IN
DEGREE PROJECT MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS
STOCKHOLM SWEDEN 2020,
Evaluation of linear force actuators in a pin-on-disc test rig application
JAKUB JAN RUPNIEWSKI
Evaluation of linear force actuators in a pin-on-disc test rig application
Jakub Jan Rupniewski
Master of Science Thesis MMK TRITA-ITM-EX 2020:574 IPUC KTH Industrial Engineering and Management
Machine Design SE-100 44 STOCKHOLM
Examensarbete MMK TRITA-ITM-EX 2020:574
En utvärdering av användning av linjära kraftmanövderdon i stift-mot-skiva-testriggar
Jakub Rupniewski
Godkänt
2020-10-28
Examinator
Martin Törngren
Handledare
Masoumeh Parseh
Uppdragsgivare
Atlas Copco
Industrial Technique AB
Kontaktperson
Mayank Kumar Erik Persson
Sammanfattning
Examensarbetet utvärderar och jämför två linjära manöverdon för att applicera en last på en stift- mot-skiva tribologitestrigg. Det första manöverdonet är en DC-motor med en kulskruv. Det andra manöverdonet är en talspole. Manöverdonen behöver följa kraftprofilsreferensen som motsvarar kontaktfriktionen i gängorna vid en skruvdragning. En Simulink modell av en stift- mot-skiva testrigg skapades för att jämföra manöverdonen. Styrenheterna för båda manöverdonen designades med samma designmetod. 27 experiment genomfördes i Simulink med varierande kraftreferenser, modellparametrar och störningar. Resultaten av alla experiment utvärderades med det kvadratiska medelvärdet för att jämföra de två manöverdonen. Talspolen var överlägsen DC-motorn med kulskruven i alla experiment. Talspolen användes därför i stift- mot-skiva testriggen för att undersöka friktionsvariationen under en skruvdragning.
Simuleringarna visade en stor betydelse av skivvåg på kraftvariation. Friktion som förekommer i linjära ställdon är en viktig fråga vid korrekt prestanda för referenskraftprofilspårning, och därför ska ställdonen utformas noggrant och väljas för att minimera friktionen. Den utvecklade simuleringsmodellen ska valideras i framtiden för att bevisa att avhandlingens resultat överensstämmer med verkligheten. När modellen väl har validerats kan den användas för att prova olika styrenhetsarkitekturer och hitta den som passar bäst i referensstyrningsprofilens spårningsapplikation.
Master of Science Thesis MMK TRITA-ITM-EX 2020:574
Evaluation of linear force actuators in a pin-on-disc test rig application
Jakub Rupniewski
Approved
2020-10-28
Examiner
Martin Törngren
Supervisor
Masoumeh Parseh
Commissioner
Atlas Copco
Industrial Technique AB
Contact person
Mayank Kumar Erik Persson
Abstract
This thesis presents an evaluation and comparison of two linear actuators that can be used as load application actuators in a pin-on-disc tribological test rig. The first actuator is a DC-motor with an external ball screw, and the second actuator is a voice coil. The actuators are required to follow the reference force profile which corresponds to the thread contact force during a screw tightening process. In order to compare the two actuators, a Simulink model of the pin-on-disc test rig was created to be used as an experimental environment. The controllers for each actuator were designed using the same design method. Further, a set of 27 experiments was performed in Simulink with different reference force profiles, model parameters and possible disturbances.
The results of each experiment were evaluated using Mean Square Error metrics and then compared between the actuators. For all the performed simulations the voice coil shows superior performance compared with the DC-motor and a ball screw. Based on these results, the choice was made to use the voice coil in the pin-on-disc test rig design for investigating the friction variation during a tightening process. The simulations showed a high importance of disc waviness on force variation. Friction occurring in linear actuators is a main concern in accurate performance of reference force profile tracking, and hence the actuators shall be carefully designed and chosen to minimize friction. The developed simulation model shall be validated in the future to prove that the results of the thesis agree with reality. Once the model is validated, it can be used to try different controller architectures and find the one that fits best the reference force profile tracking application.
FOREWORD
First and foremost, I would like to thank my parents Urszula and Mieczysław, along with my sister Anna for their invaluable support during my pursuit for a higher education.
It was a great adventure to do my thesis at Atlas Copco, and I would like to thank my supervisors Mayank Kumar and Erik Persson for their support and trust in realizing the ideas that resulted in the successful piece of work that I am very proud of. I am grateful to all the colleagues that provided me with a valuable input during my work in Atlas Copco. Special thanks to Guillermo Bossi for his energy and support in the lab.
Thank you, Zhan-Jun Lin, for your commitment to the project. It was a great time working together.
I would like to thank Masoumeh Parseh, my academic supervisor for the help in improving the quality of the following work.
I would like to thank to all my friends with whom I spent great two years of my master’s studies, especially to Lucas, Seshagopalan, Oskar, Anirudh, Gustav and Matthew.
Jakub Rupniewski Stockholm, October 2020
NOMENCLATURE
Abbreviations
AC Alternate Current
BLDC Brushless DC Motor
CAD Computer Aided Design
CAE Computer Aided Engineering
DC Direct Current
DIY Do It Yourself
FEM Finite Element Method
IAE Integral Absolute Error
ISE Integral Squared Error
ITAE Integral Time Absolute Error ITSE Integral Squared Error
MSE Mean Square Error
PID Proportional Integral Derivative
ZOH Zero-order Holding
TABLE OF CONTENTS
SAMMANFATTNING (SWEDISH) 1
ABSTRACT 3
FOREWORD 5
NOMENCLATURE 7
TABLE OF CONTENTS 8
1 INTRODUCTION 10
1.1 Background 10
1.2 Purpose 11
1.3 Delimitations 12
1.4 Method 12
2 FRAME OF REFERENCE 14
2.1 Bolt tightening 14
2.2 Tightening strategies 15
2.3 Thread contact 19
2.4 Tribometers 22
2.5 Pin-on-disc concept 24
2.6 Disc motion 26
2.7 Measurement system 27
2.8 Turbotight testing 31
2.9 Controller design 32
2.10 System performance 42
3 IMPLEMENTATION 44
3.1 System modelling 44
3.2 Controller design 70
4 RESULTS 74
5 DISCUSSION AND CONCLUSIONS 78
6 RECOMMENDATIONS AND FUTURE WORK 80
6.1 Recommendations 80
6.2 Future work 80
7 REFERENCES 81
1 INTRODUCTION
Bolts and nuts are components widely used in any mechanical application. We know them from everyday life, we used them while assembling some furniture or repairing some household equipment or a car. They are commonly used threaded elements used mainly to hold two pieces together. Holding is achieved after tightening the threaded fastener. From household perspective, tightening process of bolts is often simple, as it only demands a screw or wrench and use of human muscles. An example of bolts and screws is shown in Figure 1.
Figure 1. Bolts and screws, source: Pixabay
Bolts and nuts are part of a bigger family – fasteners. All the machines contain many fasteners, and they are the basic building blocks in machine design. The economy of scale leverages importance of improvement in fastener design, manufacturing, assembly, and quality control. For example, the Boeing 747 involves around 2.5 million fasteners – even a tiny improvement multiplied by such a large number introduces a significant difference.
1.1 Background
While designing a screw joint, an engineer requires a given clamping force between clamped members. Based on that, it is possible to determine a screw size and the amount of screws necessary for assembly. During the tightening process torque is measured which should indicate the clamping force of a joint. Torque during tightening is used to create the clamping force and overcome friction between thread of screw and nut, and between washer and nut [1]. To precisely determine the clamping force, it is necessary to predict what friction torque is generated during tightening. Hence, a good theoretical understanding of tribology of screw joints is of great importance in developing tightening techniques.
One of the Atlas Copco products are nutrunners for tightening screw joints. There are several well-established tightening techniques in nutrunner operation [2]. In the case of Turbo Tight technique, joint is tightened in 20-60 ms with small impacts – that helps nutrunner operators to
understood, which makes it more difficult to provide correct prediction on friction torque during tightening. Atlas Copco has an intention to investigate fundamental friction behaviour during short pulses. To do it, a new pin-on-disc test-rig should be developed with the focus on testing a friction behaviour during short force impacts.
1.2 Purpose
Currently existing pin-on-disc test rigs mainly focus on wear behaviour and friction investigation under steady state conditions. In that case, a linear actuator could be designed as a weight loading the pin [4], stepper motors with rack and pinion [5], or stepper motor with a ball screw and nut [6]. In contrast to above test-rigs, the new design shall perform short, transient tests with user-defined force and velocity profile during one test. This application demands special consideration of the actuator choice – for instance, the weight loaded pin is not an option. In order to perform quick 20-60ms tests with pre-defined force profile, the actuator should act as fast as possible. The higher the actuator bandwidth, the more flexibility in force-profile definition. For that reason, the thesis investigates linear actuator choice and controller design with the focus on actuator performance of tracking a high-frequency force set point.
DC motor linear actuators with nut and a screw are market available and might perform well under the transient load application. They have integrated linear transmission that allow reaching large normal force while maintaining small size of the actuator itself. If the peak force capability is larger than required, controller can be tuned with high gain which increases the system bandwidth. However, power transmission within the actuator is a source of backlash and reduces system stiffness – that will contribute to transient control inaccuracies that might lead to difficulties in meeting the set point tracking requirement. Furthermore, the integrated actuator consists of many components in the power flow, and each component model introduces series of modelling uncertainty that might have a significant influence on an actual actuator performance.
Voice coil is another solution proven to be well performing in force-control driven applications [7], including market available pin-on-disc fretting test rig with fast force application of up to 500 Hz [8]. Voice coil actuator is characterized by directly exerted force from magnetic field.
This gives an advantage from dynamic behaviour point of view as it provides stiff force transfer and lacks components that could be responsible for backlash, play or other non-linear behaviour.
For the given peak force, voice coils are more expensive and are larger than DC-motor integrated linear actuators. Since both compared actuators will be chosen at similar price range, the chosen voice coil will have smaller peak force performance, so the controller gain will not be able to increase the voice coil bandwidth as much compared with DC-motor integrated linear actuator.
Moreover, inertia of the voice coil might be larger compared with smaller integrated actuator.
Each test performed on the new machine is going to start with pre-defined pin force profile, and disc velocity profile. In order to follow the force profile as accurate as possible, force profile information shall be used to calculate a control signal based on the actuator model. In ideal case, the force profile will be perfectly followed by the actuator. Unfortunately, models never correspond reality to full extent, so all modelling uncertainties must be compensated by a feedback controller.
The research question investigated in the thesis is:
Considering a voice coil or a DC-motor with a ball screw as linear force actuators in a pin-on- disc tribological test rig, what is the better choice in force profile tracking control task investigating the friction variation during a tightening process? Mean squared error performance metrics is used to measure and compare performance of the systems under different load conditions, model parameters, and the influence of disturbances.
The output of the thesis shall help in the choice between the voice coil and DC-motor integrated linear actuator in a design of a pin-on-disc test rig for investigating transient tribological behaviour.
1.3 Delimitations
During the time of the thesis the test-rig was built and the outcomes of the thesis have been implemented in the design. However, the test-rig design is not included in the report.
The thesis is based on the simulations done in Simulink. The Simulink model hasn’t been validated due to the time constraint. The validation shall be performed in the future to improve and prove the correctness of the simulations.
The thesis focuses only on comparing two actuators: the voice coil and the DC-motor with a ball screw. There might be other feasible solutions for the linear actuator, like use of a rack and pinion mechanism, which could overperform the investigated actuators in application of pin-on- disc test rigs. In case other actuators are interesting, they shall be investigated in the future study with the help of this thesis.
Only DC-motor is investigated in combination with a ball screw. The BLDC or stepper motor might be advantageous compared with the DC-motor, and in case other motors are interesting to compare, another study with the focus on other motors shall be performed.
1.4 Method
The control performance assessment method was presented in [9] and the main activities involved are process modelling, performance specifications, performance measurement and performance analysis. The assessment shall finish with improvement suggestions and implementation of the results. The above steps are the reference for the thesis. The performance specification was defined based on [10], and the mean square error metric was used to measure the tracking performance of the system. Since there are several factors that might influence the system behaviour and the results, the influence is investigated using the design of experiments method. Based on [11], the factorial experiment will be conducted, so that several influential factors will be varied together. All the experiments are going to be performed as simulations so there is no high cost involved. Due to that, the full factorial experiment will be performed meaning that all the possible combinations of factor levels will be investigated.
The pin-on-disc test rig will be modelled using Simscape as a multi-body system. Two cases of the linear actuator are investigated – DC motor and voice coil. Both actuators will be modelled as electromechanical machines. For each actuator individual force feedback controller will be developed using the same control design method (integral time absolute error (ITAE) optimal pole placement), and the same controller design requirements. The design method and the control requirements are chosen to be the same for both the actuators in order to minimize the impact of the controller on the comparison between the actuators.
Several simulations will be performed under different load conditions, model parameters and the influence of disc surface waviness. Stiffness and damping ratio are the model parameters difficult to estimate, and they are going to be varied during the experiment. After each simulation, the actuator performance will be evaluated using the Mean Square Error (MSE) metrics.
The requirement of the test rig is to test normal force up to 240N. To have the good understanding of the performance at different load levels, the simulation will be performed for
The modelling introduces uncertainty caused by modelling errors. To consider that in the actuator evaluation, several tests will be performed for each load level. Based on the [12], the damping ratio for metal structures with joints varies approximately between 50% and 150% of the mean value 𝜁 = 0.05. Due to that, there will be two more test scenarios – one with 50%
smaller, and the other with 50% larger damping ratio than initially estimated.
The stiffness of the components is calculated either using Hooke’s Law, or FEM calculation.
Both methods are not accurate, and possible influence of wrong stiffness estimation will be considered. The stiffness will be likewise tested for 30% smaller and 30% larger of the initially estimated value.
Finally, the rotating disc is not perfectly flat, and the waviness of the disc will be considered as presented in the 3.1.12 subchapter. Two different test cases are with or without waviness.
The experiment contains of 27 simulations for each actuator, and the experimental matrix is presented in Table 1.
Table 1. Experimental matrix
Simulation No. Force Stiffness Damping ratio Waviness
1 50 N 100% 100% No
2 150 N 100% 100% No
3 240 N 100% 100% No
4 50 N 70% 50% No
5 150 N 70% 50% No
6 240 N 70% 50% No
7 50 N 130% 50% No
8 150 N 130% 50% No
9 240 N 130% 50% No
10 50 N 70% 150% No
11 150 N 70% 150% No
12 240 N 70% 150% No
13 50 N 130% 150% No
14 150 N 130% 150% No
15 240 N 130% 150% No
16 50 N 70% 50% Yes
17 150 N 70% 50% Yes
18 240 N 70% 50% Yes
19 50 N 130% 50% Yes
20 150 N 130% 50% Yes
21 240 N 130% 50% Yes
22 50 N 70% 150% Yes
23 150 N 70% 150% Yes
24 240 N 70% 150% Yes
25 50 N 130% 150% Yes
26 150 N 130% 150% Yes
27 240 N 130% 150% Yes
The overall performance metric will be an arithmetic mean of all the simulations performed.
Afterwards, the metrics will be compared between the voice coil and a dc-motor with the ballscrew. The actuator having lower Mean Square Error will be recommended to be used in further design.
2 FRAME OF REFERENCE
The frame of reference chapter provides an insight into the mechanics of tightening, and tightening strategies which is the basis for the experiments performed on the newly developed tribological test rig. Further, the pin-on-disc tribological test rig is introduced with all the components that it contains. A good understanding of the design of pin-on-disc test rig is crucial in further modelling of the one used during the thesis. The chapter continues with introduction of controller design methods, showing different possible approaches during designing the controller for the voice coil and DC-motor. The chapter finishes with the introduction of the controller performance metrics, with focus on Mean Square Error metric that is used in the thesis for evaluating performance of the actuators.
The frame of reference starts with introducing the reader with the bolt tightening techniques [13]
which is the background of the thesis purpose. Further, the tribometers are introduced [14], [15]
as laboratory equipment to investigate the friction between materials. The pin-on-disc tribometer design is described in the details with focus on linear force actuators [16], [17], [18], [19], [20].
In the end the PID controller [21] and PID controller design methods are presented [22], [23], [24], [25], [26], [27], [28]. The modelling of pin-on-disc test rig components is covered mainly in the Implementation chapter under sections corresponding to each of the components.
2.1 Bolt tightening
The tightening of fasteners is achieved with the help of the thread. Relative rotation between a bolt and a nut causes an axial movement between the two components. When the axial movement is restricted by some machine components, the further rotation starts tightening of the bolt. The machine components are clamped with the force that opposes the tightening process.
The clamping force is a crucial parameter of the connection. The bolt connection can be loaded in parallel to the bolt axis, or perpendicular. In the first case the joint is subjected to the tensile load, and the main purpose is to keep the surfaces from separating or leaking. To achieve it, the clamping force must be sufficient, so even during the maximum load the clamping force holds the machine components together. The shear load happens when the load is applied in perpendicular direction. In that case, the joint shall prevent the machine components from slipping between each other. To do so, the clamping force shall create enough friction between the machine components to prevent the joint failure. Both the loading scenarios are presented in Figure 2 [13].
Figure 2. Fastener connection loading scenarios [13]
In both the cases it is the clamping force that determines whether the joint is maintaining the function when the load is applied. When designing the jointm the clamping force is estimated based on the machine application, then the design is refined with number of bolts, bolt type, size, material, and strength. To assemble the joint, the assembly method is chosen and corresponding assembly parameter like tightening torque is calculated based on the requested clamping force.
The tightening process is subjected to uncertainty of the calculation method, so a safety factor is introduced to reduce the chance of failure. The bigger the safety factor, the more expensive is the joint itself. From that perspective, it is favourable to improve the calculation methods and understanding of the tightening process, so that the resulting assembly has higher certainty of reaching the required clamping force once the tightening is completed.
2.2 Tightening strategies
There are many ways to tighten the bolt. The simplest one, and most common in everyday life is the use of wrench with the help of human muscles. The typical wrenches are presented in Figure 3. It is often satisfactory for minor household repair, as the tools are relatively cheap, and the accuracy is not critical.
Figure 3. Typical household wrenches
When repairing the car, e.g. changing the tires, it is already recommended to use a torque wrench that allows to set the target tightening torque according to the car datasheet. The torque wrench is presented on the right side of the picture.
In industrial application the tightening tools are often powered with a compressed air, hydraulics, or electric motors. The tightening strategies that control the tools can be mainly divided into torque control, angle control, gradient control, and elongation control.
2.2.1 Torque control
The goal of the tightening is to reach the specified clamping force. It is possible to approximately calculate the tightening torque that corresponds to the given clamping force – the derivation of that calculation is presented in chapter 2.3. The first tightening strategy based on the torque control are tools using a continuous drive, with the clutch that can be adjusted for maximum torque that it can transfer. The tightening tool is rotating the bolt and once the set torque is reached, the clutch disengages. This technique is also commonly used in electric screwdrivers that are used in household application and DIY projects.
There are two more torque control strategies, both are called highly dynamic tightening. The first one is pulse tightening – the tool creates subsequent impact pulses and uses the impact to tighten the joint gradually. In Figure 4 the red colour presents the torque impact pulses, and the green colour presents the build-up of the clamping force. On the right side the conceptual view of pulse tightening is presented. The blue colour represents the residual torque remaining in the joint. It is visible that the maximum value of the torque differs compared with the one used during pulse tightening. The reason is mainly different friction value between the threads under the pulse tightening and at the end of tightening.
Figure 4. Pulse tightening, source: Atlas Copco
The second highly dynamic tightening method is called Turbotight® and it is a registered trademark symbol by Atlas Copco. The idea behind this strategy is to estimate the amount of energy needed for the tightening to be completed, and store that energy in the rotational motion of the motor before tightening starts. Once the tightening starts the energy from the rotating motor of the tool is transferred to the joint and used to tighten the bolt. Thanks to that, the tightening itself takes 30-80 ms and significantly reduces the tightening time. On the left side in Figure 5 the clamping force build-up is presented with the green plot, and the red plot shows the torque acting during the Turbotight. The torque used during the Turbotight process is smaller compared with the residual torque represented by a blue plot – the reason is different friction
conceptual view of the Turbotight is presented – the rotor of the motor storing exact amount of energy to complete tightening is conceptually similar to the car that speeds up to reach the energy that exactly allows it to climb the hill and stop right after reaching the hill.
Figure 5. Turbotight® tightening, source: Atlas Copco
The main advantage of using torque control is that it is well established method with a lot of experience in industry. There are standard torque data available for standard bolt sizes and grades. Another strong advantage is quick tightening using Turbotight strategy. The disadvantage is a high clamp force scatter caused by a high friction variation. It is especially the case for pulse tightening and Turbotight.
2.2.2 Angle control
Another possibility of controlling the tightening process is to use the information about the angle of rotation of the nut, after the nut is bottomed so that any further movement causes the bolt to stretch. The screw moves the distance of a screw pitch 𝑃 during one rotation. In that case, the angle increment 𝜃𝑅 of the screw elongated by Δ𝐿 is as follows:
𝛥𝐿
𝜃𝑅
=
𝑃360 ( 1 )
If the joint stiffness is known, the relationship between the bolt elongation Δ𝐿, joint stiffness 𝐾𝐽 and a clamping force 𝐹 can be written
𝐹 = 𝐾𝐽⋅ 𝛥𝐿 = 𝐾𝐽 ⋅ 𝑃 ⋅ 𝜃𝑅
360 ( 2 )
From that equation the angle can be determined based on the required clamping force when operating in elastic region of the bolt joint [13].
If bolt yielding is allowed in the given application, it is also possible to tighten the bolt until it reaches the plastic range – it increases the repeatability of the clamping force using angle control strategy.
The main advantage of this method is that it does not depend on the friction, and the force scatter is reduced compared with the torque control. The drawback is that the experimental analysis is needed to determine the angle, and the tool needs both the torque and angle measurement what makes them more expensive.
2.2.3 Gradient control
If application allows for it, it is advantageous to use bolts in yield working condition as the utilization of such a bolt is very high. Once that is the case, the tool can tighten the joint until it reaches the yield point, and it can be achieved by comparing the torque increase to elongation of the bolt. At the yield point the torque change is small with further increase of elongation. That point can be detected, and tightening is finished. The representation of different torque rate during tightening is presented in Figure 6.
Figure 6. Gradient control, source: Atlas Copco
The main advantage is that the method is independent on friction variation, hence low scatter in clamping force. Further, the bolt has a high utilization as it uses the full strength of the bolt. The drawback is that the joint must be analysed experimentally.
2.2.4 Elongation control
To estimate the clamping force from the angle measurement we need to know the stiffness of the joint. Unfortunately, the stiffness of the complete joint is not constant at all during the operating condition, and it might be difficult to calculate or do experiments for certain applications. To overcome that problem, it is possible to measure the elongation of the bolt itself and use the bolt stiffness to determine the clamping force. The tightening based on the elongation control can be performed by using the ultrasonic sensor, hydraulic clamping device presented in the centre of the picture, or special bolts that indicate once the specific preload has been reached presented on the right side in Figure 7.
Figure 7. Elongation control in threaded fasteners [13]
The main advantage of the elongation control is very low clamping force scatter, especially for ultrasonic measurement. The methods are very expensive and justified to use only for safety critical application like nuclear plants or airspace industry.
The big challenge when choosing the tightening strategy is having the trade-off between clamping force scatter, bolt utilization, cost of the tools capable of performing specific tightening method and time that it takes to tighten the screw. The torque-controlled tools have an advantage of fast tightening especially for Turbotight strategy, relatively low cost, and torque calculation methods that many engineers are used to use. However, due to large friction variation which currently is hard to predict, the clamping force scatter is large, what means higher safety factors, lower bolt utilization and ultimately more expensive joint design. The friction variation uncertainty is the main reason the thesis project has been initiated.
2.3 Thread contact
The transmission from bolt rotation torque to clamping force occurs at the thread of the bolt.
However, not all the torque is used to tighten the bolt – most of the torque (around 50%) is consumed to overcome friction between the nut and washer, and further part of the torque (around 40%) is consumed by the friction between the threads.
Having a closer look at the thread, it can be observed that nut movement around the bolt can be analysed through the analogy of a body climbing up the inclined plane with an angle 𝛽, as presented in Figure 8. Static analysis of the block shows that the force 𝐹𝐿 necessary to lift the body contains the longitudinal part of the clamping force 𝐹 which is 𝐹 ⋅ sin𝛽 and a friction term which is the normal force 𝐹𝑁⋅ cos 𝛽 multiplied with a friction coefficient between the threads 𝜇𝐺:
𝐹𝐿 = 𝐹 ⋅ 𝑠𝑖𝑛𝛽 + 𝐹𝑁⋅ 𝑐𝑜𝑠 𝛽 ⋅ 𝜇𝐺 ( 3 )
Figure 8. Thread analogy as an inclined plane, source: Atlas Copco
The tightening is performed by applying torque to the joint. To calculate the necessary torque, it is assumed that the force on the thread acts at the mean diameter between the top and bottom of the thread 𝑑2 = 𝑑+𝑑3
2 according to Figure 9. The normal force acting between the threads is calculated knowing the angle 𝛼 which is half an angle of the thread profile.
Figure 9. Friction diameter determination, source: Atlas Copco
𝐹
𝑁=
𝐹𝑐𝑜𝑠 𝛼 ( 4 )
The tightening torque is corresponding to a circumferential direction of the force. Since the climbing force is inclined with the angle 𝛽, the force that corresponds to the tightening torque is calculated as follows:
𝐹
𝐺=
𝐹𝐿𝑐𝑜𝑠𝛽 ( 5 )
The tightening torque on the thread is then:
𝑀
𝐺= 𝐹
𝐺⋅
𝑑22
=
𝜇𝐺⋅𝐹⋅𝑐𝑜𝑠𝛽
𝑐𝑜𝑠𝛼 +𝐹⋅𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛽
⋅
𝑑22 ( 6 )
The torque under the bolt head is calculated as friction torque acting at the friction diameter 𝐷𝐾𝑚 of the bolt head where the normal force is a clamping force 𝐹 and the friction coefficient between the bolt head and the washer is 𝜇𝐾:
𝑀𝐾 = 𝐹 ⋅ 𝜇𝐾 ⋅𝐷𝐾𝑚
2 ( 7 )
Hence, the total torque necessary to tighten the screw:
𝑀𝐴 = 𝑀𝐺 + 𝑀𝐾 =
𝜇𝐺⋅𝐹⋅𝑐𝑜𝑠𝛽 𝑐𝑜𝑠𝛼 +𝐹⋅𝑠𝑖𝑛𝛽
𝑐𝑜𝑠𝛽 ⋅𝑑2
2 + 𝐹 ⋅ 𝜇𝐾⋅𝐷𝐾𝑚
2 ( 8 )
From the geometry of the screw, we have
𝑡𝑎𝑛𝛽 = 𝑃
𝜋𝑑2 ( 9 )
where 𝑃 is the distance between two adjacent threads. Substituting it to the tightening torque equation we get the Kellerman-Klein equation:
𝑀𝐴 = 𝐹 ⋅ (𝑃
2𝜋+ 𝑑2
2 𝑐𝑜𝑠 𝛼𝜇𝐺 +𝐷𝐾𝑚
2 𝜇𝐾) ( 10 )
In that form of the equation we can clearly see the influence on the tightening torque from the screw stretching 𝐹 ⋅ 𝑃
2𝜋 , friction between the threads 𝐹 ⋅ 𝑑2
2 cos 𝛼𝜇𝐺, and friction under the bolt head 𝐹 ⋅𝐷𝐾𝑚
2 𝜇𝐾.
To clamp the joint with the required clamping force, the torque can be calculated from the Kellerman-Klein equation. The geometrical properties of the bolt joint are easy to measure.
However, the results are strongly dependent on correct determination of the friction coefficient between the thread and between the bolt head and the washer.
Friction determination is not the easiest task to do, as there are some 30 or 40 variables that affect friction that the threaded fastener experiences. Some of them are hardness of parts, surface finish, type of material, thickness and type of coating, lubricant properties, fit between threads, manufacturing method of the threaded fasteners. [13]
The above equation was derived based on static of the bolt and nut. When the tightening process is sufficiently slow, the above assumption might be justified. However, in industrial application tightening time is an important economical factor, and the tightening process might be as fast as 30 ms and the rotating speed of bolt and nut is not negligible anymore. Friction coefficient between two mating bodies with lubricant in between often follows the Stribeck curve, where the friction coefficient is plotted against product of dynamic viscosity of the lubricant 𝜂 and rotational speed 𝑁 divided by the average pressure between the bodies 𝑃. The Stribeck curve is presented in Figure 10.
Figure 10. Stribeck curve [14]
At low speeds, the lubricant only fills the empty space between the bodies, and almost all the load is transferred through the direct metal-metal contact. In that way Coulomb friction is dominating and is approximately constant. With the rise of the speed, lubrication film is building up between the contact bodies and the bodies are becoming separated by the lubricant which significantly reduces the friction coefficient. That region is called mixed lubrication. With the further speed increase, the contact bodies are fully separated, and the only friction source is the internal lubrication shearing which is proportional to the speed. In the tightening process, during the run down of the nut the load is barely anything and the speed is high. Once the tightening starts there is a rapid decrease of the speed and increase of the load. That also means power dissipation into heat and local temperature build up. Transient working condition of the tightening process suggest that the friction might change throughout the whole tightening process. There is not much knowledge about friction behaviour under the transition working condition. All these consideration makes the friction coefficient estimation difficult, and often experiments of the joints are necessary at designated bolt test rigs designed for evaluation of clamping force tendency for a particular joint design. Another, more fundamental approach, is to test the friction coefficient between two materials using standardized material samples and standardized tribological test rigs called tribometers.
2.4 Tribometers
The field of science that investigates an interaction between two contacting bodies in relative motion is called Tribology. The main topics that tribology investigates are friction behaviour and material wear during the operation of mechanical components. Tribology helps engineers to evaluate, quantify and optimize mechanical component design where contact between two bodies is a challenge. From tribology perspective, every design case that introduces tribological challenge can be represented as a tribosystem. The representation of a tribosystem is presented in Figure 11.
Figure 11. Representation of the tribosystem [14]
Two bodies loaded with the normal force 𝐹𝑛 are moving between each other with the relative velocity Δ𝑣. The bodies are characterized by material and geometry properties that influence the behaviour of the tribosystem. Material properties are strength, stiffness, hardness distribution, chemical composition, residual stress distribution or microstructure of the material. Geometry properties are dimensions, waviness, and surface roughness. Physical variables like heat conductivity, specific thermal capacity is relevant especially for heat dissipation and temperature distribution of the contact zone. Between the bodies there is almost always an inter-facial medium, which might be a liquid lubricant like oil, grease or air, or dry lubricant like graphite, molybdenum disulphide or Teflon. The properties of the lubricant have strong influence on the interaction between the bodies in contact. Once the structure of the tribosystem is defined, the loss variables 𝑧 and output variables 𝑦 can be analysed based on the input variables 𝑥. The variables 𝑥, 𝑦 and 𝑧 are shown in Figure 11. Any change in one of the properties of the tribosystem might lead to a significant change of the output and loss variables.
The tightening process is an example of a tribosystem itself. There is a bolt and a nut which are two bodies that counteract between each other. The surface of both the components might be coated. In between the lubricant might be used, otherwise air is present. When the tightening is quick, there is a large heat power dissipated to the joint that further influence the friction condition during the tightening. As previously introduced, the correct friction determination is crucial in calculating the necessary tightening torque.
Since there are so many different tribological cases in all the engineering applications, it would be hard and expensive to test and evaluate each of the cases separately. For that reason, standardized test rigs have been developed to perform fundamental analyses of the analogical tribosystems under laboratory conditions. These test rigs are commonly named as tribometers.
Fortunately, the results from the analogy tests performed in the laboratories using tribometers have great use in actual machine design application.
Tribometers can be mainly divided by a kinematics they perform and geometry of the test specimen. In Figure 12 main tribometer concepts are presented. The name of each tribometer concept is as follows: a) is block-on-ring, b) is pin-on-disc, c) is flat-on-flat, d) is pin-on-flat, e)
is ball-on-flat, f) is abrasion testing, g) is four ball testing and h) is rolling with and without sliding.
Figure 12. Tribometer concepts [14]
The general idea is that the load is applied to the specimen, and the relative movement is obtained through the actuators like electric rotary motors. Each concept differs from kinematics and tribological perspective. Moreover, different test scenarios might be applicable only for specific tribometer concepts. The choice of the tribometer is strongly dependent on the application under investigation. Once the geometry, kinematics and tribological conditions of the application are analysed, the tribometer with most suitable design shall be chosen to perform laboratory tests. That way, there is the largest chance that the test results correspond to the reality.
The thesis focuses on the development of the pin-on-disc test rig, which its basic working condition is presented in Figure 12 as a concept b). The disc is rotating, and the pin is pushed against the disc. The intention of the test rig is to investigate friction behaviour during tightening, and the results from the tests shall help in better evaluation of friction torque when performing torque control tightening. The intention of the pin-on-disc test rig is to be able to perform very fast tests that correspond to highly dynamic tightening strategies like Turbotight. The Turbotight takes 30-80 ms to complete, and that means that the analogy test on the test rig should be performed in the similar amount of time. During that short time, the clamping force increases from almost zero to the maximum value, and the bolt slows down from the initial rotational speed to stand still. Such dynamics might be a challenge to capture on the pin-on-disc test rig.
2.5 Pin-on-disc concept
In the previous subchapters threaded fasteners were introduced together with its significance on the industry nowadays. The tightening strategies were presented further. The challenge of friction determination during the bolt tightening shows that the tightening is an interesting tribological problem. There are several possibilities to measure the friction in laboratory condition using the tribometers – test machines that perform tribological experiments. Next, the
The concept of pin-on-disc tribometer is in general represented as a rotating disc and a pin that applies a force against the disc, as presented in Figure 13. During the tests, the contact between the pin and the disc is under investigation.
Figure 13. Pin-on-disc concept [14]
The main subsystem that the pin-on-disc test rig contains, are a pin load application subsystem, disc rotation subsystem, and data acquisition subsystem.
2.5.1 Pin load application
The load application can be achieved in many ways. The easiest and common method is a dead weight force application, were the load is applied with the help of gravity by using some weight mounted on top of the pin. This solution is presented in Figure 14, the weight is marked with number 4.
Figure 14. Dead weight force application [15]
The strong advantage of the method is its simplicity, but the disadvantage is the difficulty to control the normal force.
Load
Disc
With help of electric linear actuators, it is possible to have a better control on the normal force.
One of the possibilities could be to use an electric motor with a linear transmission like the Acme thread, or a ball screw. It is possible to use an integrated linear actuator which can be bought from shelf and contains the motor and a linear transmission within. The linear actuator and the pin-on-disc test rig with these linear actuators are presented in Figure 15.
Figure 15. Linear actuators in pin-on-disc application, source: Firgelli Automations, [16]
In an application characterized by a force control with quick responsiveness and short displacement, voice coils can be used as a linear actuator. The voice coil contains an electric coil through which the current flows and creates a magnetic field that acts with the magnets fixed in the stator and results in creating a linear force. The scheme of a voice coil is presented on the left side of Figure 16. On the right side, a voice coil application in a closed-loop force control grinding task is presented. Similarly, it can be used in a closed-loop force control pin-on-disc application.
Figure 16. Voice coil design, source: Motioncontroltips.com, [17]
It is also possible to create a linear force with a help of air pressure or using hydraulic systems, but these are not investigated in this thesis.
2.6 Disc motion
The disc should rotate at specific rotational speed. It can be simply achieved by any type of electric motor. Since the speed requirement of the disc might be much lower than a nominal
transmission could be achieved using belt drive or gear train. An example of a disc drive with application of AC motor and belt drive is shown in Figure 17.
Figure 17. Disc drive in pin-on-disc test rig [18]
2.7 Measurement system
Once the movement of the disc and force application is designed, the test rig is ready to perform experiments under controlled condition. The third crucial subsystem of the test-rig is measurement of physical quantities during the experiment. The behaviour of the tribosystem is dependent on many quantities and depending on the goal of investigation these quantities should be monitored, and sometimes controlled. The main quantities for every test to know are normal force, and friction force between the pin and a disc. Kinematic condition have strong influence on friction behaviour so rotational speed of the disc should also be monitored and controlled.
Contact temperature is also interesting especially during the test were the friction is strongly dependent on temperature.
Normal force measurement
The normal force measurement takes place in-line of the normal force flow. In general, the force sensors are divided into piezoelectric sensors and strain gauge sensors. The piezoelectric sensors shown in Figure 18 uses piezoelectric effect, so when the sensor is loaded with the force, charge moves through the electrode and with a help of charge amplifier the voltage signal is obtained that is proportional to applied force. The main advantage of piezoelectric sensors is its high stiffness which allows high force frequency measurement, so piezoelectric sensors are mainly suitable for dynamic application. Piezoelectric force sensors are subjected to force drift, so they are not suitable for static force measurement. Piezoelectric force sensors need additionally a charge amplifier to perform measurements, which is an extra investment to consider.
Figure 18. Piezoelectric force sensor design, source: HBM
Other types of force measurement sensors are load cells that are using strain gauges to measure the applied force. Applied load causes deformation of the strain gauge inside the sensor, and that changes electrical resistance of the strain gauge, as presented in Figure 19.
Figure 19. Strain gauge operation, source: Dewesoft
The change of resistance is measured with a full bridge configuration which allows the change of strain gauge resistance to be measured and recorded as a voltage difference, as presented in Figure 20.
Figure 20. Full bridge configuration of strain gauge cell, source: Dewesoft
Strain gauge load cells have smaller stiffness than piezoelectric force sensors, as the measurement is based on allowing the load cell to deform. For that reason, strain gauge load cells cannot measure as high force frequencies as piezoelectric force sensors. The advantage of strain gauges is simplicity of a measurement, and in comparison with piezoelectric sensors, there is no need for the expensive charge amplifier.
Friction force measurement
Friction force can be either measured using force sensors measuring tangential force acting on the pin, or by using a friction torque acting on the disc. An example of using a load cell attached
Figure 21. Friction force measurement on linear actuator [16]
In case of friction torque measurement, the torque sensor should be placed in-line of the torque flow from the motor to the disc.
Rotational speed measurement
The rotational speed can be measured using an angular encoder. Angular encoders are distinguished by its operating principle. Optical encoders use a light source that is sensed by a phototransistor. Between a light source and a phototransistor there is a disk mask that effects a signal while the shaft that the encoder is attached to rotates. The mask of an incremental encoder is presented in Figure 22.
Figure 22. The mask of an incremental encoder [19]
Incremental encoders can be used to measure relative angular position or speed. Incremental encoders provide two signals A, B which allow to determine a speed and direction of the movement.
Incremental encoders are characterized by the amount of pulses per rotation (𝑝𝑝𝑚). Therefore, the rotational speed 𝑛 can be calculated based on this parameter and the frequency of A or B signal switching:
𝑛 =𝑓𝑠𝑤𝑖𝑡𝑐ℎ
𝑝𝑝𝑚 𝐻𝑧 ( 11 )
The direction of rotation is distinguished depending whether signal B has a HIGH or LOW state when signal A changes its state from LOW to HIGH. Microcontroller is necessary to sense the rising edge of A signal and perform calculation of rotational speed.
Other types of encoders are magnetic encoders, capacitive encoders, or acoustic encoders. Their working principle differs, but application is similar for all the encoder types.
Temperature measurement
Some experiments investigate a friction or wear behaviour between materials under influence of different temperature. The friction created between a pin and a disc causes a heat generation at the contact, and that heat is transferred partially by a conduction through a pin and a disc, convection through air, and radiation from both the pin and the disc.
The temperature in a pin or a disc can be measured using a thermocouple – a sensor creating voltage signal based on measured temperature. Temperature in the pin or the disc varies at any point of the body, so it is not possible to measure the contact temperature directly, as that means that the sensor should be placed exactly at the pin and disc contact point. Hence, the temperature can be only measured in another point of the body, so the contact temperature needs to be extrapolated based on available measurements. When testing conditions are not varying and it can be assumed that the test rig reached a thermal steady state, the extrapolation is possible with the use of FEM analysis for heat transfer. However, if the tests are under transient and dynamic conditions, the estimation might be not possible or subjected to high error.
Another possibility for a temperature measurement is radiation measurement from the contact zone. Using infrared camera, it is possible to measure radiation emitted from the contact point.
This method has an advantage of allowing dynamic measurement, as the radiation generated from contact point is measured directly. The application of infrared measurement in pin-on-disc test rig is presented in Figure 23.
Figure 23. Contact temperature measurement [20]
The infrared measures amount of infrared radiation emitted from the contact point. The temperature is calculated based on the measurement and Stefan-Boltzmann law. Stefan- Boltzmann law states that the heat flux radiated from a black body with temperature 𝑇, is
𝑞̇𝑏′′ = 𝜎 ⋅ 𝑇4 ( 12 )
where 𝜎 is a Stefan-Boltzmann constant 𝜎 = 5.67 ⋅ 10−8 𝑊
𝑚2𝐾4.
However, the actual bodies emit less radiation than a black body, and it is characterized by an emissivity coefficient 𝜀 < 1. Then, the heat flux generated by any body can be represented as:
𝑞̇′′ = 𝜀 ⋅ 𝑞̇𝑏′′ = 𝜎 ⋅ 𝜀 ⋅ 𝑇4 ( 13 ) To use an infrared camera for a correct temperature estimation, it is of great importance to determine an emissivity coefficient 𝜀 of a disc or a pin. Wrong determination of emissivity coefficient directly introduces an error to a temperature calculation based on measured infrared radiation.
2.8 Turbotight testing
The pin-on-disc test rig that is investigated in this thesis is focused mainly on investigating friction behaviour of the bolt connection during the Turbotight process, so the components of the test-rig should be chosen accordingly. To make it possible, it is necessary to know what a load profile and speed profile of bolt and nut during the Turbotight process is. The results from tests performed on M10 screw coated with zinc and iron tightened to 43 Nm are presented in Figure 24.
Figure 24. Turbotight reference clamping force and rotational speed, source: Atlas Copco On the left side a clamping force profile is presented, with values reaching up to 28 N. On the right side a rotational speed of a bolt is presented during the Turbotight process. Turbotight is a fast process, the time of the tightening is between 30-80ms. To replicate the dynamics of the process, the test rig should be capable to perform that quick tests with controlled force profile of the pin and controlled speed profile of the disc. There is no test rig available in the market that is tailored for performing that quick tests, and hence there is a need to firstly investigate the feasibility of different actuator choices to reach the required performance.
Both the pin load and disc rotational speed are representing a challenge for controlling pin and disc actuators. It is already clear that pin load application using dead mass is not suitable for that application, as the force cannot be controlled during one test. The possible pin actuators could be an electric motor with a linear transmission like ball screw, or a voice coil. Having a closed-loop force control with well-tuned controller is a solution that could be suitable for performing required experiments. Both the actuators will be evaluated to understand its performance and limitations. Thanks to benchmarking parameters, it should be possible to prove which actuators fits better for the pin-on-disc application.
2.9 Controller design
As introduced in the previous subchapter, pin-on-disc test rig requires a design of a controller that controls both the pin and disc actuators to maintain required force and speed profile during the test. The general overview of a closed-loop system where control of electromechanical device is performed is presented in Figure 25.
Figure 25. Architecture of an electromechanical system [21]
The goal of the control loop is to achieve an output 𝑦(𝑡) within performance requirements based on the reference 𝑟(𝑡). The electromechanical motion device is a hardware component, like a motor or a voice coil, which is driven with power electronics e.g. transistors. The power electronics is an interface between high-power circuit and low-power digital controller. Based on an input signal from a controller, power electronics can be controlled how much power is flowing through an electromechanical device at a given time. Nowadays, controller is a digital circuit with microcontroller or FPGA integrated circuit so that it can quickly perform a control task following a programmed control algorithm and responding on the feedback signal from sensors. Sensors can measure some of physical quantities like force, speed, displacement and represent them with corresponding voltage signal. It is also important to remember about load disturbances and random noise that is always part of real world. Controller shall take care of disturbances and provide safe and reliable operation of electromechanical device.
2.9.1 PID Controller
The most common controller used in industry is proportional-integral-derivative PID controller.
The classical architecture of PID controller is presented in Figure 26.
Figure 26. Architecture of PID controller [21]
The 𝑟(𝑡) signal is a reference signal, and 𝑦(𝑡) signal is a measured system output. The error signal 𝑒(𝑡) is fed into three components of PID controller – proportional, integral, and derivative. Each of the component is described by a gain parameter 𝑘𝑝 > 0, 𝑘𝑖 > 0 and 𝑘𝑑 > 0.
The control law of the PID controller is a sum of these three components:
Reference
Time
Reference Controller (controlling/
processing hardware
Power electronics and driving circuitry
Electro- mechanical motion device
Mechanism kinematics
Loads Disturbance Perturbations Criteria and specifications imposed
Output
Time Output
Sensors
𝑢(𝑡) = 𝑘𝑝𝑒(𝑡) + 𝑘𝑖∫ 𝑒(𝑡) 𝑑𝑡 + 𝑘𝑑𝑑𝑒(𝑡)𝑑𝑡 ( 14 )
The control signal 𝑢(𝑡) is controlling power electronics that drives an electromechanical actuator. The transfer function with an error 𝑒(𝑡) as an input and a control signal 𝑢(𝑡) is
𝐺
𝑃𝐼𝐷=
𝑈(𝑠)𝐸(𝑠)
=
𝑘𝑑𝑠2+𝑘𝑝𝑠+𝑘𝑖𝑠 ( 15 )
The transfer function 𝐺𝑃𝐼𝐷 is not proper, as the degree of the numerator is deg(𝑈(𝑠)) = 2 is larger than the degree of the denominator deg(𝐸(𝑠)) = 1. The proper transfer function is obtained by adding a low-pass filter to the PID controller:
𝐺
𝑃𝐼𝐷𝐿𝑃=
𝑈(𝑠)𝐸(𝑠)
=
𝑘𝑑𝑠2+𝑘𝑝𝑠+𝑘𝑖𝑠⋅(𝑠+𝑟0) ( 16 )
2.9.2 Controller tuning
Once the controller structure is known, the next task is to determine the 𝑘𝑑, 𝑘𝑝, and 𝑘𝑖 parameters. The controller performance solely depends on the right match of these parameters which have to be carefully chosen based on the process type and behaviour, required system performance, and available processing speed of a microcontroller that the PID controller is implemented into. Since PID control is the most popular controller strategy, there are plenty of methods to tune the P, I and D parameters. The most comprehensive reference for finding the tuning guidelines depending on the process type is “Handbook of PI and PID Controller Tuning Rules” by Aidan O’Dwyer [22].
The general rules used throughout the book is to determine the process model and identify the parameters of that model. Identification of the process model might be done experimentally, one of the methods used in the industry is a relay experiment. The relay experiment is performed by putting a relay instead of controller in a closed loop system as presented on the left side of Figure 27, and based on the system response, which is presented on the right side of Figure 27, the model parameters can be defined.
Figure 27. Relay experiment for process identification [23]
Another method used in process modelling is an analytical model development, which is based on the governing equations for simplified models of electromechanical systems, e.g. electric motors, gearboxes, or deformed structural elements.
Once the model parameters are defined, the tuning guidelines are simply providing relations
Pole placement with transfer function
Another technique used in 𝑘𝑑, 𝑘𝑝 and 𝑘𝑖 determination is the pole placement technique. The main idea behind this method is to reach a desirable closed loop system behaviour by defining the desirable poles of the closed loop transfer function, and based on that the 𝑘𝑑, 𝑘𝑝 and 𝑘𝑖 parameters are calculated so the desirable poles have been achieved.
Having a 1st order process with a PI controller as presented in Figure 28, the closed loop transfer function is:
𝐺(𝑠) =
(𝑘𝑝⋅𝑠+𝑘𝑖)⋅𝐾 𝜏 𝑠2+1+𝐾⋅𝑘𝑝
𝜏 ⋅𝑠+𝑘𝑖⋅𝐾 𝜏
( 17 )
Figure 28. PI controller with a 1st order process
In that case, the denominator of the closed loop transfer function is of 2nd order, and the behaviour of the system can be approximated by the 2nd order system. Since the numerator is of 1st order, the closed loop behaviour will differ from 2nd order system, but the approximation provides satisfactory results.
The 2nd order system with unity gain is characterized by a transfer function:
𝐺
2(𝑠) =
𝜔02𝑠2+2𝜁𝜔0⋅𝑠+𝜔02 ( 18 )
Where 𝜔0 is a natural frequency of the system, and 𝜁 is a damping ratio. Substituting the closed loop transfer function 𝐺(𝑠) to the 2nd order unity gain transfer function, the natural frequency and damping ratio are:
𝜔
0= √
𝑘𝑖⋅𝐾𝜏 ( 19 )
𝜁 =
𝐾⋅𝑘𝑝+12⋅√𝑘𝑖⋅𝐾⋅𝜏 ( 20 )
