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Engineering Failure Analysis 44 (2014) 285–298

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Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal

Analysis of fatigue failure on the keyway of the reduction gear input shaft connecting a diesel engine caused by torsional vibration Hyung-Suk Han ⇑ Naval System Research Team, Busan Center, Defense Agency for Technology and Quality, 525-2, Gwangan 1 dong, Busan, Republic of Korea

a r t i c l e

i n f o

Article history: Received 26 November 2013 Received in revised form 14 May 2014 Accepted 20 May 2014 Available online 2 June 2014 Keywords: Torsional vibration Lateral vibration Fatigue Propulsion shaft

a b s t r a c t The vibratory torque of a diesel engine caused by the reciprocating motion of the mass and gas pressure force of a cylinder is one of the main causes of the failure of the driving shaft of the diesel engine and the connecting shaft to the reduction gear. Because high cycle torsional fatigue can occur in the reduction gear shaft connecting the engine under vibratory torsional stress, the US Navy restricts it under the MIL G 17859D(SH) standard and suggests a procedure for evaluating the safety of the shaft for the reduction gear. In this study, the structural safety of the reduction gear input shaft in which fatigue failure occurs in typical naval vessels is investigated in accordance with the VDI 3822 RCA (root cause analysis) procedure based on the MIL G 17859D(SH) standard. When evaluating the safety factor in accordance with the MIL G 17859D(SH) standard, the alternating bending moment from the lateral vibration and the stress concentration factor under static load are considered. In addition, an improved design is suggested by CAE to satisfy the safety factor suggested by the MIL G 17859D(SH) standard. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Recently, shipbuilders have been manufacturing many types of ships. These ships usually adopt a diesel engine for their propulsion system. Since a diesel engine is operated by the force of the cylinder from the explosion of the gas, the torsional vibration from the fluctuation torque is bigger than that of other types of engines, such as gas-turbine and electrical propulsion motors. Therefore, the propulsion shafts in ships frequently fail due to the extreme torsional vibration from diesel engines. The engines of naval vessels that require more power and revolution speed usually adopt V type, 4 stroke diesel engines and reduction gears in order to increase the output torque. Therefore, the healthy design of shafts is strongly required for naval vessels. Engine shaft failures usually occur at stress concentration areas such as the fillet and chamfer under a dynamic load. Peterson [1] suggested the stress concentration factor for various mechanical designs such as a hole, flange, and keyway, and their study serves as the most commonly used reference for stress concentration factors. The stress concentration factor at the end of the keyway dominantly affects the life of the shaft when torque is transmitted through the key. Okubo [2] suggested the stress concentration factor in keyways of the shaft from experiments with fine-grained carbon steel. Pedersen [3] ⇑ Address: Defense Agency of Technology and Quality, 525-2, Gwangan 1-dong, Suyeong-gu, Busan 613-808, Republic of Korea. Tel.: +82 51 750 2533; fax: +82 51 758 3992. E-mail address: [email protected] http://dx.doi.org/10.1016/j.engfailanal.2014.05.012 1350-6307/Ó 2014 Elsevier Ltd. All rights reserved.

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H.-S. Han / Engineering Failure Analysis 44 (2014) 285–298

suggested a new design for a keyway modeled as a hyperbola, which could reduce the stress concentration factor compared to the standard design as per DIN 6885 [4]. Fracture analysis reports of a shaft with a keyway have been published in many journals. Goksenli and Eryurek [5] studied the fatigue fracture of the drive shaft of an elevator with a keyway. He estimated the safety factor of the driving shaft using the Goodman method and concluded that fracture was caused by torsional–bending fatigue through the evaluation of the microstructural, mechanical, and chemical properties of the driving shaft. Bhaumik et al. [6] reported cracks in the hollow shaft of a single-stage helical gear box. Subsequent investigations revealed that the crack initiated by fatigue at one of the keyway edges and propagated in a helical manner. He suggested possible root causes as fault machining, inadequate radius at the keyway run out radius, and elongated MnS inclusion. Parida et al. [7] reported the root cause of the torsional fatigue failure of a coal pulverizer mill shaft. Through mechanical and chemical analysis, it was found that the initiation and growth of cracks were facilitated by low-toughness brittle microstructures resulting from improper heat treatment. In this research, the root cause analysis (RCA) of the failure of the reduction gear input shaft connecting to a diesel engine is described in accordance with the VDI 3822 [8] RCA procedure, as shown in Fig. 1, considering the torsional vibration of a diesel engine as well as the bending moment from the input shaft, which comes from the weight of the shaft and the lateral vibration of the connecting engine.

2. Failure description and record of the history Pictures of the failure of the shaft in this research are shown in Fig. 2. As illustrated, the crack of the shaft was developed from the keyway in a 45-degree direction with a cup and corn shape as shown in Fig. 2(a)–(c). In Fig. 2(c), it can be found that the crack initiated at the end of the keyway and propagated to the rotational direction with 45 degree helical manner. It is a representative pattern of torsional fatigue. SEM pictures on the fracture surface at the crack initiating and propagation zone are also shown in Fig. 2(d). Upon SEM analysis of the failure surface, the initial crack appears to have occurred at the end of the keyway and developed toward the center of the shaft with the sequence of beach marks having spiral shape striation. Therefore, it can be concluded that this failure occurred by torsional fatigue based on the records referred to above, and the RCA is performed to address the hypotheses in the next chapter.

Description of the failure Document of the failure mode Survey of special characteristics of the design, material or processing

Record of failure history Failure case history View of entire system Survey of the nominal state Operation and environmental conditions Specific chronological and/or local conditions Frequency periodicity Change in the material

Failure hypothesis (hypotheses) Guide of the analysis Assessment of verification cost (time and money)

Instrumental analysis Investigation plan Sample collection Test and analysis Simulation and reconstruction trials

Investigation results Nominal/actual comparison Iteration loop (if needed)

Cause(s) of failure Primary and secondary failure influences (when given)

Failure collection Actual and preventive measures

Report Knowledge management

Fig. 1. Performance of a failure analysis.

287


45 ° Initiation of crack

(b) view at the keyway side

(a) crack propagation

Crack initiation zone

45 ° line

Final rupture

(c) fracture surface at the flange side

SEM on the initial crack position

SEM on the crack propagation zone Beach Mark

Crack initiation point

Crack initiation

Fatigue striation

(d) SEM of the initial crack and crack propagationzone Fig. 2. Failure pattern of the reduction gear input shaft connecting to the diesel engine.

3. Failure hypotheses As referred in the previous chapter, failure hypotheses for the shaft failure are as follows: (a) The failure occurred from torsional fatigue due to the bad material and production error. (b) The initial crack occurred when the shaft was manufactured before installing it in the ship and developed during the ship’s operation period.

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(c) The shaft does not have sufficient safety factors to endure the force induced by the torsional and lateral vibration of the engine. Based on these hypotheses, an RCA logical tree can be drawn, as shown in Fig. 3 and RCA can be performed. The instrumental analysis for each item in Fig. 3 is described in the next chapter. 4. Instrumental analysis and investigation When the thermal stress and corrosion in Fig. 3 was investigated, there was no special problem. Therefore, the instrumental analysis about the mechanical stress including the mechanical and material properties is performed and described in this chapter. 4.1. Material and mechanical properties In this research, the material of the reduction gear input shaft connecting to the diesel engine is 826M40 (Nickel Chromium Molybdenum Steel) hardened and tempered according to BS970. Tables 1 and 2 depict the analysis results of the material and mechanical properties. As shown in these tables, the material and mechanical properties of the reduction gear input shaft are satisfied with required specification. Therefore, hypothesis 1 is not the main root cause for the shaft failure based on the instrumental analysis as above.

Fig. 3. RCA logical tree.

Table 1 Material analysis result (unit: wt%). Contents

Specification

Inspected value

C Si Mn Ni Cr S P

0.36–0.44 0.10–0.35 0.45–0.70 2.30–2.80 0.50–0.80 Max. 0.025 Max. 0.025

0.39 0.26 0.59 2.38 0.58 0.002 0.015

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H.-S. Han / Engineering Failure Analysis 44 (2014) 285–298 Table 2 Mechanical analysis result. Item

Specification

Inspected value

Yield strength Ultimate strength Elongation Hardness

740 MPa min 925–1075 MPa 15% min 269–331 HB

847 MPa 981 MPa 18% 282–296 HB

Fc(coupling weight), Fv(force from lateral vibration) Keyway p(weight per unit length)

Fig. 4. Assumption of the simply supported beam of the reduction gear input shaft.

Fig. 5. Test setup of the lateral vibration of the diesel engine.

When microscopic and macroscopic analyses were performed for the failure surface, the initial crack could not be found. In addition, when investigating the inspection data about the shaft for the delivery conditions, such as liquid penetrant testing (PT) and magnetic particle testing (MT), there was no record for the initial crack. Therefore, hypothesis 2 also is not the main root cause for the shaft failure based on the recording of the shaft at the delivery condition.

290


(a) Vibration displacement 0.0020

acc1-x acc1-y acc1-z acc2-x acc2-y acc2-z acc3-x acc3-y acc3-z

0.0018

Displacement [m]

0.0016 0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000

10

100

Frequency [Hz]

(b) Vibration displacement (Ship 1) 0.0020

acc1-x acc1-y acc1-z acc2-x acc2-y acc2-z acc3-x acc3-y acc3-z

0.0018

Displacement [m]

0.0016 0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 0.0002 0.0000

10

100

Frequency [Hz]

(c) Vibration displacement (Ship 2) Fig. 6. Lateral vibration level of the diesel engine.

4.2. Mechanical stress analysis 4.2.1. Applied load The definition of the applied load is necessary to analyze the mechanical stress of the shaft. In this research, the applied load is defined considering the mean and alternating diesel engine torque as well as the bending moment that comes from the lateral vibration and weight of the shaft. Assuming that the reduction gear input shaft is simply a supported beam, as shown in Fig. 4, the bending moment from the weight of the shaft, including the coupling weight, can be determined.


291

The bending moment of the shaft from the engine vibration can be estimated with the measured vibration of the engine according to ISO 10816-6 [10], as shown in Fig. 5. In Fig. 5, the engine vibration was measured with three axis accelerometers (PCB Type 356A02) and a data acquisition system (B&K Type 3560B). Fig. 6 is the measured vibration for two ships that used the same diesel engine and reduction gear described in this research. In Fig. 6, the vibration levels of these two ships are quite different. When analyzing the spectra of vibrations for these ships, it can be found that the difference comes from the vibration of the engine and mounting system whose frequency range is 2–10 Hz. This vibration comes from the movement of the engine supported by an elastic mount and should be dependent on the sea and ship operating conditions. In this research, the vibration level of ship 1 is adopted for the conservative analysis. The bending moment from the lateral vibration of the engine can be calculated based on the stiffness of the flexible coupling in the lateral direction and its vibration displacement, as shown in Fig. 7. Here, the vibration displacement can be calculated based on the double integral with the measured acceleration. In Fig. 7, the bending moment considering only the weight of the shaft and coupling is shown, and the bending moment considering the lateral vibration of the engine is much bigger than that considering the weight of the shaft and coupling. The torque of the diesel engine can be classified as the mean torque and alternating torque. The mean torque can be calculated with Eq. (1), and Fig. 8(a) is the calculated mean torque from Eq. (1) for the revolution speed range of the diesel engine in this research.

QT ¼

60 W x 2 K 1000 N m 2p xmax xmax

ð1Þ

Here, QT is the mean torque, W is the output power (kW), xmax is the maximum revolution speed (rpm), x is the revolution speed, and K is the safety factor (=1.1). The alternating torque was calculated with measured alternating angular velocity with a laser velocity meter and the torque per unit alternating angular velocity from TV calculation of the diesel engine suggested by its supplier as shown in Fig. 8(b). Fig. 8(c) shows the measured alternating torque at each rpm step. In Fig. 8(c), the revolution speed is 1148 rpm, at which the alternating torque is at the maximum level (8.81 kN m). Through Figs. 7 and 8, the load applied on the reduction gear shaft can be defined, and the stress analysis is performed employing the theory and CAE described in the next chapter. 4.2.2. Stress calculation procedure In this research, the stress analysis is performed in accordance with MIL G 17859D, Appendix D [9]. The resultant steady stress (Sr) can be written as given in Eqs. (2) and (3) based on the maximum shear stress theory.

Sr ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S2c þ ð2Ss Þ2

ð2Þ 4

Sc ¼ 0; Ss ¼

QTd pd ; J¼ 2J 32

ð3Þ

Here, Sc is the steady compressive stress, Ss is the steady shear stress, and d is the shaft diameter Eq. (4) [1] is the effective stress concentration factor.

K f ¼ 1 þ qðK t 1Þ

ð4Þ

Fig. 7. Bending moment of the diesel engine.

292


(a) Mean torque

(b) Test setup for alternating torque measurement

(c) Alternating torque Fig. 8. Torque of the diesel engine as revolution speed.

Here, Kf is the effective stress concentration factor, Kt is the ideal stress concentration factor, and q is the notch sensitivity index.In Eq. (4), the notch factor under the dynamic load is almost 1.0. However, the notch factor of the ductile metal under the static load is 0 due to the hardening from the local plastic deformation. Therefore, it is 0 in MIL G 17859D when calculating the resultant steady stress. However, the notch factor of a ductile metal may be able to increase under the condition that inhibits plastic slip. For the impact load, the notch factor is recommended to have a value between 0.4 and 0.6 for ductile metals and 1.0 for brittle materials. The notch factor of the brittle material for which the elongation ratio is under 5% under a static load is usually 0.15–0.25. The stress concentration factor of the keyway, as shown in Fig. 9, is given in Eqs. (5) and (6) for the bending moment and torsion, respectively.

2 0:1 0:1 0:0019 K t;B ¼ 1:426 þ 0:1643 ; r=d r=d

0:005 6 r=d 6 0:04; d 6 165:1 mm

ð5Þ


293

Fig. 9. Shaft with keyway.

2 0:1 0:1 0:0021 ¼ 1:953 þ 0:1434 ; r=d r=d

K t;T

0:005 6 r=d 6 0:07

ð6Þ

Here, Kt,B is the ideal stress concentration factor for the bending moment, Kt,T is the ideal stress concentration factor for the torsion, r is the fillet radius, and d is the shaft diameter.The notch factor under the alternating load can be represented as given in Eqs. (7) and (8) [1].

q¼

1 ; 1 þ a=r

q¼

1 ; 1 þ 0:6a=r

for bending & axial loading

for torsional loading

ð7Þ

ð8Þ

Here, a is the material constant; quenched and tempered steel is 0.0025, annealed and normalized steel is 0.01, and aluminum alloys is 0.025. Considering above stress concentration factor, the resultant alternating stress can be written as given in Eqs. (9)–(11).

Sar ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi K f ;B S2b þ ð2K f ;T Sas Þ2

ð9Þ

3

Sb ¼

Mb pd ;Z ¼ Z 32

ð10Þ

Sas ¼

Ta Sr T max

ð11Þ

Here, Sar is the resultant alternating stress, Sb is the alternating bending stress, Sas is the alternating torsional shear stress, Kf,B is the effective stress concentration factor for the bending moment. Kf,T is the effective stress concentration factor for the torsion, Mb is the bending moment from the weight of the shaft and the lateral vibration of the engine, and Ta, Tmax are the alternating and maximum torque of the engine, respectively. 4.2.3. Stress calculation by MIL G 17859D The yield strength of the shaft in this research is 847 MPa as shown in Table 2 in the previous chapter, and the fatigue limit can be calculated to 304 MPa, which is 0.5 times the ultimate strength of applying an additional modification factor (k = 0.62) as given in Eqs. (12)–(16) [11]. 0

Se ¼ kSe ¼ ka kb kc kd ke kf S0e

ð12Þ

ka ¼ aSbut

ð13Þ 0:107

2:79 < d < 51 mm

0:157

51 < d < 254 mm

kb ¼ 1:24d

¼ 1:51d

kc ¼ 1:0ðBendingÞ; 0:85ðAxialÞ; 0:59ðTorsionalÞ

ð14Þ ð15Þ

294


kd ¼ 0:975 þ 0:432ð103 ÞT F 0:115ð105 ÞT 2F þ 0:104ð108 ÞT 3F 0:595ð1012 ÞT 4F

ð16Þ

Here, ka is the surface condition modification factor (a = 1.58, b = 0.086 for grounded steel), kb is the size modification factor, kc is the load modification factor (=1.0 when using the effective von Misses stress), kd is the temperature modification factor (=1.0 in this research), ke is the reliability factor (=1.0 in this research), kf is miscellaneous-effects modification factor (=1.0 in this research), Se0 is the rotary beam test specimen endurance limit and Se is the endurance limit at the critical location of a machine part in the geometry and condition of use. Through these stress values, the Soderberg plot can be drawn, as shown in Fig. 10, for the straight and zigzag maneuver conditions of a ship at the keyway end of the reduction gear input shaft. In Fig. 10, the safety analysis is performed when the notch factor for calculating resultant static stress is 0 and 0.15, respectively, related to the maneuver conditions. The stress concentration factor is considered in the static load condition because the shaft is high-strength steel and the maximum stress is under yield stress at the keyway. Fig. 10(a) shows that the safety factor is not satisfied with the limit value of MIL G 17859D(1.75) under some operating conditions when notch factor is 0. In Fig. 10(b), the safety factor is initially reduced when the notch factor is 0.15. In

(a) q s =0

(b) q s =0.15

(c) Safety factor as RPM Fig. 10. Soderberg plot and safety factor of the reduction gear input shaft.


295

Fig. 10(c), the minimum safety factor is 1.36 and 1.21 at 1130 rpm when the notch factor is 0 and 0.15, respectively, in the zigzag maneuver condition. The Soderberg plot indicates that the safety factor is not sufficiently related to MIL G 17859D and high-cycle fatigue can occur since the safety factor can be additionally reduced according to the ship operating conditions and sea state. 4.2.4. Stress calculations using CAE In this chapter, stress analysis is performed with CAE. MSC.Patran/Nastran is used for CAE in this research. The CAE is performed with two cases in which the assumptions of the boundary condition are different. The boundary condition of the 1st case is that the torque is applied at the end of the input shaft and the opposite end (coupling assembling flange) is constrained. The boundary condition of the 2nd case is that the end of the flange is constrained and the torque is input to the keyway surface. (1) Case 1 The FEM model is shown in Fig. 11(a). The input torque is 37,703 N m at 1148 rpm of the engine. Fig. 11(b) shows the resultant stress from CAE, in which the maximum stress occurs at the fillet edge of the keyway. Through the maximum shear stress theory, it can be found that the resultant stress is 325 MPa and the alternating stress is 75.9 MPa when the alternating torque is 8810 N m. The analysis of case 1 shows that the safety factor can be calculated to 1.58 based on the Soderberg safety equation at 1148 rpm, where the torsional vibration has a maximum value. (2) Case 2 The FEM model is shown in Fig. 12(a), in which the maximum stress occurs at the end of the keyway similar to the real fracture. The resultant static stress is 416 MPa, and the resultant alternating stress is 97.2 MPa when the alternating torque is 8801 N m.

(a) FEM model

Max. Stress Position

(b) Max. stress on the keyway: 325Mpa Fig. 11. Result of linear static analysis for case 1.

296


The analysis of case 2 indicates that the safety factor can be calculated to 1.23 based on the Soderberg safety equation at 1148 rpm, where the torsional vibration has a maximum value. Upon investigating the FEM results, the safety factor from case 2 appears to be 1.28 times lower than that from case 1, and the safety factor from all cases cannot satisfied with the limit of MIL-G-17859D, which should be over 1.75. In CAE, the stress concentration factor can be estimated by comparing the maximum stress of the shaft with a keyway to that without a keyway, which is 1.92 for case 1 and 2.31 for case 2. These stress concentration factors were applied to the resultant static stress as well as the alternating stress together, different to the stress concentration factor in MIL G 17859D. Therefore, CAE considers a lower stress concentration factor for an alternating load and a higher one for a static load rather than one factor for both.

5. Investigation results and cause of the failure Through the instrumental analysis referred to in the previous chapter, the safety factor of the reduction gear input shaft does not satisfy the requirements of MIL G 17859D, even though the safety factor from the Soderberg safety equation is over 1.0. Since a shaft can frequently become abnormally loaded over the design level when a ship is sailing, the safety factor should have a sufficient margin to endure under such conditions. Therefore, it can be concluded that the root cause of the shaft failure in this research is the poor design of the shaft with respect to the maximum operating load.

6. Corrective action Through the instrumental analysis about failure of the reduction gear input shaft, the failure seems to be caused by insufficient safety factors at the keyway end of the shaft under mean and alternating torque.

(a) FEM model


(b) Max. stress on the keyway: 416Mpa Fig. 12. Result of linear static analysis for case 2.


r=0.59mm

(a) r=0.59

r=1.0mm

(b) r=1.0


(c) FEM result for r=1.0 (Max. stress on the keyway: 288Mpa) Fig. 13. Increasing the fillet radius on the keyway edge.

(a) d = 130.04

(b) d = 145

(c) FEM result for r=1.0 (Max. stress on the keyway: 240Mpa) Fig. 14. Increasing the diameter of the shaft.

297

298


Methods to increase the safety factor are reducing the torsional vibration level or changing the design of the shaft to be more healthy design. Since reducing an engine’s torsional vibration is more difficult than changing a shaft’s design, the latter is investigated in this research. Design changes are suggested for two cases, in which the fillet radius on the edge of the keyway is increased and the shaft’s diameter is increased. Fig. 13 shows the design change for the fillet radius on the edge of the keyway. When increasing the fillet radius from 0.59 to 1.0 mm, the stress on the edge of the keyway is reduced from 325 to 288 MPa, and the safety factor increases from 1.58 to 1.78 for the boundary condition of case 1. When increasing the diameter of the shaft from 130.04 to 145.0 mm, as shown in Fig. 14, the maximum stress is reduced from 325 to 240 MPa and the safety factor increases from 1.58 to 2.2 for the boundary condition of case 1. Therefore, increasing the shaft diameter is a more conservative correction action than increasing the fillet radius on the keyway edge in order to protect this failure. 7. Conclusion RCA of the failure of the reduction gear input shaft in a typical naval vessel is investigated according to VDI 3822 in this study. RCA shows that failure appears to be caused by poor design of the shaft’s keyway. The following conclusions are derived from this study. (a) Based on RCA of the failure of the reduction gear input shaft, it is estimated that the shaft cracks owing to torsional fatigue caused by an insufficient safety factor (<1.75), which is suggested in the MIL G 17859D(SH) standard. (b) When the notch factor calculated based on the stress concentration factor for the static load is considered to be 0.15 for the reduction gear input shaft, the safety factor reduces from 1.36 to 1.21 at 1130 rpm. Therefore, it is recommended that the notch factor for static load be considered when the shaft material is high-strength grade steel and that plastic slip does not occur at the maximum stress to evaluate the safety of the shaft more conservatively. (c) Through CAE, the safety factor is evaluated to be 1.58 when the torque is input at the end of the shaft constraining the end of the opposite side of the shaft and 1.23 when the torque is input at the keyway surface constraining both ends of the shaft. (d) Even though the safety factor is over 1.0 for the reduction gear input shaft, the safety factor of the reduction gear input shaft with a keyway is clearly not sufficient to satisfy the limit suggested in the MIL G 17859D(SH) standard, and it may reduce more further the applied load on the shaft is varied according to the sea state and sailing condition of the ship. (e) Through design changes from CAE, it can be estimated that the safety factor increases from 1.58 to 1.78 when the fillet radius is increased from 0.59 to 1.0 mm and from 1.58 to 2.2 when the diameter of the shaft increases from 130.04 to 145 mm for the reduction gear input shaft. Through the corrected actions estimated using CAE, increasing the shaft diameter is a more conservative corrective action than increasing the fillet radius on the keyway edge to prevent high-cycle fatigue and satisfy the limit of the safety factor (>1.75) suggested by the MIL G 17859D(SH) standard.

Acknowledgement This research was performed in the Defense Agency of Technology and Quality, and DTAQ verified that it did not contain any information related to military security. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]

Peterson RE. Stress concentration design factors. New York: John Wiley & Sons Inc.; 1953. Okubo H, Hosono K, Sakaki K. The stress concentration in keyways when torque is transmitted through keys. Exp Mech 1968;8(8):375–8. Pedersen NL. Stress concentration in keyways and optimization of keyway design. J Strain Anal 2010;45:593–604. DIN 6885, 1968, Drive type fastenings without taper action; Parallel keys, keyways, deep pattern (FOREIGN STANDARD). Goksenli A, Eryurek IB. Failure analysis of an elevator drive shaft. Eng Fail Anal 2009;16:1011–9. Bhaumik SK, Rangaraju R, Parameswara MA, Venkataswamy MA, Bhaskaran TA, Krishnan RV. Fatigue failure of a hollow power transmission shaft. Eng Fail Anal 2002;9:457–67. Parida N, Tarafder S, Das SK, Kumar P, Das G, Ranganath VR, et al. Failure analysis of coal pulverizer mill shaft. Eng Fail Anal 2003;10(2003):733–44. VDI-Gesellschaft Material Engineering. VDI 3822 Failure analysis: fundamental and performance of failure analysis; 2011. D.o.D. MIL-G-17859D(SH): Gear Assembly, Production (Naval Shipboard Use); 1993. ISO. IS0 10816-6: Mechanical vibration – Evaluation of machine vibration by measurements on nonrotating parts – Part 6: Reciprocating; 1995. Shigley JE. Shigley’s mechanical engineering design. Tata Macgraw-Hill Education; 2011.

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