Master’s thesis in Engineering Physics
Author Sofi Backman
June 20, 2018 Supervisors
Martin Nilsson, Joakim Ekspong, Markus Nyberg Examiner
Magnus Andersson
Industrial robots are often equipped with large cables mounted on the outside, i.e. dress- packs, to provide their instruments with what they need, such as power and signal trans- mission. The robots extensively repeat motions as they work resulting in deformation of their dresspacks. This will over time cause enough damage on the dresspack, resulting in breaking of the signal cables thus requiring dresspack replacement. Currently there are few methods for predicting the effect of these smaller damages inside the dresspack and how they affect the lifespan of it. However, these are either very time-consuming or can only be used for comparison to see if one motion is more damaging than another. Here we develop a model trying to predict the effects of dresspack damage and the expected lifespan of the dresspack, by focusing on the deformations of the inner wires of the signal cables and their fatigue life.
The developed model uses simulations from Algoryx’s physics engine AGX Dynamics to extract deformations of the complete dresspack together with a model for deformation of a second order helical structure in an electrical cable. The model can explain dresspack damage caused by strain of the inner parts of the signal cables and estimate the fatigue life of these parts.
The cable damage model gave correct results on what motions of the dresspack that caused it most damaged and also gave good results on where the dresspack was most likely to break. The lifespan calculations of the model gave values of too short lifespans, hours instead of months, but this was not unexpected since all information about the dresspack was not available to set the all model parameters correctly. Even though the exact values of expected lifespan was too low, the model can be used to compare different dresspack motions and see which one is safer for the dresspack, making it possible to lengthen the lifespan of the dresspack. With the right parameters for the lifespan calculations, the prediction of the dresspack life could also be improved to give more realistic results. As this is mainly a model of the signal cables of the dresspack, it is not a complete model for dresspack damage, but it sets a good foundation for further work on this subject.
1 Introduction 1
1.1 Background . . . 1
1.2 Purpose and goal . . . 2
2 Theory 2 2.1 Terminology . . . 2
2.2 Appearance of the dresspack . . . 3
2.3 Mechanisms behind dresspack failure . . . 5
2.4 Stress and strain . . . 6
2.4.1 Bending strain . . . 7
2.4.2 Torsional strain . . . 8
2.5 Fatigue life . . . 8
2.5.1 Strain-life curve . . . 9
2.5.2 Mean stress effects . . . 10
2.5.3 The Palmgren-Miner rule . . . 10
2.5.4 Rainflow counting . . . 11
3 Method 12 3.1 Cable model . . . 12
3.1.1 Wire strain . . . 15
3.2 Calculating deformation of dresspack in AGX . . . 15
3.2.1 Curvature . . . 16
3.2.2 Twisting . . . 17
3.2.3 Elongation/contraction . . . 17
3.3 Limitations . . . 17
3.4 Testing cable damage model . . . 18
3.4.1 Bending cable . . . 18
3.4.2 Dresspack on robot . . . 19
3.4.3 Parameters in simulation . . . 19
4 Results 20 4.1 Simulation of bending cable . . . 20
4.2 Simulation of dresspack on robot . . . 22
5 Discussion 26
6 Conclusion 27
References 29
iii
1 Introduction
1.1 Background
Industrial robots are a common sight in most large factories around the world. Many of these robots are equipped with large cables to provide their tools with, for example, power and the ability to send and receive signals. Since these cables, or dresspacks, are different for different tools they are not an integrated part of the robot but are often mounted on the outside, see Fig. 1.
Figure 1: Schematic robot with dresspack mounted on the top of the upper robot arm and going down the side. [10]
Industrial robots often repeat the same pattern of motions when they are working and each motion leads to some kind of bending, stretching or twisting of the dresspack.
This will eventually damage the cable and the robot tools will malfunction, causing unpredicted stops in a production line, which can be costly.
Some motions can cause catastrophic damage to the cable, for example if it gets stuck and tugged or is bent more than it can resist. These kinds of damages can be avoided by programming the motion pattern of the robot in a way that is safe for the cable. This is often done by first testing the robot motions in a simulation where the cable is also included and visually making certain that the cable does not get stuck or is bent too much. In these simulations it is however not always possible to see the effects of how the smaller stresses and deformations, that will not immediately break it, affect the lifetime of the cable.
Having a tool that can simulate cable damage from the smaller deformations for a certain set of motions and predicting the lifetime of the cable can then be of great help, both for planned maintenance and for programming the robot motions such that the cable can be used longer before it is replaced. This master thesis work focus on developing such a simulation tool.
This thesis work is performed at Algroryx Simulation AB in collaboration with Volvo GTO and is a part of the EU research project ENTOC, which stand for Engineering Tool Chain. The goal of ENTOC is to increase efficiency, maturity and innovation in the engineering tool chain by automated generation of virtual product systems.
Algoryx’s multi-purpose physics engine, AGX Dynamics, can simulate cable motion and has a model for cable damage. This model is largely based on the work developed by Kressin [1]. More precisely the damage model by Kressin is used when the motion of the robot is optimized to be as effective and still cause as little damage as possible to the dresspack. Even though this model can tell if one motion is more damaging than another, the data coming from it does not not have a physical meaning and the model does not say anything about the expected lifespan of the cable.
In Volvo’s factories the welding robots experience the largest deformations and are there- for of certain interest for this master thesis work. After interviewing people with expe- rience of these cables at both Volvo and ABB, who manufactures both industrial robots and their dresspacks, it has become clear that when the cable starts to malfunction it is often due to signal cable failure in the dresspack. Therefore these signal cables are of extra interest.
1.2 Purpose and goal
The purpose of this master thesis is to increase the knowledge about the cause and physical mechanism of cable damage on industrial robots and present new ideas and improvements on how to predict and extend cable lifetime.
The goal of the thesis is to find and implement a working model for predicting cable damage for a given set of motion patterns for an industrial robot, that in the future might replace or complement the current model in AGX Dynamics.
2 Theory
2.1 Terminology
To make the discussion about the dresspack a little easier, we will call the complete dresspack just dresspack, and the first layers of cables inside the protective hose will be
called cables. The smaller cables inside these cables will be called conductors and the thin metal wires inside these will be called wires. This is illustrated in Fig. 2.
Figure 2: Illustration of the different layers of the inner structure of a cross-section of a dresspack. Note that the scaling and structuring of cables and conductors are not exactly as for the real dresspack and that the empty space between the cables is smaller in real life.
2.2 Appearance of the dresspack
To understand what happens with the dresspack when it is deformed one needs to under- stand what it looks like on the inside. Note that the appearance and structure described in this section is for one type of welding dresspack and that other types of dresspacks can have other cables, hoses or inner cable structures. This type will however be the focus of this work.
The outermost layer is the corrugated protective hose that encloses and protects all the cables of the dresspack. Inside this hose there are four cables responsible for transporting cooling water to the welding tool, these are the orange ones in Fig. 3. These cables are ignored in the damage model since they are never mentioned as being a reason for dresspack failure. In the middle of the dresspack there is one thick power transmission cable, which in turn consists of three conductors made of copper wires.
Figure 3: One end of a welding dresspack, with its cables visible. The orange ones are for cooling water, the thickest one in the middle is the power transmission cable and the three smaller black cables, merging at the large gray contact, are the signal transmission cables.
In Fig. 3, the three smaller black cables are signal cables, which have the most complex appearance. They all consists of conductors of various shapes and sizes, that are twisted around each other, see Fig. 4-5. Simulating the exact appearance of these cables would be rather time consuming so they are simplified to have a more homogeneous appearance, where all the conductors are the same size inside each signal cable, described more later.
Figure 4: The cables inside of one of the signal cables in the dresspack.
Figure 5: The cables inside of two of the signal cables in the dresspack.
2.3 Mechanisms behind dresspack failure
One very important thing to understand before discussing how to simulate the damages of the welding dresspack is how and why it actually breaks. In many cases the first thing to break in the dresspack is the plastic corrugated hose that protects all the cables of the dresspack. This may cause severe changes in the cable motions, so that the cables bend much more than previously and thus exposing them to much larger deformations, which can dramatically shorten the dresspack lifespan. When the hose breaks it sometimes starts to wear on the cables themselves, damaging or breaking them.
When a protective hose breaks it is usually mended in some way to minimize these kinds of damages. According to employees working with these dresspacks at Volvo a damaged hose is often detected and mended within in a week. After a dresspack has been mended the time left before it has to be completely replaced varies a lot, from a couple of weeks to months. The dresspack is usually completely replaced when signal errors appear, which suggests that the signal cables are the part of the dresspack that is most sensitive and therefore important to focus on.
It is also important to mention that sometimes the dresspack fails, even though the protective hose has not. In these cases it is either the braided screening of the signal cables that has failed or the metal wires in one of the signal cables that has cracked due to repeated stress. When something is repeatedly deformed the stresses in the material will build up over time, weakening it. This type of weakening is called fatigue and is described more in section 2.5.
2.4 Stress and strain
Mechanical stress is the force per unit area applied to some material and is often used when calculating how much a material can take before it breaks. The stress can normally be divided into normal stress and shear stress. The normal stress, which is perpendicular to the surface the stress acts on, is often the effect of tension or compression, and shearing stress can occur when a component is twisted, i.e. torsional stress [2].
Strain describes how much something has been deformed and for a simple, homogeneous rod being elongated, the strain can be expressed as
= ∆L
L , (1)
where ∆L is the difference between the original length and the length after elongation, and L is the original length.
Stress can be computed from the strain in a simple, linear relationship;
σ = E, (2)
where E is Young’s modulus or elastic modulus and describes the stiffness of a material.
This relationship however only holds for small, elastic deformations. When the defor- mations become plastic, i.e. when the deformation is irreversible, the relationship is no longer linear and the situation becomes more complex. An example of the relationship between stress and strain is shown in Fig. 6, where A marks the elastic region. Note that this type of stress-strain curve looks different for different materials, and often different for the same material at different temperatures [3].
Figure 6: An example of engineering stress-strain relationship for a material. A marks the elastic region, B marks the region where the deformations become plastic. Between B and C strain hardening occurs, meaning that the material is hardened by the plastic deformations. Between C and D necking occurs, meaning a reduction in cross section diameter due to the deformation [11].
2.4.1 Bending strain
When it comes to deformation of cables, one very common deformation is that of bending.
Therefore it is important to understand how a simple rod is deformed when it is bent.
Fig. 7 illustrates how this happens by looking at the differences in length of different parts of the cylinder rod.
Figure 7: An unbent cylinder to the left and a bent cylinder (in profile) to the right.
a, b, c, d all describe the length of a cylinder segment at different distances from the cylin- der center. The red dotted line marks the center and is also the neutral bending axis. θ is the bending angle
When bending the cylinder the upper part will be subject to tension and the lower part compression, leading to that a < a0, b > b0, but at the central axis c = c0, as seen in Fig. 7. Given that r is the distance from the neutral axis to the point of interest in the cylinder and using the equation for the length of a circle sector we have that
d0
c0 = (R + r)θ
Rθ = R + r
R , (3)
where R is the bending radius. Strain at r from the central axis will then be
= d0− d
d = d0− c
c = (R + r)θ − Rθ
Rθ = r
R (4)
2.4.2 Torsional strain
The torsional deformation, or shear strain, of a cylinder rod is described by the angle of how much the rod has been twisted, in Fig. 8.
Figure 8: The deformation, , of a cylindrical rod where one end is fixed and the other is being twisted. The right part shows the cross section of the part where the cylinder is twisted.
For the cylinder in Fig. 8, using trigonometry and the assumption of small angles, we have that
L = rϕ ⇒ = rϕ
L (5)
2.5 Fatigue life
Fatigue is one common cause for materials to crack and happens when a material is exposed to cyclically applied loads, that do not break the material immediately but slowly
weakens it until it breaks. The loads are often still large enough to cause microscopic cracks in the material, that grows larger for each cycle of loading until it reaches a critical size and the structure fractures. The amount of time it takes for this to happen is often referred to as the fatigue life [3].
One often mentions two different types of fatigue; high cycle and low cycle fatigue. High cycle fatigue is when a material is exposed to smaller, often elastic deformations, meaning that it often takes more cycles for the material to fail. Low cycle fatigue is when the deformations are mostly plastic and the material therefore can handle fewer cycles before it fails [3].
When computing the fatigue life for high cycle fatigue, the number of cycles a material can handle of a certain cyclic load is often computed using a so called Wöhler curve or stress-life curve. This curve describes how many cycles of a certain amplitude of stress the material can handle and can often be described by the Basquin equation [4];
σa= σ0f(2Nf)b, (6)
where σa is the stress amplitude, Nf the number of cycles to failure, σ0f the fatigue strength coefficient and b is the fatigue strength exponent or Basquin exponent [4]. The values of σf0 and b are material specific and described more the in the next section.
2.5.1 Strain-life curve
In many cases materials are exposed to elastic deformations, and a strain-life approach to finding the fatigue life might be more appropriate in these cases. This means that a curve with the strain, instead of the stress, as a function of the numbers of cycles to failure is used for calculation of the expected lifespan.
In 1954 Coffin and Manson (working independently) found that the plastic strain am- plitude, a, related to the number of cycles to failure for metallic materials, Nf, in the following way;
a= 0f(2Nf)c, (7)
where 0f is the ductility coefficient and c the fatigue ductility exponent [4].
Since the total strain amplitude can be written as the sum of the elastic part and the plas- tic part of the amplitude, combining Eq. (2), (6) and (7) the Coffin-Manson relationship becomes
a= σ0f
E(2Nf)b+ 0f(2Nf)c. (8)
Parameters 0f and σ0f both have values rather close to the true fracture ductility and fracture strength in monotonic tension for many metals [4]. Concerning the exponents b and c, these often has to be determined experimentally, and typical values are c = −0.6 [−0.5, −0.8] and b = −0.085. For soft metals, as for example aluminum or lead, b = −0.12 is common and for highly hardened metals, as for example hardened steel, b = −0.05 is more common [3].
However, since a material often is exposed to many different kinds of loads, with different amplitudes, these curves cannot be used to calculate the fatigue directly for a more complicated case. To solve this problem the Palmgren-Miner rule is often used.
2.5.2 Mean stress effects
The mean stress is, as the name suggest, the average of the maximum and minimum value of cyclic stress. The mean stress may be zero, as in cases of completely reversed stressing, but is often not. However, most stress-life or strain-life curves assume a mean stress of zero. This means that for cases when the mean stress is larger than zero, the strain-life curve will underestimate the numbers of cycles to failure.
One way to include the mean stress is by the Smith, Watson and Topper method, or SWT method. This modifies the Coffin-Manson relationship to be
σmaxa= σf0(2Nf)bhσf0
E(2Nf)b+ 0f(2Nf)ci
, (9)
where σmax= σa+ σm and σa then is the stress amplitude and σmis the mean stress [3].
2.5.3 The Palmgren-Miner rule
If a material is exposed to stress of different amplitudes, there must be a way to sum the effect of these amplitudes up. A stress-life or strain-life curve only describes the lifespan of cycles with one amplitude, but the Palmgren-Miner makes it possible to use them in more complicated cases.
The Palmgren-Miner rule assumes that the damage done from one amplitude of stress can be calculated by dividing the number of cycles of that amplitude, nj, by the number of cycles the material is supposed survive for that amplitude, Nf j. This is then seen as a fraction of how much of the material’s lifespan is consumed. The Palmgren-Miner rule states that by summing up all these fractions for each amplitude we get the total life used for that sequence. Fatigue failure is expected when the fractions sum up to unity, i.e.
X
j
nj
Nf j = 1, (10)
where j says which number we are at in a sequence of amplitudes.
However, this rule does not consider how the order of when the different amplitudes appear may affect the material and the rule’s linear behavior is not always correct [4].
2.5.4 Rainflow counting
When using the Palmgren-Miner rule one must know how many cycles there are of a certain amplitude. This is something that is not easily extracted for more complicated cases. Cycle counting techniques are then often used to reduce these complex loading histories into discrete events, thus giving the information of how many cycles a certain amplitude appears. One of the most common approaches to this is the so called rainflow cycle counting and is illustrated in Fig. 9 [3].
Figure 9: Rainflow counting example, showing how the "rain water" flows down the rotated strain history [12].
The algorithm for the rainflow counting follows: First the loading history must be reduced to only one sequence of the peaks and valleys. Then the reduced history is turned 90◦ clockwise, so that the positive time axis points downward. This is then imagined as a pagoda roof with rainwater flowing down from each peak, see Fig. 9. The number of half-cycles is then counted by looking for terminations in the flow. These occur when the flow reaches the end of the time history, it merges with the flow that started at an earlier peak or when an opposite peak has greater magnitude.
The above steps is then repeated for the valleys. The half cycles of identical magnitude, but opposite direction, are then paired to count the number of complete cycles. The
magnitude to a half cycle is seen as the strain difference between start and termination [5].
3 Method
Even though the protective hose usually breaks first, this is not what we will concentrate on, since a broken hose does not automatically mean a completely broken dresspack and sometimes the dresspack fails without the hose breaking. This thesis work mainly focus on the signal cables, or more precisely, the fatigue life of the small wires inside them.
The method used to calculate the expected lifespan of the signal wires can be described in five steps:
1. Calculate deformation of complete dresspack at each time step using AGX 2. Calculate strain in signal cables from dresspack strain
3. Use rainflow counting to find how often a certain strain amplitude appears
4. Calculate expected number of cycles for each strain amplitude by solving the Coffin- Manson relation with mean stress.
5. Use the Palmgren-Miner rule to sum up the damage
3.1 Cable model
The model used for calculating the strain inside the signal cables is based on the de- formation of wire ropes. This means that it describes the twisted wires in the core of conductors that are also twisted around each other. Using this model, some assumptions has to be made, where one assumption is that the cables in each layer is of the same size and material. The model used in this project is based on the work done by Kenta Inagaki, Johan Ekh and Said Zahrai in the paper called Mechanical analysis of second order helical structure in electrical cable, where they use theory of deformation of wire rope to calculate a cable’s inner strain but also investigate when the smaller wires in a cable start to slide against each other when the cable is bending [6]. However, the part about wire slipping is not included in this damage model mainly due to the limited time to complete this work.
In this model, the complete set of conductors are called the cable, the first helical struc- ture will be called conductors, and the second, inner one, will be called wires. The letter c will be used to refer to the conductors and w the wires. This model makes it possible to calculate the strain in the wires from the deformation of the cable. These deformations are elongation, , twisting, τ , and bending, κ.
The center position of helically twisted conductors in the cables reference system is described in cylindrical coordinates by the angle θc and the vector r, where the angle is the angle from the neutral bending axis, see Fig. 10.
Figure 10: Cable geometry. (a) Side view of cable showing lay angle, α, when elongated.
(b) Cross-section of cable with helical radius for both layers, Rc1 and Rw1, and angle of cable position θc. [6].
For the conductor, the vector r and the angle θc are calculated as r = Rcncos θcx + Rˆ cnsin θcy +ˆ Rcnθc
tan αcn
ˆz (11)
and
θc= 2πi
Kcn +l tan αcn
Rcn , (12)
where Kcn describes the number of conductors in layer n where n = 1 is the outermost layer. i describes which conductor in that layer we are looking at, i = 0 is the conductor at the neutral axis as seen from the top of the cable, and l is the length of the cable. Rcn is the distance from the cable center to the centers of the conductors in layer n. αcn is the lay angle for conductors in layer n and can be calculated from the initial lay angle as
αcn= tan−1 tan ¯αcn+ Rcnτ 1 +
, (13)
where ¯αcn is the initial lay angle of the cable. Knowing this angle, the position angle θc and the deformations of the cable, it is possible to calculate the elongation of the conductor as
c= cos2αcn( + Rcnsin θcκ) + Rcnsin αcncos αcnτ. (14)
To be able to study the direction of the conductors, a local coordinate system for the conductors is introduced, where Fig. 11 shows the origin of this system at the center of the conductor. The unit vectors in this frame are given by
ˆt ˆ n ˆb
=
− sin αcsin θc sin αccos θc cos αc
− cos θc − sin θc 0 cos αcsin θc − cos αccos θc sin αc
ˆ x yˆ ˆ z
. (15)
In this frame ˆt is tangent to the axis of the conductor, ˆn is the normal vector always pointing to the center of the cable and ˆb is the bi-normal vector perpendicular to the other two.
Figure 11: Cross-section of cable showing local coordinate system of the conductor in the cable, where θw is the position angle of a wire and κnoc is the bending curvature component in the normal direction and κbic in the bi-normal direction [6].
The conductor is also subject to a bending and a twisting strain and by projecting the bending vector in direction of ˆt we get the torsional strain;
τc= κ sin αccos αcsin θc. (16) The curvature of the conductor is then calculated as
κnoc = κ cos αccos θc, (17)
κbic = κ cos2αcsin θc, (18) where κnoc is the curvature component in the normal direction and κbic in the bi-normal direction.
3.1.1 Wire strain
To find the strains in the helically twisted wires inside the conductor, the wires are assumed to be related to the conductor as the conductor is to the cable. This means that given the strains in the conductor, the strains in the wires can be calculated. Now the local coordinate system used for calculating the strains in the conductor is seen as the global one. This gives that the position angle for the center of a wire can be calculated as
θw = 2πj
Kwm + Rcnθc
Rwmtan αwmcos αcn + (π − θc), (19) where m is the layer number and j is the number of the wire in that layer. αwmis the lay angle of the conductor in its deformed state at layer m and is computed in a the same way as for the conductor in Eq. (13), but using c and τcinstead of and τ .
The equation of the strain in a wire in the conductor can then be calculated in a similar way as for the conductor, that is
w = cos2αwm c+ Rwmsin θwκbic − Rwmcos θwκnoc + Rwmsin αwmcos αwmτc, (20) where the bending now has been divided into two components instead of one. The twisting of the wire is then calculated as
τw = κbicsinθw− κcnocos θw sin αwcos αw, (21) and the curvature is then given by
κnow = κnoc sinθw+ κbic cos θw cos αw (22) and
κbiw = κbicsinθw− κnoc cos θw cos2αw. (23) Note that this model only mentions two helical structures, but for the actual dresspack there will be three; the signal cables, the conductors in the signal cables and the wires in the conductor. This means that the for the cable the "conductor" equations will be used, and for the conductors in the dresspack the "wire" equations will be used. For the actual wires in the dresspack the wire equation will be used again but then with the results from the previous helical level, since it is just another level with the same relations to the previous one.
3.2 Calculating deformation of dresspack in AGX
For simulation of the welding robot and its dresspack, Algoryx’s physics engine AGX Dynamics is used. AGX uses a method called lumped element method, LEM, and is based on dividing the cable into equally large segments and having constraints between them deciding how each segment can move. Each segment is a rigid body that is not
deformed. It is only the distance and position of the segments relative to each other that changes.
The method used for the cable model is then used on each segment, so that we know how strain in each of the cables segments occur. However, to use the cable model for the wires inside the dresspack, the complete deformation of the dresspack must be known first. This is also calculated for each segment, but since each segment of a cable is stiff, the deformation cannot be calculated looking only at one segment. One has to look at the segments right next to that segment as well and compare their positions to each other.
3.2.1 Curvature
In the cable model, the bending is describes as the curvature of the cable, κ, and is the inverse of the radius of a circle describing the bending. To calculate the radius and position of a circle, at least three points are needed. For the model these three points are chosen as the center positions of three cable segments, see Fig. 12. The equation used to calculate the radius is
r = ABC
4K , (24)
where A, B, C are the length of the sides of the triangle created by the three points and K is the area of the same triangle. This formula comes from how the radius of a circumcircle made from a triangle is calculated [7].
Figure 12: The bending radius, r, of the middle cable segment. The black "capsules"
are three cable segments and the red dots mark their center position.
To get the actual strain caused by bending there is one thing to keep in mind: Multiplying the radius of the cable with the curvature, as in Eq. (4), gives the largest strain in the cable. The strain will however not be the same all over the cable surface, for example at the neutral axis it will be zero, and thus it is important to keep track of which direction the cable is bending. In this work this is done by looking at the position of the next, and previous, cable segments in the center segment’s own reference frame.
3.2.2 Twisting
The twisting, τ , in the cable model is described as the twisting angle divided by the length of the cable, or cable segment in this case. This angle is labeled ϕ in Fig. 8.
Using AGX, ϕ is calculated by looking at how the reference frames of the cable segments are twisted relative to each other. Since the angles are in quaternions a cable segment’s rotation is simply multiplied with the conjugate of the previous segment rotation, then the relevant rotation direction is translated to Euler angles.
When ϕ is calculated it is then simply divided with the cable segment length to get τ . The actual value for τ in the model is the mean of the value for when looking at the segment before and the segment after.
To get the actual shear strain as a result of the twisting of the cable, the value of τ must be multiplied with the radius of the cable.
3.2.3 Elongation/contraction
Cable elongation is the most simple to calculate. Since the cable segments does not actually change shapes, the difference between the end and start of each segment is instead calculated. The mean of the difference of the segment before and after is then taken as the actual elongation of the cable. To get the strain used in the cable model, , the elongation is divided by the cable segment length.
3.3 Limitations
Neither the manufacturer of the welding dresspack we investigated or ABB does perform tests of how long the their type of welding dresspack survives. According to ABB the reason why they to not do this or developed their own model for predicting dresspack life is due to the complicated nature of the problem. There are so many factors that play a role in how long a dresspack will survive, such as wear, changes in dresspack motion over time and the effects of stress in a lot of different components, that a lot of simplifications have to be done to be able to handle the problem.
One of the major simplifications in this thesis work is that all time dependency of the strain is ignored. This means that creeping effect in the material, change in motion over
time, the order of the motions and the effect of strain rate are all ignored. The reason for this is the time it would consume to integrate all these effects into the result and the fact that for metals at room temperature effects of creep and strain rate are both rather small.
The temperature of where the dresspack is located is assumed to be close to room tem- perature, which means that no effects due to temperature changes are accounted for.
This means that this model will not work if the dresspack is located at places that are much hotter or colder than room temperature.
The effects of cyclic hardening is also ignored for simplicity. Cyclic hardening is the effect of repeated plastic deformations that hardens the material so that for each cycle it becomes more difficult to deform.
The simulations of the cable are run in AGX, and they are assumed to be correct even though the behavior of the cable in the simulation might not be exactly the same as in the real case.
3.4 Testing cable damage model
To test the developed cable damage model, with both the part calculating the strain and the part predicting the expected lifespan, two different tests was conducted: One simple, to only test the computation of the strain, and one with cables on robots in i a situation close to real life to test the complete model in a more complex case.
3.4.1 Bending cable
A simple test case was created using simulations in AGX to first determine that the model was implemented correctly. The test case was to be similar to the test done by Inagaki et al [6], with a cable extended between two blocks, vertically, with the upper block slowly moving downwards, causing the cable to bend more and more.
Inagaki et al. [6] compares the curvature with the stress by multiplying the strain with the Young’s modulus of the material, which in this case was copper and has a value of about 12 · 1010 P a [8]. By simulating the same thing, the results can be compared and used to validate the method. One important thing to note is that Inagaki et al. had also used a model for how the inner wires was slipping or sticking when the cable was bent, making the strain smaller when the wires was slipping. However, for smaller strains the wires are sticking and the values should be close to the same.
3.4.2 Dresspack on robot
To test the model for the damaging of the dresspack, we ran a simulation using AGX Dynamics and data from Volvo GTO. The data contained a movie where two welding robots where visible and some statistics on how often the dresspack had to be either fixed or changed completely on these robots.
By visually trying to copy the motions of the robots for the three first minutes of the film, the damage done to the dresspack can be compared between the two robots, where one was more often damaged than the other. This also gave a chance to compare the expected lifespan predicted by the fatigue analysis, even though the lack of data on these dresspacks made it difficult to determine all parameters correctly for the strain life equation in Eq. (8).
3.4.3 Parameters in simulation
Due to the complicated inner structure of the signal cables, the cable with the simplest structure was chosen for the tests, which is the orange one in Fig. 5. In this signal cable the thickest of the conductors in it was chosen, meaning that in the simulation all conductors in the signal cable have this size. The thickest one was chosen due to bending and twisting increases with the radius and here it is interesting to find the spot where the damage is largest. This also means that the damage was only calculated for the outermost layers. All the values used can be seen in Table 1. The lay angle was roughly estimated, but not actually known.
Table 1: Values used for the dresspack in the simulation, measured from a dresspack signal cable. The diameter of the parts was measured with a verier caliper and thus the radius has an error of ±2.5 · 10−5 m. Kn is the number of cables/conductors/wires at the outermost layer.
Layer: cable conductor wire
Tot. radius [m] 0.00530 0.001175 0.000075 R1 [m] 0.01845 0.002825 0.00075
Kn 10 7 31, 25, 18, 12, 6
Lay angle [◦ ] 0 25 5
Since no actual tests were performed on the dresspack or the cables inside it, the pa- rameters that are material specific in the Coffin-Manson relation, Eq. (8), cannot be exactly determined for this case. Instead parameters is used from a similar case made by McCorquodale, C. in a paper called "Development of a Fatigue Analysis Tool to Predict Cable Flex Life" [9], where a copper wire was tested. Since an equation very similar to the Coffin-Manson equation was used, the parameters of Coffin-Manson could be calcu- lated from those copper wire results. The same test was also performed with values for
one type of aluminum taken from a table in [3], to see the difference and the effect on the results. The values can be seen in Table 2.
Table 2: Values for the parameters of a copper wire in the Coffin-Manson equation, transformed from parameters used in i similar case in [9], and for 7070-T6 aluminum [3].
Metal E[P a] σ0f[P a] 0f b c
Cu 117 · 109 983 · 106 2.43 -0.112 -0.6 7070-T6 Al 71 · 109 1466 · 106 0.262 -0.143 -0.619
4 Results
4.1 Simulation of bending cable
The simple bending test, performed in AGX Dynamics, gave a visual result seen in Fig.
13. There the cable segment experiencing the largest damage is marked red, and as expected it is in the middle, where the curvature seems to be largest.
Figure 13: The bending cable used in the AGX simulation. The most damaged segment is marked with red.
In Fig. 14 the strain values of elongation, twisting and bending can be seen for each
segment of one wire in the cable. The wire which we see the values for is the one that had the largest damage done to it. In Fig. 13 it is obvious that the effect of twisting and bending on the single wire is quite small, since when the complete cable bends the effect on the single wire is more that it is elongated than anything else. Looking at Fig.
15 we see how the stress was changing when the curvature increased as the cable was bending and as expected the stress increases with the curvature. The lack of data point for curvature in the beginning is due to the fact that the cable is completely straight in the beginning of the simulation, then "pops" out a little when it is compressed enough and it has to start bending.
When comparing the values in Fig. 15 with results from Inagaki et al. [6], the results are not exactly the same. For example, for values of κ = 0.25 the stress is about 15 MPa in [6], and in the simulation this value is about 17 MPa. The stress is also increasing more with curvature in the results from the bending test, when compared to the results of [6]. This can however be explained by that the model of slipping wires was not used, and when the wires starts to slip the stress will not increase as quickly. The important thing was to see that the order of magnitude was the same and had the right kind of behavior, i.e. stress increases with bending curvature.
0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 Cable segment nr.
0.0000 0.0001 0.0002 0.0003 0.0004 0.0005
Strain amplitude
Last time step, complete cable
Stretch Twist Bend
Figure 14: The strain in each segment of the cable, at the wire which was subjected to the largest damage.
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Curvature [1/m]
0 1 2 3 4 5 6
Stress amplitude [Pa]
1e7
Figure 15: Stress as a function of curvature for the bending cable test case in the segment and wire subjected to the largest damage as the cable was bending.
4.2 Simulation of dresspack on robot
Testing the dresspack on the robot, with the robot motions copied as good as possible from the video of the moving robots, gave the results seen for robot 1 in Fig. 16 and for robot 2 in Fig. 17. The figures show the strain in the part of the wire that was most damaged for both robots. Using these values of the strain and calculating how much of their expected lifespan these motions consumed, gave a result of 3.6% for robot 1 and 2.9% for robot 2. This means that after repeating these motions 27 times the wire would break for robot 1 and for robot 2 it would break after about 35 times, which is rather low values since this means that the wire would survive less than two hours of repeating the motion pattern. Even though one broken wire does not break the dresspack, these numbers are too low. A dresspack should at least survive a couple of months, as observed in factories where they are used.
One might argue that it is only one wire that is very damaged, but looking at the numbers of the wire one row closer to the center of the conductor, it has a value of life consumed at 1.6%. This means that it would survive a little more than three hours of the repeating the motion pattern, which is not much longer when compared to the more damaged wire.
Also note that wires close to each other in the same level often have rather similar values of strain and consumed life. So according to the used life prediction model more than a few wires would probably be broken after one day and this means that the numbers for consumed life seems to be too high overall.
The high numbers of consumed life is however not unexpected due to how some values of the parameters for the fatigue models were set. Some assumptions was involved when it comes to what material the cables actually consist of, since the exact information was not available. Since copper is a common metal in conductors and the values was available from fatigue life tests, this was the metal used in the model. The test with aluminum was performed to see how different material parameters affect the results, and as expected the results are very similar in where the largest damage happens. However, the consumed life is a lot larger; 20% for robot 1 and 15% for robot 2, meaning that the material parameters for copper was a better choice for the model in this case.
0 500 1000 1500 2000 2500
Time step nr.
0.005 0.000 0.005 0.010 0.015 0.020 0.025
Strain amplitude
Figure 16: The strain value of the wire subjected to the largest damage in the most damaged segment for the first robot.
0 500 1000 1500 2000 2500 Time step nr.
0.015 0.010 0.005 0.000 0.005 0.010 0.015
Strain amplitude
Figure 17: The strain value of the wire subjected to the largest damage in the most damaged segment for the second robot.
Since it is the robot’s motion that is copied, all cable motions are decided by the physics engine AGX Dynamics. By visually comparing the motions of the simulated cable and the cables in the movie, it seems they do not move exactly the same way. For example, the cable can bend in the wrong direction. This is because there are a few parameters to be set for the cable in the simulation, such as the bending stiffness. These could only be estimated and then slightly altered to make the motions in the simulation more similar to the motion in the movie. Getting the perfect combination of all parameters is not possible when there is only a movie to compare to and thus the simulated cable motions are not exactly similar as those in the movie. However, even though the cable might, for example, bend in the wrong direction the amount of how much it bends increases for the right type of motions in most cases. This means that the same types of motions should cause most damage to the dresspack both in the real case and in the simulation. The results from the damage done to the cable in the simulation should therefore at least have some similarity to the real world case.
According to people working close to this type of industrial robots the dresspack of welding robots should have a lot of deformation close to the head of the robot, and this correlates with both robot simulations. The segment of the simulated dresspack that is subject to the largest damage in the simulations was the 16th from the head of robot 1 and 3rd for robot 2, see Fig. 18 and 19.
Figure 18: The end position of the first simulated robot, with the green cable simulated and the segment subjected to the largest damage marked red.
Figure 19: The end position of the second simulated robot, with the green cable simulated and the segment subjected to the largest damage marked red.
What is also promising is that the correct robot consumed most of its lifespan when comparing the results from the simulation to the real case. In the Volvo factory robot 1
had the dresspack that needed to be fixed or changed most often.
One important thing to mention is that only three minutes of each robots motions was simulated, because of the time consuming nature to try to copy the robot motions by hand. These three minutes does not represent the robots complete trajectories and thus some motions that could be more or less damaging could have been excluded. How- ever, these three minutes should still give some hint of how damaging their motions are since many of the motions are similar but not exactly the same as the ones used in the simulations.
5 Discussion
The results from the cable bending test seem promising. The values of strain are a little larger compared to the results from the tests done by Inagaki et al. [6], but as mentioned this was expected since the effect of wires slipping is not taken into account and this should give a larger value of the stress.
Even though expected, one might argue that the larger strain results is not a good thing.
However, when it comes to damage and fatigue life it is always better to overestimate the damage, than to underestimate it. This does however mean that deformation of the inner wires when the cable is bending might be a bit overestimated. A wire slipping model would probably give more accurate results but to do this friction coefficients between wires and cables and the pressure the plastic jacket of a cable has on the wires inside it are needed. The reason why the slipping wire model by Inagaki et al. [6] was not used was because it assumes that the complete set of cables are not twisted.
The most important results of the simulation of a dresspack on a robot is that the damage appears close to the head and that the robot with the most damaged dresspack in the movie also took most damage in the simulation. This means that the model can be used to compare robot motions, but also to see where the dresspack is most likely to break.
The model predicts the damage for the robot dresspack and does so with numbers that actually have a physical meaning. Even though the number of the expected life length was unexpectedly low, it is difficult to say if the fatigue methods used were not ideal for this case or if the parameters chosen were incorrect. The model should also be tested for more cases of robot motions, preferably where the parameters for the cable in the simulation is better determined, to be able to be completely certain of what is causing the large values of consumed life.
To make the life estimation model more reliable a thorough study of the dresspack should be done. This means bending, twisting and stretching the dresspack until it breaks, to know how many times it can be deformed to a certain amount. Preferably such infor- mation should also be produced for the signal cables and the protective hose separately.
Comparing the results from separate tests with tests on the whole dresspack should give an idea of how they affect each other. Alternatively more dresspack manufactures can be
contacted to see what information they have about their expected lifespan. Having more data about dresspack life would mean that the parameters of the fatigue models, and more precisely Eq. (8), could be set more accurately, which would improve the lifespan calculation.
Another factor that might impact the results of expected lifespan is that there is some room between the cables inside the dresspack. This means that the signal cables are probably not placed at the same distance from the center the entire time as the dresspack is deformed. This is assumed in the damage model and is a good assumption for the inside of the signal cables since the conductors and wires are more closely packed. However, for the signal cables there is more room for them to move and if they at some instances could move closer to the center of the dresspack, this would decrease the deformation they are experiencing and therefore partly explains why the lifespan calculations are too low. The exact impact of this is however difficult to determine, since it is not exactly known how the cables move inside the dresspack hose. One test that might be performed to see the how much this affects the results is by replacing the rigid cable that represents the dresspack in the simulation with a more realistic model of the inside of the dresspack.
This would mean replacing the rigid cable with a hose with some smaller rigid cables inside it, of the same sizes as the ones in the dresspack. Then the deformation of the signal cables could be taken directly from the simulation, and not by calculating it from the dresspack deformation. This would then make it possible to better understand how the cables move inside the dresspack, and understand how much it affects the results.
The next step to the dresspack damage model should be to add a life estimation model of the dresspack’s corrugated hose, as this cause a lot of problems. However, since it is made of plastic, which does not behave in the same way as metals, and has a corrugated shape it makes the computation of how it is damaged when it is deformed a bit more difficult. The deformation of the outermost part of the dresspack is however already available and can be used for estimation of hose deformation. What should be added is another fatigue model that is better for the hose. Finally, the model of the hose could be used together with the model for the signal cables to give a better picture of the damage to the dresspack.
6 Conclusion
The main goal of this master thesis work was to implement a model to predict the damage done to robot dresspacks. To reach this goal, we developed a model that can explain cable damage caused by strain of different parts and estimate the fatigue life of these parts. The results from the strain calculations looks promising from the tests done in this thesis and can be useful for seeing how and where the cable is damaged even without the fatigue model.
The part of the dresspack that has been the focus in this work is the signal cables. The
results from the fatigue life of these cables was not expected to be the same as the real values due to the lack of data to be able to set all the parameters correctly. However, even though the resulting numbers of consumed life does not completely match the real case, they still give important information about were the cable is most damaged and a possibility to compare the damage between different motion patterns for robots where the damage for the complete motion is taken into account, as the results from the simulations with dresspacks on robots show. Also, the resulting numbers from the method developed in this thesis work has a physical meaning, in strain and consumed life, that makes the results of cable damage easier to understand, as compared to the current model in AGX Dynamics.
Even though the method developed in this work is not a completely finished tool for dresspack damage predictions, it has set a good foundation for further work on the subject to create a complete method to predict the damage for the whole dresspack.
References
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Pictures
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