2009:158 CIV MASTER’S THESIS
Design comparison for piston rod solution
Johan Olofsson
MASTER OF SCIENCE PROGRAMME Mechanical Engineering
Luleå University of Technology Department of Applied Physics and Mechanical Engineering Division of Computer Aided Design
2009:158 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 09/158 - - SE Universitetstryckeriet, Luleå ii Abstract The ever increasing energy consumptions and growing environmental awareness requires a steady development of hydro power efficiency. This development puts hard demands on the internal components of a Kaplan runner. Therefore is this design comparison performed to find differences between an old design solution and a new solution untested for larger runners.
The work has been performed at Andritz Waplans located in Vaplan. In the design comparison four design aspects have been evaluated; structural properties, assemblage, manufacturing and procurement. Focus has been on the structural calculations where the new designs fatigue properties have been evaluated, since this was where the most benefits were thought to be. The comparisons have been made by comparing two design solutions with the same premises. It was done by choosing an existing example of the old design and adapting the new design to its size and other prerequisites. The chosen existing example was from Näsaforsens hydro plant.
The fatigue calculations that have been performed are according to the FKM guideline. The basis for the calculations are the use of FEM simulations and a load case composed by a service load measurement that is scaled to fit Näsaforsen and to give 40 years of service. The whole calculation procedures are described in detail.
The other aspects of this comparison have been evaluated by interviews with experts within each field. During these interviews were chosen evaluation points used to find differences between the two designs. The depths of those evaluations are more shallow than the structural evaluation.
It has been found that the two designs have practically the same fatigue properties and it is possible for the new design to fulfill other structural criterions as well, such as nominal stress and buckling. It has also been found that when making a specific case comparison between the two designs for Näsaforsens premises it is possible to reduce the total costs, due to the large difference in material cost when comparing a wrought bar to an ordinary round bar.
In the comparison it has also been seen that the new design might take longer time to assemble due to control measurements and possible position adjustments. It was also established though that it is possible to assemble the new design without any drastic changes of assemblage routines.
In the comparison the two designs are only compared for the premises of Näsaforsen. The results are only valid under those conditions. Further delimitations are that no structural analysis calculations have been performed on the runner hub.
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iv Acknowledgements This document is the collected outcome of my Master’s thesis. It is the final step of my Master of Science degree in mechanical engineering at Luleå University of Technology (LTU). The work has been performed at Andritz Waplans (AW) in Jämtland. The subject of the thesis was to compare two design solutions for a piston rod in a Kaplan runner.
First of all I would like to thank Andritz Waplans for giving me the chance to get an insight of what hydro power development is about. Among the people that I would like thank are of course my supervisor at LTU Stefan Sandberg and my supervisor at AW Henrik Boström. I would also like to direct a special thank to those who have helped me with their expertise during this process, especially Mikael Helin whose help was critical during the structural analysis calculations but also Håkan Hedman and Peter Sverresson for their expert opinions. Besides these mentioned persons I thank everyone that during my education has helped me and supported me along this long and interesting journey.
Johan Olofsson October 2009
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vi 1 Introduction...... 9 1.1 Company presentation...... 9 1.2 Background hydro power...... 9 2 Design background ...... 11 2.1 Kaplan blade adjustment mechanism...... 11 2.2 Background to the new design ...... 12 2.3 Functional difference ...... 12 2.4 Pretension – Superbolt ...... 14 2.5 Expectations on the new design ...... 14 3 Design comparison theory...... 15 3.1 Structural comparison ...... 15 3.1.1 Fatigue...... 15 3.1.2 Fatigue comparison ...... 16 3.1.3 FKM...... 16 3.1.3.1 Fatigue calculation procedure...... 16 3.1.3.2 Service measurements ...... 17 3.1.3.3 Choosing evaluation point...... 17 3.1.3.4 Rainflow counting ...... 18 3.1.3.5 Stress spectra ...... 18 3.1.3.6 Material properties...... 19 3.1.4 Evaluation according to FKM guideline ...... 23 3.1.4.1 Reading the results ...... 24 3.1.5 Other structural evaluation criterions ...... 24 3.1.5.1 Nominal stress levels...... 24 3.1.5.2 Threads...... 25 3.1.5.3 Buckling ...... 25 3.2 Comparison of other design aspects...... 27 3.2.1 Assemblage comparison...... 27 3.2.2 Manufacturing comparison ...... 27 3.2.3 Procurement comparison...... 28 4 Design comparison procedure...... 29 4.1 Implementation and software...... 29 4.2 Fatigue comparison calculations procedure ...... 29 4.2.1 Measurements of service loads...... 29 4.2.2 Scaling the forces ...... 30 4.2.3 Forces to stress ...... 31 4.2.3.1 Boundary conditions...... 31 4.2.3.2 Pretension ...... 32 4.2.3.3 Contacts in the model ...... 32 4.2.3.4 Mesh...... 33 4.2.3.5 Locating evaluation point ...... 33 4.2.3.6 Transforming the forces to stress...... 35 4.2.3.7 Transformation ...... 36 4.2.4 Rainflow counting...... 37 4.2.5 Stress spectrum...... 37 4.2.6 Material properties ...... 38 4.2.7 Evaluation according to FKM guideline ...... 40 4.2.8 Degree of utilization...... 41 4.2.9 Other evaluation criterions ...... 41 4.2.9.1 Nominal stress levels...... 41 4.2.9.2 Stress amplitude in threads...... 41 4.2.9.3 Buckling ...... 42 4.3 Evaluation of other design aspects ...... 43 4.3.1 Assemblage comparison...... 43 4.3.2 Manufacturing comparison ...... 45 4.3.3 Procurement comparison...... 46 5 Results...... 47 5.1 Results for structural evaluation...... 47 5.2 Results from assemblage comparison ...... 47 5.3 Results from manufacturing comparison ...... 48 5.4 Results from procurement comparison...... 48 6 Conclusions...... 49 7 Discussion...... 50 7.1 The new design ...... 50 7.2 Discussion regarding structural calculations...... 50 7.3 Discussion regarding other design aspects...... 50 8 Future work...... 51 9 References...... 52
Appendix A – Basic dimensions for Näsaforsens piston rod Appendix B – Basic dimensions for new design piston rod Appendix C – Basic dimensions for new design upper sleeve
8 1 Introduction Hydro power has been used by humans for hundreds of years but it is only during the last two centuries that it has been used for production of electricity. To make this electricity production possible a lot of development has been made over the years. Although with today’s increasing use of energy and growing focus on environmental sustainability the development continues; in this case with focus on the blade adjustment of a Kaplan runner. In this introduction chapter the background to the problem is given.
1.1 Company presentation Andritz Waplans (AW) was founded under the name Waplans Mekaniska Verkstad in 1836 and has since then been at the same location in Vaplan, Jämtland. The main business areas are hydro power and pulp and paper industry. AW is a part of the Andritz group. The Andritz group has its head quarter in Graz, Austria and has a staff of approximately 13400 employees. The group’s five main business areas are hydro, pulp and paper, environment and process, metals and feed and bio fuel [1].
1.2 Background hydro power The basic principal for a hydropower plant is to convert the potential energy of the dammed up water to a mechanical motion which can be transformed into electric power via a generator [2], see Figure 1. The amount of electricity produced depends on several factors such as head, flow, type and size of turbine etc. The term head is referring to the height that the water travels downwards before it reaches the turbine. It is measured between the upper water surface in the dam and lower water surface after the downstream outlet; more head gives the water more kinetic energy before it reaches the turbine. Flow does also affect the possibility to produce electricity; more flow gives more kinetic energy that can be converted. But also the type of turbine plays a big role, different turbines has different efficiency, with efficiency meant how much of the waters potential energy that can be converted into mechanical motion to drive the generator with. The efficiency is normally in the span of 91-96% [3].
Figure 1. Basic principle for electricity production in a hydro power plant [4].
In Sweden it is mainly two types of turbines that are used; Francis and Kaplan. Common for most turbine types is that the water is collected from a dam and is from there guided through a tunnel into the inlet tube where the water is concentrated into a spiral case where the waters direction and flow is controlled. The flow is controlled with guide vanes in the wicket gate which can be adjusted from fully closed to fully opened positions to produce different flows. After the guide vanes the water reaches the turbine and causing it to rotate. The main difference
9 between the two turbine types is the direction of the water flow, in a Francis turbine the water flows horizontally in to the turbine (radial machine) whilst in a Kaplan turbine it flows axially in to the turbine (axial machine), see Figure 2.
Figure 2. The two most common types of turbines in Sweden, Francis (left) and Kaplan (right) [5].
There are also other types of turbines, such as Pelton and bulb turbine. Pelton is used for very high heads and is common in Norway. The bulb turbine can be seen as a variant of a Kaplan turbine but with its runner main shaft placed horizontally, it is used for very low heads with large flows [3]. The different turbine types have different fields of application. This is due to their different efficiencies over different combinations of head and flow, see Figure 3.
Figure 3. Diagram over usage of turbine types depending on head and flow, blue area is Pelton, red area is Francis, orange area is diagonal turbines, yellow area is Kaplan and green area is bulb turbine [6].
Francis and Kaplan are the two most used types in Sweden because there are not so many rivers with high head but a lot of them instead have large flows. Besides the water flow direction, the two types have another significant difference; the Kaplan turbine has adjustable turbine blades. That makes it more suitable for plants were the flow and head might vary over time, since the adjustable blades gives it a higher operating efficiency range.
10 2 Design background In this chapter the necessary background to the design is given. First is the blade adjustment mechanism explained and after that the functional differences for the new design. As a final point the expectation on the new design is enlightened.
2.1 Kaplan blade adjustment mechanism The mechanism to adjust the runner blades is driven by hydraulic oil pressure. The oil is led down to the runner hub via pipes inside the main shaft, then into the piston rod and out into the cylinder. The piston rod is mounted to the hub and then the piston and the sleeve is mounted on the rod. Around the piston the cylinder is mounted and the cylinder top is integrated with the cross-head. When the need to adjust the blades arises, the oil pressure is raised on one side of the piston, forcing the cylinder to move. That motion is transferred from the cross-head to the blades by the links and levers causing the blades to rotate. This mechanism makes the runner quite complicated and it requires a lot of internal parts in the runner hub, see Figure 4
Figure 4. Cross section of Kaplan turbine runner with named internal components.
Depending on the water supply conditions and the turbine regulator characteristic the regulations occur more or less often. How often the blades are adjusted is also dependent on the type of grid that it is connected to. The frequency for the regulations can vary over time from stand still over days to several adjustments per minute. This causes problems with fatigue in structural parts of the runner design. This is mainly a problem with the piston rod and the parts connected to it. The plant owners have high demands on regulation possibilities since unfavourable blade positions will waste water which in its turn means less profit. Due to these high demands, the fatigue criterions are hard to meet. In the design used at AW today the most problematic area of the piston rod is the notch where the piston is supported. A new design is needed where fatigue is not a problem and without the need to increase the dimensions of the piston rod. The size of the piston rod is important for several reasons; the most important one is the very limited space within the runner hub. A smaller piston rod gives more space for the trunnion and its bearings. Another important aspect of the piston rod size is the cost; a bigger rod means higher material costs.
11 2.2 Background to the new design At AW a new design became available through their owner Andritz Group. The new design originates from German built compact hydro machines. The term compact refers to their size and that they are assembled and shipped as one to the plant. This new design is quite similar to the design used today, which makes a replacement uncomplicated. A lot of the old relating parts would not need any redesign. This design is untested on larger runners and is new to AW. To evaluate the design it needs to be adapted for larger runners and their circumstances. For comparison of the difference in needed components between the two designs see Figure 5. As the figure shows the difference between them is that the new design has an upper sleeve around the piston rod and it has a large nut instead of a flange to secure it to the hub.
New design Old design Nut
Runner hub
Upper sleeve
Piston rod Piston
Piston sleeve
Superbolt
Figure 5. Comparison of components between new and old design.
2.3 Functional difference The functional advantage of the new design is that it directs a part of the load differently. When opening the runner (cylinder moving upwards) there is no difference between the two designs since then the force on the piston is transferred via the lower sleeve to the Superbolt threads, which causes tension in the piston rod. When closing the runner, the force in the old design goes directly into the piston rod whilst in the new design it is transferred into the upper sleeve and from it into the runner hub, see Figure 6.
12 Opening pressure
Reaction force when opening
Closing p ressure
Reaction force when closing
Figure 6. Difference between new and old designs regarding reaction forces on the components.
This makes an important difference in the stress scenario for the piston rod; since the new design does not have the notch it will have other fatigue properties. In the new design, the whole piston rod is under tension and the whole upper sleeve is under compression. In the old design the piston rod was mostly under tension while the upper oil inlet hole was under compression stress. Combining this with the large stress concentration in the notch radius caused a need for a large dimension on the old piston rod.
Some details of the design have not been specified but they are important for design properties and the evaluations validity. The most important of these details is the location of the seals; in which component they are placed. In the original design all the sealing slots are placed in the piston rod. In the adapted new design they are all placed in the sleeves and piston, see Figure 7.
Figure 7. Sealing slots placed in the sleeves and in the piston in the adapted design, not in the rod as in the original design.
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2.4 Pretension – Superbolt Both the new and the old designs have a need for pretension of the piston rod. It is needed to make sure that there is no clearance between the piston and its connecting parts during service. The size of the pretension is determined of the maximum hydraulic pressure, the piston surface area and a safety factor. To create such large pretension a Superbolt is used. The Superbolt is a pretension device for large threads; it is a large threaded nut with several smaller bolts in it. Each one of these smaller bolts can be tensioned individually with small hand tools to generate a well controlled pretension for the large nut, see Figure 8.
Figure 8. Superbolt pretension nut [7].
2.5 Expectations on the new design The purpose of this comparison between the new and the old designs is to verify if the new design has the expected advantages and if there are any other drawbacks with it. The expected advantages can be seen in Table 1.
Table 1. Expectations on the new design. Expectations Benefit Diametrically smaller base material for piston rod Lower material cost Better or equal fatigue properties Size reduction Less or equal space required in runner hub More space for the trunnions Lower or equal total production costs More profit More or equal assemblage possibilities Simpler assemblage Adaptable for large and small runners Wide range of usage possibilities
14 3 Design comparison theory The design comparison was divided into four steps, structural analysis, assemblage, manufacturing and procurement. The first step was absolutely the largest one since if the design would not have been structurally satisfying there would have been no need to evaluate it further, it was also the step that required the most time consuming calculations. The theory behind these calculations and the procedure to perform them are described in detail. The other aspects have more experienced based evaluation and were performed with help of interviews with experts in each field. The decision was taken to make the comparison on a newly designed runner. The runner that the design would be compared to was Näsaforsen. The reason for this was that the Näsaforsen runner had recently been designed and dimensioned according to the latest guidelines. It was also a clear example of how the old design solution could be implemented.
3.1 Structural comparison The first comparison that needed to be done was to make sure that the new design had at least the same or better structural properties, and if there was any possibility to reduce the total space needed in the runner hub. The evaluations were done by comparing the designs fatigue strength and by assuring that the new design fulfilled the structural demands that were set up for it.
3.1.1 Fatigue Fatigue is a phenomenon that occurs when a component is under a cyclic load, that meaning that the load is not constant but varying over time. This variation in stress leads to a gradual breakdown of the material. Fatigue is without a doubt the most common failure type in mechanical components [8]. The fatigue process can be separated into three phases; crack initiating, crack growth and final failure, see Figure 9. Several aspects influence the fatigue sensitivity for a component, some of them are:
Component geometry – Stress concentration regions Material properties – Yield strength. Material defects – Slag or other impurities. Loading – Number of cycles and cycle complexity. Component environment – Temperature and corrosiveness
Crack initiation site
Crack growth
Final failure
Figure 9. Fatigue failure on an aluminium crank, with the three phases of failure distinguished [9].
There are some different ways of evaluating fatigue and the simplest is to use an S-N curve known as Wöhler curve. It is created through a series of material tests where a test specimen is subjected to a sinusoidal load until it breaks. The number of load cycles at each load amplitude is plotted to a curve, see Figure 10. The curve shows a linear reduction in strength with increased number of load. The curve has a breakpoint where the stress does
15 not decrease any further; it is called the fatigue limit. For more complex loads and more precise results other evaluation methods are needed.
Log σ Stress Stress
Number of load cycles Log N
Figure 10. Figure of a simple S-N curve, called a Wöhler curve. The allowable stress is decreasing with increasing number of cycles.
3.1.2 Fatigue comparison To be able to verify if the new design had the expected fatigue benefits the comparison was needed to be done in a careful way so only the design differences was compared and not other influencing parameters. This was done by using as much geometries as possible from Näsaforsen. The evaluation was to be done according to FKM guidelines which are newly adopted at AW. To enable this comparison between the two designs first a CAD- model had to be done for the new design but with dimensions that would fit the Näsaforsen runner. It was done with help of scaling and adapting the design to Näsaforsen’s runner hub dimensions. See Appendix A to Appendix C for the components basic dimensions. The original design had a different oil inlet system than Näsaforsen and therefore it also had to be adapted to Näsaforsen.
3.1.3 FKM FKM stands for “Forschungskuratorium Maschinenbau” and is a German guideline in assessments of analytic strength for mechanical components. The guideline has been available since 1994 and is based on the former German standards TGL and VDI 2226. FKM separates analysis of rod-shaped, shell-shaped and block-shaped components, it also separates welded from non-welded components. The guideline gives several ways to analyze fatigue and the calculation procedure is almost completely predetermined, leaving only some decisions to the user [10].
3.1.3.1 Fatigue calculation procedure When analyzing fatigue according to the FKM guidelines there are a lot of input needed. To be able to understand what the different inputs are and why they are needed it is first important to have an overview of the whole procedure, see Figure 11. Each step of this procedure will now be described in a theoretical way and later the steps will be described in the details concerning the new designs actual calculations.
16 Analyzing Forces from measured measurements signal Material properties Fatigue limitations Scaling forces Choosing evaluation point Design parameters Stress gradient Force and stress relations
Component Degree of needing utilization fatigue analysis
Type of overloading Critical damage sum Creating Safety factor stress spectra Adapting stress spectra Evaluation Distinguishing to R=-1 according to load cycles with FKM Rainflow counting
Figure 11. Schematic timeline of fatigue calculations procedure.
3.1.3.2 Service measurements There are different ways to determine a load case for a component, sometimes it is possible to assume a load scenario, otherwise a standard load scenario might be used and in some cases when available a measured service load can be used. In this case the last scenario was applied because it would involve the least approximations. The measured signal that describes the runner blade adjustments is a measurement performed on Sollefteås hydro power plant. The measurement was made by recording the pressure in the hydraulic unit. After this the pressure signal was analyzed with help of a sign check of the first order derivative to isolate distinctive local maximums and minimums. Measurements were made during roughly 22h and during that time the machine had a standstill for approximately 5h, despite the quite short time it gives a picture of the service conditions for the components in the runner. Since the measurement was performed on Sollefteå hydro power plant it had to be scaled to fit Näsaforsens runner premises. These machines are very different in size, head and flow. These differences lead to different blade forces and therefore different loads on the components in the hub. The scaling is done with help of linear interpolation between known points, for both Sollefteå and Näsaforsen, regarding needed force to achieve a blade adjustment at a certain blade position.
3.1.3.3 Choosing evaluation point The FKM guideline uses local stresses from one point of the component to determine the fatigue strength. To find this point Finite Element Method (FEM) simulations were used, the needed components were modeled and three simulations were performed. Only areas where fatigue was suspected were chosen for evaluation since no more than one point at a time can be evaluated with this method. But this was seen as sufficient since if the worst point fulfill the demands then the rest will also be good enough. These three simulations were used to create a
17 linear relation between pressure on the piston and stresses in the most exposed regions on the components. With a function derived that expresses the relation between piston load and stresses in the most stressed areas of the components it is possible to transform the scaled forces into stresses.
3.1.3.4 Rainflow counting The analyzed and transformed signal containing peak values does not give any information of what the levels consists of, meaning there is nothing distinguishing any difference between mean stress and amplitude stress. Therefore it is necessary to separate the signal into these two components. The separation can be done in different ways but the Rainflow counting method is seen as one of the more appropriate when dealing with complex load variations [8]. Rainflow counting is performed with a program script, the script searches through the signal and find full or half cycles of loads at different mean points and with different amplitudes, see Figure 12. As the example picture shows the Rainflow script has found a number of cycles in a random signal. It has found a cycle with small amplitude and with a negative mean point, colored cyan, but it has also found a dark blue half cycle with a mean point near zero. The data collected from this analyze is then saved to a matrix.
Figure 12. Example picture of Rainflow counting algorithm, generated with help of demo script included with the Rainflow algorithm.
3.1.3.5 Stress spectra As with all types of strength calculation, stress is always compared to the material properties. These properties are based on numerous tests and analyses. A materials fatigue properties are determined by tests where the mean stress is zero and the amplitude is held constant. Therefore the load matrix from the Rainflow counting have to be transformed, otherwise the material properties will not be valid. The transformation is done according to the FKM guideline, and is achieved by assumptions of an overload where the ratio between amplitude and mean stress is held constant and the materials mean stress sensitivity is taken into account, see Figure 13.
18 3 1 2
Figure 13. Schematic figure over the mean stress transformation. The stress σa in point 1, is projected on to the overload stress curve that has constant relations between mean stress and amplitude stress. This creates an A/B ratio which is reproduced for the overload that would be produced at R=-1 [10].
The transformation can be explained in three steps. First a load consisting of a mean stress and stress amplitude, called σa in the picture, at point 1. At point 2 the load is extended along the R σ =constant line and the original load is projected onto the extended one, this forms an A/B ratio. In the third step the A/B ratio is reproduced at point 3, meaning at zero mean stress. This transformation is then done on every recorded set of loads in the matrix, resulting in a stress spectrum that can be used for evaluation against measured material properties. There is a significant difference between the two components mean stress transformation since the piston rod is under constant tension and the upper sleeve is under constant pressure. That gives that all the loads for the upper sleeve is on the left side of the R σ =-1line which gives that the mean stress gets less influence since there is not the same concern taken to the yield limit under compression when dealing with fatigue.
3.1.3.6 Material properties In the new design two different materials were used, one for the Piston rod and one for the upper sleeve. The materials that are used are the same that was used in Näsaforsen. This is done to make sure that structural comparison is made without influence from the material. Since there is no upper sleeve in Näsaforsen it has been given the same material as the lower sleeve instead. The piston rod material is an alloyed construction steel while for the upper sleeve the material is stainless steel. The materials properties can be seen in Table 2 [10]. Fatigue is a complex phenomenon and hard to make simple assumptions about. Therefore when analyzing fatigue strength there are a lot of aspects about the material that needs to be taken into account.
Table 2. Material properties for the two materials used in the components. Material Property SS2541 – Piston rod SS2387 – Upper sleeve E – Young’s modulus [GPa] 210 210 Yield strength RP [MPa] 749 680 Tensile strength R m [MPa] 910 840 Poisson’s ratio 0.3 0.3
19 3.1.3.6.1 Limiting factors It is well known that a high number of cycles effect the material in a negative way. The more load cycles the more the material will be broken down. Depending on material the degradation will have different speed and might also come to a point where the material will not break down any further. That limit is called the fatigue limit, but not all material has such limit. Aluminium lacks this property. Other factors might affect that limit, for instance welding or corrosion can diminish the effect. In this case the load cycles over 40 years are more than 10^6 and therefore the material strength can be reduced with help of equation (1), with the fatigue strength factor
fW ,σ according to Table 3.
σ = ⋅ (1) W ,zd fW ,σ Rm
Table 3. Constants for material types for calculations of various factors in the evaluation.
Type of material aG bG aR, σ Rm,N,min fW ,σ Case hardening steel 0.40 - - 0.22 400 Stainless steel 0.40 0.4 2400 0.22 400 Forged steel 0.40 - - 0.22 400 Steels, other 0.45 0.5 2700 0.22 400 GS – Cast steel 0.34 0.25 2000 0.2 400 GGG – Nodular cast iron 0.34 0.05 3200 0.16 400 GG – Cast iron with lamellar 0.30 -0.05 3200 0.06 100 graphite GT – Malleable cast iron 0.30 -0.05 3200 0.12 350 Wrought aluminium alloys 0.30 0.05 850 0.22 133 Cast aluminium alloys 0.30 -0.05 3200 0.20 133
There are also other aspects of a component that influences the materials fatigue strength. The aspects that are dealt with in FKM are: design factor, roughness factor, surface treatment factor, surface coating factor and non- linear elastic stress strain factor.
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3.1.3.6.2 Design factor K f The design factor depends on the stress concentration factor and stress gradient in the chosen area of evaluation. The stress gradient is approximated with help of FEM in most cases, with simpler geometries there are some analytic equations to calculate it. In this case when FEM was used it was approximated with help of equation (2) and Figure 14. The stress concentration factor is calculated differently depending on the geometry in the area, for instance is a notch calculated in one way and a hole in another. In this case were both a hole and a groove of interest. For a hole in a rod it was calculated according to Figure 15 and equations (3) to (6) and for a groove it could be derived with help of Figure 16. The larger the stress concentration factor and the stress gradient are the greater the strength compensation is, meaning higher strength.
Figure 14. Graphical explanation of variables needed to calculate the stress gradient σa is stress at the surface of the area where the gradient is calculated.
20 1 σ G = 1− 2a (2) σ ∆ σ s 1a
Figure 15. Graphical explanation of variables needed to calculate the stress concentration factor for a rod with transverse hole [11].
2r 2r K = C + C + C ( ) 2 (3) t 1 2 D 3 D = (4) C1 .3 000 = − + 2 − 3 (5) C2 .0 427 .6 770 (d / D) 22 .698 (d / D) 16 .670 (d / D) = + − 2 + 3 (6) C3 11 .357 15 .665 (d / D) 60 .929 (d / D) 41 .501 (d / D)
Figure 16. Graph from which stress concentration factors for a U-groove can be determined with help of dimensions for the groove [12].
When the stress concentration factor and the stress gradient have been established it is possible to calculate the fatigue strength influence that detail has on the component. This is done with first calculating K f / K t ratio called nσ, how to calculate it depends on the size of the stress gradient according to equations (7) to (9) and Table 3. After that it is possible to calculate the design factor with equation (10).
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− If G ≤ 1.0 mm 1 then
R −(a − 5.0 + m ) G ⋅ bG MPa nσ = 1+ Gσ ⋅10 (7)
− − Or if 1.0 mm 1 < G ≤ 1mm 1 then
R −(a − 5.0 + m ) G ⋅ bG MPa (8) nσ = 1+ Gσ ⋅10
− − Or if 1mm 1 < G ≤ 100 mm 1 then
R −(a − 5.0 + m ) G ⋅ bG MPa (9) nσ = 1+ Gσ ⋅10
~ K t K f = (10 ) nσ
3.1.3.6.3 Roughness factor K Rσ The surface finish influences the fatigue strength through the crack initiating potential. A smoother surface gives a higher strength. A rough surface has much higher risk of inducing a crack. The roughness factor is calculated with equation (11), Table 3 and Table 4.
= − ⋅ µ ⋅ ⋅ (11) K R,σ 1 aR,σ lg( RZ / m) lg( 2 Rm / Rm,N ,min )
Table 4. Variable explanations for equation (11). Variable Explanation R Average roughness of the surface of the component in m Z R Materials tensile strength m Constant from table a σ R, R Constant from table m,N ,min
3.1.3.6.4 Other influencing parameters K S , KV , K NL ,E In fatigue analyzes there are even more parameters that influence the material strength but they do so to a very limited extent in most cases. In some cases they can have a significant impact on the fatigue strength. If the material is a cast iron with lamellar graphite, a so called grey cast iron, then the constant for non-linear elastic stress strain behavior K NL ,E must have a value higher than 1. If it is an aluminium alloy with a surface coating, then the coating factor K S with regard to the coating thickness needs to be accounted for. The last parameter is the surface treatment factor KV which is used if the material has a surface treatment. This factors size is dependent on type of material and what kind of treatment that is used, but they all get the value 1 if they are not in use or seen as non significant.
22 3.1.3.6.5 Design parameters When all of the needed design parameters have been calculated the final design parameter can be calculated. It is the final parameter that determines the materials fatigue strength. It is calculated according to equation (12).
1 1 1 1 K = ⋅ 1( + ( − ))1 ⋅ (12 ) WK ,σ ~ ⋅ ⋅ nσ K R,σ KV K S K NL ,E K f
The final design parameter can now be used to calculate the fatigue strength for the component, it is done with equation (13).
σ = σ (13) WK W ,zd / KWK ,σ
3.1.4 Evaluation according to FKM guideline There are several different ways to evaluate the fatigue strength for a component and in FKM some of them are presented. The evaluation is made by comparing the components final fatigue strength to the load that it is subjected to. Before this evaluation is possible the component fatigue strength first has to be calculated, it is done by taking the previously calculated material strength and regulate it for the spectrum characteristics and type of evaluation chosen. Depending on what kind of evaluation that is used the components fatigue strength is calculated differently, although they all use damage summation to establish the spectrums effect on the component. Damage summation in its basic form can be described by equation (14) but in the different evaluations it is used a bit differently. The total damage sum that the spectrum causes to the component is calculated by summation of the damage from each step, according to equation (14) and Table 5 . Each step is made up by an amplitude stress and the number of cycles expected. The number of cycles in a step is compared to how many cycles that are needed to failure at that amplitude. The result from each partial sum can be plotted together to form a graphical view of the spectrums characteristics and then be compared to Wöhler curves.
n ∑ i = Total damage sum (14) Ni
Table 5. Variable explanations for equation (14). Variable Explanation Number of cycles in step i of load spectrum ni Number of cycles at step i until failure Ni
In FKM some different ways of calculating the fatigue strength is given, the most strict of them is Miner’s elementary rule, this evaluation does not imply a fatigue limit at 10^6 cycles. Miner’s consistent rule which is less strict does take the fatigue limit into account and it has another view of the materials strength reduction. The difference in strength reduction between the two fatigue evaluation methods is how the variable amplitude fatigue strength factor is calculated. In Miner’s elementary rule the same variable amplitude strength factor is used for all the steps in the stress spectrum. In the consistent version of Miner’s rule the variable amplitude fatigue strength factor is calculated iteratively for different values of σa,1 until the required total number of cycles is obtained. This means that a different variable amplitude strength factor is used for every step in the load spectrum. This leads to a decrease in fatigue strength when the damage sum increases. For detail description of the calculation procedure for the variable fatigue strength factor see [10]. With a determined component fatigue strength factor can the components amplitude strength be calculated according to equation (15) and Table 6.
σ = σ ⋅ (15 ) BK AK K BK ,σ
23 Table 6. Variable explanations for equation (15). Variable Explanation σ Component variable amplitude fatigue strength BK σ Component fatigue limit AK Variable amplitude fatigue strength factor K BK ,σ
In the calculation process there are two parameters that the user can control. The first one is the safety factor; it works like a normal safety factor that reduces the strength of the material with a chosen limit. How to choose the limit is described in FKM, see Table 7. The second one is the critical damage sum; this is a parameter that controls how far the user wants the fatigue damage to have propagated. That means that when the damage sum is 1, a failure has occurred, therefore a critical damage sum is chosen to control how far from failure that is accepted. FKM gives that for steel the suitable critical damage sum is 0.3.
Table 7. Table for determining the safety factor for fatigue calculations according to FKM. Safety factor jD Consequences of failure Severe Moderate Regular inspections no 1.5 1.3 yes 1.35 1.2
3.1.4.1 Reading the results The evaluation leads up to a result that it is called the degree of utilization. It is a level of how much of the component’s strength that has been consumed by the load spectrum. If the degree of utilization is greater than one the component does not fulfill the requirements that the user has set up. The degree of utilization is calculated with equation (16) and Table 8. The result from the damage summation can also be plotted against a Wöhler curve giving a graphical display of the components fatigue strength.
σ a 1, a = (16 ) BK ,σ σ BK jD
Table 8. Variable explanations for equation (16). Variable Explanation σ Largest stress amplitude in spectrum a 1, σ Component variable amplitude fatigue strength BK jD Total safety factor
3.1.5 Other structural evaluation criterions There is not only the fatigue criterion that needs to be met when the design is evaluated. There are also other criterions such as nominal stress levels in the component, stress amplitude for the threads in the Superbolt and since the upper sleeve is under high compression load there might be risk for buckling. These criterions are evaluated with help of a set of simpler structural calculations.
3.1.5.1 Nominal stress levels The nominal stress level in the components is evaluated with help of the maximum load and the stress level is calculated for the smallest cross section. It is calculated with equation (17). The criterion that is used is the ASME criteria for nominal stresses for component under cyclic load, see equation (18) [13].
F σ = (17 ) A
24
⋅ Rm 2 Rp Maximum allowable no min al stress = Min , (18 ) 3 3
3.1.5.2 Threads An assumed normal load cycle gives the stress amplitude used to evaluate the threads. The assumed normal load cycle is based on the servo forces to yield a certain blade angle at a certain position. The worst case is used, meaning to open and close the runner at near fully opened position. The criteria for maximum nominal stress is according to BSK99 [14] and is based on the type of joint and 10^6 load cycles.
3.1.5.3 Buckling The risk for buckling of the upper sleeve is calculated with help of BSK99 [14]. According to BSK99 the criteria for steel constructions load carrying capacity can be calculated with equation (19) and equations (20) to (25) with help of Figure 17 and Table 9. The upper sleeve is seen as free in its lower end and fixed in its upper end; see Figure 17. The calculated capacity can then be compared to the maximum expected load.
= ω NRcd c Agr f yd (19 )
With:
α − α 2 − 4.4 λ2 ω = c (20 ) c λ2 2.2 c
Were:
l f yk λ = c (21 ) c π i Ek
α = + β (λ − )+ λ2 (22 ) 1 1 c 2.0 1.1 c
And
I i = (23 ) A
= β (24 ) lc L
π (D4 − d 4 ) I = (25 ) 64
25 F
L L β = c l
Figure 17. Load case for upper sleeve buckling, fixed in one end and free in the other. The figure also shows relations between actual length and buckling length.
Table 9. Variable explanations for equations (19) to (25). Variable Explanation Compression force load capacity N Rcd ω Reduction factor for buckling c λ Slenderness ratio c Buckling length lc i Inertia radius I Area moment of inertia α Constant for determining the reduction factor Cross section area Agr Value of characteristic tensile strength limit f yk Value of dimensioning tensile strength limit f yd Characteristic young modulus Ek β Enlargement factor for actual length L Actual length D Outer diameter d Inner diameter β Constant for determining α, dependent on type of cross section. 1
26 3.2 Comparison of other design aspects Besides the structural comparison there is also need for several other aspects of the designs to be compared. The other aspects that were chosen for evaluation were assemblage, manufacturing and procurement. The depths of the comparisons for these other aspects are quite shallow due to time limitation. That there are so many factors that influence the result that a definite and universal result would be hard to reach. The comparisons are therefore made on two levels, first a more general comparison were the designs principals are compared and on a second more specific level were the designs are compared in more detail as designed for Näsaforsen. The results given from the specific comparison is to give an example of how the two designs may differ in a specific case. In the more general comparison simple evaluation points are used to distinguish the differences between the two designs.
3.2.1 Assemblage comparison The assemblage comparison is performed by interviews with experts in the field of assemblage. Before the interview a set of questions were formed that regarded the praxis of assemblage. The goal with the comparison was to find differences between the two designs, and where possible decide which of the two that is preferable. The evaluation points used during the comparison can be seen in Table 10. Since the assemblage is not so very case sensitive this comparison is made quite general but with Näsaforsen used as base. With that meant the pictures and drawings from Näsaforsen were used to show principal design ideas and included components during the interview.
Table 10. Evaluation points for assemblage aspects. Evaluation point Question formulation Assemblage order In which order would the new design be assembled? Assemblage of other components Does the new design affect the assemblage of the other components? Space and access Does the new solution require more space for fitting the components into the hub? Tools Are any extra tools needed for the new design? Hub orientation During assemblage of the new design does it require more rotation and repositions than the old design? Assemblage time Does the new design take longer time to assemble? Quality control Are there differences for quality control between the two designs? Incorrect assemblage Is the risk for incorrect assemblage higher for the new design? Scaling effects Are there any scaling effects?
3.2.2 Manufacturing comparison The manufacturing comparison is performed with the same procedure as for the assemblage. To be able to compare the manufacturing cost to the specific level drawings for the two designs were needed, both for the piston rod and the upper sleeve. These were done with the correct dimensions and tolerances. The tolerances that were used were the same as those originally used in Näsaforsen. The basis for the comparison is made out by interviews with a manufacturing engineer. The drawings were used to estimate manufacturing time in the specific examples and they were also used to compare principal differences between the designs. From this a series of simple cost calculations was made to establish differences between the two designs in the specific example. The evaluation points used for the general comparison can be seen in Table 11.
27 Table 11. Evaluation points for manufacturing aspects. Evaluation point Question formulation Total manufacturing time Does the new design take longer total time in manufacturing? Machine requirements Is there any difference in which machines that is needed? Tool requirements and tool wear Do the materials require different tools and does the amount of machining lead to different tool wear? Quality control Are there any differences in possibilities to take control measurements of the components? Influence on manufacturing of runner How does the new design influence the machining of the hub runner hub?
3.2.3 Procurement comparison The procurement comparison is hard to make on a general level since in procurement a lot is depending on size and material etc. Consequently the most of the comparison is made out by the more specific example. Most of the costs involved in manufacturing of components of this size are the material costs and they are very much depending on the economic situation in the world. It is therefore not possible to compare Näsaforsens old designs actual cost against the new design with today’s material prices. Therefore the material costs for the new design is based on the old designs actual cost and on material costs from that time period, and by this making the comparison more accurate. The procurement comparison is also made with help of interviews with a production engineer. Evaluation points used in the general procurement comparison can be seen in Table 12.
Table 12. Evaluation points for procurement aspects. Evaluation point Question formulation Delivery time Are there differences in delivery time for the two designs? Delivery condition What delivery conditions exist for the two designs? Coating and laser Does the reduced amount of laser welded stainless coating give any cost weld reduction? Material cost What are the total material costs for the two designs? Suppliers Does the new design lead to more potential suppliers?
28 4 Design comparison procedure In this chapter the comparison procedure is described. First the structural calculations are described step by step and after that the other comparisons are describe as they were performed.
4.1 Implementation and software The calculations were carried out with help of a numerical calculation program named Octave [15]. It was used in a Linux-like environment called Cygwin [16]. Other software used during the evaluations was the CAD software SolidWorks [17] and its FEM module SolidWorks Simulations [18]. The implementation of the calculations was divided in 4 Matlab-scripts and to them other smaller function scripts were used. Table 13 gives an overview of which script that calculated what and which sub scripts that were used in each.
Table 13. Overview of implementation scripts used to perform fatigue calculations. Main script Subscript Calculation 1. solforce_to_nasastress.m - Transforms the Measured forces from Sollefteå into stresses in Näsaforsen 2. rainflow_nasa.m rainflow.m Analyzes the stress signal with Rainflow counting. 3. lastspektra_nasa.m kaksf2.m/kaksf2b.m Transforms the Rainflow data into a stress spectrum 4. utv_FKM_nasa.m material.m Evaluates the component and haigh2.m/haigh4.m calculates its degree of utilization. px.m p2km.m minerkonsdiff.m cyl1.m damagediff.m cyl2.m wf1.m wf2.m
4.2 Fatigue comparison calculations procedure In this section the calculations will be described step by step for the actual analysis of the new design solution. The description will be valid for all the analyzed parts, but most of the examples and figures that are presented show the piston rod.
4.2.1 Measurements of service loads As described earlier the first step of the analysis was to create a stress spectrum from a pressure measurement. That process began with the scaling of the forces from Sollefteå to fit with Näsaforsen. Measured forces from Sollefteå can be seen in Figure 18. Since the fatigue calculations were to make out a basis for comparing the two designs the fatigue calculations for the old design were needed to be done in the same way. Therefore the same procedure was used to evaluate the fatigue strength for the old design. Since Näsaforsen recently was designed there already existed FEM simulations and calculations that could form a base for the comparison calculations.
29
Figure 18. The complete measured force signal from Sollefteå hydro power plant.
4.2.2 Scaling the forces The forces were scaled linearly with help of known values for the runner positions from both Sollefteå and Näsaforsen. These values come from calculations of the forces that are needed to do a certain adjustment at a certain position. When the measurement of the hydraulic pressure was made the runner position was also recorded and therefore it was possible to do this scaling. Figure 19 shows how the force is related to the runner positions for both Sollefteå and Näsaforsen.
Servo forces to obtain certain blade angle at certain positions
3200
2400
1600
800 Fservo opening Näsaforsen Fservo closing Näsaforsen 0 [kN] Fservo opening Sollefteå Fservo closing Sollefteå -800
-1600
-2400
-3200 0,00 20,00 40,00 60,00 80,00 100,00 Runner blade Opening [%]
Figure 19. Forces to obtain a blade adjustment at certain blade positions for both Sollefteå and Näsaforsen
30 4.2.3 Forces to stress With the forces now scaled to fit Näsaforsen the next step was to form a relation between those forces and the stress affecting the piston rod. To find these stresses and to determine an evaluation point FEM was used. To save calculation time a simplified model of the design was used and only the parts that could have any structural interest were included in the model. The simulation model consisted of a quarter of the design and some of the details on it were removed to simplify meshing, see Figure 20. Examples of simplified details are oil inlet tubing and piston surface. To further simplify calculations the model was given three dividing lines axially to enable the use of finer mesh on small areas. An additional simplification was that the Superbolt was modeled as a part of the rod; this was done since it would not be possible to get any useful information from a threaded part.
Figure 20. Geometries used for FEM simulations to determine evaluation points and distinguishing force and stress relations for the evaluation points. Dividing lines on the components surfaces is also visible in the figure.
4.2.3.1 Boundary conditions The upper part of the design was given fixed constraints to simulate the nut on the piston and to simulate the runner hub on the sleeve. To verify these boundary conditions tests were made with the use of a quarter runner hub, the results were the same for both models and therefore the one without the runner hub were chosen. This reduces calculation time since it involves fewer contacts and fewer elements. To compensate for the quarter model symmetry was used, see Figure 21.
Figure 21. Boundary conditions used in FEM simulations, red arrows being fixed constraints, green arrows being symmetry constraints and blue colored lower sleeve being of different temperature than the other components.
31 4.2.3.2 Pretension The Superbolt gives a very big pretension of the piston rod. The purpose of the pretension is to make sure no clearance between the components occur during blade adjustments. The needed pretension is given by the piston surface area and the maximum available hydraulic pressure and a safety factor. It is calculated with equation (26), with input and result according to Table 14. This is nothing that can be simulated directly in FEM; since the pretension is set on the unloaded piston and the pretension vary over different loads it could not be applied just as a constant force. Therefore it was solved with help of a temperature difference between the lower sleeve and the rest of the parts, this causes the lower sleeve to grow and that gives a force on the piston contact area that resembles the pretension force, see Figure 21. To find the correct temperature some FEM simulations were needed, first one with just a random temperature difference, after that it was possible to linearly calculate a theoretical value. Repeating this one more time gave a very accurate contact force between the surfaces on the piston and lower sleeve.
= ⋅ FPretension S f FServo (26 )
Table 14. Table showing variable values for equation (26), and the result from equation (26).
FServo S f FPretension 3060kN 1.3 ≈4000kN
4.2.3.3 Contacts in the model In the model there were several points were contact between different parts were used, the type of contact that was used are “no penetration”, meaning that the chosen surfaces can not penetrate each other. Points where this was used can be seen in Figure 22.
Contact search surfaces
Figure 22. Points where contact search is used to be able to transfer force between components in the simulation.
32 4.2.3.4 Mesh Since these components are quite large with some small details it was not possible to have a small mesh over the whole model. Therefore mesh control were used to control the mesh size on chosen features, such features were the oil inlet holes, radiuses on the piston rod and contact surfaces, see Figure 23. The mesh size on the rest of the model was chosen larger to reduce calculation time. Several simulations were performed on the same model and with varying mesh size to verify that the results converged, after this was the same mesh size used for all simulations.
Figure 23. Mesh size variation in the FEM model, finer mesh around oil inlet holes and on contact surfaces. Pressure applied for closing, blue arrows on lower surface of the piston.
4.2.3.5 Locating evaluation point Three FEM simulations were needed to be able to form a linear relation between load and stresses. The three were maximum closing pressure, maximum opening pressure and pretention only. With maximum the maximum available hydraulic pressure is meant, which is 150Bar. The difference between opening and closing is which side of the piston that the pressure is applied, see Figure 23. The results from the simulations show several areas of high stresses but some of them could however be neglected. Such areas were the radius towards the solid
33 modeled Superbolt, surfaces where fixed constraints were used and on the absolute edge of the contact surface between the upper sleeve and the piston. The two parts that are of interest for the analysis were the upper sleeve and the piston rod. On these two components the areas with the highest stresses were identified with help of probing tools. In these areas the nodes with the highest stress were identified, see Figure 24.
Figure 24. Results from one of the FEM simulations with load case where maximum opening pressure is applied. Zoomed view to the right showing the evaluation point for the piston rod, marked with a red ring in the larger picture.
The results that could be read out from the first simulations gave the evaluation point. It also gave the node id which was to be used to read the results from the other load cases. In the piston rod the area with highest stresses was the oil inlet hole. To choose evaluation point for the upper sleeve was not so obvious since there were two areas that could have high stresses, but only one had been included in the model. The sealing slots in the upper sleeve had been left out of the model due to its small details. Therefore a new set of simulations were done with the sealing slots as the only area with fine mesh. The reason for not including them in the same model was due to computer memory capacity, since it would have lead to multiple areas with fine mesh. But with these two models it was possible to extract values for both the sealing slot and the oil inlet hole on the upper sleeve. For results from the two simulation models see Table 15. For the piston rod the first principal stress is used and for the upper sleeve the third principal stress is used. The reason for this is that the FKM calculations are made according to the calculations that regard one dimensional rod shaped components.
34
Table 15. Results from the three FEM simulations. Load case Component Place Node P1/P3 stress [MPa] Maximum close Piston rod Lower oil inlet hole 71987 412.8 Upper sleeve Oil inlet hole 327345 -883.7 Sealing slot 40676 -898.9 Pretension Piston rod Lower oil inlet hole 71987 536.3 Upper sleeve Oil inlet hole 327345 -486.7 Sealing slot 40676 -589.6 Maximum open Piston rod Lower oil inlet hole 71987 659.8 Upper sleeve Oil inlet hole 327345 -1170 Sealing slot 40676 -279.7
4.2.3.6 Transforming the forces to stress The results from the FEM simulations were used in a simple linear calculation. From that a linear function was derived that can be used to transform forces into stress, see Figure 25 for the piston rod’s function. As the figure shows it was clear that there is a linear relation between forces and stress, and the function that could be derived from it was equation (27) for the piston rod, equation (28) for the upper sleeve oil inlet hole and equation (29) for the upper sleeve sealing slot.
Linear function of force to stress transformation
7,00E+08
6,00E+08
5,00E+08
4,00E+08 Closing 3,00E+08 Opening
2,00E+08 First principal stress [Pa] principal First 1,00E+08
0,00E+00 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 Force [kN]
Figure 25. Force and stress relation for the piston rods evaluation points.
σ = −40359 48. ⋅ F + 36.5 ⋅10 8^ (27 )
σ = −125277 8. ⋅ F − 87.4 ⋅10 8^ (28 )
σ = −101160 13. − 90.5 ⋅10 8^ (29 )
To verify the function it was tested against a FEM simulation with a pressure chosen in-between the earlier used pressure span. This shows a good accuracy, see Table 16 for results from this test. Due to the good result from this test only the function for the piston rod was tested.
35
Table 16. Results from validation test of the function derived from the FEM simulations. Function verification at 55kN opening force Calculated value 534.1MPa FEM value 534.3MPa Deviation 0.04%
4.2.3.7 Transformation With the linear function defined it was possible to transform the scaled forces. This was simply done by just using the function on all the force values in the script. With the forces normalized and plotted together with the positions it gives a good picture over how the position altering affects the stress levels on the design, see Figure 26. Only a segment of the time is plotted to easier show the variations in the signal. Clear stress peaks can be seen at the very start of a blade angle adjustment. When viewing the full stress plot one can clearly see that the stress amplitude is not so large but that the mean stress is quite large, obviously this comes from the large pretension that the Superbolt gives. To more clearly show this, a plot over a segment of the time is plotted in Figure 27.
Figure 26. Segment of the transformed stresses and blade positions, percentage of opened and percentage of maximum force. Shows stress peaks at the start of every blade adjustment.
Figure 27. Segment of stress in the piston rod, showing a high mean stress and low amplitude stress.
36 4.2.4 Rainflow counting As earlier described Rainflow counting is a method of signal analysis where mean points and amplitudes are extracted from the signal via an algorithm. The script divides the mean stresses and the amplitude stresses into intervals and then it stores these intervals in vectors, it also stores the number of times a cycle in the specific interval has occurred. After this it is possible to make a color contour plot to show how the stresses are distributed. In this script was also the scaling of the time done. Since the measurement only lasted for 17h and the dimensioning time for the runner is 40 years it was necessary to multiply this measurement up to 40 years. The plot shows amplitude stress on the x-axis and mean stress on the y-axis, the color represents the number of times that combination of amplitude and mean stress has occurred during 40 years of normal service, see Figure 28 for the piston rod’s Rainflow plot. Notable in the figure is that the most common of the amplitude stresses are below 10MPa.
Figure 28. Color contour plot of extracted Rainflow matrix, colors representing the number of times that the specific combination of mean stress and stress amplitude occurs during 40 years of normal service.
4.2.5 Stress spectrum With the now extracted stress prognosis over 40 years it was possible to create a stress spectrum that can be used to evaluate the fatigue risk based on the material properties. As described earlier the spectrum was derived by using a constant ratio between amplitude and mean stress and by that transforming the loads to be of the type with zero mean stress, i.e. R=-1. The stresses were also normalized. The largest stress gets value 1 and the rest of them get a value representing their size as a fraction of the largest stress. They are also sorted in size with the largest one first to be able to evaluate them. A plot of the normalized stress steps with zero mean stress for the piston rod can be seen in Figure 29.
37
Figure 29. Compensated mean stress spectrum, sorted and normalized to have the largest stress first at value 1, following stresses are fractions of the biggest stress.
4.2.6 Material properties The material in the piston rod is SS2541 and in the upper sleeve it is SS2387. Depending on the type of loading and which area that is being evaluated the material get different property degradation according to FKM. The first parameter that was accounted for was the number of load cycles. Since the analysis is done over 40 years there are a lot of load cycles. Both of the materials are steels so they have a fatigue strength factor of 0.4 according to Table 3. With use of equation (1) the fatigue strength for completely reversed stress could be calculated for the two materials, see Table 17.
Table 17. Material properties at 10^6 cycles. Material σ Rm [MPa] fW ,σ W ,zd [MPa] SS2541 910 0.4 364 SS2387 840 0.4 336
The next step was to calculate the design factors. Since the design factor consists of both the stress gradient and the stress concentration factor, these two needs to be calculated first. The stress concentration factors were determined according to the analytic expressions in equations (3) to (6), and Figure 15 and Figure 16. To calculate them dimensions were needed, see Table 18 for dimensions and calculated stress concentration factors.
38 Table 18. Stress concentration factors for the three evaluation points.
Components Area Dimensions [mm] Kt Piston rod Oil inlet hole D=210 3.0716 d=70 r=8 Upper sleeve Oil inlet hole D=280 3.0827 d=210 R=8 Sealing slot a=7.6 4.3 r=1 t=4.4
The areas that were evaluated were very small in comparison to the whole design, therefore smaller FEM models were needed to be able to have a mesh fine enough to get useful values for calculating the stress gradient. The smaller models were made only by a 30 degree model and only the area surrounding the evaluation point was included. They were given fixtures, loads and mesh according to Figure 30. With help of the controlled mesh size in the evaluation point it was possible to determine the distance needed in the gradient calculations. The results from the gradient calculations can be seen in Table 19. The sizes of the applied loads are calculated from the large models tensions in a cross section of the region were the load is to be applied.
Figure 30. FEM models used to determine stress gradients for the small evaluation areas. Red arrows are fix constraint, green arrows are symmetry constraints and blue arrows are force loads.
Table 19. Results from FEM and variable values needed to calculate gradients. Component Evaluation area ∆ σ σ S (Mesh size in 1a [MPa] 2a [MPa] Gσ area) [mm] Piston rod Oil inlet hole 0.8 685 500 0.34 Upper sleeve Oil inlet hole 0.8 -750 -575 0.29 Sealing slot 0.5 -1200 -680 0.87
The last of the factors that needed to be calculated was the roughness factor. It was done with equation (11), an assumed surface finish of 3.2 m from turning or 6.3 m from drilling [19] and factors from Table 3. The result can be seen in Table 20 . With all the needed factors determined it was possible to calculate the final design parameters with equation (12) and earlier determined factors and the remaining of the factors according to Table 20. The resulting design factors can be seen in Table 20.
39 Table 20. The different factors needed to calculate the design parameters and the calculated design parameters for the evaluation points. Component Evaluation K − K Roughness Design Surface Surface Non- Design area t f factor coating treatment linear parameter factor K rσ ratio ~ factor factor factor KV KWK ,σ K f K S K NL ,E Piston rod Oil inlet 1.086 0.88 2.83 1 1 1 0.9635 hole Upper Oil inlet 1.108 0.89 2.78 1 1 1 0.9421 sleeve hole Sealing slot 1.160 0.93 3.7 1 1 1 0.8792
The final material fatigue strengths for completely reversed stress in the components evaluation areas were then determined with equation (13), see results in Table 21.
Table 21. Final fatigue strengths for the components in the evaluation points. Evaluation area Fatigue strength for completely reversed stress [MPa] Piston rod oil inlet hole 378 Upper sleeve oil inlet hole 357 Upper sleeve sealing slot 382
4.2.7 Evaluation according to FKM guideline The component is evaluated according to two different criterions. The first one is Miners rule which is the more conservative of the two, the other one is Miners consistent rule which is a modified version of the first one. The main difference between them is the regard to the fatigue limit. That means that if Miners rule is used there is no possibility to reach infinite component life. The reason why both are used is that if Miners rule is not fulfilled then the Miners consistent rule might be refined enough to give a suitable result with out the need for component design change. Or if the component is far from failing the elementary criteria then there may be room for design optimizations.
The degree of utilization determines if the component has the required fatigue strength. If this value is larger than 1 then the component does not fulfill the criterions. In this case the safety factor was chosen to be 1.5 according to Table 7, since there are no possibilities to inspect the components regularly and the consequences of a failure would be severe. As mentioned earlier the critical damage sum was chosen to be 0.3 due to that the components are made of steel.
The calculated component amplitude fatigue strengths for the different evaluations were calculated with equation (15) and the results can be seen in Table 22. This clearly shows that Miner’s elementary rule is more conservative.
Table 22. Amplitude strengths for evaluated components for the two different evaluation criterions. Component Evaluation Miner’s elementary Miner’s consistent point σ σ rule BK [MPa] rule BK [MPa] Piston rod Oil inlet hole 164 376 Upper sleeve Oil inlet hole 283 404 Sealing slot 308 440
40 4.2.8 Degree of utilization The degrees of utilization are calculated for the different components with equation (16) and Table 22, the results from this can be seen in Table 23.
Table 23. Degree of utilization for evaluated points. Component Evaluation Largest stress Degree of utilization Degree of utilization point amplitude in aBK ,σ Miner’s aBK ,σ Miner’s consistent spectrum σ a 1, elementary rule rule. [MPa] Piston rod Oil inlet hole 244 2.24 0.97 Upper sleeve Oil inlet hole 183 0.97 0.68 Sealing slot 148 0.72 0.50
4.2.9 Other evaluation criterions In this section the other structural design evaluations are presented. The evaluations were nominal stress levels in the components, thread stress amplitude and buckling. For each evaluation their criterions are calculated and presented.
4.2.9.1 Nominal stress levels The nominal stress levels were calculated for each components smallest cross section and the maximum occurring load. The nominal stress criterions were calculated with equation (18), results from this can be seen in Table 24. The nominal stress levels for the two components smallest cross sections can be seen in Table 25 and are calculated with equation (17).
Table 24. Results from calculations of critical values for nominal stress levels. Component Material Chosen Rm 2Rp critical value 3 3 [MPa] [MPa] [MPa] Piston rod SS2541 303 499 303 Upper sleeve SS2387 280 453 280
Table 25. Results from nominal stress level calculations. Component Region for smallest Smallest Load case Force[kN] Nominal stress cross section. cross section in cross area [mm 2] section [MPa] Piston rod Oil inlet hole 25198 Maximum open 4940 196 Upper sleeve Sealing slot 23975 Maximum close 6128 255
4.2.9.2 Stress amplitude in threads The stress amplitude in the threads needed to be evaluated separately since they were not a part of the FEM simulation and could therefore not be evaluated with the same method. They could not be included in the FEM model since that would lead to a large area of very small elements and with a very complex contact search between the Superbolt and the piston rod. The stress amplitude was determined by assuming a normal load cycle. The worst case from Figure 19 was used. It is to yield opening and closing at near fully opened runner. The evaluated stresses were the nominal stresses in the cross section where the thread is placed. The stresses were calculated with equation (17) and Table 26, also for results see Table 26. The two calculated nominal stresses gives the width of the load cycles and the amplitude is given by dividing the width with two. The calculated stresses were then compared to the criteria that BSK99 gives for bolts for 20^6 load cycles with constant amplitude. Critical amplitude for this type of joint can also be seen in Table 26.
41 Table 26. Stress amplitude in threads. Load case Force Resulting Cross section Nominal stress Amplitude Critical [kN] force [kN] [mm 2] [MPa] stress [MPa] amplitude [MPa] Closing 55 4000 30450 131.4 10.2 22.5 Closing 105 844 30450 110.8
4.2.9.3 Buckling With use of equations (19) to (25), and with help of Table 9 and values according to Table 27, the load carrying capacity could be calculated. The load carrying capacity could then be compared to the maximum occurring load. If the load is lower than the capacity there is no risk for buckling of the upper sleeve. Results from these calculations can be seen in Table 28.
Table 27. Values for constants used to calculate the load carrying capacity for the upper sleeve under compression load. Variable Explanation Values Cross section area 0.026929m 2 Agr Value of characteristic tensile strength limit 680MPa f yk Value of dimensioning tensile strength limit 567MPa f yd Characteristic young modulus 210GPa Ek β Enlargement factor for actual length 2 L Actual length 0.978m D Outer diameter 0.280m d Inner diameter 0.210m β Constant for determining α, dependent on type of cross 0.21 1 section.
Table 28. Results from load carrying capacity calculation and maximum occurring load. Load carrying capacity Maximum occurring load 14510kN 6000kN
42 4.3 Evaluation of other design aspects The other design aspects that were evaluated in this comparison are described in this section. The evaluations have been performed with help of interviews where a set of evaluation points were discussed. The design comparison is made on two levels, one general and one specific regarding Näsaforsen to give an example of how the designs may differ in a specific case. The evaluation points used in each comparison are to find general differences. Where it is possible to make specific comparisons calculations have been done to give a case specific example of how the two designs may differ.
4.3.1 Assemblage comparison The first point on the assemblage comparison was to determine the assemblage order for the new design. It was soon discovered that is was not so easy to give a universal answer to that question. But after some discussion a suggestion was given of how the assemblage probably would be carried out. It is important to understand the order of assemblage since it affects some of the details in the design, this will be explained later.
The suggested assemblage order starts with that all the components have been tried in its positions one by one and without seals [20]. This is done to make sure that there is not any component which does not fulfill the tolerances and that there is not any grip between parts that should have clearance. The assemblage performed in four steps is described below and Figure 31 shows each step.
1. The first step of the actual assemblage would be to mount the upper nut on the piston rod. It should then be measured so that it is at the correct height and after that secured to the rod 2. The rod is lowered into the hub. With the piston rod and the nut secured to the hub it is rotated so the bottom of the hub is facing upwards. 3. After this the upper sleeve is lowered down into the hub and around the piston rod with its seals in place. 4. Next the piston rod is measured to make sure that it is on the correct height in relation to the piston. If the piston rod is on the wrong height then the upper nut must be rotated to alter the height.
1 2 3 4 Figure 31. Assemblage order described in four steps. In the first step the nut is mounted and secured on the correct height of the piston rod. In step two the piston rod is lowered into the hub and secured to it. The hub is rotated upside down and the upper sleeve is mounted in step three. The last step is to control measure the piston rod height, and possibly adjust it by rotating the upper nut.
43 After this the assemblage is as with the old design, the piston and the lower sleeve are mounted and the rod is put under pretention with the Superbolt, see Figure 32 for Näsaforsen at that state of assemblage.
Figure 32. Näsaforsen runner hub turned upside-down ready for mounting of the lower sleeve.
Since the assemblage comparison could only be made very general the outcome of it was mostly the answers of the questions given in Table 10. The new design does not affect the assemblage of the other components nor does it require more space to be fitted into the hub. The hub orientation during the assemblage is not either affected. The first question in Table 10 that indicates a difference is regarding the tools needed. The question does not aim at hand tools but on tools that are needed for lifting and fitting the components, and this is the reason why it is important to know the assemblage order. Here are of course differences since the design contains parts that have other dimensions, but what was stated as important was that holes for lifting must be placed accurately out of center of gravity points since it affects how easy it is to smoothly fit the components. Other tools that was seen as important was some kind of locking device to lock the upper nut to the piston rod to assure that the preset distance from the nut to the top of the rod would be held constant. A third important remark was that the upper nut will need some screws to lock the piston rod to the hub body. Not as rigorous as the old design but just so that it can hold the piston rod in place while the hub is turned upside down during the assemblage.
The total assemblage time was estimated to be a little longer due to the extra measurements that are needed to make sure that the piston rod is on the correct height. It was not the actual measurements that were estimated to take longer time but the adjustments if it would be on the wrong height. The two following questions regarding quality control and incorrect assemblage are also connected to this part of the assemblage. There may be a risk that the height of the piston rod is hard to adjust absolutely correct. How big this problem would be is hard to evaluate because it is depending on several factors. First of all there are not so tight tolerances on the actual rod height since the piston position is not affected by it, and therefore it is possible that the preset of the upper nut is enough to give a correct position. The problem may only occur if there is very little clearance between the rod and the upper sleeve. This problem is enhanced when the surfaces are of stainless steel since that increases the risk for galling. In this case the stainless steel coated part of the rod is fitted into the stainless steel sleeve so it may be a risk for galling.
The last evaluation point was if there would be any scaling effects with the new design. It was stated that there are always more problems when things get really big since they get more and more difficult to handle smoothly the bigger they get. And that the bigger the components get the harder it is to achieve the correct tolerances. The two scaling effects in combination leads to that the new design might be more sensitive for becoming problematic to assemble.
44 4.3.2 Manufacturing comparison The manufacturing comparison that was carried out was based on a set of evaluation points, see Table 11. As earlier mentioned the comparison was made on two levels, one general level and one specific regarding Näsaforsen. For the more general comparison some conclusions about principal differences could be drawn, and from the specific evaluation some calculations could be done for the total manufacturing time for the two designs in Näsaforsen. The manufacturing time for the two designs in Näsaforsen has been estimated by a production engineer. The times for the old design are based on the actual time spent when it was finished and the time that it should have taken. The time estimated for the new design was based on the components size, shape, material and tolerances.
Before it is possible to make these estimations one must make a judgment of how it is being produced. In the old design the piston rod was produced from a wrought bar, which was turned and milled to the final shape and tolerances. In the new design it is possible to produce the piston rod from machining a round bar. The upper sleeve would be made with centrifugal casting in the same was as the lower sleeve. The reason for that it has to be casted is the dimensions and the material. The machining has been divided in three parts for the piston rod and into two for the upper sleeve. This is due to different operation types and sometimes different machines. The machines that are needed [21] and the cost factor for each operation [22] can be seen in Table 29.
Table 29. Machines needed for manufacturing and their hourly rates. Machine type Machine id Machine cost factor NC-mill 665 1 Lathe 670 1.155 Boring machine 681 1.350
In the comparison it was assumed that the cost and time for the upper nut in the new design was equal to the threaded holes in the hub. The other differences in the hub were seen as equal in manufacturing time. For manufacturing cost calculation see Table 30. The set-up time was included in the time approximations.
Table 30. Manufacturing cost calculations for the two designs. Component Operation Time unit [A] Machine id Machining cost Rough turning 1 670 1.155 Piston rod Fine turning 5 670 5.775 New design Drilling and threads 3 681 4.05 Turning 3 670 3.465 Upper sleeve Drilling 0.375 665 0.375 Total 12.375 14.820
Rough turning 1 670 1.155 Old design Piston rod Fine turning 7 670 8.085 Drilling and threads 5 681 6.750 Total 13 15.990
The more general comparison in this section is made out by the remaining questions from Table 11. They were evaluated in terms of if they would be affected if the new design was to be used. The tool wear would not be affected since the two materials are practically the same to machine, and there would not be any additional tools needed since the lower sleeve would be machined for both designs. When it comes to quality control and control measurements there may be some difficulties for large runner hubs. Since the hub body has two areas of high tolerances these two areas could be forced to be made from different directions, meaning that the hub must be rotated between these two operations. This could occur if the hub is too deep to machine both areas from one side. The problem that it could lead to is to control measure that the two areas are concentric enough after the machining.
45 4.3.3 Procurement comparison Procurement is very case sensitive and therefore hard to make general comparisons about. Both designs are possible to make alterations to that would have large impacts on the procurement for both of them. Example of this is that if it is a very large runner then the wrought bar may be replaced by a round bar to reduce the costs. This would lead to the need of a bolted flange and extra machining of the bar. Another example is if the upper sleeve would be really small then it might be possible to buy a pipe instead of a casted piece. This leads to that the procurement comparison is mostly done on the specific case.
This specific case can be seen as in general valid for this size of runner. In the specific case the costs for material and services is bought from other companies are regarded. Since the piston rods are made out of steel, they need surface coating of laser welded stainless steel on some surfaces. The two designs need different amount of coating and the costs for this is estimated based on the actual costs from Näsaforsen. Mutual for the two designs is the oil inlet, this requires a long hole drilling operation which is not performed at AW and is purchased from another company. The costs for this operation are seen as equal in both cases. The costs for purchased services and materials [21] can be seen in Table 31, all values calculated into cost units.
Table 31. Comparison of purchased services and material for the two designs with Näsaforsen premises. Component Material cost Duroc coating and Deep hole Total laser welding drilling Piston rod 5.083 4.621 6.470 New design 21.026 Upper sleeve 4.852
Old design Piston rod 16.174 7.394 6.470 30.037
In the comparison the other aspects listed in Table 12 were also evaluated. This was also done with the specific case seen as generally valid for this runner size. It was then found that there are differences between the two designs when it comes to delivery time, see Table 32 for delivery times [21]. Both designs need a lower sleeve so the upper sleeve in the new design does not affect the total delivery time. The delivery time for Näsaforsen is the actual delivery time plus time for offers, for the new design the time for the lower sleeve is used but the time has been reduced due to the lower sleeve was ordered during vacation months. With the new design the number of available suppliers does not increase, so in that sense the two designs are equal.
Table 32. Delivery time comparison for the materials. Component Delivery time New design Piston rod 1 Week Upper sleeve 8 Weeks Old design Piston rod 13 Weeks
46 5 Results In this chapter the results from the different evaluations are collected and evaluated. Each evaluation aspect is given its own section. All costs in the tables in this section are calculated into a cost unit.
5.1 Results for structural evaluation The fatigue results are compared to the old design; the other structural results are compared against its critical limits. For collected results see Table 33 and Table 34. For each result an additional safety factor is calculated, it is done to show how close the result is to fail the criteria. If the factor has a value larger than 1, the design fulfills the criteria.
Table 33. Fatigue evaluation results for the new and old designs. Evaluation Design Component Evaluation Criteria Degree of Degree of Criteria Leaves an type point utilization utilizatio fulfilled? additional Miner’s n Miner’s safety factor of elementary consistent criteria/load rule rule level Fatigue New Piston rod Oil inlet <1 2.24 0.97 Yes – Miner’s 1.03 hole consistent rule Fatigue New Upper Oil inlet <1 0.97 0.68 Yes – Miner’s 1.03 and 1.47 sleeve hole elementary rule and Miner’s consistent rule Fatigue New Upper Sealing slot <1 0.72 0.50 Yes – Miner’s 1.39 and 2 sleeve elementary rule and Miner’s consistent rule Fatigue Old Piston rod Notch <1 2.31 1.0 Yes – Miner’s 1 consistent rule
Table 34. Structural evaluation results for the new design. Evaluation Component Evaluation Criteria Nominal Amplitude Buckling Criteria Leaves an type point stress stress in fulfilled additional levels threads safety factor of [MPa] [MPa] criteria/load level Nominal Piston rod Cross <303MPa 196 - - Yes 1.546 stress section at levels oil inlet hole Nominal Upper sleeve Cross <280MPa 255 - - Yes 1.1 stress section at levels sealing slot Amplitude Piston rod Treads <22.5MPa - 10.2 - Yes 2.2 stress in threads Buckling Upper sleeve - >6000kN - - 14510kN Yes 2.48
5.2 Results from assemblage comparison The most important result from the assemblage comparison is that the new design would be possible to assemble without any drastic changes. The comparison also gave knowledge of that it is important to have locking devices for the piston rod since it would not be possible to assemble without. It also needs some locking for the whole rod to the hub so that the hub can be placed upside down during the assemblage. It also gave some other results such as that the new design probably takes slightly longer time to assemble and that it may be problems with positioning the piston rod at the correct height.
47 5.3 Results from manufacturing comparison The manufacturing comparison show in the specific case that there may be some cost reductions with the new design. The reduction in the specific case can be seen in Table 35. The cost reduction comes mostly from the reduced need to drill holes in the flange for mounting the piston rod to the hub. In the more general case it is likely to assume that there is some time differences between the designs and that they are approximately the same percentile as in the specific example. This is possible to assume since the new design has slightly simpler geometries than the old design. How big these differences are is very case sensitive and as mentioned in the procurement comparison alterations are possible in both designs and that would change the manufacturing time too.
Table 35. Results from manufacturing comparison. Total manufacturing Total manufacturing cost time New design 14.820 12.375 Old design 15.990 13
Reduction 7.3% 5%
5.4 Results from procurement comparison As described in the procurement comparison it was mostly done on the specific example and due to the case sensitivity in procurement it was hard to make a general evaluation. From the calculations in the specific case it is clear that if the new design has any real benefits then they probably are in procurement, see Table 36. The new design has its largest benefits from the lower material costs and some of the cost reductions comes from the reduced need of coating. In the table the reduced delivery time are also listed, the new designs delivery time is controlled by the upper sleeve whilst for the old design it is the wrought rod that controls the total time.
Table 36. Results from procurement comparison. Procurements Delivery time New design 21.026 8 weeks Old design 30.037 13 weeks
Reduction 30% 38%
With the manufacturing and procurement costs for the specific example added together it is clear that the new design may have some cost reduction potential. The total cost reductions can be seen in Table 37.
Table 37. Total cost reduction possible for the two designs in Näsaforsen. Total costs New design 35.846 Old design 46.027
Cost reduction 22.1%
48 6 Conclusions In this chapter conclusions from the comparison are collected. The results from the comparison make out the base for the conclusions and some come from own insights learned during the evaluation. After the evaluation it is clear that some of the expectations on the new design were not completely fulfilled. While some of them were proven true. The results chapter shows that the new design has some important advantages. These are valid under the conditions listed throughout the report. Conclusions from the evaluations:
Structurally there are very small differences between the two designs. Their fatigue strengths are practically the same when given the same space in the runner hub.
To assemble the new design does not require any radical changes but it might take longer time due to control measurements and possibly some extra adjustments.
The manufacturing comparison shows that there may be difference between the two designs but they are very small. The calculated difference in the specific example is so small that it probably is within the accuracy for the estimations.
There are definitely procurement differences between the two designs when the old design is produced from a wrought bar. It is probably also lower costs for the new design when the old design is machined from a large bar, but this has not been evaluated.
From these conclusions it is obvious that the two designs are in general quite similar. Therefore it is hard to give a definite answer to which of them that is superior. It is probably so that they have different areas were they are the better choice. It is mostly dependent on the exact design solutions and the planned production. To this come also a lot of other aspects that could affect which of the two to choose, e.g. is size of the runner, current material prices and available time for design.
49 7 Discussion In this chapter the whole design evaluation is discussed, first the new design in general is discussed and after that the comparison is discussed. Some sources of error are enlightened and discussed.
7.1 The new design The new design has proven to have some of the expected advantages. According to this evaluation it is possible to change to it with some cost benefits. It is important to remember under which conditions that this has been evaluated and that the biggest differences come from the different bars used for the rods. Structurally one must also remember some of the details in the design during the comparison. Especially the position of the sealing slots since this gives an important difference when it comes to fatigue properties. Since all the sealing slots are placed in the components that is under compression. This gives the design better fatigue strength. If the sealing were to be placed in the rod they would be under tension and that would make the rod much more sensitive for fatigue. Also important is simplicity of the rod in general since the fatigue properties were the dimensioning factor. It does not allow any vast changes which would induce stress concentrations such as sharp notches. The new design does not give any extra fatigue strength with reduced total space required in the hub. The reason for this is that in the upper sleeve it is not the fatigue strength that is critical; instead it is the nominal stress levels. This makes it hard to make big reductions on the total size, although there is room for some small optimization, but that would only reduce the sleeve diameter with a few millimeters.
7.2 Discussion regarding structural calculations The structural calculations are described in their full extent as they are performed. But their validity must be discussed. In the fatigue calculations the whole result is based on a one point read out from the FEM simulations results. That makes the readout very important for the whole result. Therefore the nodes are chosen with the highest value so that the result is as conservative as possible. How conservative it actually gets is an uncertainty. It is suspected that it might be quite conservative, since the maximum node value is higher than the average node values in the region surrounding the nodes. Other uncertainties in the fatigue calculations are the measured service loads. The signal has not been analyzed in such way that it can be determined if it is a hard or easy load case. The signal also contains a lot of fast and short regulations and it has not been established if this is noise from the measurements or if the machine in Sollefteå actually behaves like that. This gives some additional uncertainties of how conservative the calculations are.
In the calculations two things has been left out. It has not been calculated how the hub body is loaded or how its fatigue is affected by the new design. The other thing that has been left out is the effects of corrosion, since the piston rod is made out of steel it might be affected by corrosion. The design has been adapted to this by using a seal in the top of the upper sleeve to reduce the risk for moist on the piston rod.
7.3 Discussion regarding other design aspects The other aspects of the two designs that could be discussed is mostly that the cost comparison is only made on Näsaforsen, this gives uncertainties on how the costs are for the two designs on a machine of another size. The comparison is fairly correct for machine sizes similar to Näsaforsen. Simple study shows that there are no problems to purchase piston rods for the new design with twice the diameter. It is suspected that the cost for the upper sleeve may increase more rapidly due to the centrifugal casting technique. As shown in the results chapter the new design has advantages when it comes to delivery time. They are valid for Näsaforsen but are universal when comparing the wrought bar against the round bar. The advantages with this might be several. Initially this gives the design engineer longer time to complete the design. The shorter delivery time may have an advantage in manufacturing. If something would go very wrong during the manufacturing there may be time to order a new bar without that much time lost. The earlier mentioned problem with the need to rotate a large hub to be able to machine both the areas with high tolerances is something that both the designs have. The problems it could lead to are probably higher in the new design due to that the sleeve and the piston rod needs a high degree of concentricity to be possible to assemble.
50 8 Future work There are still areas were the new design could be improved, and areas of further evaluation that is needed before a design change could be fully implemented. The comparison performed so far is only done at one hydro power plant, to further establish the differences and advantages more comparisons are needed. They should be done at both smaller and bigger plants then Näsaforsen. This is needed to verify if there are any significant scaling effects, i.e. if the two designs have different advantages at different sizes. Since the new design is an adaption of an existing design it has a development potential. The design was adapted to Näsaforsen with its existing flaws and compromises. The most problematic area of manufacturing in the new design is the deep hole for the oil inlet. This is hard to produce with high tolerances and it is very hard to confirm that it is correctly assembled. Therefore a suggestion is to try to find an oil inlet solution that neither needs the deep hole nor needs the drilled channels that the original design has. A possible way to solve this is to have an inserted sleeve in the bottom of the rod. This solution would not need a high tolerance long hole in the rod.
Further simple optimizations that could be done is to move the oil inlet chambers in the rod to the sleeves instead, this would give the rod slightly better fatigue properties, which could make some small size reduction possible. This in its turn could reduce the size of the sleeve and by that give a little more space in the runner hub but it is probably in the range of millimeters.
Depending on the hub design there might be problems with room for the upper nut, in these cases alternatives are needed. A suggestion then is to secure the rods threads in a large thread directly in the hub body. This alternative needs to be structurally evaluated. Since the runner hub is made out of a simpler material and the stress amplitudes in the threads therefore cannot be too high.
An additional aspect that may need an overview if the new design would be implemented is the assemblage routines. The new design leads to a slightly altered assemblage order and that needs to be documented and established in a correct way. The assemblage order that is suggested under the assemblage comparison is only one alternative, but if it is the best way or not has not been evaluated.
Future work is also needed in the calculations procedure. As mentioned in the discussion it is necessary to evaluate the service signal, since there are uncertainties of how conservative it is. Also an evaluation method where not only one value determines the final result, a method where more nodes or all the nodes were evaluated without the need of performing it one by one and with a lot of manual work would be useful and less time consuming.
51 9 References
[1] ANDRITZ: Company Profile (ANDRITZ AG: 2009) http://www.andritz.com/ANONIDZ63CC61C04DE2A6FC/about-us [9 September 2009]
[2] NATIONALENCYKLOPEDIN: Vattenenergi (Nationalencyklopedin: 2009) http://www.ne.se/vattenkraftverk [9 September 2009]
[3] Leif Vinogg and Ivar Elstad: Hydropower development vol. 12, Mechanical Equipment (Norwegian University of Science and Technology: 2003)
[4] U.S. Army Corps of Engineers: File:Water_turbine.jpg (Wikipedia, the free encyclopedia: June 2005) http://en.wikipedia.org/wiki/File:Water_turbine.jpg [9 September 2009]
[5] Arne Morten Lundhaug Johnsen: Technologies for storage reservoirs, dams and waterways (renewable.no) http://www.renewable.no/sitepageview.aspx?sitePageID=1113 [9 September 2009]
[6] OJSC Power machines: Equipment for small hydro power stations (OJSC Power machines: 2002-2006) http://english.power-m.ru/themes/english/materials-document.asp?folder=1456&matID=2108 [9 September 2009]
[7] Superbolt: Products (Superbolt, Inc.: 2009) http://www.superbolt.com/products.html [9 September 2009]
[8] Ingvar Rask and Staffan Sunnersjö: HÅLLFASTHETSTEKNISK DIMENSIONERING (Sveriges verkstadsindustrier: 1992)
[9] Wikimedia commons: File:pedalarm_Bruch.jpg (Wikipedia, the free encyclopedia: June 2007) http://commons.wikimedia.org/wiki/File:Pedalarm_Bruch.jpg [9 September 2009 – altered by rotation and crop view]
[10]E. Haibach: FKM-Guideline ANALYTICAL STRENGTH ASSESSMENT OF COMPONENTS IN MECHANICAL ENGINEERING (Forschungskuratorium Maschinenbau (FKM): 2003)
[11] Walter D. Pilkey: Formulas for Stress, Strain, and Structural Matrices (2nd Edition) (John Wiley & Sons, Inc.: 2005)
[12] Walter D. Pilkey and Deborah F. Pilkey: Peterson's Stress Concentration Factors (3rd Edition) (John Wiley & Sons, Inc.: 2008)
[13] Mikael Helin, Structural Analysis Engineer , (September 2009)
[14] Lars Göransson and Sture Åkerlund: Stålkonstruktioner, BOVERKETS HANDBOK OM STÅLKONSTRUKTIONER BSK99 (Boverket, byggnadsavdelningen:1999)
52
[15] Octave (University of Wisconsin: 2009) http://www.gnu.org/software/octave/index.html
[16] Cygwin (Red Hat, Inc.: 2009) http://www.cygwin.org/cygwin/
[17] SolidWorks Premium 2009 (Dassault Systémes 2008) http://www.solidworks.com/
[18] SolidWorks Simulations 2009 (Dassault Systémes 2008) http://www.solidworks.com/sw/products/fea-design-simulation-software.htm
[19] Karl Björk: Formler och Tabeller för Mekanisk Konstruktion, sjätte upplagan (Karl Björks Förlag HB)
[20] Peter Sverresson, Assemblage technician , (October 2009)
[21] Håkan Hedman, W ork preparation leader , (October 2009)
[22] Peter Knutsson, Sales engineer , (October 2009)
53 Appendix A – Basic dimensions for Näsaforsens piston rod
Appendix B – Basic dimensions for new design piston rod
Appendix C – Basic dimensions for new design upper sleeve