dec 2019] [8] P. Ringdahl, 2019.Personal Interview. [9] Pico Technology. [Online]. Available at: https://www.picotech.com/oscilloscope/2000/picoscope-2000-overview [accessed 11 Dec 2019] [10] PCE Instruments. [Online]. Available at: https://www.pce-instruments.com/english/measuring-instruments/test-meters/data-logger-data-logging-instrument-kat_40040.htm?gclid=CjwKCAiAxMLvBRBNEiwAKhr-nPxN5j0aNN_u6OJwMo1aDslFoLveNRIo5RpptGcPejh-dLZaTPOYUxoCHv4QAvD_BwE [accessed 11 Dec 2019] [11] Arduino. [Online]. Available at: https://www.arduino.cc/en/Guide/Introduction [accessed 11 Dec 2019] [12] C. Petersen. 2013. [Online]. Available at: https://projektkvalitet.dk/wp-content/uploads/the-practical-guide-to-project-management.pdf [accessed 16 Dec 2019]

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Appendix A: Project charter

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Appendix B: Links to components of choice Bill of materials -

Test Rig

Test rig

Amo

unt Link Comments

Quick release for wire 1

https://lyfta.se/shop/product

/6616?fbclid=IwAR1fm2mGM

lKRlOKYhOdDNxiDDQvimib4d

5P7fYPO9g94dqS0v6FHy993Y

Z4

Rope 15

https://shop.poly.se/sv/MEN

Y/TAGVIRKE/Rep-_-Snoren/P

olyester/Poly-Braid-32/Spole/

POLY-BRAID-32-gra-rod?id=20

8281

8mm, length

15*1m=15m total

would be enough

Pulleys 4

https://lyfta.se/shop/product

/6783 Max 16mm rope

Thimbles 4

https://shop.poly.se/sv/MEN

Y/TAGVIRKE/Metallvaror/Kau

ser/KAUS-galvad-10-mm--(2st

_frp)?id=4908050910

need 8 = 4 * 2

(comes in 2-pack)

Clips 4

https://shop.poly.se/sv/MEN

Y/TAGVIRKE/Metallvaror/Wir

elas/WIRELAS-varmgalvat--8-

mm-(2st_frp)?id=4908059008

need 8 = 4 * 2

(comes in 2-pack)

Shackles 4

https://shop.poly.se/sv/MEN

Y/TAGVIRKE/Metallvaror/Sch

acklar/Rak-SCHACKEL-varmgal

vad--8-mm-5_16_-(2st_frp)?i

d=4908050707

need 8 = 4 * 2

(comes in 2-pack)

eye-bolt (M12) 2

https://lyfta.se/shop/product

/5177 5T211-M12

Weights 1

Coupling end MAYR ROBA-ES

24/940.022.A bore of 17mm

(H7?) 2

https://www.aratron.se/sv/va

ra-produkter/kopplingar/klok

opplingar/

Carrier load sharing unit 1

47 KTH

Frame (steel) + bolts, welds, etc 1

Linear guide rails 2

Shock absorber for LSU, before

frame 2

https://www.mekanex.se/pro

dukter/komponenter/industri

stotdampare/

model: SES 10 * 40

B

Bearings for ball screw 2

Tyre (for weight/floor

suspension) 1

Nuts for shock absorbers, M20 *

1,5 2

https://www.svith.s

e/bygg-garage-och-l

yft/bygg/bultar-mut

trar-och-brickor/mu

ttrar-finganga/mutt

er-20x1-5.html

Fixing support for rig vs. roof 1

https://www.hornbach.se/sh

op/Stamp-160-300-cm-max-1

800-kg/5069983/artikel-detalj

er.html?wt_mc=se.paid.sea.g

oogle.alwayson_assortment...

1585902475.59881002956.&

wt_cc1=1585902475&wt_cc2

=59881002956&wt_cc3=2980

15765576&wt_cc4=&wt_cc6=

5069983&wt_cc7=&gclid=Cjw

KCAiA8K7uBRBBEiwACOm4dy

idmxhsuNqxP-ei0zr6UTJalfNL

RRZyF-ZdI5CR4iQuJcMuSpJQ

wxoCt-8QAvD_BwE

Bearing blocks UCP204 2

https://www.mecmove.se/wp

-content/uploads/UCP2.pdf UCP204

Threaded plug insert 8

https://www.mecmove.se/wp

-content/uploads/ganginsatse

r.pdf

VG 40x40x1,5 - 2,0

M8”S”

Adjustable feet 8

https://www.mecmove.se/wp

-content/uploads/SF_SFK.pdf SFK30 8x50

Brake Assembly Kit 1

https://www.radne.se/Produ

ct/8245/Bromssystem-Kompl

ett-Universal-2PN100-WP-Sva

rt?fbclid=IwAR2tJCQWvAXA9

DSerrcxuo92IOR5F9ZtVPVBBV

48 KTH

f8CYlUpYivUQCdXhZ2y28

Hub for Brake Assembly Kit -

30mm 1

https://www.radne.se/Produ

ct/5181-1/Bromsskivenav-sva

rt-30-mm-6-8-mm

Brake fluid 1

https://www.radne.se/Produ

ct/49809/Bromsvatska-DOT-4

-Xeramic-250-ml

Brake reservoir 1

Vetek Load Cell 1t 1

Power supply 1

100 Nm Non contact rotary

torque sensor WTQ-66 1

HX711 amplifier 8

https://www.elfa.se/sv/hx711-lastcellfoerstaerkare-sparkfun-electronics-sen-13879/p/30145509?track=true&no-cache=true

Arduino Mega 1

https://www.elfa.se/sv/mikrostyrenhetskort-mega2560-r3-arduino-a000067/p/11038920?q=arduino+mega&pos=17&origPos=34&origPageSize=10&track=true

Wachendorff encoder 1

Vetek donut Load Cell 100 kg 6

Socket red 1

https://www.elfa.se/sv/kontakthyls

a-4mm-roed-schuetzinger-bu-403-n

i-rt/p/30040239?track=true

Socket black 1

https://www.elfa.se/sv/kontakthylsa-4mm-svart-schuetzinger-bu-403-ni-sw/p/30040240?queryFromSuggest=true

Jumper wire female to male 3

https://www.elfa.se/sv/byglingstrad-hane-till-hona-paket-med-10-delar-150-mm-mangfaergad-rnd-components-rnd-255-00013/p/30115111?q=byglingstr%c3%a5d&pos=6&origPos=6&origPageSize=10&track=true

Honlist 10 stift 5

https://www.elfa.se/sv/genomgaende-hal-kretskortsuttag-rak-10-stift-stift-54mm-stiftavstand-rnd-connect-rnd-205-00650/p/30093670?q=RND&pos=1&origPos=2278&origPageSize=10&track=true

Hanlist 9 stift 5

https://www.elfa.se/sv/genomgaende-hal-kretskortslist-rak-stift-stift-54mm-stiftavstand-rnd-connect-

49 KTH

rnd-205-00630/p/30093650?q=RND&pos=18&origPos=3722&origPageSize=10&track=true

USB A to USB B cord 1

https://www.elfa.se/sv/usb-plug-to-usb-plug-cable-600mm-svart-rnd-connect-rnd-765-00066/p/30125784?q=*&pos=2&origPos=23&origPageSize=10&track=true

Bill of materials - LSU

Load sharing unit Amount Link

Ball screw 1

Ball nuts 3

Hydraulic housing 3

Doughnut load cells 6

Fresh hydraulic oil 1

Threading tape 1

Assembly Spacers 6

Existing Pressure Gauge 1

https://www.roemheld-g

ruppe.de/shop/en/9820

000.html

Additional Pressure Gauge 1

https://www.roemheld-g

ruppe.de/shop/en/9820

000.html

Pressure Gauge union 2

https://www.roemheld-g

ruppe.de/shop/en/f9-30

0-fittings-with-24-cone-a

s-per-din-en-iso-8434-1/

9208011.html

T union 8mm 3

https://www.roemheld-g

ruppe.de/shop/en/f9-30

0-fittings-with-24-cone-a

s-per-din-en-iso-8434-1/

9208009.html

Check Valve 8mm 2

https://www.roemheld-g

ruppe.de/shop/en/9208

012.html

Flow Control Valve (Bleeder) 6mm 2

https://www.roemheld-g

ruppe.de/shop/en/c2-94

0-flow-control-valve-wit

50 KTH

h-locking-screw/2956311

.html

Hydraulic tube 8mm (1m) 1

https://www.roemheld-g

ruppe.de/shop/en/f9-30

0-fittings-with-24-cone-a

s-per-din-en-iso-8434-1/

3128112.html

Existing Hydraulic Hose (0,5m) 1

Additional Hydraulic Hose (0,5m) 1

https://www.roemheld-g

ruppe.de/shop/en/f9-36

1-hydraulic-high-pressur

e-hoses/9375100500.ht

ml

Existing Male Stud 6mm 6

https://www.roemheld-g

ruppe.de/shop/en/f9-30

0-fittings-with-24-cone-a

s-per-din-en-iso-8434-1/

9206028.html

Existing Male Stud 8mm 2

Additional Male stud 6mm 6

https://www.roemheld-g

ruppe.de/shop/en/f9-30

0-fittings-with-24-cone-a

s-per-din-en-iso-8434-1/

9206028.html

PTFE Tape 1

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Appendix C - Work Breakdown Structure Chart

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Appendix D - GANTT chart

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Appendix E - Torque Sensor

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Appendix F - Doughnut Load Cells Data Sheet

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Appendix G - Arduino Data Sheet

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Appendix H - S-Shaped Force Sensor Data Sheet

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Appendix I - Encoder Data Sheet

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Appendix J - Ball Screw Data Sheet

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Appendix K - Matlab Code clear all, close all, clc  %Higher Course II Machine Design MF2077 %Fall 19  %% variables f3=2;  f1=3.8; v=1; %m/s m=100; %kg, load g=9.81; h=1; %m, height load is traveled    % Main ball screw,SKF SL/TL 32x40 R d_0=32; %mm, nominal d_2=26.9; %mm, root diameter mu=0.006; %coefficient of friction P_h=40; %mm, lead L=1.5e3; %mm, distance between supporting bearings %% Efficiency eta=1/(1+pi*d_0*mu/P_h); etad=2-1/eta;  %% Buckling F_c=34*1000*f3*d_2^4/(L^2); %N, safety factor 3 included in equation  %% Critical speed n_cr=0.8*49*10^6*f1*d_2/(L^2); %rpm, 80% recommended according to SKF v_cr=10^-3*d_2*pi*n_cr/60; %m/s   %% Flywheel wrev=v/(P_h*10^-3); %rev/s w=wrev*2*pi; %rad/s I_fw=2*m*g*h/(w^2); %kgm2, assumption of zero losses   %% Acceleration m_2=200; m_lsu=20;  g=9.81; h=2; %height of drop mu=0.004; %friction coeff of linear guide a=(2*m_2*g-mu*m_lsu*g)/(2*m_2+m_lsu);  

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v=sqrt(2*a*h); 

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Appendix L - Arduino Code // Machine Design Advanced course II // Fall 2019 // Final Arduino code for testing load sharing  #include "HX711.h"  //HX711 scale1; //HX711 scale2; HX711 scale3; HX711 scale4; HX711 scale5; HX711 scale6; HX711 scales;  // HX711 circuit wiring //const int LOADCELL1_DOUT_PIN = 2; //1 //const int LOADCELL1_CLK_PIN = 4; // //const int LOADCELL2_DOUT_PIN = 13; //2 //const int LOADCELL2_CLK_PIN = 11;  const int LOADCELL3_DOUT_PIN = 34; //3 const int LOADCELL3_CLK_PIN = 40;  const int LOADCELL4_DOUT_PIN = 29; //4 const int LOADCELL4_CLK_PIN = 33;  const int LOADCELL5_DOUT_PIN = 23; //5 const int LOADCELL5_CLK_PIN = 24;  const int LOADCELL6_DOUT_PIN = 2; //6 const int LOADCELL6_CLK_PIN = 4;  const int LOADCELLS_DOUT_PIN =45; // S const int LOADCELLS_CLK_PIN = 51;  // Calibration factors for each load cell //float calibration_factor1 = -27680; // 1st sensor calibrated for 2 kg //float calibration_factor2 = -33100; // 2nd sensor calibrated for 2 kg float calibration_factor3 = 47580; // 3rd sensor calibrated for 2 kg float calibration_factor4 = 66340; // 4th sensor calibrated for 2 kg 

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float calibration_factor5 = 53900; // 5th sensor calibrated for 2 kg float calibration_factor6 = 103440; // 6th sensor calibrated for 2 kg float calibration_factors = -4420; // s sensor calibrated for 2 kg  void setup() {  Serial.begin(9600);     // Set up for saving data to excel  Serial.println("CLEARDATA");  Serial.println("CLEARSHEET");  Serial.println("LABEL,Date,Time,Timer,LC 3 [kg],LC 4 [kg],LC 5 [kg],LC 6 [kg],LC S [kg]");  Serial.println("RESETTIMER");   // Initiating load cells // scale1.begin(LOADCELL1_DOUT_PIN, LOADCELL1_CLK_PIN); // //scale1.set_scale(); // scale1.tare(); //Reset the scale to 0 // // scale2.begin(LOADCELL2_DOUT_PIN, LOADCELL2_CLK_PIN); // //scale2.set_scale(); // scale2.tare(); //Reset the scale to 0   scale3.begin(LOADCELL3_DOUT_PIN, LOADCELL3_CLK_PIN);  //scale3.set_scale();  scale3.tare(); //Reset the scale to 0   scale4.begin(LOADCELL4_DOUT_PIN, LOADCELL4_CLK_PIN);  //scale4.set_scale();  scale4.tare(); //Reset the scale to 0   scale5.begin(LOADCELL5_DOUT_PIN, LOADCELL5_CLK_PIN);  //scale5.set_scale();  scale5.tare(); //Reset the scale to 0   scale6.begin(LOADCELL6_DOUT_PIN, LOADCELL6_CLK_PIN);  //scale6.set_scale();  scale6.tare(); //Reset the scale to 0   scales.begin(LOADCELLS_DOUT_PIN, LOADCELLS_CLK_PIN);  //scales.set_scale();  scales.tare(); //Reset the scale to 0 }  void loop() { 

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//Adjust to this calibration factor // scale1.set_scale(calibration_factor1); // scale2.set_scale(calibration_factor2);  scale3.set_scale(calibration_factor3);  scale4.set_scale(calibration_factor4);  scale5.set_scale(calibration_factor5);  scale6.set_scale(calibration_factor6);   scales.set_scale(calibration_factors);     // Printing values in excel // Serial.println((String) "DATA, DATE, TIME, TIMER," + scale3.get_units()+ "," + scale4.get_units()+ "," + scale5.get_units()+ "," + scale6.get_units() + "," + scales.get_units());  // Serial.println(scale1.get_units(), 3); Serial.print(",");  // Serial.println(scale2.get_units(), 3); Serial.print(",");  //Serial.print("Reading:");  Serial.println(scale3.get_units(), 3); //Serial.print("\n");  Serial.println(scale4.get_units(), 3); //Serial.print("\n");  Serial.println(scale5.get_units(), 3); //Serial.print("\n");  Serial.println(scale6.get_units(), 3); //Serial.print("\n");  Serial.println(scales.get_units(), 3); Serial.print("\n");  } 

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Appendix M - Matlab Code for Test Data % Machine Design Advanced course II % Fall 2019 % Code for importing the data from the arduino to matlab for analysis   clear all, close all, clc   formatSpec = '%f'; test1 = fopen('newtest1.txt','r'); T1 = fscanf(test1,formatSpec);   LC3 = T1(1:5:end); LC4 = T1(2:5:end); LC5 = T1(3:5:end); LC6 = T1(4:5:end); LCS = T1(5:5:end);   t = 1:1:length(LC3);   Figure(1) plot(t,LC3,'r'); hold on plot(t,LC4,'c'); plot(t,LC5,'b'); plot(t,LC6,'g'); title('Forward test round 1'); ylabel('Weight [kg]'); xlabel('Time [s]'); legend('LC3','LC4','LC5','LC6');   % LC3 = LC3 + 1; % LC6(36:71) = LC6(36:71) + 3; %  % Figure(2) % plot(t,LC3,'r'); % hold on % plot(t,LC4,'y'); plot(t,LC5,'b'); plot(t,LC6,'g'); % title('Test round 1'); % ylabel('Weight [kg]'); % xlabel('Time [s]'); % legend('LC3','LC4','LC5','LC6') 

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