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Palmgren-Miner rule
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Use of the Palmgren-Miner rule for life prediction for variable amplitude l...
Available to PurchasePublished: 01 January 1996
Fig. 6 Use of the Palmgren-Miner rule for life prediction for variable amplitude loading that is completely reversed. Source: Ref 1 (p 383)
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Book: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002365
EISBN: 978-1-62708-193-1
... on their manner of use and limitations. The use of the Palmgren-Miner rule for life prediction for variable amplitude loading is also discussed. fatigue life Palmgren-Miner rule strain-based approach stress-based approach variable amplitude load FATIGUE LIFE ESTIMATES are often needed...
Abstract
This article discusses two major approaches in estimating fatigue life from the viewpoint of their use as engineering methods. These include the stress-based (S-N curve) approach and strain-based approach. The stress-based and strain-based approaches are compared, with some comments on their manner of use and limitations. The use of the Palmgren-Miner rule for life prediction for variable amplitude loading is also discussed.
Image
Example of Palmgren-Miner damage summation rule for two different load ampl...
Available to PurchasePublished: 30 August 2021
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Example of Palmgren-Miner damage summation rule for three different load am...
Available to PurchasePublished: 30 August 2021
Image
Comparison of prediction and observed results for spectrum fatigue data of ...
Available to PurchasePublished: 01 January 2001
Fig. 9 Comparison of prediction and observed results for spectrum fatigue data of Schutz and Gerharz ( Ref 14 ), Schaff and Davidson ( Ref 18 ), Yang and Du ( Ref 31 ), MRLife ( Ref 32 ), and Palmgren-Miner rule ( Ref 27 , 28 )
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Book: Composites
Series: ASM Handbook Archive
Volume: 21
Publisher: ASM International
Published: 01 January 2001
DOI: 10.31399/asm.hb.v21.a0003382
EISBN: 978-1-62708-195-5
... incorporated into existing design practices. These models are simply applied to multistress-level loading and are traditionally associated with safelife. Palmgren-Miner Rule Perhaps the most simple life prediction model is the Palmgren- Miner rule ( Ref 27 , 28 ): (Eq 6) ∑ i = 1 m n...
Abstract
In the design of composite structures for durability and damage tolerance, the primary concerns are out-of-plane failures, such as delamination, material degradation associated with environment, stability under compression loading, large degree of scatter in fatigue life, and bearing failure of joints. This article presents an introductory discussion on the fatigue damage process, methodologies assessing fatigue behavior, and life prediction models. It describes the damage mechanisms introduced for a quasi-isotropic laminate under tension-compression fatigue loading. Delamination is a critical issue in fatigue and generally results from high interlaminar normal and shear stresses. The article schematically illustrates the structural elements in which high interlaminar stresses are common. It concludes with a discussion on the classification of fatigue models such as mechanistic or phenomenological, for composite materials under cyclic loading.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003516
EISBN: 978-1-62708-180-1
... in Fig. 3 , is more likely to be encountered by structural components in actual service. In order to calculate the life of a component subject to variable loading, a method is needed that relates constant-amplitude fatigue test data to a random stress history. The Palmgren-Miner cumulative damage rule...
Abstract
This article discusses the fundamental variables involved in fatigue-life assessment, which describe the effects and interaction of material behavior, geometry, and stress history on the life of a component. It compares the safe-life approach with the damage-tolerance approach, which employs the stress-life method of fatigue life assessment. The article examines the behavior of three different metallic materials used in the design and manufacture of structural components: steel, aluminum, and titanium. It also reviews the effects of retardation and spectrum load on component life. The article concludes with case studies of fatigue life assessment from the aerospace industry.
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
...: σ a S e + σ m σ f = 1 Fig. 6 Comparison of mean stress equations from (a) Soderberg, (b) Goodman, (c) Gerber, and (d) Morrow. Adapted from Ref 6 Fatigue Damage Summation The Palmgren-Miner damage summation rule ( Ref 32 – 34 ), sometimes referred...
Abstract
This article offers an overview of fatigue fundamentals, common fatigue terminology, and examples of damage morphology. It presents a summary of relevant engineering mechanics, cyclic plasticity principles, and perspective on the modern design by analysis (DBA) techniques. The article reviews fatigue assessment methods incorporated in international design and post construction codes and standards, with special emphasis on evaluating welds. Specifically, the stress-life approach, the strain-life approach, and the fracture mechanics (crack growth) approach are described. An overview of high-cycle welded fatigue methods, cycle-counting techniques, and a discussion on ratcheting are also offered. A historical synopsis of fatigue technology advancements and commentary on component design and fabrication strategies to mitigate fatigue damage and improve damage tolerance are provided. Finally, the article presents practical fatigue assessment case studies of in-service equipment (pressure vessels) that employ DBA methods.
Book Chapter
Life Extension and Damage Tolerance of Aircraft
Available to PurchaseBook: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002392
EISBN: 978-1-62708-193-1
... from constant amplitude loading tests. One such method is the Palmgren-Miner Rule ( Ref 6 , 7 ), which has the mathematical form: ∑ i = 1 m n i N i = 1 where n i represents the number of cycles of damage and N i represents the life of a component...
Abstract
This article describes two analysis methods that are used to determine the life of aircrafts: fatigue life and fracture mechanics methods. The life limiting factors that control the durability of the aircraft are also discussed. The article provides an overview of the various approaches to corrosion identification and prevention. These include safe-life, fail-safe, and damage tolerance approaches. The article discusses their application to the process of extending the life of aircraft structural components.
Book Chapter
Fatigue Crack Growth under Variable-Amplitude Loading
Available to PurchaseBook: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002356
EISBN: 978-1-62708-193-1
... now. Many test programs were carried out to check the famous Miner rule (Σ n / N = 1), which Miner published in 1945 ( Ref 19 ). The rule was published earlier by Pålmgren in 1924 ( Ref 20 ). Another noteworthy publication came from Langer in 1937 ( Ref 21 ). He divided the fatigue life...
Abstract
This article summarizes fatigue phenomena in metallic materials. It discusses fatigue under variable-amplitude (VA) loading, with emphasis on crack growth. The article presents the prediction models of crack initiation and crack growth under VA loading. It concludes with a discussion on the conditions associated with engineering applications of VA loading.
Book Chapter
Friction and Wear of Rolling-Element Bearings
Available to PurchaseSeries: ASM Handbook
Volume: 18
Publisher: ASM International
Published: 31 December 2017
DOI: 10.31399/asm.hb.v18.a0006426
EISBN: 978-1-62708-192-4
... and the reliability and lifetime expressions from Weibull and Palmgren led to the first bearing ratings and life theories and various fatigue and material constants. This led to methods on computing stresses for basic bearing geometries and considerable fatigue testing. Following the work of Grubin in 1949 ( Ref 2...
Abstract
Rolling-element bearings, also called rolling bearings and antifriction bearings, tend to have very low friction characteristics compared to plain bearings or simple sliding bearings. This article discusses the types of rolling-element bearings, namely, ball bearings and roller bearings. It provides information on the bearing component materials. The article describes the lubrication requirements and lubrication methods, namely, elastohydrodynamic lubrication and grease lubrication. It reviews the adjustment factors influencing fatigue life of the bearing. The article also provides information on bearing load ratings, standard bearing geometries, rolling bearing friction factors, and wear and its control methods. It concludes with a discussion on damage modes of bearings.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006779
EISBN: 978-1-62708-295-2
... by Miner ( Ref 7 ). According to the Palmgren/Miner rule, the application of n i cycles at a stress amplitude S ai , for which the number of cycles to failure in the S - N curve is N i ( Eq 5 ), causes a fatigue damage that is expressed by the damage sum: (Eq 16) D i = n i / N i...
Abstract
Fatigue failures may occur in components subjected to fluctuating (time-dependent) loading as a result of progressive localized permanent damage described by the stages of crack initiation, cyclic crack propagation, and subsequent final fracture after a given number of load fluctuations. This article begins with an overview of fatigue properties and design life. This is followed by a description of the two approaches to fatigue, namely infinite-life criterion and finite-life criterion, along with information on damage tolerance criterion. The article then discusses the characteristics of fatigue fractures followed by a discussion on the effects of loading and stress distribution, and material condition on the microstructure of the material. In addition, general prevention and characteristics of corrosion fatigue, contact fatigue, and thermal fatigue are also presented.
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002432
EISBN: 978-1-62708-194-8
... be exercised as this is similar to the Palmgren-Miner rule in fatigue failures, which is recognized as a crude approximation in many cases. Abu Haraz and Ermer ( Ref 29 ) used the cumulative damage theory with some success. They also were successful in using the Arrhenius equation in accelerated testing...
Abstract
Reliability is a measure of the capacity of equipment or systems to operate without failure in the service environment. This article focuses on reliability in design and presents equations governing the instantaneous failure rate, general reliability function, mean time to failure, mean time between failures, and useful life period. The article describes the calculation of reliabilities for series and parallel arrangements of a complex system. It provides a comparison of probabilistic and deterministic design and concludes with a discussion on reliability growth.
Book Chapter
Fundamentals of Modern Fatigue Analysis for Design
Available to PurchaseBook: Fatigue and Fracture
Series: ASM Handbook
Volume: 19
Publisher: ASM International
Published: 01 January 1996
DOI: 10.31399/asm.hb.v19.a0002364
EISBN: 978-1-62708-193-1
... a is the alternating-stress amplitude; S cr is the completely reversed stress amplitude for a given life (i.e., 10 6 , 10 5 , etc.); S u is the ultimate tensile strength of the material; S y is the yield strength; and S o is the mean stress. For the case of tensile mean stresses, as a rule-of-thumb...
Abstract
Fatigue crack initiation is an important aspect of materials performance in design. This article summarizes some fundamental concepts and procedures for the fatigue life prediction of relatively homogeneous, wrought metals when a major portion of total life is exhausted in crack initiation. It presents an overview of the strain-based, as opposed to stress-based, criterion of material behavior and fatigue analysis. The article describes the cyclic stress-strain behavior of metals to illustrate the inadequacy of the monotonic or tensile stress-strain curve in accounting for material instabilities caused by cyclic deformations. It discusses the effect of mean stress on fatigue life and presents the analysis of cumulative fatigue damage. The article concludes with examples of application techniques for fatigue life prediction.
Book Chapter
Failures of Rolling-Element Bearings and Their Prevention
Available to PurchaseSeries: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006834
EISBN: 978-1-62708-329-4
... Temperature domain (Δ T ), °C (°F) −30 to +100 (−20 to +210) −30 to +120 (−20 to +250) −20 to +150 (−4 to +300) −10 to +220 (+14 to 430) −40 to +130 (−40 to +265) Media resistance guide Mineral oil Good Good Dedicated Dedicated Not recommended Synthetic oil Not indicated Good Dedicated...
Abstract
This article is dedicated to the fields of mechanical engineering and machine design. It also intends to give a nonexhaustive view of the preventive side of the failure analysis of rolling-element bearings (REBs) and of some of the developments in terms of materials and surface engineering. The article presents the nomenclature, numbering systems, and worldwide market of REBs as well as provides description of REBs as high-tech machine components. It discusses heat treatments, performance, and properties of bearing materials. The processes involved in the examination of failed bearings are also explained. Finally, the article discusses in detail the characteristics and prevention of the various types of failures of REBs: wear, fretting, corrosion, plastic flow, rolling-contact fatigue, and damage. The article includes an Appendix, which lists REB-related abbreviations, association websites, and ISO standards.
Series: ASM Handbook
Volume: 8
Publisher: ASM International
Published: 01 January 2000
DOI: 10.31399/asm.hb.v08.a0003318
EISBN: 978-1-62708-176-4
... loading using the concept of cumulative damage (e.g., Palmgren-Miner mean accumulation rule). While this concept has strength in crack initiation models, it does not capture the role of overload type or order in the loading sequence and the subsequent effect on a propagating crack. Application...
Abstract
This article provides a review of fatigue test methodologies and an overview of general fatigue behavior, fatigue crack initiation and fatigue crack propagation of advanced engineering plastics. It also describes the factors affecting fatigue performance of polymers and concludes with information on fractography, a useful tool in failure analysis.
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006792
EISBN: 978-1-62708-295-2
... follow a statistical distribution, the life prediction is a statistical probability. The life prediction used is typically L 10 (the number of cycles before which 10% of the bearings are expected to have failed). Lundberg and Palmgren ( Ref 7 , 8 ) developed an experimental life method that is still...
Abstract
Rolling-contact fatigue (RCF) is a common failure mode in components subjected to rolling or rolling-sliding contact. This article provides a basic understanding of RCF and a broad overview of materials and manufacturing techniques commonly used in industry to improve component life. A brief discussion on coatings to improve surface-initiated fatigue and wear is included, due to the similarity to RCF and the increasing criticality of this failure mode. The article presents a working knowledge of Hertzian contact theory, describes the life prediction of rolling-element bearings, and provides information on physics and testing of rolling-contact fatigue. Processes commonly used to produce bearings for demanding applications are also covered.
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0001810
EISBN: 978-1-62708-180-1
Abstract
Rolling-element bearings use rolling elements interposed between two raceways, and relative motion is permitted by the rotation of these elements. This article presents an overview of bearing materials, bearing-load ratings, and an examination of failed bearings. Rolling-element bearings are designed on the principle of rolling contact rather than sliding contact; frictional effects, although low, are not negligible, and lubrication is essential. The article lists the typical characteristics and causes of several types of failures. It describes failure by wear, failure by fretting, failure by corrosion, failure by plastic flow, failure by rolling-contact fatigue, and failure by damage. The article discusses the effects of fabrication practices, heat treatment and hardness of bearing components, and lubrication of rolling-element bearings with a few examples.
Book Chapter
Fatigue Failures
Available to PurchaseSeries: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003544
EISBN: 978-1-62708-180-1
.... The most widely used method of estimating fatigue under complex loading is provided by the linear-damage law. This is a hypothesis first suggested by Palmgren and restated by Miner, and is sometimes known as Miner's law ( Ref 2 ). Application of n i cycles at a stress amplitude S i , for which...
Abstract
This article describes three design-life methods or philosophies of fatigue, namely, infinite-life, finite-life, and damage tolerant. It outlines the three stages in the process of fatigue fracture: the initial fatigue damage leading to crack initiation, progressive cyclic growth of crack, and the sudden fracture of the remaining cross section. The article discusses the effects of loading and stress distribution on fatigue cracks, and reviews the fatigue behavior of materials when subjected to different loading conditions such as bending and loading. The article examines the effects of load frequency and temperature, material condition, and manufacturing practices on fatigue strength. It provides information on subsurface discontinuities, including gas porosity, inclusions, and internal bursts as well as on corrosion fatigue testing to measure rates of fatigue-crack propagation in different environments. The article concludes with a discussion on rolling-contact fatigue, macropitting, micropitting, and subcase fatigue.