presentation of the revised standard “richtlinien fÜr … · 2019. 4. 15. · due to its...

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PRESENTATION OF THE REVISED STANDARD “RICHTLINIEN FÜR WERKSTOFFE IN HYDRAULISCHEN

MASCHINEN – RWHM“ PART 2: COMPONENT DESIGN USING K-FACTORS – A

CRITICAL REVIEW

Ch.A. Schenk, St. Leitner

Abstract: In this part, the application of traditional design factors, in Austria also known as k-factors, is critically reviewed. For this purpose, the widely accepted FKM guideline [1] is utilized in order to assess the inherent safety when applying k-factors for component design. Results of this work will be included in a forthcoming, revised edition of RWhM [2].

1 Component design using k-factors By long tradition and common practice, the design of mechanical components in hydropower engineering is based on design factors. Especially in Austria, these design factors are also known as k-factors. k-factors are frequently included in the invitation to tender as part of the technical specification. Quite often, also legal authorities require k-factors to be applied for the design of such components. In the course of the design using k-factors, the load carrying capacity is referred to the yield strength , i.e. = . (1) k-factors are usually applied to both machine and pressurized components, respectively, their actual values do depend on the stress approach to be applied as well as on the relevant load case. Some typical values are given in Table 1.

Stress Approach Normal Operating Condition Unusual Operating

Condition Extreme Operating

Condition Nominal Stresses 0.5 0.6 0.75

Local Stresses 0.65 0.78 0.98

Table 1: Typical k-factors for component design

20th Intern. Seminar on Hydropower Plants – Celebrating 40 Years of Industry-Academic Engagement Copyright: Institute for Energy Systems and Thermodynamics – Vienna 2018

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The practical application of k-factors is quite simple, but does not account for several effects on static strength:

Distinction between non-welded and welded components (FKM: welding factor and partial safety factor for cast components)

Effect of component size and material production on strength parameters (FKM: technological size factor and anisotropy factor )

Larger strength variations of cast components (FKM: technological size factor and partial safety factor for cast components)

Support effect in case of non-uniform stress distribution (FKM: plastic support number )

Distinction between local failure (exceedance of permissible local strain) and global failure (exceedance of collapse load)

Effect of multi-axial stress state on permissible local strain (FKM: = (ℎ), where ℎ describes the degree of multiaxiality of the stress state)

It is also a common assumption, that fatigue strength within service life is ensured if k-factors have been applied for the design of mechanical components. Especially in the past, a dedicated fatigue analysis might thus have not been carried out for fatigue loaded components.

2 FKM guideline Due to its conceptual design, the FKM guideline "Analytical Strength Assessment of Components" [1] tries to give a framework for a uniform strength assessment of non-welded as well as welded components in mechanical engineering. The guideline includes both static and fatigue strength assessment, respectively. The sequential arrangement for static strength assessment is shown in Fig. 1.

Fig. 1. Assessment of static strength according to FKM

Material Properties

Design Parameters

Assement of Static Strength

Characteristic Service Stresses

Component Static Strength Safety Factor


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Fig. 2. Calculation of component static strength according to FKM

Fig. 3. Assessment of fatigue strength according to FKM

Assement of Fatigue Strength

Material Properties Design Parameters

Component Fatigue Strength

Component Finite Life Fatigue Strength Safety Factor

Characteristic Service Stresses

Component Alternating Strength


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Fig. 4. Calculation of component fatigue strength according to FKM

The calculation of the component static strength according to FKM is shown in Fig. 2. The yield strength is obtained by reducing the yield strength of the semi-finished steel product by means of a technological size factor and an anisotropy factor. In case of non-uniform stress distribution, the plastic support number can utilize additional load bearing capacities. Formally, the yield strength is increased by taking into account this support effect, yielding the component static strength. The permissible component static strength is obtained by incorporating the safety factor. The sequential arrangement for the fatigue strength assessment is shown in Fig. 3. The calculation of the fatigue component strength according is shown in Fig. 4. The ultimate strength is obtained by reducing the ultimate strength of the semi-finished steel product again by means of a technological size factor and an anisotropy factor. The alternating strength is defined as a fraction of the ultimate strength. In presence of stress gradients, the support number can utilize additional load bearing capacities. Formally, the alternating strength is increased by taking into account this support effect, yielding the component alternating strength. By considering the mean stress sensitivity together with an appropriate safety factor, one finally arrives at the permissible component finite life fatigue strength.


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3 Review of component design using k-factors 3.1 Static loading In the following, an attempt is made in order to assess the inherent safety in the design using k-factors by means of FKM. Hereby, k-factors for extreme operating condition are being used, as in general this load case causes the largest service stresses. The safety factor according to FKM accounts for high damage and low probability of occurrence of the service stress. The actual comparison is based on safety against yielding. As can be seen from Table 2, for unnotched components under tensile, compressive or shear loading, respectively, the design by k-factors yields similar safety margins when compared to the assessment of static strength according to FKM. For flexural or torsional loading, FKM yields a less conservative design when compared to the design using k-factors. According to FKM, for welded components (assumption: all welds are through or back welded, respectively, 10% of all welds are tested and free of flaws), the welding factor

equals 1. So for both FKM and k-factors, there is no distinction between non-welded and welded components. Only exception with regard to FKM are welded joints with base material S690, here the weld factor is set to = 0.9.

Component Safety margin applying k-factors Safety margin applying FKM

Tension bar = 1/0.75 = 1.33 = 1.35 → = 1.35 Bending bar (rectangular section)

= 1/0.75 = 1.33 = 1.35; , = 1.5; = / , = 0.9 Torsion bar (circular section) = 1/0.75 = 1.33 = 1.35; , = 1.33; = / , = 1.0

Table 2: Comparison of safety margins for unnotched components by applying k-factors and according to FKM for nominal stresses

For notched components it follows from Table 1, that the ratio between k-factors for nominal and local stresses, respectively, does not dependent on the load case. Provided a component is loaded with the maximum permissible nominal stress, the corresponding notch factor is = 1.3. This in turn corresponds to a rather slightly notched component, where no yielding is permitted in the root of the notch. Larger notch factors are allowed only for lower nominal stress levels. Contrary, FKM allows for nominal stresses notch factors up to = 5 or a maximum strain of 5%, if elongation at break of the material in question is larger than 6%.


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3.2 Fatigue loading Similar to section 3.1 but now for fatigue loading, the inherent safety in the design using k-factors by means of FKM is investigated. Hereby, k-factors for normal operating condition are being used, as in general this load case causes the largest number of stress cycles. The corresponding safety factor according to FKM accounts for high damage and non-regular in-service inspection. In what follows is restricted to non-welded components. For the actual comparison, some additional parameters for the assessment of fatigue strength according to FKM have to be defined:

Design factor : grinded surface with = 12,5 µm; no surface treatment, i.e. = = 1; notch factor = 1,3 (for nominal stresses) respectively =2 (for local stresses)

Support effect is not taken into account, i.e. support number = 1 (conservative assessment)

Cyclic loading, no mean stress is considered, i.e. ( = −1) and = 1 In doing so, one can define a material dependent k-factor according to

(2)

Hereby, the component alternating strength is normalized by the yield strength. In addition, the corresponding safety factor and the assumptions given above have been taken into account. Correspondingly, ∙ , represents the maximum cyclic stress amplitude, where no damage due to fatigue for the respective material occurs. For materials commonly used in hydro engineering, is shown in Fig. 5. As can be seen, for all listed materials is smaller than 0.5 ( = 0.5 for normal operating condition and nominal stresses, see Table 1). It follows that a nominal cyclic stress amplitude corresponding to = 0.5 causes a finite component life due to high cycle fatigue. The corresponding cycle numbers are shown in Fig. 6. It should be mentioned, that stainless cast steel GX4CrNiMo 13-4 is rather sensitive to fatigue loading, yielding endurable load cycle numbers below 1E4. This is beyond the scope of FKM, thus no load cycle numbers are presented for various variants of GX4CrNiMo 13-4.

≔ 1, ∙ , .


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Fig. 5. Factor for infinite component life in presence of fatigue loading

0.300.250.25

0.220.22

0.250.25

0.220.22

0.200.200.20

0.220.220.22

0.260.260.26

0.230.20

0.360.33

0.300.32

0.260.230.23

0.200.27

0.230.22

0.170.13

0.18

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

S235 JRS355 N

S355 NLS460 N

S460 NLS355 M

S355 MLS460 M

S460 MLS690 Q

S690 QLS690 QL1

S500 QS500 QL

S500 QL1P355 N/NH

P355 NL1P355 NL2

X3CrNiMo13-4 +QT 780X3CrNiMo13-4 +QT 900

C35E N20Mn5 N

S355J2G3 NC35E Q

20Mn5 QX3CrNiMo13-4 +QT 650X3CrNiMo13-4 +QT 780X3CrNiMo13-4 +QT 900

42CrMo430CrNiMo830CrNiMo8

GX4CrNiMo 13-4 +QT1GX4CrNiMo 13-4 +QT2GX4CrNiMo 13-4 +QT3

k


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Fig. 6. Material dependent cycle number for = 0.5 (normal operating condition)

76,644 32,829 32,829

18,354 18,354

32,829 32,829

16,887 16,887

11,084 11,084 11,084

16,632 16,632 16,632

39,677 39,677 39,677

18,516 10,691

204,229 131,490

72,132 112,660

36,916 21,199 20,058

10,691 49,260

20,843 17,755

---

-

50,

000

100

,000

150

,000

200

,000

250

,000

S235 JRS355 N

S355 NLS460 N

S460 NLS355 M

S355 MLS460 M

S460 MLS690 Q

S690 QLS690 QL1

S500 QS500 QL

S500 QL1P355 N/NH

P355 NL1P355 NL2

X3CrNiMo13-4 +QT 780X3CrNiMo13-4 +QT 900

C35E N20Mn5 N

S355J2G3 NC35E Q

20Mn5 QX3CrNiMo13-4 +QT 650X3CrNiMo13-4 +QT 780X3CrNiMo13-4 +QT 900

42CrMo430CrNiMo830CrNiMo8

GX4CrNiMo 13-4 +QT1GX4CrNiMo 13-4 +QT2GX4CrNiMo 13-4 +QT3

N


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4 Summary The static design using k-factors provides similar safety margins as obtained by a formal assessment of static strength according to FKM. This is true for tensile, compressive or shear loading, respectively, for non-welded and welded components, as well as for slightly notched components. For non-uniform stress distribution, as well as for components with rather pronounced notch stresses, the design using k-factors is considerably more conservative when compared to the design according to FKM. Consequently, expenses of material for such components are correspondingly higher. In addition, according to the prerequisite of elastic strains at the root of the notch ( ≤0.98 for local stresses, see Table 1), serious difficulties might arise in the construction of such components if k-factors are applied. The assessment of static strength according to FKM is recommended for such highly stressed components. However, care should be taken with regard to fatigue strength, if k-factors have been applied for the design of mechanical components. In particular, it has been shown, that a nominal cyclic stress amplitude corresponding to = 0.5 does not yield necessarily a fatigue endurable design for the materials considered, i.e. ≥ 1 6. In this regard, for a rough assessment, the load cycle number to be expected within service life for a particular material should be well below the one given in Fig. 6. Unsurprisingly, results presented in this work clearly emphasizes again the importance of well defined loading conditions, especially for fatigue loading. In this respect, Fig. 6 tries to give an overview on the sensitivity to fatigue loading for various materials. In addition, Fig. 6 might provide a basis for the decision whether or not the application of traditional k-factors yield a well designed mechanical component, i.e. if an assessment of the structural strength according to the FKM guideline might be more expedient. References

[1] Analytical Strength Assessment of Components, Forschungskuratorium Maschinenbau (FKM), VDMA Verlag, 6th edition, 2012.

[2] Die Richtlinien für Werkstoffe in hydraulischen Maschinen, Österreichs Energie, 2009.


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Author(s)

Dr. Christian A. Schenk TIWAG-Tiroler Wasserkraft AG Eduard-Wallnöfer-Platz 2 6020 Innsbruck [email protected] Ch.A. Schenk graduated from the Technical University of Munich in Mechanical Engineering. He carried out his doctoral studies at the Institute of Engineering Mechanics in Innsbruck. After receiving his doctoral degree, Schenk joined TIWAG in 2003, where he is team leader in the department of electrical and mechanical engineering. Dipl.-Ing. Stefan Leitner KELAG Kärntner Elektrizitäts-Aktiengesellschaft Bereich Erzeugung Arnulfplatz 2, 9020 Klagenfurt, Austria Tel.: +43 463/525-1542 E-mail: [email protected]


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