AAR M-101

AAR Manual of Standards and Recommended Practices Wheels and Axles

S-660

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S-661


GAUGE, WHEEL—MAXIMUM FLANGE THICKNESS, HEIGHT, AND THROAT RADII GAUGE FOR AAR-1B NARROW-FLANGE STEEL WHEEL Standard S-661 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-602.

Notes:

1. Unless noted, all other tolerances are ±0.0250. 2. Hanging holes optional. 3. Minimum 0.120-in. steel with minimum 55 RC hardness.

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S-662


GAUGE, WHEEL—MINIMUM FLANGE THICKNESS, HEIGHT, AND THROAT RADII GAUGE FOR AAR-1B NARROW-FLANGE STEEL WHEEL Standard S-662 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-603.

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S-663


GAUGE, WHEEL—REFERENCE LIMIT GAUGE FOR VERIFYING AAR 1B NARROW FLANGE WHEEL GAUGE S-661 Standard S-663 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-604.

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S-664


GAUGE, WHEEL—REFERENCE LIMIT GAUGE FOR VERIFYING AAR 1B NARROW FLANGE WHEEL GAUGE S-662 Standard S-664 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-604.

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S-665


GAUGE, WHEEL—MAXIMUM FLANGE THICKNESS, HEIGHT, AND THROAT RADII GAUGE FOR AAR-1B WIDE-FLANGE STEEL WHEELS Standard S-665 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-605.

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S-666


GAUGE, WHEEL—REFERENCE LIMIT GAUGE FOR VERIFYING AAR 1B WIDE FLANGE WHEEL GAUGE S-665 Standard S-666 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-606.

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S-667


GAUGE, WHEEL—MINIMUM FLANGE THICKNESS, HEIGHT, AND THROAT RADII GAUGE FOR AAR-1B WIDE-FLANGE STEEL WHEELS Standard S-667 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-607.

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S-668


GAUGE, WHEEL—REFERENCE LIMIT GAUGE FOR VERIFYING AAR 1B WIDE FLANGE WHEEL GAUGE S-667 Standard S-668 Adopted: 1991 1.0 SCOPE 1.1 This standard became effective March 29, 1991. 1.2 This standard supersedes MSRP S-608.

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S-669


ANALYTIC ANALYTIC EVALUATION EVALUATION OF LOCOMOTIVE LOCOMOTIVE WHEEL WHEEL DESIGNS DESIGNS Standard S-669 Adopted: 2011 1.0 OBJEC JECTIVE

The objective of this procedure is to provide a method, using the AAR Manual of Standards and S-660 as a basis, to evaluate the performance of a proposed loco Recommended Practices Standard S-660 as motive wheel design under normal railroad operating service conditions. The objective will be achieved by comparing the results obtained from the application of this procedure to a fatigue criterion and prescribed vibration performance limits. The first step is to ensure that the computations will be of sufficient accuracy and reproducibility where and by whom they are made. This procedure permits the use of all computational techniques that can be demonstrated to provide accurate results and that permit the analysis to be performed under a standard set of assumptions (i.e., material property data and loading conditions). This procedure shall be operative under MSRP Specification M-107/M-208, M-107/M-208 , Appendix A , paragr paragraph aph 2.2 2.2.. This standard applies to new wheel designs that have not yet received approval for use in service pursuant to the requirements of Standard S-660. S-660 . 2.0 BACKGROU ROUND

Computational finite element methods may be applied to obtain the results required by this standard. These results form the basis of the AAR evaluation of the wheel design. Because the evaluation process consists of comparisons of results for wheels of different designs, the magnitude and manner of design load application to the wheel as well as the accuracy requirements for the computational technique must be specified if consistent, comparable results are to be obtained. 3.0 ANALYST ANALYST AND CODE CODE QUAL QUALIFI IFICAT CATION ION

To ensure accuracy and consistency of the results of an analysis, analysts and software must be qualified by the AAR. Qualification shall be obtained by performing a benchmark analysis of a prescribed wheel design and heat-treatment schedule (identifying the initial temperature, quench duration, quenched region, and annealing temperature and duration) that shall be obtained from the committee coordinator of the Wheels, Axles, Bearings, and Lubrication (WABL) Committee. The analysis shall be conducted using the procedures and material properties provided herein, and a report of the results res ults obtained shall be submitted to the committee coordinator. 4.0 RESULTS

Specific results reporting requirements are described below. Stress results must be reported in pounds per square inch (psi) at each nodal location.

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5.0 SOLUTI SOLUTION ON QUALI QUALITY TY AND AND REQUIR REQUIRED ED ANALYS ANALYSES ES 5.1 Solutio Solution n Quality Quality and Anal Analysi ysis s Overvi Overview ew

The analytical procedures applied to produce the results required by this standard must be accurate and convergent. Accuracy can be determined by comparison with a standard set of calculated results. Convergence must be examined to ensure that the choice of finite element size and density or the number of terms in the series representations (if employed) do not appreciably affect the results of the calculations. For the purpose of compliance with the requirements of this standard, convergence is achieved when the maximum von Mises effective stress predicted by the analytical procedure employed is less than 500 lb/in. 2 (psi) for successive complete mesh refinements. Five analyses are required to evaluate the conditions described in this standard as described in paragraph paragraphss 5.2 5.2 to to 5.6 5.6 and and paragr paragraph aphss 7.0 7.0 and and 8.0 8.0.. The first analysis is performed according to the current requirements in Standard S-660 (with S-660 (with additions) as described in paragr paragraph aph 5.2 5.2 and and consists of an elastic analysis of the wheel in the new and worn (to the condemning limit) conditions. This analysis may be performed using a two- or three-dimensional finite element model. The second analysis consists of an elastic-plastic simulation of the wheel heat treating process as described in paragr paragraph aph 5.3 5.3 and and may be performed using a two- or three-dimensional finite element model. This analysis also considers the wheel in the new and worn (to the condemning limit) conditions. Mechanical properties for this analysis are specified s pecified in paragraph paragraph 10.0 10.0.. Because the purpose of this analysis is for comparison of wheel designs only, analysts who wish to extend this analysis to consider conditions not specified here may wish to apply different properties for such analyses. The third analysis involves calculation of the elastic stresses resulting from the wheel-to-axle interference fit as described in paragr paragraph aph 5.4 5.4 and and may be performed using a two- or three-dimensional finite element model. This analysis also considers the wheel in the new and worn (to the condemning limit) conditions. The fourth analysis identifies fatigue-prone locations in the proposed wheel design through application of the Sines criterion as described in paragr paragraph aph 5.5 5.5.. This is accomplished by combining selected results from the three analyses described above according to the procedure outlined in paragr paragraph aph 7.0 7.0.. The fifth analysis requires determination of certain vibration characteristics characteristics of the proposed wheel design as described in paragr paragraph aph 5.6 5.6 A A three-dimensional model of the wheel is necessary to perform this elastic analysis (for the full-thickness rim condition only) according to the procedures outlined in paragr paragraph aph 8.0 8.0.. To simplify the task of manipulating and interpreting the results, the cross-sectional finite element mesh (in the radial-axial plane) of all models used to satisfy the requirements of this standard for a particular wheel design must be identical.

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5.2 5.2 S-66 S-660 0 Ana Analysi lysis s

An analysis pursuant to the requirements in Standard S-660 (most S-660 (most recent version) shall be completed. Compliance with this standard expands the requirements of Standard S-660 paragr paragraph aph 7.2 to include the V1+L1 and V2 load cases for the worn rim condition. Two types of finite element models may be used to perform the Standard S-660 analysis. S-660 analysis. The first model type consists of a mesh of structural or thermal elements as required. The structural element will have three displacement degrees of freedom at each node, and the thermal element will have a single degree of freedom (temperature) at each node. The second model type that may be utilized to perform the Standard S-660 analysis S-660 analysis comprises a mesh composed of harmonic structural or thermal elements. The structural element will have three displacement degrees of freedom at each node, and the thermal element will have a single degree of freedom (temperature) at each node. The difference is, with this type of element, the structural and thermal loads are characterized by Fourier series approximations. Compared with the first model type, run times are faster and file sizes are smaller using harmonic elements. If this technique is employed, a sufficient number of terms must be considered in the Fourier series representation of the loading to obtain an accurate solution. 5.3 5.3 Heat Heat-T -Tre reat atme ment nt Analy Analysi sis s

The state of residual stress in the wheel following wheel rim heat treatment (quenching, tempering, and cool down) shall be determined. The heat-treatment analysis shall be performed independently of all other analyses required by this standard. The complete thermal and stress transient history, beginning at the start of the quench process (assuming a uniform temperature) and ending when the wheel reaches ambient thermal conditions, shall be calculated. Viscoelastic creep effects shall be accounted for in the heat-treatment analysis. Because the fatigue analysis methodology requires combining results from different analyses at particular nodal locations, the same model used to perform the Standard S-660 analysis must be used for the heat-treatment analysis. Results of the heat-treatment analysis shall be presented as four contour plots depicting the axial, radial, circumferential (hoop), and in-plane shear stress components individually for the new and worn rim conditions. 5.4 5.4 Inte Interfe rfere rence nce Fit Fit Anal Analys ysis is

An interference fit of 0.010 in. (referenced to the diameter) between the wheel bore and axle shall be applied. The interference fit analysis shall be performed independently of all other analyses required by this standard. Because the fatigue analysis methodology requires combining results from different analyses at particular nodal locations, the same model and material properties used to perform the Standard S-660 analysis must be used for the interference fit analysis. Results of the interference fit analysis shall be presented as four contour plots depicting the axial, radial, circumferential (hoop), and in-plane shear stress components individually for the new and worn rim conditions. 5.5 5.5 Fatig atigue ue Anal Analys ysis is

The fatigue analysis specified in this standard shall be performed by applying the Sines criterion to the results obtained from the preceding analyses. In the Sines criterion context, the live (alternating and mean) stresses are those that occur as a result of the applied loading, and the as-manufactured residual stresses and the stresses due to interference fit represent the static stresses. The analytically-determined stresses are combined with certain material constants to evaluate the Sines criterion at each node in the model. The outcome of o f this evaluation determines whether the proposed wheel design is likely to experience fatigue failure before its desired lifetime.

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5.6 Vibration Analysis

The objective of this analysis is to evaluate the dynamic performance of the proposed wheel by simulating the dynamic reaction between the wheel and the track. A 360° model of the wheel, as shown in Fig. 5.1, shall be created using solid (brick) elements with a minimum of eight nodes. The use of higher-order solid elements is permitted. If a two-dimensional (axisymmetric) model is used to perform the analyses described in paragraphs 5.2, 5.3, and 5.4, that model shall be revolved as described below to generate the three-dimensional model. The portion of the S-660 compliant model that represents the hollow axle shall be retained. The elastic material properties prescribed in Standard S-660 (most recent version) shall be used in the vibration analysis. Interference pressure between the hollow axle and wheel hub shall be ignored in this analysis. 90°

180°

0°

270°

Fig. 5.1 3-D rendering of locomotive wheel identifying angular reference positions (view is of front face of wheel)

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The elements generated in the hoop direction shall have a maximum angular length of 10° or less. The model shall have a plane of nodes at 45°. The angular length of the elements on either side of the 45° plane shall extend in the hoop direction by no more than 5°. These requirements are illustrated in Fig. 5.2. The 0° plane is the plane on which the specified loads are applied. The 45° plane is the plane at which the stress results are reported.

Note: Shaded sectors represent minimum 10° arc length segments. Black and white segments represent minimum 5° arc length segments on opposite sides of 45° plane. Red arrow indicates direction of tractive load applied to tread surface. Fig. 5.2 Illustration of 3-D model created by revolution of 2-D axisymmetric model (view is of front face of wheel)

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6.0 LOADING CONDITIONS 6.1 Standard S-660 Stress Results

Obtain the orthogonal (normal) stresses for the following loading combinations from the Standard S-660 analysis (using the material properties defined therein) for all nodes in each model (new and worn rim conditions): Vertical Load V1 + Lateral Load L1 Vertical Load V2. Orthogonal (normal) stresses at each node in the region identified in Fig. 6.1 for each model shall be retained.

Fig. 6.1 Portion of model (red regions) in which stresses due to applied loads (L1 + V1 and V2) must be retained for fatigue analysis of the new and worn rim conditions 6.2 Heat-Treatment Residual Stresses

The heat-treatment schedule shall be provided by the AAR WABL Committee for the benchmark analysis to be performed for analyst qualification. The schedule identifies initial temperature, quench duration and extent, annealing temperature and duration, and any dwell time that may exist between any steps in the heat-treatment process. Convective and radiative heat transfer shall be accounted for on all exterior surfaces of the wheel as described in paragraph 10.0. All other submissions to the WABL Committee according to this standard must utilize the heat-treatment schedule proposed for the actual wheel design for which approval is sought. 6.2.1 New Rim Geometry

The purpose of this analysis is to establish the state of residual stress for the new rim geometry due to the heat-treatment process including cool-down to room temperature. In a decoupled analysis, the temperature history at each node shall be calculated first using thermal elements. Time begins (t = 0) when the wheel exits the austenizing furnace at a uniform elevated temperature. The material is considered to be strain-free at this point in time. The analysis ends ( t = tn) when the wheel reaches ambient temperature at the end of the cool-down period. This condition is satisfied when the temperature at all nodes is within the range of ambient temperature plus 5 °F.

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In the second part of the decoupled analysis, the time-dependent nodal temperatures are applied to the structural elements to obtain the residual stresses. The relevant temperature-dependent material property data in paragraph 10.0 shall be used. At the conclusion of the heat-treatment simulation, orthogonal (normal) stresses at each node in the model in the region identified in Fig. 6.1 shall be retained. 6.2.2 Worn Rim Geometry

To determine the residual stress distribution in the worn wheel, elements are removed from the model described above to arrive at the worn rim geometry. Element removal alters the residual stress distribution. This technique involves modifying the stiffness matrix. The relevant temperature-dependent material property data in paragraph 10.0 shall be used. After removal of the rim material, orthogonal (normal) stresses at each node in the model in the region identified in Fig. 6.1 shall be retained. 6.3 Interference Fit Analysis

The interference fit shall be accomplished by inserting a hollow axle stub into the wheel bore. A nominal interference of 0.010 in. referenced to the diameter is assumed. For convenience, the hollow axle geometry shown in Fig. 5.2 (in which the axle bore diameter is 2 in.) may be used. The interference fit stresses shall be determined for the new and worn rim conditions. The element removal technique described above may be used to obtain the interference fit stresses for the worn rim geometry. Material properties for the wheel and axle shall be as defined in Standard S-660 (current version). Orthogonal (normal) stresses at each node in each model in the region identified in Fig. 6.1 shall be retained. 6.4 Required Stress Results

The analyses performed according to paragraphs 6.1, 6.2, and 6.3 yield eight sets of stress results, or eight load cases, as shown in Table 6.1. Table 6.1 Summary of load cases

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Load Case

Required Result at Each Node

Condition

1

Orthogonal normal stresses under load (S x L, Sy L, Sz L, T xy L, Tyz L, T xz L)

V1+L1, new (full) rim

2


V2, new (full) rim

3


V1+L1, worn rim

4


V2, worn rim

5

Orthogonal normal stresses (S x R , Sy R , Sz R )

Heat-treatment residual stresses, new (full) rim

6

Orthogonal normal stresses (S x R , Sy R , Sz R )

Heat-treatment residual stresses, worn rim

7

Orthogonal normal stresses (S x P , Sy P , Sz P )

Interference-fit stresses, new (full) rim

8

Orthogonal normal stresses (S x P, Sy P, Sz P)

Interference-fit stresses, worn rim

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7.0 FATIGUE ANALYSIS ACCORDING TO SINES CRITERION

Combinations of static or residual stress with superimposed alternating stress were examined by Sines [1, 2, 3, 4] and it was found that the permissible alternation of stress is a reasonably linear function of the orthogonal normal static stresses expressed as follows:

J ′ 2 ≤ A – α ( J 1 M + J 1 R + J 1 P )

Equation (1)

in which J' 2 represents the octahedral shear stress and is defined as follows: 1 2 = -- [ ( S x – S y ) + 3

J ′ 2

( S y – S z )

2

+

( S z – S x )

2

2 2 2 + 6 ( T xy + T yz + T xz )]

1 -2

Equation (2)

which, for the purposes of this standard, is characterized by the amplitudes of the stresses due to the applied load as derived from the stress states on the load application plane (at 0°) and on a radial plane located 180° from the load application plane. The amplitude of each nodal stress component ( S , i T ij) in Equation (2) is defined as follows:

S i

1 L = -- [ ( S L i ) 0 ° – ( S i ) 180 ° ] and 2

T ij

1 L = -- [ ( T L ij 0 ° ) – ( T ij 180 ° ) ] 2

Equation (3)

in which the subscripts 0° and 180° denote the value of each stress component on the respective model planes (the regions identified in Fig. 6.1), and the superscript L denotes the stresses due to the applied loads. These stresses are obtained from the analysis performed according to paragraph 6.1. J 1 M is the mean of the sum of the orthogonal (normal) components of the alternating stresses ( Si L) at each node as determined by the analysis performed according to paragraph 6.1 and is defined as follows:

J M 1

1 L + S L + S L ) + = -- [ ( S x y z 0 ° 2

L ) ( S x L + S y L + S z ] 180 °

Equation (4)

in which ( S x L + S y L + S z L)0° are the orthogonal (normal) stress components at the nodes on the radial plane upon which the load is acting (at 0°), and ( S x L + S y L + S z L)180° are the orthogonal (normal) stress components at the nodes on a radial plane 180° away (the regions identified in Fig. 6.1), and J 1 R is the sum of the orthogonal (normal) components of the residual (static) stresses ( Si R) at each node as determined by the analysis performed according to paragraph 6.2 and is defined as follows:

J R 1

=

S x R + S x R + S x R

Equation (5)

and J 1 P is the sum of the orthogonal (normal) components of the interference fit (static) stress ( Si P) at each node as determined by the analysis performed according to paragraph 6.3 and is defined as follows:

J P 1

=

P S x P + S y P + S z

Equation (6)

The values of the constants ( A = 28 ksi and

= 0.16) have been experimentally determined [5, 6].

α

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Equation (1) shall be evaluated at each node in each model in the region identified in Fig. 7.1 for the four combinations of load cases shown in Table 7.1. If, under any load combination, Equation (1) evaluates to false (the alternating stresses are greater than the static stresses) at any node in the model(s), then fatigue is predicted, rendering the design unacceptable.

Note: Area comprises portion of wheel cross-section between red lines that connect inboard and outboard hub outer diameters and inboard and outboard rim inner diameters.

Fig. 7.1 Region in which Sines criterion is applied

Table 7.1 Load combinations to which Equation (1) shall be applied Load Combination

J’ 2

J 1M

J 1R

J 1P

A

Load Case 1

Load Case 1

Load Case 5

Load Case 7

B

Load Case 2

Load Case 2

Load Case 5

Load Case 7

C

Load Case 3

Load Case 3

Load Case 6

Load Case 8

D

Load Case 4

Load Case 4

Load Case 6

Load Case 8

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7.1 Results

The results obtained by application of the Sines criterion for the four load combinations described in paragraph 7.0 shall be presented as four contour plots in the plane of the wheel cross-section on which the mechanical loads act in a format similar to that shown in Fig. 7.2.

Fig. 7.2 Sample contour plot of Sines parameter on portion of wheel cross-section identified in Fig. 7.1 (legend omitted)

For each of these plots, the value to be contoured at each node location is the Sines parameter, SP, which is the difference between the left-hand and right-hand sides of Equation (1), or

SP

=

J ′ 2 – [ A – α ( J 1 M + J 1 R + J 1 P ) ]

Equation (7)

Negative contour data ( SP less than 0) indicate locations at which the Sines criterion is satisfied. Positive contour data ( SP greater than 0) represent fatigue-prone locations at which the Sines criterion is violated. Fatigue-prone locations are unacceptable, and if identified through application of this procedure, the proposed wheel design must be revised and the analysis procedure repeated until no Sines criterion violations remain ( SP < 0 everywhere in the specified plate region). The minimum safety factor and the location in the wheel plate at which it occurs shall be reported for each load combination. The safety factor represents the fatigue margin for the proposed wheel design and is determined in the following way. The analysis described in paragraph 7.0 yields a value for the Sines parameter ( SP) at each node for each of the specified nominal loading conditions. The stresses due to the mechanical loads are recomputed assuming the nominal load (L1, V1, V2) is increased by a load factor n. Because the model is linearly elastic, the stresses due to the mechanical loads (load cases 1 through 8 in Table 6.1) increase proportionally.

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The Sines parameter SP is recomputed for each node for each load combination described in Table 7.1. Each node is now characterized by two values for SP: one due to the nominal load (load factor = 1) and one resulting from the increased load (load factor = n). The safety factor at each node is the multiplier (load factor) on the mechanical load necessary to cause the left-hand and right-hand sides of the Sines criterion to be equal at this location ( SP = 0). This concept is graphically depicted in Fig. 7.3:

Fig. 7.3 Schematic illustrating method for determining safety factor

Table 7.2 Reporting format for fatigue analysis results

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Load Combination

Loading Description

Rim Condition

Maximum SP

Safety Factor

A

V1 + L1

NEW

B

V2

C

V1 + L1

D

V2

WORN

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8.0 VIBRATION ANALYSIS 8.1 Modal Analysis

A modal analysis shall be conducted to determine the vibration characteristics (natural frequencies and mode shapes) in the frequency range of 0 Hz to 500 Hz. The saddle mode of vibration (as shown in Fig. 8.1) is the subject of this analysis. The natural frequency associated with this mode shall be used in a harmonic response analysis to determine the stress field in the wheel. Damping is ignored.

0° - 180° reference plane

Fig. 8.1 Wheel in saddle-mode of vibration with reference plane for applied load 8.1.1 Finite Element Model

The three-dimensional model described in paragraph 5.6 shall be used. 8.1.2 Material Properties

Relevant material properties as defined in Standard S-660 (current version) shall be used. Thermal effects are not considered in this analysis. The modal and harmonic response analyses are performed assuming elastic material behavior. 8.1.3 Boundary Conditions

The outer surface of the hollow axle stub shall be fixed to the inner surface of the wheel hub. Axle bore nodal degrees of freedom are fixed. Interference pressure between the hollow axle and wheel hub is ignored in this analysis. 8.1.4 Modal Analysis Results

The lowest frequency at which the wheel vibrates in the saddle-mode shape as shown in Fig. 8.1 shall be reported to a minimum of three decimal places.

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8.2 Harmonic Response Analysis

A harmonic response analysis shall be conducted for the saddle mode of vibration to predict the sustained dynamic behavior and the steady-state response of the wheel to a tractive load that varies sinusoidally with time. The forcing frequency of the applied load is 0.002% greater than the saddle-mode natural frequency obtained in paragraph 8.1.4 (i.e., f = f n·[1+0.00002] to a minimum of three decimal places). The same model used for the modal analysis shall be used for the harmonic response analysis. Three load cases shall be considered. Tractive loads shall be applied in the rail running direction on the wheel tread surface in the 0° plane identified in Fig. 5.2 at the locations shown in Table 8.1. A force magnitude of 300 lb is sufficient to provide adequate excitation. Damping is ignored. Table 8.1 Load locations for harmonic analysis Load Case

Load Location on Wheel Tread

H1

1 in. from front rim face

H2

3 1/16 in. from the back rim face for wide flange wheels 2 27/32 in. from the back rim face for narrow flange wheels

H3

1 1/2 in. from the back rim face for wide flange wheels 1 9/32 in. from the back rim face for narrow flange wheels

8.3 Harmonic Response Analysis Results

For each load case identified in Table 8.1, provide the following graphical results: • A three-dimensional view of the model depicting the wheel in the saddle mode of vibration as shown in Fig. 8.1 • Two-dimensional contour plots of circumferential (hoop), axial, and radial stresses in the cross-sectional plane located 45° from the 0° plane at which the excitation is applied (as identified in Fig. 5.2) when the amplitude of the forced vibration is maximum For each load case identified in Table 8.1, report the following data as shown in Table 8.2: • The maximum residual circumferential (hoop) tensile stress in the wheel rim resulting from the heat-treatment analysis as identified in Fig. 8.2 (paragraph 6.2) • The circumferential (hoop) stress range due to the forced vibration at the location of maximum residual circumferential (hoop) tensile stress in the wheel rim (in the cross-sectional plane located 45° from the 0° plane at which the excitation is applied as identified in Fig. 5.2) resulting from the heat-treatment analysis (paragraph 6.2) • The maximum circumferential (hoop) tensile stress in the wheel rim (in the cross-sectional plane located 45° from the 0° plane at which the excitation is applied as identified in Fig. 5.2) that occurs during the forced vibration analysis (paragraph 8.3)

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Fig. 8.2 Arrow indicates typical location of maximum residual circumferential (hoop) tensile stress in wheel rim following simulated heat treatment. This is referred to as cross-sectional “Location X” in Table 8.2 (legend omitted)

Table 8.2 Reporting format for stresses due to heat treatment and forced vibration (ksi)

Load Case

Maximum Rim Circumferential (Hoop) Tensile Stress Following Simulated Heat Treatment at Location X (see Fig. 8.2 )

Circumferential (Hoop) Stress Due to Forced Vibration at Location X

Maximum Rim Circumferential (Hoop) Tensile Stress Due to Forced Vibration

H1

H2

H3

9.0 RESPONSIBILITY 9.1 Deviations

Once an analytical procedure has been qualified, it shall be the responsibility of the vendor to inform the AAR if he deviated from the conditions for which he is qualified. The vendor must demonstrate that the new code still qualifies. 9.2 Auditing

In auditing the analysis done by vendors, the AAR may, at its discretion, require any vendor to rerun the standard solution in its entirety or in part. Failure on the part of the vendor to comply shall be grounds for disqualification.

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10.0 MATERIAL PROPERTIES

Material properties are specified so that the results of various computational techniques may be compared. 10.1 Material Properties (Constants) for Heat-Treatment Simulation

Initial temperature (after residual stress calculation): 75 °F Ambient temperature for cool-down portion of residual stress analysis: 75 °F Mass density: 0.283 lbm/in.3 Convection coefficient (wheel to air): H = 9.6450 ×10 -6 BTU/sec-in.2-°F (assume constant) or H = 5.0 BTU/hr-ft2-°F (assume constant) Convection coefficient (wheel to water) [7]: H = 1.0417 ×10 -3 BTU/ sec-in.2-°F (assume constant) or H = 540.0 BTU/hr-ft2-°F (assume constant) Stefan-Boltzmann constant: 3.30632716e-15 BTU/sec-in. 2-R4 Emissivity: 0.80 View factor: 1.0

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10.2 Material Properties (Temperature-Dependent) for Heat-Treatment Simulation Table 10.1 Specific heat [8]

Table 10.2 Thermal conductivity [7]

Temp (°F)

(BTU/lbm-°F)

Temp (°F)

(BTU/sec-in-°F)

0

0.1059

0

0.000672

75

0.1106

75

0.000664

1292

0.1866

392

0.000629

1337

0.4079

1292

0.000403

1382

0.1487

1472

0.000329

1652

0.1309

1800

0.000361

1800

0.1309

10.3 Material Properties (Temperature-Dependent) for Stress Calculations Table 10.3 Modulus of elasticity (E) and hardening modulus (Etan) Temp (°F)

E (kips/in.2)

Etan [9, 10, 11, 12]a/ (kips/in.2)

0

29368

2016

75

29000

2192

100

28955

2250

200

28543

2484

300

28130

2719

400

27718

2953

500

27306

3187

600

26859

3028

700

26407

2804

800

25741

2514

900

24784

2151

1000

23553

1790

1100

20542

1431

1200

17531

1071

1300

14424

726

1400

11698

557

1500

9952

424

1600

9114

384

1700

8577

343

1800

7390

303

a/

Table 10.4 Poisson's ratio [ 9, 11, 13] Temp (°F)

ν

0

0.2820

75

0.2836

514

0.2927

752

0.2980

932

0.3020

1292

0.3200

1472

0.3400

1800

0.3461

Table 10.5 Coefficient of thermal expansion [8]

Temp (°F)

Thermal Expansion Coefficient per °F

0

6.22E-06

75

6.22E-06

212

6.22E-06

400

8.58E-06

1292

8.58E-06

1472

9.61E-06

1800

9.61E-06

Temperature-dependent values for hardening modulus have been interpolated such that they are presented for the same temperatures as the modulus of elasticity.

G [S-669] 140

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S-669

Table 10.6 Yield strength

03/2011

Table 10.7 Creep strain rate [7]

σy

Temp (°F)

(kips/in.2)

0

80.00

75

80.00

100

79.94

200

79.69

300

79.44

400

79.20

500

78.95

600

77.71

700

76.32

800

67.77

900

54.91

1000

41.95

1100

32.77

1200

23.59

1300

14.63

1400

10.50

1500

8.94

1600

7.79

1700

6.63

1800

5.48

&

ε

– 08

= 4.6410

– 53712 -----------------T + 460

12.5 ( σ ef f ) e

in which

&

ε

=

the creep strain rate (1/°F)

σeff

= von Mises effective stress (ksi)

T

=

G [S-669] 141

temperature (°F)


S-669

11.0 REFERENCES

1. Sines, G. 1955. Failure of Materials Under Combined Repeated Stresses with Superimposed Static Stresses. NACA Technical Note 3495. 2. Sines, G. 1969. Elasticity and Strength. Needham Heights:Allyn and Bacon. 3. Sines, G., and J.L. Waisman, eds. 1959. Metal Fatigue. London:McGraw-Hill. 4. Stephens, R.I., A. Fatemi, R.R. Stephens, and H.O. Fuchs. 1980. Metal Fatigue in Engineering, Hoboken:Wiley and Sons. 5. McKeigan, P.C., F.J. McMaster, and J.E. Gordon. 2002. Fatigue Performance of AAR Grade B Wheel Steel at Ambient and Elevated Temperatures. ASME Paper IMECE2002-33240. 6. McMaster, F. J., G.P. Robledo. and J.E. Gordon. 2005. Fatigue Performance of AAR Grade A Wheel Steel at Ambient and Elevated Temperatures. ASME Paper IMECE2005-82519. 7. Kuhlman, C., H. Sehitoglu, and M. Gallagher. 1988. The Significance of Material Properties on Stresses Developed During Quenching of Railroad Wheels. Proceedings of the 1988 Joint ASME IEEE Railroad Conference. 8. Metals Handbook. 1948. Vol. 1, 9th edition. Cleveland:American Society for Metals. 9. Slavik, D., and H. Sehitoglu. 1986. Constitutive Models Suitable for Thermal Loading. ASME J. Eng. Mats. Techn. 108:108-312. 10. Lunden, R. 1991. Contact Region Fatigue of Railway Wheels Under Combined Mechanical Rolling Pressure and Thermal Brake Loading. Wear. 144:57-70. 11. Orringer, O., D.E. Gray, and R.J. McCown. 1993. Evaluation of Immediate Actions Taken with Cracking Problems Observed in Wheels of Rail Commuter Cars. DOT-VNTSC-FRA. 93:3. 12. Berg, N. A., and R. Alber. 1972. Tread Braking Versus the Wheel. Proceedings of the 64th Annual Convention of the Air Brake Association . 13. Metals Handbook. 1948. Vol. 1, 10th edition. Cleveland:American Society for Metals.

G [S-669] 142

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03/2011

RP-608

GAUGE, WHEEL—REFERENCE MASTER DISK FOR VERIFYING WHEEL CIRCUMFERENCE GAUGES S-612 AND S-613 Recommended Practice RP-608 Adopted: 1937; Last Revised: 2004  

   



    

 

        

     



 

                 

   

      

 



 

    

 

 

    

 

                              

  

 

   

         

                

  

             



             

   

  

                 

             

MATERIAL: ASTM A-47 Grades 32510 or 35018 03/2011

         

G [RP-608] 143

                                   


RP-608


G [RP-608] 144

03/2011

03/2011

RP-609


INSPECTION STAND FOR USE WITH MASTER DISKS Recommended Practice RP-609 Adopted: 1937; Last Revised: 2004

MATERIAL: COLD ROLLED STEEL, CAST IRON

03/2011

G [RP-609] 145


RP-609


G [RP-609] 146

03/2011

03/2011

RP-612


MOUNTING PRESSURES FOR WROUGHT AND CAST STEEL WHEELS ON GEAR-DRIVEN AND IDLER AXLES OF LOCOMOTIVES OTHER THAN STEAM Recommended Practice RP-612 Adopted: 1951; Last Revised: 2004 Diameter of Wheel Seat (in.)

Minimum

Desired Mounting Pressure (ton)

Maximum

6.000 to 6.346, inclusive

75

80

95


75

85

100


75

90

110


75

95

115


80

100

120


85

105

125


90

110

130


90

115

140


95

120

145


100

125

150


105

130

155


110

135

160


110

140

170


115

145

175


120

150

180


125

155

185


130

160

190


130

165

200


135

170

205


140

175

210


145

180

215

Desired mounting pressures are based on 13 ton/in. of diameter, expressed in the nearest 5 ton with an allowable variation of 20% over and under, except the first three minimum pressures, which are shown as 75 ton, being considered better practice for these sizes.

03/2011

G [RP-612] 147


RP-612


G [RP-612] 148

03/2011

03/2011

RP-613


GAUGE, AXLE—MASTER GAUGE FOR VERIFYING AXLE JOURNAL AND FILLET GAUGE S-614 Recommended Practice RP-613 Adopted: 1937; Last Revised: 2004 1.0 SCOPE This master gauge applies to Gauge No. 34401, described in the AAR Manual of Standards and Recommended Practices , S-614.

MATERIAL: ASTM A-576, Grade 1020

03/2011

G [RP-613] 149


RP-613


G [RP-613] 150

03/2011


03/2011

RP-614

GAUGE, WHEEL—MASTER GAUGE FOR VERIFYING WHEEL GAUGES S-617 AND S-618 Recommended Practice RP-614 Adopted: 1937; Last Revised: 2004 1.0 SCOPE This master gauge applies to the steel wheel gauges described in the AAR Manual of Standards and Recommended Practices , Standards S-617 and S-618.

MARK: MASTER FOR WHEEL GAUGE (3/32-in. STAMPS) MATERIAL: ASTM A-576, Grade 1020 FINISH: CHROMIUM PLATE

03/2011

G [RP-614] 151


RP-614


G [RP-614] 152

03/2011

03/2011

RP-615


GAUGE, WHEEL—SIMPLIFIED Recommended Practice RP-615 Adopted: 1975; Last Revised: 2004 1.0 SCOPE 1.1 This gauge can be used for checking high-flange, thin-rim, and grooved tread for all freight car wheels. 1.2 This recommended practice became effective October 1, 1976.

     

MATERIAL: .093-in. STAINLESS STEEL. UNLESS OTHERWISE STATED. ALL TOLERANCES ARE ±.010 in. REMOVE BURRS AND SHARP EDGES.

03/2011

G [RP-615] 153


RP-615


G [RP-615] 154

03/2011

03/2011

RP-619


REFERENCE GROOVE FOR MULTIPLE-WEAR DIESEL WHEELS Recommended Practice RP-619 Adopted: 1970; Last Revised: 2004

NOTE: THIS REFERENCE GROOVE IS OPTIONAL AND IS MACHINED AT THE REQUEST OF THE CUSTOMER UNLESS SPECIFIED AS REQUIRED.

DESIGN

“D” (in.)a/

CH 33

29

H 33

29

CA 34

30

A 34

30

CF 36

32

F 36

32

CA 38

34

A 38

34

CE 40

36

E 40

36

CA 42

38

A 42

38

CC 42

38

C 42

38

a/ TOLERANCE = 1/32 IN.

03/2011

G [RP-619] 155


RP-619


G [RP-619] 156

03/2011

03/2011

RP-622


AXLE, WEIGHT—MACHINED FINISH, RAISED WHEEL SEAT Recommended Practice RP-622 Adopted: 1966; Last Revised: 2007 Nominal Weight (lb) Classification of Axles

Roller Bearing

03/2011

Size of Journal (in.)

Rough-Turned Journal and Wheel Seats Freight Car

Passenger Car

D

5 1/2 × 10

810

840

E

6 × 11

975

1005

F

6 1/2 × 12

1175

1220

G

7 × 12

1415

—

K

6 1/2 × 9

1168

—

L

6×8

900

—

M

7×9

1325

—

G [RP-622] 157


RP-622


G [RP-622] 158

03/2011

03/2011

RP-629


GAUGE, WHEEL—FOR MEASURING CONDEMNABLE OVERHEATED WHEELS Recommended Practice RP-629 Adopted: 1980; Last Revised: 2004 Note: See RP-630 for application.

MATERIAL: 16 GAUGE BLACK STEEL

03/2011

G [RP-629] 159


RP-629


G [RP-629] 160

03/2011

03/2011

RP-630


GAUGE, WHEEL—APPLICATION FOR MEASURING CONDEMNABLE OVERHEATED WHEELS Recommended Practice RP-630 Adopted: 1980; Last Revised: 2004 Note: See RP-629 for gauge drawing.

 

03/2011

G [RP-630] 161


RP-630


G [RP-630] 162

03/2011

03/2011

RP-636


GAUGE, WHEEL—APPLICATION DRAWING FOR AAR 1B WHEEL GAUGES S-662 AND S-667 Recommended Practice RP-636 Adopted: 1991 1.0 SCOPE This recommended practice can be used when checking with the following gauges: S-667 (wide flange) and S-662 (narrow flange).

 

 

 

 

 

03/2011

G [RP-636] 163


RP-636


G [RP-636] 164

03/2011

03/2011

RP-637


GAUGE, WHEEL—APPLICATION DRAWING FOR AAR 1B WHEEL GAUGES S-661 AND S-665 Recommended Practice RP-637 Adopted: 1991 1.0 SCOPE This recommended practice can be used when checking with the following gauges: S-665 (wide flange) and S-661 (narrow flange).

 

 

 

 

 

03/2011

G [RP-637] 165


RP-637


G [RP-637] 166

03/2011

03/2011

RP-638


GAUGE, WHEEL—APPLICATION DRAWING FOR REFERENCE GAUGE TO VERIFY WHEEL GAUGES S-661, S-662, S-663, S-664, S-665, S-666, S-667, AND S-668 Recommended Practice RP-638 Adopted: 1991 1.0 SCOPE This recommended practice can be used when checking with the following gauges:

Maximum Flange Thickness, Height and Throat Radii Gauges: Maximum Limit Wear Gauges: Minimum Flange Thickness, Height and Throat Radii Gauges: Minimum Limit Wear Gauges:

 

 

 

03/2011

S-665 and S-661 S-663 and S-666 S-667 and S-662 S-664 and S-668

 

G [RP-638] 167

AAR M-101

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