sae arp 5429-2001(r2006) landing gear fatigue tests with equivalent damage spectra

AEROSPACE RECOMMENDED PRACTICE

ARP5429

Issued 2001-07

Landing Gear Fatigue Tests With Equivalent Damage Spectra

1. SCOPE:

This SAE Aerospace Recommended Practice (ARP) applies to fatigue testing of landing gear and landing gear components.

1.1 Purpose:

Advancements in fatigue analysis methodology, combined with larger and faster computers, have led to more thorough and accurate fatigue life predictions. Traditional methodology involved the analysis of block loading spectra using S-N curves excluding the effect of plastic strain, residual stresses and the effect of the loading sequence. Today’s methodology employs “strain-life” analysis combined with the application of Neuber’s equation and the effects of the loading sequence to determine the true state of stress of every load set in a flight-by-flight spectrum. While providing the ability to analyze the “real world” our advancements in analytical methodology have surpassed the practicality of physical testing. While it is relatively simple to analyze a flight-by-flight spectrum, the cost and time required to test a flight by flight spectrum is prohibitive.

The purpose of this document is to provide a method and rationale for creating a physical test spectrum which is significantly reduced from the analytical spectrum and yet provides an accurate accumulation of the analytical damage for all critical areas of the article under test. While the focus of this document is the fatigue testing of landing gear, the approach is applicable to most mechanical structures subject to safe life fatigue analyses.

2. REFERENCES:

2.1 Applicable Documents:

The following publications form a part of this document to the extent specified herein. The latest issue of SAE publications shall apply. The applicable issue of other publications shall be the issue in effect on the date of the purchase order. In the event of conflict between the text of this document and references cited herein, the text of this document takes precedence. Nothing in this document, however, supersedes applicable laws and regulations unless a specific exemption has been obtained.

Reaffirmed 2006-08

RATIONALE This document has been reaffirmed to comply with the SAE 5-year Review policy.

SAE Technical Standards Board Rules provide that: “This report is published by SAE to advance the state of technical and engineering sciences. The use of this report is entirely voluntary, and its applicability and suitability for any particular use, including any patent infringement arising therefrom, is the sole responsibility of the user.” SAE reviews each technical report at least every five years at which time it may be reaffirmed, revised, or cancelled. SAE invites your written comments and suggestions. Copyright © 2006 SAE International All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of SAE. TO PLACE A DOCUMENT ORDER: Tel: 877-606-7323 (inside USA and Canada) Tel: 724-776-4970 (outside USA) Fax: 724-776-0790 Email: [email protected] SAE WEB ADDRESS: http://www.sae.org

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2.1.1 FAR/FAA Publications: Available from Federal Aviation Administration, 800 Independence Avenue, SW, Washington, DC 20591.

FAR Part 25, Paragragh 25.571FAA Advisory Circular 25.571-1C

3. BLOCK SPECTRA AND STRESS LIFE FATIGUE METHODOLOGY:

Prior to the development of flight-by-flight spectra and the introduction of strain-life methodology, block spectra typically were provided based upon alternating pairs of conditions such as spin-up and spring-back, right and left turns, towing forward and aft, and left and right steering. The total number of cycles expected during the life of the aircraft was assigned for each pair of conditions. A typical block loading spectrum is shown in Table 1. The total number of cycles represented are 990,840 for four aircraft lifetimes. The relatively low number of cycles indicates that the spectrum was clipped/truncated based upon previous experience and knowledge of the endurance limit of the materials being used.

Using the mission profile provided in Table 1, the mission segments are then grouped in pairs by maximum and minimum for each segment thus creating the analytical ground load spectrum. This spectrum is provided in Table 2 as an example. From this ground load information, external reactions and key member loads are determined at various fatigue critical sections of the structure. The state of stress at sections determined to be critical is then calculated using standard methods of elastic stress analysis. In most practical cases, the state of stress at the surface of a part is biaxial, defined by the normal stresses fx and fy and the shearing stress fs. The combined effect of these stresses is expressed as an “equivalent uniaxial” stress, F, for which the octahedral shear stress criterion yields the following equation:

(Eq. 1)

For each pair of loads, or load cycle, in the spectrum, equivalent stresses Fmax and Fmin are obtained. Using this range of stresses, the alternating stress, Sa, and the mean stress, Sm, is expressed as follows:

(Eq. 2)

The equivalent fully reversed stress is then calculated using the Modified Goodman diagram, or stress range diagram. The stress range diagram is assumed to be a straight line connecting the points (Sm=0, Sa=S) and (Sm=Ftu, Sa=0), where S is the equivalent fully reversed stress.

F fx2 fy

2 fx fy 3fs2+–+=

SmFmax Fmin+( )

2-----------------------------------= Sa

Fmax Fmin–( )2

----------------------------------=



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TABLE 1 - Typical Block Loading



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TABLE 2 - Analytical Spectrum (Block Loading)



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FIGURE 1 - Modified Goodman Diagram

3. (Continued):

Mathematically, the equivalent fully reversed stress may be expressed as follows:

(Eq. 3)

With the value of the equivalent fully reversed stress having been determined, the number of cycles to failure, N, may be determined by entering the material stress-life (S-N) curve with the appropriate stress concentration factor, Kt. The value of N is then determined for each load pair in the loading spectrum for the respective equivalent fully reversed stress; N1, N2, N3, etc. The values of Ni are divided into the number of applied cycles for the given load cycle, ni, to determine the damage ratio for to that particular pair. The sum of the damage ratios

(Eq. 4)

is considered the accumulative damage ratio. An accumulative damage ratio of 1 or less is acceptable.

The relatively small number of conditions allows the analyst to survey the member loads for the sections to be analyzed and determine which pairs are likely to cause damage. The state of stress and the resulting damage ratio can then be tabularized to determine the accumulative damage ratio for the section. Table 3 presents an example of a typical section analysis. This process is then repeated for all potentially fatigue critical sections throughout the structure.

SSa

1SmFtu---------–

------------------Fmax Fmin–( )

2Fmax Fmin+

Ftu------------------------------

–---------------------------------------------= =

n1

N1------

n2

N2------

n3

N3------ .................+ + +

nN----∑=



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TABLE 3 - Typical Section Analysis

3. (Continued):

While this method of analysis has been used in the design of numerous landing gears and aircraft components, it differs from current methodology in several respects.

1. The order of application of loads is not considered.2. The absolute maximum and minimum stress for any given section may not be paired (see Table 3).3. The effect of residual stresses is not considered.4. Areas generally loaded in compression are not considered critical.



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3. (Continued):

As noted previously, the spectrum used in this example consisted of less than 125,000 load reversals, or 250,000 discrete load applications per lifetime. Based upon the analysis, it would be possible to eliminate complete mission segments from a fatigue test spectrum if the analysis indicates it did not cause damage for any section of the landing gear.

The running time to complete one lifetime of testing for the complete spectrum could be completed in approximately 15 days, or two months for four lifetimes (assuming a cycling rate of six per minute). If the low level taxi cycles of load steps 16 and 17 (Table 1) were found to not cause damage, the test time could be reduced to five days per life. Keeping these times in mind, we will now investigate the effects of analyzing and testing to the true flight-by-flight spectra now in use.

4. FLIGHT-BY-FLIGHT SPECTRA AND STRAIN LIFE METHODOLOGY:

In recent years much of the aerospace industry has transitioned to “strain-life” fatigue analysis techniques rather than the stress-life approach described above. The strain-life method is generally accepted to be more accurate than the stress-life approach, particularly in the plastic stress regime, in that it considers the following:

- The plastic stress at the notch using Neuber’s rule.- The strain hardening/softening of structural materials subjected to cyclic loading.- The order of load application.- The pairing of the highest and lowest applied strain regardless of when it is applied.- The affect of residual strains.- Life data based upon strain controlled testing which in effect accurately represents notch stress in

the plastic range.

Neuber’s rule which relates the nominal stress and notch factor to the true stress and strain may be stated as follows:

(Eq. 5)

In addition to defining the true stress and strain at a notch, use of Neuber’s equation allows the determination of the residual strain or stress due to plastic stress at the notch.

Most high strength metals will strain harden, or soften, relatively quickly when subjected to cyclic loading in the plastic range. The resulting cyclic stress-strain curve may vary dramatically from the monotonic curve as shown below for 4340 steel heat treated to a 180 ksi strength level. The cyclic stress-strain curve should always be used when notch stresses are expected to exceed the proportional limit.

KtS( )2

E----------------- σε=



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FIGURE 2 - Stress/Strain Curve

4. (Continued):

Given Neuber’s rule and the cyclic stress-strain curve for a given material, the fatigue analysis of any section of any component may be accomplished in the following manner:

1. Determine the nominal stresses at the desired location using classical analytical techniques. In the case of biaxial stresses, an equivalent uniaxial stress must be determined using the Octahedral Shear Theory discussed previously or by a similar method.

2. Digitally plot the flight-by-flight spectrum of nominal stresses for each loading condition beginning with the highest stress, tension or compression.

3. Using a “Rain Flow” or “Range Pair” method, determine the paired load conditions throughout the spectrum.



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FIGURE 3 - Rain FlowCounting

4. (Continued):

4. Using the cyclic stress-strain curve, the stress concentration factor, and Neuber’s equation determine the true strain and residual strain at the notch for each loading condition. Determination of the equivalent fully reversed stress may vary but is generally a function of the strain range and mean stress and may be expressed as shown below:

(Eq. 6)

Where E is the modulus of elasticity of the material and β is a material constant.

5. Determine the damage for each pair using the appropriate strain-life curve for the material being used in the design and simply add the damage from each pair to determine the resulting life of the component.

Typical results from such an analysis are shown in Table 4. This table presents only a portion of the total spectrum for the example being used. The constants A, E, and XN define the cyclic stress strain curve and β is the material constant for determination of the fully reversed stress. This analysis is repeated for every critical component/section on the structure. Depending on the size and complexity of the structure, the number of sections analyzed may approach or exceed 100.

εEQ

εmax εmin–2

---------------------------σmean

E---------------

β

+=



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TABLE 4 - Section Fatigue Analysis Sample



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4. (Continued):

The spectrum for this particular example, the landing gear of a modern day military aircraft, contained 1,132,270 load conditions per aircraft life. It must be noted that this spectrum was previously truncated and clipped based upon criteria established by the airframe supplier and the end user. Again assuming that six load cycles per minute are achievable in the test laboratory, the running time required to complete a fatigue test for this particular landing gear would be 65 days per life or nearly nine months for four life times.

A similar example might be stated for a business jet or regional aircraft. In these cases the flight-by-flight spectrum may not be truncated or clipped resulting in a number of load conditions per life exceeding 8 million. Test running time for such a case would approach six years. This, of course, is an unacceptable situation based upon both test cost and risk to the fleet in service.

5. DEVELOPMENT OF AN EQUIVALENT DAMAGE TEST SPECTRUM:

Perhaps the most obvious approach is not to test conditions that do not contribute to the total damage of the component. That is, review the analytical spectrum thoroughly for all pairs of load conditions that do not cause damage and eliminate them from the test spectrum. While this approach is indeed feasible, there are certain criteria that should be met before such an undertaking.

a. A thorough and accurate fatigue analysis must be completed. Thorough in the sense that all potentially fatigue critical areas are analyzed and accurate in that all contributing factors are included in the analysis. In this respect, a strain-life approach is preferred in that it considers the true and residual strains at the notch.

b. A spectrum sensitivity study should be completed during the fatigue analysis. High plastic strains result in residual stresses that may be detrimental or have a “healing” effect. In either case, the effect of such loads on the total damage should be investigated and a decision made as to whether the load case is realistic and should be included.

c. While a reduced test spectrum that simply eliminates non-damaging load conditions will be fairly representative, it must be examined to assure that all sections are adequately enveloped with respect to damage ratio. Therefore a tolerance, plus or minus a certain percent of damage, should be established as a success criteria. For example, it may be decided that the resulting test spectrum must envelope all damage ratios greater than 0.25 within +5%/-0% and all damage ratios less than or equal to 0.25 within ±20%. In any case, the final test spectrum damage must be carefully compared to the analytical damage and sound engineering practice applied. ht

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5. (Continued):

Given these criteria, determining an equivalent damage test spectrum from analytical test spectrum is relatively straightforward with the aid of the proper computer resources.

1. For each section analyzed, sort the resulting pairs by damage ratios in decreasing order.

2. Eliminate all pairs that cause zero damage, i. e., those pairs which have an equivalent fully reversed strain less the endurance limit of the material. Short of only eliminating pairs that cause no damage, it may be acceptable to choose an agreed upon minimal amount of damage such as 0.0000005.

3. Save the remaining pairs to a separate collection file.

4. Repeat the steps 1.) and 2.) for all sections analyzed. Save any previously unused pairs in the file created in step 3.). Pairs that already exist in the collection file need not be repeated.

5. Create a “equivalent damage test spectrum” from the pairs collected in step 3.) applying them in as close to the same order as possible.

6. Repeat the analytical fatigue analysis of each section using the test spectrum and compare the results to the original analysis. If all sections are enveloped within the agreed upon tolerance, the test spectrum is complete. If all sections are not enveloped properly, adjustments may be made to the pairs contributing to the damage of that particular section. However, care must be taken not to “overtest” or “undertest” other critical sections when making such adjustments.

Applying this technique to the example of the military aircraft previously used resulted in a 94% reduction of the load cycles in the spectrum. Table 5 summarizes the results for the four most critical sections on the landing gear.

TABLE 5 - Analytical Versus Test SpectrumMilitary Aircraft

Similarly, Table 6 provides a damage ratio comparison for the business jet example. The analytical spectrum contained 3,752,400 load pairs per life and would require 217 days of test running time for one life. The equivalent damage spectrum contained 101,000 loads conditions requiring only six days of running time.



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TABLE 6 - Analytical Versus Test Spectrum DamageRegional Business Jet



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6. EQUIVALENT DAMAGE TEST SPECTRA - OTHER ISSUES:

While the development of an equivalent damage test spectrum is relatively straight forward, there are issues and questions that arise concerning its use. These include such things as certification requirements, the effect of design or load changes, and the concern of missing a critical section or underestimating a stress concentration factor.

Certification issues, whether military or commercial, must be agreed upon between the landing gear supplier, the aircraft manufacturer, and the regulatory agency. Thorough documentation of the fatigue analysis and the test spectrum development will provide rationale that will allow for sound decision making and providing of a safe product at an economically acceptable cost.

Design and load changes are to be expected during the development and service life of any aircraft. The effect of such changes on the fatigue life of the landing gear must be considered in the same manner whether the fatigue test is conducted using a full flight-by-flight or equivalent damage test spectrum. A complete re-analysis must be conducted and the effect of the changes thoroughly reviewed. A decision can then be made as to whether to rely on the structural analysis or consider additional fatigue testing. If additional fatigue testing is required, element testing of the affected components may be considered in lieu of a complete fatigue test.

A fatigue analysis is prepared to identify critical areas and address possible sources of problems during the design phase. It is not intended to replace a fatigue test. Due to the physical complexity of landing gear components, it is possible that the designer may miss a critical section or underestimate a stress concentration factor. However, experience has shown that fatigue damage to a landing gear is generally accumulated by a relatively small number of ground handling or landing conditions. A thorough fatigue analysis will capture these conditions and they will be included in an equivalent damage spectrum thus identifying any structural weakness during the fatigue test.

It must also be noted that the method presented in this document does not provide for increasing the applied loads to accelerate the accumulation of damage. Increasing the loads is not a recommended practice since increased residual stress effects may retard damage in some cases while it increases the damage in others. This, in turn, makes enveloping the damage for all of the components much more difficult.



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7. SUMMARY:

It is generally acknowledged that relatively few of the load conditions and cycles applied to a landing gear throughout its service life contribute to fatigue damage of the gear. While a complete flight-by-flight fatigue test is the ideal scenario, this type of testing is very costly and time consuming to accomplish. Today’s analytical tools, both hardware and software, allow the fatigue analyst to do a more in-depth and accurate fatigue analysis relatively quickly. Using these tools to investigate the source of fatigue damage and eliminate non-damaging loading conditions from the test spectrum will effectively reduce test time and cost while maintaining the integrity of the qualification test and assuring product safety. It must be noted that the method presented in this document is certainly not the only method that may used to identify non-damaging loads in a fatigue spectrum. However, it has been employed and has met acceptance in the aerospace community.

PREPARED UNDER THE JURISDICTION OFSAE COMMITTEE A-5, AEROSPACE LANDING GEAR SYSTEMS

