ML20091M545

Design Review of Connecting Rods for Tdi DSRV-4 Series Diesel Generators, Final Rept Prepared for Tdi Diesel Generator Owners Group

ML20091M545
Person / Time
Site:	05000000, Shoreham
Issue date:	05/31/1984
From:	FAILURE ANALYSIS ASSOCIATES, INC.
To:
Shared Package
ML20091M472	List: ML20091M520 ML20091M545 ML20091M551
References
FAAA-84-3-14, FAAA-84-3-14-01, FAAA-84-3-14-1, NUDOCS 8406110336
Download: ML20091M545 (60)

Text

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FaAA-84-3-14 PA07396/GKD-03340A(2)

DESIGN REVIEW OF CONNECTING RODS FOR TRANSAMERICA DELAVAL DSRV-4 SERIES DIESEL GENERATORS The -report is final, pending confirmatory reviews required by FaAA's QA operating procedures.

Prepared by Failure Analysis Associates Palo Alto, California Prepared for TDI Diesel Generator Owners Group May 1984 i

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O STATEfENT OF APPLICABILITY This report addresses the structural integrity of connecting rods in the Transamerica Delaval Inc. (TDI) DSRV-16-4, DSRV-20-4, and DSRV-12-4 j ,

V-series engines. The articulated connecting rod design analyzed in this i

report is the same in all TDI R-4 V-series engines. However, the oolting securing the pin joint to the articulated and master connecting rods is dif-ferent in the DSRV-16-4 engines installed in Mississippi Power & Light Com-pany's Grand Gulf Nuclear Station in that the link red box is secured to the master rod by 1 7 /8-inch diameter bolts. Other TDI owners have engines with 1 1/2-inch diameter bolts in this joint. Both versions are evaluated in this report.

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x EXECUTIVE SUMARY The Transamerica Delaval Inc. DSRV-4 articulated connecting rod assem-bly consists of a link rod box containing the pin bearing bolted to the master rod across a lapped serrated joint. The upper pair of bolts nearest the connecting rod bearing has been prone to fatigue failure, and in several instances fatigue cracks have been found in the bolt holes. Two different bolt diameters , 1 7/8-inch and 1 1/2, and two levels of pretorque for both diameters have been employed in service.

The inertial and gas pressure loading has been calculated for the connecting rod assembly and applied to a two dimensional finite element model of the rod box to master rod assembly. The stress range for the 17/8-inch bolt holes is greater than that for the 1 1/2-inch bolt holes by approximate-ly 8%. At the high levels of pretorque, 2600 and 1700 ft-lb, respectively, fracture mechanics calculations show that the stress intensity range at thread roots of 1 7 /8-inch bolt holes is in the range of the lower limit of fatigue crack propagation threshold.

The stress calculations assumed perfect contact along the lapped joint under the specified bolt pretorque. Lack of perfect contact could result in fretting wear, relaxation of bolt preload and increased stress range in the bolts and bolt holes.

In view of the criticality of this assembly, it is recommended that inspections of the bolts and bolt holes be carried out at regular intervals.

Based on the resolution of eddy current inspection, this interval should not exceed 200 hours0.00231 days <br />0.0556 hours <br />3.306878e-4 weeks <br />7.61e-5 months <br /> of operation at full load, 248 hours0.00287 days <br />0.0689 hours <br />4.100529e-4 weeks <br />9.4364e-5 months <br /> at 85% load, or 286 hours0.00331 days <br />0.0794 hours <br />4.728836e-4 weeks <br />1.08823e-4 months <br /> at 75% load. The breakaway torque should also be measured, and the fit between the mating surfaces of the serrated joint should be inspected for signs of fretting wear. In the event of fretting indications or low breakaway bolt torques, the bolts and contact areas require more detailed examination.

An ultrasonic bolt stress measurement device is preferable to measurement of breakaway torque.

11

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(_j - TABLE OF CONTENTS Page STATEMENT OF APPLICABILITY................................................i E X E C U T I V E SUMMA R Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 s

1.0 INTRODUCTION

..................................................... 1-1 1.1 Se rvi ce Expe ri en ce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2 1.2 Observations of Cracked Rod.................................. 1-2 Se ct i o n 1 Re fe re n ce s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 - 3 2.0 CONNECTING R00 EVALUATION......................................... 2-1 2.1 Rod Bow An a ly s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2- 1 2.2 Analysis Of The Lower Connecting Rod Assembly................ 2-2 2.2.1 Fi n i t e El emen t Model i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-3 2.2.2 Loading Conditions.................................... 2-6 2.2.3 Finite Element Stress Analysis Results . . . . . . . . . . . . . . . . 2-7 2.2.4 Fracture Mechanics Analysis of Bolt Holes. ... .. . . .. ... 2-9 2.3 Rod - Ey e Ana l y s i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2- 14

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4 Section 2 References............................................. 2-13

3.0 CONCLUSION

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APPENDIX A: Derivation of Piston Acceleration for Articulated Rod......A-1 APPENDIX B: Comp onent Ta sk Des cri pti ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B-1 4

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1.0 INTRODUCTION

This report addresses the structural integrity of connecting rods in the Transamerica Delaval Inc. (TDI) DSRV-4 16, 20, and 12 cylinder engines used in emergency generator sets in nuclear power stations.

The connecting rods used in the V-series engines are of an articulated design that operates two pistons off each crank throw. The V-series engine connecting rods have been manufactured with either 1 7/8 or 1 1/2-inch dia-meter bolts connecting the link rod box to the master rod. The 1 7/s-inch version is installed in the DSRV-16-4 engines at Grand Gulf Nuclear Station; other owners have engines with 1 1/2-inci. bolts. The master rods have either round or H-shaped shank cross sections.

The function of the connecting rod is to transmit cylinder firing forces from the piston pins to the crankshaft such that the reciprocating forced motion of both pistons is translated into rotation and torque at the crankshaft. The connecting rod must have sufficient column strength and fatigue resistance to withstand repeated cylinder firings and inertial load-ings. Both master and link rods must carry cooling and lubricating oil to pistons and piston pin bearings. Finally, the design of the link-rod-box-to-master-rod joint incorporates mating serrations which must be protected from fretting and local stress concentration effects. The configuration of the V-series engine connecting rod is shown in Figure 1-1.

The bushings of the reciprocating bearings in the connecting rod eyes and the crankpin bearing shells have been evaluated in previous reports [1-1, 1-2]. The key subjects of this report are the rod eye, link pin housing, and connecting rod bearing housings.

i The Component Task Description for the V-series engine connecting rod is contained in Appendix B. The evaluation focuses on those areas for which service experience indicates a significant incidence of failure. This experi-ence is summarized in Section 1.1.

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1.1 Service Experience The survey of industry experience with DSRV-4 connecting rods summar-ized in this section ~ has not been independently confirmed by FaAA and, there-fore, is not subject to FaAA's usual quality assurance procedures.

TDI has supplied information concerning two failure mechanisms that have been experienced in non-nuclear installations.

, The first mechanism is fatigue failure of the link rod bolts resulting from loss of bolt preload. The problem and its solution were addressed by TDI in Service Information Memo No. 349, dated September 18, 1980 [1-3]. Accord-ing to this SIM, engines manufactured between 1972 and February, 1980, may 2

have been shipped with an insufficient locating dowel counterbore depth in the link rod or link pin, resulting in clearance between the link rod and link pin as assembled. - Under firing load, this locating dowel will yield, allowing the above clearance to disappear and resulting in loose link rod bolts. There must be zero clearance under the specified bolt torque of 1050 ft-lb, in spite

$O of SIM 349, 'which recommends checking clearance with a 0.0015-inch feeler gage.

The second mechanism is fatigue cracking of the connecting rod bolts and/or the link rod box in the mating threads. Figure 1-2 shows schematically the location and origin of the crack path.- TDI indicated knowledge of numer-

{ ous instances of bolt or rod fatigue of this nature where low assembly torque values were specified. FaAA examined one crack in a rod which was assembled with a nodified specification of a higher bolt torque, documented in the following section. TDI attributed these rod cracks to " thread fretting".

This " thread fretting" was concluded by TDI to result from distortion of the j rod and bolt under operating loads in the area 'of the mating threads which

! could occur if the bolts had been installed with the originally specified lower preloads. TDI produced results of a static load strain gage test of an assembled connecting rod with 1 7/s-inch diameter bolts that indicated the alternating stresses were reduced 25% by increasing the assembly torque from 2200 ft-lb to . 3200 ft-lb. According to TDI, the effect of this increased preload is to stiffen. the threaded joint by distributing load over more 1-2

(3 1 threads, thus reducing the concentrated stress both in the bolt and the bolt hole. The current torque specification for the 17/8-inch diameter bolts is 2600 ft-lb [1-4].

Later DSRV-16-4 engines have connecting rods with 1 1/2-inch diameter bolts. At the present time only the four DSRV-16-4 engines at Grand Gulf Nuclear Station are reported to have the 17/8-inch diameter design in emer-gency generator sets in nuclear installations. TDI indicated that the design change to the smaller diameter bolts was intended to provide greater section thickness in the link rod box around the bolt threads [1-5]. The specified torque for the 1 1/2-inch diameter bolts is 1700 ft-lb. [1-4].

According to TDI [1-5], there have been no reports of cracked connect-ing rods with either bolt size when the specified torque is applied during assembly. FaAA has been unable to confirm this conclusion to date, since two cracked rods have been found in a marine engine assembled and operated during the time period when the higher specified torque level was apparently in effect. However, recent inspection of all 8 connecting rods for bolt and bolt hole cracking in the 1A engine at Catawba Nuclear Power Station after more than 800 hours0.00926 days <br />0.222 hours <br />0.00132 weeks <br />3.044e-4 months <br /> of operation disclosed no relevant indications.

Another potential problem reportedly encountered with H-section con-necting rod shanks is distortion leading to axial misali gnment . This cond-ition is analyzed in Section 2.1.

1.2 Articulated Connecting Rod Failure A metallurgical failure analysis was performed on a failure which occurred in the link rod box at the lower pair of four bolt holes. This particular articulated connecting rod was removed from a TDI DMRV-12-4 en-gine. The location of the failure is shown in Figure 1-2.

Metallurgical and mechanical tests were performed on material removed from the link rod box. This material, AISI 4140 or AISI 4142, had a yield strength of ~88.5 ksi, ultimate strength of ~115 ksi, and elongation of

( ~20%. The average measured hardness was 20 HRC (230 BHN). The metallurgical 1-3

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microstructure was that of a well-tempered martensitic structure, which is to be anticipated with the measured hardness and strength values.

The failure was the result of progressive fatigue crack growth from a threaded bolt hole. A photograph showing the entire fracture surface is shown in Figure 1-3. Fractography, geometry, and coloration indicate the primary l origin was at the root of a thread. The origin, Site A, is shown in the macrophotograph, Figure 1-4.

A secondary origin, Site B, occurs at a step in the thread flank. This step was probably introduced when the bolt was torqued, or in tia event bolt fracture preceded the cracking in the rod, when the bolt fractured. No record of the condition of the bolt from this hole apon disassembly was available.

The sharp step acted as a stress concentrator which subsequently acted as the crack initiator. Both cracks initiated at stress concentrators that showed evidence of yielding. No evidence of fretting was observed on the thread sur-faces. Greater than 75% of the fracture is attributable to fatigue crack growth.

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'Section I lieferences 1-1 Failure Analysis Associates, " Design Review of Connecting Rods of Transamerica Delaval Inline DSR-48 Emergency Diesel Generators,"

Fa AA-84-3-13, April 1984.

1-2 Failure Analysis Associates, " Design Review of Connecting Rod Bearing Shells for Transamerica Delaval Enterprise Engines," FaAA-84-3-1, March 12, 1984.

l 1-3 Service Information Memo No. 349, Transamerica Delaval Inc., Sept. 18, i 1980.

1-4 TDI Owners Manual, Cleveland Electric Company.

1-5 Maurice Lowrey, Transamerica Delaval Inc., personal communication, May 1984.

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O 2.0 C0lutECTING ROD EVALUATION An analysis was performed (Section 2.1) to determine the degree of centerline bow that can be tolerated by the V-Series engine (RV-4) H-section connecting rod. In Section 2.2, the finite element stress and fracture mechanics analyses of the lower connecting rod assembly are presented. The fatigue resistance of the rod eye is discussed in Section 2.3 2.1 Rod Bow Analysis The connecting rods in the TDI RV-4 Series engines may incorporate either a round machined shank, or an as-forged. H-section shank (see Fig-ure 2-1). Forging practices may have resulted in the manufacture of rods with slightly cr:ved centerlines. The purpose of this analysis is to deter-mine what degree of centerline bow can be tolerated without exceeding the requirements of related components. Specifically, the axial misslignment of the connecting rod bearing resulting from flexure of a bent or bowed connect-ing rod with various degrees of centerline bow is calculated and related to published standards [2-1] to determine the acceptance / rejection criterion for this condition.

The forging practice mentioned above may be that of placing a hot forging on its side (bearing axis vertical) supported only on either end to cool after forming. At forging temperatures the material could sag under its own weight, and the resultant bend could be in the direction which would lead to the greatest bearing misalignment.

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, If misalignment is slight compared to bearing clearance, as it is in this case, axial misalignment is analogous to crankpin taper wherein the amount of taper is equivalent to twice the amount of misalignment. It has been suggested that crankpin taper be limited to 0.0003 inch over the length of a bearing more than 2 inches in diameter to afford optimum bearing life [2-1].

Therefore, this analysis considers an axial misalignment of 0.00015 inch to be the maximum allowable. I O

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Axial misalignnent causes the oil film pressure profile of a journal bearing to shift such that a restoring force is generated [2-2]. The entire oil film pressure profile is skewed, with pressures being higher on the side of the bearing where the oil film thickness is reduced by the tipping of the hearing housing relative to the shaft. A relationship exists between the size of the bearing, its clearance and loading, the degree of misalignment, and the equivalent offset of the reaction forces. In the TDI model RV-4 engine at full load, an axial misalignment of a connecting rod bearing of 0.00015 inch over the length of the bearing will produce an offset in the position of reaction forces of 0.029 inch [2-2]. This offset, then, defines the equi-librium position of a connectir:9 rod at maximum axial misalignment.

For the example of a bowed connecting rod, the offset can further be broken down into two components. The components are, first, that offset which results directly from misalignment or tilting of the connecting rod and, secondly, the further offset that develops as the result of loading a curved beam in compression. The tilting is a simple geometric relationship and accounts for 0.010 inch of the allowable 0.029 inch of offset. Therefore, the balance of 0.019 inch of offset is the maximum allowable transverse motion of the connecting rod-eye with respect to the bearing bore that can be tolerated by the system. Solving for the degree of bow that yields this offset using curved beam equations [2-3] reveals that the TDI model RV-4 engine can toler-ate a centerline bow in an H-section connecting rod of up to 0.47 inch.

2.2 Analysis of the Lower Connecting Rod Assembly A finite element (FE) stress analysis of the lower connecting rod assembly is discussed in this section. This analysis was performed to assess the range of cyclic stresses caused by the cylinder gas pressure plus dynamic loads exerted on the connecting rod. Emphasis was on the region of the four upper bolts (Figure 2-2). A fracture mechanics analysis was subsequently performed based on the FE stress analysis results to assess whether or not the cyclic stresses in connecting rods can cause a fatigue failure.

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A two dimensional FE stress analysis of a V-engine connecting rod was performed.

The model was developed with the interactive mesh generation code, Patran [2-4] and the analysis performed using the MARC [2-5] general purpose finite element code. A plane-stress analysis was performed selecting eight-node isoparametric elements [2-6]. These elements provide quadratic displace-ment fields (linear strain variation within the element) and model the curved edges of the crankpin hole and link pin hole. Figure 2-2 shows the lower connecting rod assembly model and Figure 2-3 shows the finite element mesh.

The mesh consists of 289 elements and 948 nodes. The model includes the lower portion of the master rod and the link rod box assembly. The interface between the master rod and the link rod box, indicated by the serrated line in 1

Figure 2-2, is modeled with gap elements. These elements allow separation of the two sides. However, because of the serrated attachment, it was decided to assume no relative shear displacement could occur. Actually, relative dis-placement across the serrated joint is able to occur between the tangents to the tooth profile at the pitch line, an angle of 45'. The master rod and link rod box are connected with bolts above and below the crankpin as illustrated in Figure 2-2. Bolts below the crankpin extend entirely through the connect-ing rod assembly. Therefore, any prestressing of these bolts will create compressive stresses in the connecting rod itself; on the other hand, tighten-ing of the bolts located above the crankpin would cause tensile stresses near the threads in the link rod box.

The bolts were represented by truss elements, as in Figure 2-4, and bolt prestresses were modeled by applying a thermal strain to the bolt. To account for the reduced stiffness due to the bolt holes, the regions of the 2-D mesh which included the bolts were represented by equivalent material with Young's modulus, E,q, given by the following equation:

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E = the Young's modulus of the connecting rod = 29 x 106 psi D = the diameter of the bolt hole = 1.906 inch (for 17/8-inch bolt) h = the thickness of the connecting rod = 6.941 inch n = the number of bolts through the thickness = 2 This representation is common in situations where it is necessary to

, approximate a three-dimensional geometry by a two-dimensional model. The model developed here thus represents the load in the shank of the bolt from l

the underside of the head to the middle thread by an elastic tension member of the same . axial stiffness as the bolt. Within the width of the elements representing the bolt holes, the longitudinal and transverse stiffnesses of the rod were adequately represented by the reduced equivalent modulus, and no stiffening effect of the bolt was assumed, as is reasonable in view of the radial clearance between the bolt and the bolt hole. In the region of the mating threads, the bore of the hole is to some extent more resistant to distortion because of the ability to transmit stresses across the pitch dia-meter. According to TDI [1-5] this is the primary effect of the increased bolt preload. It is apparently intended that the threads closest to the head of the bolt deform plastically and transmit more contact force to adjacent threads. This effect was bounded in our analysis by first assuming that the mating threads exerted no reinforcing effect and then by representing the i

region of the mating threads as solid metal, i.e., no hole. The effect of these bounding assumptions on the cyclic stress range in the hole surface along the axis of the hole is less than 5%.

In addition to the stresses caused by tightening of the bolts, large cyclic loads are exerted on the connecting rod assembly due to the gas pres-sure in the cylinders and the inertial loads due to the mass of the pistons and the connecting rods.

Inertial loads were determined by lumping masses at the two pistons and the crankpin and determining the acceleration of these points from the kine-matics of the V-engine. The mass lumped at the center of the crankpin has a

, circular motion, causing a centrifugal force egal to:

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Fg = the centrifugal force = 56301 lbs m = mass lumped at the crankpin = 933 lbs (weight) e w = the angular velocity 2n (450) radians / minute R = the radius of the rotation, i.e., the distance between the cen-ters of the crankpin and the crankshaft = 10.5 inch The direction of the centrifugal force is radially outward from the center of the crankshaft to the center of the crankpin. This force was modeled in the finite element analysis by distributed body forces. Appendix A describes the derivation of the acceleration of the pistons for a V-ende with an articulated rod configuration as in the TDI RV-4 diesel engines. A computer program called CONROD was written to implement this analysis and determine the inertiel forces as a function of crank angle. CONROD combines

, the gas pressure and inertial loads on the piston. On the master rod the combined gas pressure and inertial loads are applied at the surface designated by C in Figure 2-2. The force along this face is predominantly axial with a O, small shear component and a moment. The force acting on the lin,k rod due to the gas pressure and inertia is primarily axial since rotary inertia of the link rod is negligible; this load is transferred to the connecting rod assem-bly at the link pin with an oil film pressure distribution, assumed to be a cosine pressure distribution.

The applied forces are balanced by an oil film pressure distribution on

'ie crankpin also approximated by a cosine dist;ibution. Although the reac-tion force at the crankpin is in equilibrium with the applied forces, boundary constraints are needed for the finite element analysis. Therefore, Points A 3

and B, as shown in Figure 2-2 below the crankpin, were constrained in the vertical direction, and Point A was additionally constrained in the horizontal direction. As expected, the reactions at Points A and B were very small.

Geometry. The dimensions of the FE model are based on those given on numerous TDI drawings. Figure 2-5 shows these dimensions. The bolts connec-ting the master rod and link rod box are of either 1 7/8-inch diameter or l /O 1 1 /2-inch diameter.

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Material Properties. The master rod and the link rod box are made from 4142 Steel [2-7] which has the following properties:

Young's Modulus L

• 29,000 ksi Poisson's Ratio v = 0.3 Yield Stress ey = 88.61 ksi J

Ultimate Stress ou = 114.94 ksi t

Materials A and C shown in Figure 2-2 were assigned the above proper-ties. The region of the bolt hole (material 8) was modeled with a reduced equivalent Young's Modulus:

For the 1 7/s-inch diameter bolt:

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The Poisson's ratio was assumed to be unchanged.

2.2.2 Loading Conditions Combined gas pressure and inertial loads, plus bolt prestresses, are exerted on the lower connecting rod assembly. The load conditions analyzed are described next.

Bolt Prestress. The master rod and the link rod box are connected with eithtr 1 7 /8-inch diameter or 1 1/2-inch diameter bolts. The 1 7/e-inch bolts are torqued to 2600 ft-lbs with a corresponding clamping force of 90 kips

[2-8]. The 1 1/2-inch bolts are torqued to 1700 ft-Ibs with a corresponding clamping force of 90 kips. [2-8] This clamping . force was based upon data generated by Crane Co. for threaded fasteners lubricated by graphite and 4

oil. The conventionally calculated preload, e.g., according to Shigley, [2-8]

y 2-6

e

=

would yield 83 kips and 68 kips respectively. The clamping force is modeled by applying a thermal strain - (MT) to the elements representing the bolts.

-The magnitude

• of eT is chosen such that the resulting force in each bolt is 89.754 kips in the 17 /8 inch diameter bolts and 89.781 kips in the 1 1 /2 inch i

bolts.

The gas pressure in the cylinder at full load was Gas Pressure Force.

measured at l' intervals of crank angle from 0* to 720* for the Shoreham diesel engine DG103. This pressure is shown in Figure 2-6. The peak gas pressure in V-engine cylinders was measured at Catawba and Grand Gulf plants to be approximately the same as that of Shoreham's DG103 tested engine.

The force acting on the connecting rod due to the gas pressure is equal to the pressure times the piston area of 227 inch2, Inertial Force. Dynamic loads are generated due to the motion of the mass of the pistons and the connecting rod itself. The derivation of these inertial forces is presented in Appendix A.

Load Conditions Analyzed. Several load cases corresponding to specific

, crank angles are analyzed here to determine the maximum range of cyclic stress that the connecting rod is subjected to at full load. At any crank-angle position the connecting rod will be loaded by a combination of inertial force, gas pressure _ force, and the bearing reaction. The computer program CONROD computes these forces and their directions. Figure 2-7 shows the forces acting on the connecting rod. The magnitude and orientation of these forces change as a function of the crank angle.

J

, Table 2.1 lists the load cases anaylzed, along with the different loads considered for the analysis. The crank angles shown in Table 2.1 are measured from the TDC of the articulated rod during its combustion stroke.

C

• eT is. a negative value.

2-7

+y --y -

smyv g - --w.-y-*--g- ,ew--y,

,w--- , - , ,e---e y-w

. = .

2.2.3 Finite Element Stress Analysis Results Tables 2.2 and 2.3 summarize results of the finite element stress analysis. From the results of the finite element analysis, it was found that:

e Maximum tensile stresses in the area investigated are produced in the link rod box near TDC of the link rod when peak firing pressure occurs, e Maximum stresses occur at the crankpin hole near a line connecting the crankpin center to the link pin center, e Tensile stresses in the connecting rod result from the noncolinear loads exerted at the link pin hole and the reaction on the crankpin hole. This offset in loads pro-duces a bending moment which causes tensile stresses in the link rod box above the crankpin and adjacent to Bolt 1 (Figure 2-2).

e Nominal stresses near the upper bolts are slightly lower than at the crankpin hole; however, because of the presence of the threads, higher stresses occur near the bolts due to stress concentration effect of the threads.

~e Maximum compressive stresses in the ' element adjacent to Bolt 1 occur for Load Case 17 which corresponds to the 185*

crank angle after TDC of the link rod.

e The angle of the bearing pressure distribution along the crankpin hole has a relatively minor influence on the maximum stresses produced near Bolt 1. By reducing the angle of pressure distribution from 120' ' to 60* (i .e. ,

concentrating the reaction force at the crankpin hole), the maximum stress is effectively unchanged.

v .

2-8 1

_i__'.____.._______.______.____m . _ , , , .. _ . . _ _,- . . . . -

o Timing of the peak gas pressure has a small effect on stresses in the link rod box. Maximum principal stress at Bolt Hole No.1 increases from 16.38 ksi to 17.55 ksi when peak pressure occurs 2 after TDC instead of 7* after TDC. For peak pressure occurring 12* after TDC, stresses are reduced to 15.46 ksi at Bolt Hole No.1.

, e For the 1 7/e-inch diamete- bolt design, the maximum range (i' e., double amplitude) of cyclic principal stress at the bolt hole is 9.88 ksi. The direction of this stress is 49.4" to the axis of the bolt hole (see Figure 2-2).

e For the 1 1/2-inch diameter bolt, the maximum range of cyclic stress at the bolt hole is 9.01 ksi. The direction of this stress is 57.8* to the global axis of the bolt hole. This angle agrees well with the direction normal to the fracture surface examined (56*).

e The maximum cyclic stress range occurs at the link pin bearing hole at the minimum ligament between the crankpin hole and link pin hole. The maximum stress range here is 28.36 ksi. There are no stress concentration effects assumed at this location because the oil hole is removed

, sufficiently to produce a negligible effect. Therefore, this ' stress range is less critical than that at the bolt hole.

Figure 2-8 shows the distribution of the stress range for both 17/8-inch bolt. and 11/2-inch bolt configurations in the bolt hole region of 1

Bolt 1. Elements in the bolt hole region are shown in Figure 2-9.

l 2.2.4- Fracture Mechanics Analysis of Bolt Holes In this section, crack initiation at the bolt holes and fatigue crack

, propagation rates are assessed. The cyclic . stress intensity factor, which controls crack growth rate, is based on the maximum cyclic stress range deter-mined from the FE analysis.: The cyclic stress intensity factor is compared 2-9 l j

i

,- . ~ _ . ..

l F gg = 0.60 AKy= 9.88 h (.043) 0.60 = 2.179 ksi/E The effective stress intensity is given by [2-10):

1 AK,ff = (1.5-R)A 1 where R = "i" the ratio of the minimum to maximum stress =

" max For stresses exceeding the flow stress, the R ratio is defined as:

R = II*-A = 101.8 - 9.88 = 0.9 of j g, 101.8 The flow stress is defined as:

O Q

ofjg, , " ultimate + " yield , 114.94 + 88.6 2 2

= 101.8 ksi Hence, for the 1 7/8-inch diameter bolt, the stress intensity factor range is:

AKeff * (1.5 0.9) 2.179

=

5.474 ksi vin.

This effective stress intensity factor range is very close to the threshold of fatigue which ranges from 5.0 to 7.5 ksi (In.

l l

Fatigue Crack Propagation (1 1/2-inch Diameter Bolt) l I

The maximum range of principal stress computed by the FE analysis at the bolt hole is:

.Ao,,x = 9.01 ksi 3

(0 2-11

I l

with the fatigue threshold for the connecting rod material (4142 Steel) [2-7]

'to assess whether o.a not fatigue crack propagation is pes'.'ile.

Fatigue Initiation The bolt prestress creates a large mean stress. Locally, yield or above yield stresses occur near the first few threads. Because of this yield level mean stress near the Bolt Hole No. I threads, fatigue crack initiation is possible in this location. The next section addresses whether fatigue crack propagation is possible by comparing the effective stress intensity

, factor range to the fatigue threshold.

Fatigue Crack Propagation (1 7 /s-inch Diameter Bolt)

The maximum range of principal stress computed by the FE analysis at the bolt hole is:

Ao max = 9.88 ksi To compute the cyclic stress intensity factor, AK ,g assume a crack model which has a series of edge cracks, each with length a and separated by a distance of 2h [2-9]. The cyclic stress intensity factor is given by:

AKg = Aomax Fgi(s) b where Fig (s) is a parameter which characterizes the assumed crack configura-tion model [2-9].

8 "

a+h For a 1 7 /s-inch diameter bolt:

-a = thread depth = 0.043 inch 2h = thread pitch =.0.0833 inch l

'- =

.043 l s = 0.508

.043 + .0833 l

2-10

The stress intensity factor is computed assuming a crack model which has a series of edge cracks, each with length a and separated by a distance of

^

l 2h [2-9].

The 11/2-inch diameter bolt has the same pitch and thread depth as the 17/s-inch bolt. Hence, for the 1 1/2-inch bolt the stress intensity factor range is given by:

AKg = 9.01 /w (0.043) 0.60 = 1.99 ksi /E The R-ratio equals:

R= 101.8 - 9.01 = 0.91 101.8 The effective stress intensity factor for the 11/2-inch bolt is given by:

f AK,ff = 1.5 - 0.91 1.99 = 2.549 (1.99) = 5.072 ksi /Iii The 1 1,'2-inch bolt is less critical than the 17/8-inch bolt, which has about an 8% higher stress intensity factor range.

The cyclic stress intensity range determined is unaffected by the level J

of bolt prestress as long as the prestress is sufficient to prevent separation along the master rod and link rod box joint.

The calculations assume perfect contact along the serrated joint under the specified bolt torque. If perfect contact is not achieved, the stress intensity range will be greater than the values calculated above and may exceed the threshold for crack propagation. It is not possible to evaluate the acceptable amount of contact area on the faces of the joint by simplified FE analysis. Therefore, the adequacy of the assembly and consequent suscepti-bility to fretting and fatigue cracking must be determined by inspection of

! the bolt holes.

i

[J 2-12

Section 2 References 2-1. Swanger, Lee, i

" Selection of Crankshaft Materials for Optimum '

Performance," SME technical paper No. CM80-329.

2-2. Cameron, Alastair, Basic Lubrication Theory. Third Edition.

! 2-3. Roark, R. J. and Young, W. C., Formulas for Stress and Strain. Fifth

]

Edition McGraw Hill,1975.

2-4. PDA/Patran-G Computer Program, 1980.

)

2-5. MARC General Purpose Finite Element Program, Version K,1983.

2-6. Zienkiewics, O. C., The Finite Element Method. Third Edition, McGraw Hill, 1977.

2-7. Telephone Conversation with Maurice Lowery, Transamerica Dela val ,

March 9, 1984.

2-8. Torque Manual, presser Industries, Inc., Hand Tool Division, Bolt

Chart, p. 36.

. 2-9. Tada, H., Paris, P., and Irwin, G. "The Stress Analysis of Cracks Handbook," Del Restarch Corporation, June 1973.

2-10. Hopkins, S.W. , Rau, C.A., Leverant, G.R., and Yuen, A. , "Effect of

• Various Programmed Overloads on the Threshold for High Frequency Fatigue Crack Growth," ASTM, STP 595, 1976, pp. 125-141.

2-11. "81GIF Fracture Mechanics Code for Structures" by Failure Analysis j Associates, July 1978. EPRI NP-838, pp. 4-26.

2-12. Rolfe S. T., and Barsom, J. M., Fracture and Fatigue Control in Struc-3 tures Applications of Fracture Mechanics. Prentice Hall Inc., 1977.

2-13. Failure Analysis Associates Report No. FaAA-84-3-13. " Design Review of Connecting Rods of Transamerica Delaval Inline DSR-48 Emergency Diesel i

Generators," April 1984.

l f,

i i

O 2-15

i 2.3 Rod Eye Analysis While the overall dimensions of the DSRV-4 connecting rod-eye are the same as those of the inline DSR-48 rod-eye, the cross section of the wall is either larger than or similar to the inline engine rod-eye. The rods in service can either be round or H-section. The round section rod-eyes are the same thickness as the inline engine rod-eyes, whereas the H-section rod has a thicker rod-eye.

The rod-eye bushing is subject to essentially the same loads in both the inline and V-engines. Accordingly, the same inspection procedures and acceptance / rejection criteria previously reported [2-13] apply to the V-engine.

4 2-14

Fatigue Life Prediction The maximum stress intensity factor determined for the 17/8-inch and 1

1/2-inch diameter bolt connecting rods (5.47 ksi M and 5.07 ksi M respectively) lies near the lower side of the available data for the fatigue crack propagation threshold. Therefore, inspection of the Bolt Hole No. 1 thread area is recommended to detect fatigue cracks. However, any inspection l

procedure at this location is limited to detecting cracks that exceed 1/8-inch l depth. Therefore, it is necessary to determine the remaining life of a con-necting rod which has an initial crack at the bolt hole thread of 1/8-inch depth. The smallest ligament between Bolt Hole No. I and the crankpin bearing bore is 0.8 inches. Assuming a maximum tolerable crack depth of 1/2-inch, the number of hours required for a semielliptic crack [2-11] 1/8-inch deep to propagate to a 1/2-inch deep crack is determined.

Numerical crack propagation analysis was performed using the BIGIF code

[2-11]. A three-dimensional elliptical surface crack model in a finite body was assumed [2-11, p. 4-26]. Crack propagation rate is based on Paris's rule

[2-12] and for this material equals:

h=a.0x 10 10 (ag I)3 where a = crack length in inches-N = number of cycles AKy = maximum stress intensity factor range i

The above equation applies when the R-ratio (R = o,,x/ min) is zero. The l BIGIF program incorporates the effect of nonzero R-ratio.

i The numerical analysis shows that a semicircular crack 1/8-inch deep could grow to a depth of 1/2-inch in approximately 200 hours0.00231 days <br />0.0556 hours <br />3.306878e-4 weeks <br />7.61e-5 months <br /> of engine opera-tion at full load firing pressure (1579 psig). At lower loads and pressures, the engine operating hours are given in Table 2-4. *

\

J 2-13

t' A

b TABLE 2.la LOADING CONDITIONS ANALYZED Parameterr Considered in the Finite Element Analysis Load Crank Gas Pressure (psig) Angle for Case Angle Amount of thaber Bearing (Degrees) Clamping Pressure Link Rod Master Rod Force Distribution Cylinder Cylinder (Percent)* (Degrees) 0 -

0 0 100 -

1 0 1485 34 100 120 2 0 1485 34 50 120 3 0 1485 34 10 120 4 715 1317 31 100 120 5 710 1113 31 100 120 6 700 784 36 100 120 7 0 1485 34 100 60 8 715 1485 31 100 60 l 9 3 1577 36 l 100 60 10 315 39 1485 100 60  :

11 0 1485 34 100 60 12 8 1577 36 100 60 13 5 1485 34 100 60 I 14 315 39 1485 50 60 I 15 315 39 1485 10 60 16 158 129 49 100 60 17 185 99 56 100 60 18 200 80 54 100 60 l 100% clamping force is:

e 89.754 kips which corresponds to 2600 ft-lb torque on the 17/s-inch bolts, e 89.781 kips which corresponds to 1700 ft-lb torque on the 1 1/2-inch bolts.

! O i

l

'Q) l l

2-16

T 2.lb LOAD CASES ANALYZED Crank Inertial Force Bearing Pressure Forces and Manents Bearing Pressure Load Angle at Crank Pin Link Rod Box at Master Rod End Reaction at Crank Pin Case at Fg 6 F2y T Fg y Fs , F3 ,*d R 8 Mr (Deg) (kips) (Deg) (kips) (Deg) (kips) (ktps) (kip-in) (kips) (Deg) 0 - - - - - - - - --

1 0 56.3 4.1 279.05 5.81 -25.586 -8.222 -191.43 202.338 10.95 2 0 56.3 4.1 279.05 5.81 -25.586 -8.222 -191.43 202.338 10.95 3 0 56.3 4.1 279.05 5.81 -25.586 -8.222 -191.43 202.338 10.95 4 715 56.3 -1.69 241.66 6.2 -31.16 -7.6 -176.83 164.78 16.443 5 710 56.3 -7.56 196.72 6.5 -35.723 -6.475 -150.76 123.46 25.29 6 700 56.3 -19.46 126.435 6.79 -42.233 -4.351 -101.30 75.75 56.45 7 0 56.3 4.1 279.05 5.81 -25.586 -8.222 -191.43 202.338 10.95 81 715 56.3 -1.69 279.846 6.2 -30.989 -8.796 -204.80 201.463 14.32 98 3 56.3 6.43 300.288 5.63 -23.295 -8,571 -199.56 224.112 9.088 10 315 56.3 -49.75 25.163 -174.19 278.287 0.741 17.253 208.717 -55.252 11 0 56.3 4.1 279.05 5.81 -25.586 -8.222 -191.43 202.338 10.95 12 8 56.3 13.28 300.24 5.0 -16.988 -7.608 -177.14 228.513 5.339 132 5 56.3 8.73 271.923 5.43 -22.348 -7.491 -174.413 197.103 8.585 14 315 56.3 -49.75 25.163 -174.19 278.287 0.741 17.253 208.717 -55.252 15 315 56.3 -49.75 25.163 -174.19 278.287 0.741 17.253 208.717 -55.252 16 158 56.3 148.36 71.147 -20.22 48.94 7.154 166.567 174.871 -29.78 17 180 56.3 166.38 65.273 -19.16 48.207 6.232 145.10 166.387 -23.86 18 200 56.3 183.85 56.573 -16.66 41.236 4.719 109.873 146.436 -16.207 8 Peak pressure occurs 2* af ter TDC. Note: - Angles 8 and 0 are positive clockwise at C1 with CgC2 as 2 Peak pressure occurs 12* af ter TDC. All other reference. See Fig. 2-7.

cases: Peak pressure occurs 7* af ter TDC.

- Angle Y is positive clockwise at C2 with C2Cs as reference.

See Figure 2-7.

TABLE 2.2a MAXIMUM CYCLIC STRESSES FOR 1 7/8-INCH DIAMETER BOLT l CONNECTING R0D IN BOLT 1 REGION l

'. Cyclic Element / Angle with Stress Integration respect to Load Cases (ksi) Point the x-axis '

7 and 17 9.88 219 / 7 -49.362 '

7 and 16 9.56 219 / 7 -44.750 7 and 18 9.59 219 / 7 -52.305* ,

I and 17 9.67 219 / 7 -38.764*  !

I and 16 9.57 219 / 7 -33.945 1 and 18 9.21 219 / 7 -42.637*

l See Figure 2-9 for location of elements and integration points.

t l

i O

2-18

TABLE 2.2b i

MAXIMUM CYCLIC STRESSES FOR 13/2-INCH DIAMETER BOLT CONNECTING R0D NEAR BOLT 1 REGION i

Cyclic Element / Angle with Stress Integration respect to Load Cases (ksi) Point the x-axis 7 and 17 9.012 219 / 7 -57.80 7 and 16 8.566 216 / 7 -56.49 7 and 18 8.830 219 / 7 -58.97*

See Figure 2-9 for location of elements and integration points.

O O

2-19 l

l

__ - . . , _ _ . _ _ . _ _ , . . . . _ . . . . _ _ _ . _ _ , . . - , . . _ - - . ~ . . . _ _ _ _ . , . _ _ _ , _ . . - _ . . . .

TABLE 2.3a AXIAL STRESSES IN THE BOLTS OF THE 1 //8-INCH DIAMETER BOLT CONNECTING R00 Load Averaga Axial Stress in ksi Case Lower Number Bolt 1 Bolt 2 Bolt 0 32.51 32.51 32.51 7 32.80 32.58 33.03 1 32.90 32.51 33.09 17 32.38 33.14 32.47 16 31.94 32.99 32.13 18 32.29 32.61 32.21 4 32.86 32.58 33.08 12 32.62 32.61 32.91 10 33.99 33.29 32.57 O 8 13 32.70 33.23 32.58 32.90 32.96 33.44 Maximum Stress Range (ao max) 2.05 0.78 0.96 For Load Cases 10 and 16 10 and 1 1 and 16 i

=i 4

U l

1 2-20 i

TABLE 2.3b AXIAL STRESSES IN THE BOLTS OF THE 1 1/2-INCH DIAMETER BOLT CONNECTING R00

~

Lead Average Antal 5 tress in ksi Case Lower lhamber Bolt 1 Bolt 2 Bolt

. 0 50.81 50.81 50.81 i 7 51.05 50.90 51.33 l 16 50.26 51.32 50.45 l 17 50.37 -

51.15 50.46 18 50.60 50.94 50.52 1

1 O

i i

l i

1 i

i O

2-21

i TABLE 2.4 ENGINE OPERATING HOURS i

Hours of Crack Percent Load Peak Firing Pressure Growth Lifetime 100% 1579 psig 200 hr 85% 1485 psig 248 hr 755 1414 psig 286 hr i

3 l

O '

4 i

l l

1 1

I O

t-22

k 5 { r i I l l

I t

J l

-+ i: , Centerline bow i

i:

).

t I

I

> 1 i

2  %

r 7 4

l l

i i

e i

I

\

. i f.

w a I

l l

l 1

Figure 2-1. Schematic of connecting rod bow.

l-

' N

Material A Surface C Material C Master rod f fh'$hkhhIkhbfh khkfhh  ;

Upper bolt I$M((M,,

$[TM,;, .,,,,,,,, ..  !!!'3

,.,w.,,~..:,,h,

,:.,,,$a$j f  ?

Material B i

Lower bolt s

~> Link rod box hhf fkhkhkh!'h kkIk hbh2hh

$ 08 m I A"

I I

s Figure 2-2. V-engine connecting rod assembly. I l

i l

L

l 1

~

'sg .

1 >

l ,

~w f

4 1 2

- - - J s

\ '

O m

1

]

/

y i

1 \ ,

., I t

1

-! l l

l 4

1 Figure 2-3. Finite-element model of connecting rod.

FaAA-84-3-14

O 1 l

i 1

3~ \

s

e-4 g , *gn

=. a y

>;  ; . ~ - 9,

^

y

' \

\\ . >#*

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'g 9.0 31 *

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e N m 80  :

e v- N** i e e ' '

1 t

}

~

e ..

9 '

d

" 3 (a  !

)

• --- 8.8 2 5 ' r  :

8.12 5 * ---*

Figure 2-5.

Main structural dimensions'in inches.

O FsAA-84-3-14 l

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I I i  ; )

AI I.l-

i. 3 , I I \! ,Y /

l I

\l (k I, I ii! '

l

\

o Truss

/

- elements modeling i

/

W I bolts f

7 x I Fi j l i l 6

I l

Figure 2-4. Modeling of bolts and bolt-prestress force.

N _,./

FaAA-34-3.14

-s - s a a~ -e- A =- ---au 5 g 3

O

-Q t.

A 1

G d8"Ilt b

o a e e

1

(

w W T

= 1 l' = @

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Ln m v

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<, O c.

t

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• > Q v

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. 3 4

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a e

a A g Q Q 8

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" 10 g (I5d) 3Wn553Wd SYD PaAA M 14 . _ . . _.

. . . . . . .. .. -~ - -.

l 1

M F1xd p U /

i V

g Bearing pressure in connecting rod box a

t C2

\ f W

\i  ?

h m

\\

\

0

'/

O ,al Bearing pressure dt Fhe -Inertial force at crank pin applied as body force Figure 2-7. Loads acting on the connecting rod.

O l 15 , , , , ,

=

.I w

, 1-7/8* dia.

C 2

y 10 -

9.88 kal -

p. - -~~~.:^,z.

9.01 ksi h

> 1-1/2" dia. N

! C 2

s 3 5 -

x _

4 2

1 M

e l E .

j Beginning Threads End

)

O A 8 0 1 2 3 DISTANCE (in)

Master rod and link rod box interface o Figure 2-8.

Maximum cyclic stress range at bolt hole (Bolt 1).'

i l

1 a.

'E'

.. ._ .-. . - .- . . - . . _ . , - ~ . , . - - - . - _ . - . - - .

. -FeAA 44

--. _ 14-

Master rod and link rod box interface

)

[ Integration point t number t

5 Bolt y

, Bolt / bolt hole h

/

h/HHH/

~

/nHs///////H/ H//H///

7 i 243 .l pe218 .jjlr7 r7

.tf,1 4 .,r N gtg l yyy o i / /

I- Element nu'mber

\

/ '

O

\

\

see detail above -

x!

x v i

in to >, )\ -

Xl '

P / /

m ( i s <

Bolt 1 213 k 216

~[ 219 222 i (

[

/

r .

g i

l

)

Figure 2-9. Locations of elements of interest in the finite element model of connecting rod.

- - - _. ,. ._ _ _ _ . . --FaAA-84-3_14

3.0 CONCLUSION

S v

Based on the design review, FaAA concludes that the connecting rods for the TDI DSRV-4 Series engines are adequate for their intended service under the conditions specified below.

3.1 Link Pin Locating Dowel Interference Clearance between the link pin and link rod should be examined. SIM 349 recomends that this dimension be checked with a 0.0015 inch feeler gage. This dimension must be zero when the specified bolt of 1050 ft-lb is applied.

3.2 Rod Bow The maximum permissible centerline bow in an H-section connecting rod is 0.47 inch based upon a calculation of axial misalignment under firing pressure. This allowable dimension should be verified.

O O 3.3 Connecting Rod Bolts and Bolt Holes The first pair of bolts above the crank pin should be removed and inspected by magnetic particle method and the threads of the hole examined for cracking by eddy current or other methods. ine allowable time at full load between inspections based upon the reliability of the eddy current inspection is 200 hours0.00231 days <br />0.0556 hours <br />3.306878e-4 weeks <br />7.61e-5 months <br />. This time assumes that the specified assembly torque is ade-quate to prevent separation along the serrated joint. Adequacy of the torque depends upon the initial fit between the mating surfaces. It has not been possible to quantify the effect of manufacturing tolerances on this fit. A joint that has been assembled with less than uniform contact may result in loss of bolt preload during operation and consequent fatigue failure. Break-away torque should be measured and complete dimensional checks of both sur-faces made if the breakaway torque is less than 1600 ft-lb for the 1 1/2-inch diameter bolts or less than 2400 ft-lb for the 17/s-inch diameter bolts. As additional experience is accumulated it may be possible to relax the inspec-tion requirements.

,A]

L 3-1

3.4 Rod Eye .

i.

l The rod-eye of the link rod and the rod-eye bushings are similar to l j those in the inline DSR-48 connecting rods and are subject to the same j maintenance procedures recomended for those rods.

f, h

i i

f.

I i

i I

l 1

5 1

I {

i  !

i i i  :

a i

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i i

4 l

l 3-2

_ _ . _ _ . - _ _ _ _ _ _ . _ _ _ . _ ~ . _ _ _ . . _ _ , _ . _ . _ . _ . . _ _ _ . _ . , _ . _ . . . _ _ _ _ _ _ _ _

l O

O APPENDIX A DERIVATION OF PISTON ACCELERATION FOR V-ENGINE ARTICULATED ROD CONFIGURATION In this appendix, the dynamic loads that act on the connecting rods are determined by lumping the appropriate masses at the two pistons and the crank pin. Inertial loads are determined by first evaluating the motion of the pistons and the crank pin center. The center of the crank pin has a simple circular motion; therefore, the only inertial load will be that of the radial-ly outward centrifugal force equal to:

F; =mwR e where me = the mass lump at the crank pin w = the angular acceleration

=

R the radius of rotation.

/

The motion of the piston is more complex. However, for a given crank angle, wt, the position of the pistons can be analytically assessed from the known kinematics. The acceleration of the pistons are determined by differen-t1ating the position of the pistons with respect to time. The pistons undergo a one-dimensional motion along the centerlines of the cylinders.

Consider the schematic description of a V-engine shown in Figure I-1, where the symbols designate:

P g

a the master rod piston P2 = the link rod piston Cg = the center of the crank pin 0 = the center of the crank shaft C2 = the center of the link pin 13 = the master rod length 1

2 = the distance between centers of the crank pin and link pin x./

A-1

I h 13 = the link rod length R = the distance between the centers of the crank shaft and crank pin a = the fixed angle between P C C 3 32 eo = the V-engine angle et = the crank angle y = the cartesian coordinate along the centerline of the articulated rod cylinder.

x = the coordinate normal to y C ', C2 ', P ', P '2 designate the locations of C , C 3 3 3 2

, P , P2 for a 3

crank angle of wt.

y = the angle between OP' and CjPj n = the angle between the y axis and CjPj Y

= the angle between CjCj and CjPj 6

= the angle between a radial line OC{ and C iCj y, n, t, 8 are all functions of the crank angle.

CoordinatesofCj O

Coordinates of C{ are given by:

x = R sinwt (A.1) y = R coset.

(A.2)

CoordinatesofP{

Coordinates of P{ are given by:

x = -r 3

sine o (A.3) y= r 3cose o (A.4) where r3 = the distance from the center of the crank pin to the master rod piston,OP{.

12 3 = (R sinut + r 3sineo)2 + (R coswt - r 3coseo)2 (A.5)

..]

A-2

Solving for r :

3 r 2 3 = R cos(so + wt) + [1 2 - R2 sin 3 (so + wt)] 2 (A.6)

The acceleration of the master rod piston is equal to the second deri-vative of r ,3 which is determined by differentiating Eq. A.5 twice.

Differentiating E4. A.5 once gives:

dt (r1-Rcos(so+wt))+Rwrisin(so + wt) = 0, (A.7) from which the velocity jt is determined, dri , , Ru r1 sin (Bo + wt) dt (r1-Rcos(so+wt)) (A.8)

O Differentiating Eq. A.7 again gives:

2

' dri 2

d r1 = -(dri)+2R"dt dt sin (Oo + wt) + Rw2 r1 cos(so + wt) dt2 (A.9) r1 - R cos(so + wt) d2r1 where represents the acceleration of the master rod piston.

2 Angle y between OPjC{ for any crack angle is determined from the fol-lowing two equations:

R cos (0, + wt ) + Ag cosy = r 3 (A.10) 1 siny = R sin (oo + wt) 3 (A.11) .

Hence,

. p.

Y A-3

R sin (e + wt) h d

tan y =

ri - R cos(0, + wt)

(A.12)

To simplify the determination of the motion of the link rod piston, l define transformed coordinates x', y' at Cj origin such that x' is parallel to x, and y' is parallel to y. Then,

, x = x' + R sinwt (A.13) y = y' + R coswt (A.14)

Next, define transformed coordinates x", y" at C{ origin such that y" isalongC{P{andx"isorthogonaltoC{P{.

The rotation angle 4 between the x' and x" axes is related by:

r1 Cos0o - R coset cos 4 = '

(A.15) 11 O- r1 sineo + R sinet sin 4 =

11 (A.16)

Coordinates x" and y" are related to x' and y' by:

x' = x" cost - y" sint (A.17) y' = x" sin 4 + y" cos4 (A.18)

Coordinates of C' Coordinates of point C' in the x", y" plane are given by:

x{j = 12 sina (A.19) y{j=12 cosa (A.20)

In the x, y cartesica plane, the coordinates of C' are given by:

i O i V l A-4

xC' " A2 sina cost - 1 2cosa sint + R sinwt (A.21) yCj"1 2 sina sin 4 + 12 cosa cost + R coswt (A.22)

CoordinatesofPj Coordinates of Pj can be evaluated from the foregoing two equations:

x,=0, and (A.23)

P2 (yp . - J C,) +x,=1 r (A.24) 2 2 2 12

/

y.*J'+ ^*

p 2 C2 ~*C'2 O For brevity, let yp = yp ;, xp = xp ;; xC " *Ci' #C"#Ci' A.22 can be written as:

(yp -y) +x C

= j (A.26)

Differentiate above equation with respect to time using dots to desig-nate time differentiation; (y p -y

• C (P ~

C + *C C (^* }

Rearranging Eq. A.27 gives the velocity of the link rod piston:

i i

O A-5

l l

8p

• y y [(Y p -Y C C ~ *C C (A.28)

Differentiating Eq. A.27 again produces the link rod piston accelera-tica:

1 1

Yp

• J +*C*C] (A.29)

C~(Yp-Y)[(P-C C) + ( C)

Time derivatives of x C, and y ,C are determined from Eqs. A.18 and A.19 2 2 as follows:

let

" cos'4 = d (cost) (A.30) dt O Then; 5

Cj = Re coset + 12 (sina cos't - cosa sin'4) (A.31) yCi = -Re sinwt + 1 2 (sina sin'4 + cosa cos 't) (A.32)

X Ci = -Rw sinwt + 12 (sina cos"4 - cosa sin"4) (A.33) yCi = -Rw 2 coswt + 1 2 (sina sin"4 + cos"4.cosa) (A.34)

Time derivatives of sin 4 and cos4 are determined from Eqs. A.12 and -

A.13 by direct differentiation of those equations:

-O' V

A-6

sin'$ = (r3 sin 6,+Rwcoswt) (A.35)

I sin"$ = - (h sine, - Rw2 sinwt) i (A.36) cos '$ = (rcose +Rwsinet) i (A.37) cos"$ = (hicose, + Rw2 coswt) (A.38)

The angle n between the link rod and the y axis is given by:

• Cl *Ci tan n = =

(A.39) y2 (YPJ ~ # )) (13 2_x C J O Direction of centrifugal force is given by:

8=0 + wt + y - a.

Direction of forceacting on the link rod is given by:

$=n+a-0 - y.

The combined forces acting on the connecting rod are shown in Figure I-2. On the master rod an axial and horizontal force are exerted. On i the link rod, only an axial force is applied. From a simple free body diagram l consideration, F2 is given by: l 5

t (F1 2+F92) v F2

," cosn A-7 l

._ - -_ -_- --_.__-----. -- - - - - - - - - - ' - - - - ^ ~ - ~ ~ ~ ~ ~ ~ ~ ~ ~

where l F

I2 = the inertial force of the mass lumped at the link rod piston.

F 92

= the gas pressure force.

The inertial force equals:

2 dy p 12

• *2 dt2 The acceleration was given by Eq. A.29.

The gas pressure force is determined from the pressure, which is a function of the crank angle times the piston area. This force will be com-pressive.

The horizontal force acting on the master rod is determined by requir-ing moment equilibrium at the crank pin center.

A2 Fi x

=pF 2y sin t.

The axial force along the master rod is given by equating the sum of the forces along the master red piston to the gas pressure plus inertial load. That is; F +F =F 1 cosy - F siny 1

1 . gi y 3 x

or It+ gi .

F = +F l tany l

y cosy x

A-8

1 1

The reactions at the crank pin (point C1) are given by force equilibriura:

Rg = F2 cost + Fi cosa - F ycoss - F sina i y y C X R =F 2 sint + F i sina + Fg sins + Fi cosa y y C x where F =

the inertial force due to the lumped mass at the crank pin center.

Rj.and Ry are the components of the reaction at the crank pin hole.

!O i

4

O A-9

. . . . . . . , _ _ .-._ _ . - - - - - - , . . - - . . - . - - . _ . . _ - . . . . . , _ . . , ~ . _ _ . - , - -

..c..

O

/

A P p2  !

3 v'

P'2 t

P'y 13 7 #U l

/ 13

/

/

/

/

/ -$

11 /

r1 O Cpl/

/ C '2 l2 / x.

/

I2 0

, ci

/

/

00 / cet c.i .

l l /

0  %

, 'N N X.

Figure A-1. Kinematics of V-engine connecting rods.

FaAA-84-3-14

F 2y F ty F ix P

2 Pg "Y

O ,

\C 2 O

h4 4

B Y

C1 Rx l

1

\

Figure A-2. Free body diagram of actions and reactions on the V-engine connecting rod.

(

p g a-s4-3-S'

, - , - . . - -.e.- - - - . . - _ . _ _ . . . - _ - - - . . - , - - - , - - - - - . - -, _ _ _ - - .e.--, - - - . ..- , - - . -

APPENDIX B 1

COMPONENT CESIGN REVIEW l TASK DESCRIPTION CONNECTING R0D Classification A I PART N0. 03-340A Completion 3/20/84 I PRIMARY FUNCTION: The connecting rod transmits engine' firing forces from the l pistons and piston pins through the rods to the crankshaft such that the reciprocating motion of the pistons induces rotation and output torque of the crankshaft.

FUNCTIONAL ATTRIBUTES:

1. The connecting rod must have sufficient column buckling strength and fatigue resistance to withstand cylinder firing forces and inertial loads.

2. In the RV engine design, the three oscillating bearings two (2) wrist pin bearings and one (1) link pin bearing and the rotating crank pin bearing all require support from the connecting rod. In the R-48 design, a single wrist and crank pin bearing are supported. The flexure of the rod must be such that bearings are not unacceptably distorted.

3. Passages within the rod wst provide cooling and lubricating oil to the bearings and pistons.

4. Stress levels, both mean and alternating, must fall within the endur-ance limits for the material utilized.

5. In the RV design, the two bolted joints (link rod to link pin and master rod to link rod box) must maintain sufficient contact I

pressure. The R-48 design likewise requires sufficient clamping forces on the crank pin bearing cap.

6. The rod cap bolts must support the necessary preload without yielding, b).

fracture or unacceptable thread distortion.

l B-1 l l

= ,-. r ,,w,- -,er- my w , ,- , ---,w-- . , - - - - ,w * + - + - , , , ,

7. The wrist pin (or rod-eye) bushing must acceptably support the gas

{

pressure and inertia forces transmitted by the pistons during the unique nuclear standby required starting cycle' and normal operation. l SPECIFIED STANDARDS: None EVALUATION:

1

1. Determine the service histories of the connecting rods. In particu-lar, evaluate the two V-style connecting' rods (the 1 7/8-inch bolt diameter connecting rod and the 1 1/2-ir/ch bolt diameter rod) and the R-48 style connecting rod.

2. Incorporate firing load profile data for the crankshaft analysis and the results of the 13-inch diameter rod bearing analyses to produce a connecting rod static load profile, with the addition of inertia loads for a complete time-load map.

3. Evaluate the significance of possible rod bow as it affects bearing centerline angular misalignment.

O- 4. Review and report on failure of connecting rod at Copper Valley Electric, Glenn Allen, Alaska.

5. Conduct journal orbit analysis of the wrist pin bearing.

6. Using examples of fractured rods to focus the area of investigation, develop finite element models of the 1 7/8-inch bolt diameter V-type rod, to define deformation and the possibility of crack initiation and propagation.

7. Evaluate the necessary preload and acceptable design requirements (yielding, thread distortion) of the rod cap bolts for the R-48 and RV designs.

8. Evaluate the loading, fabrication and installation requirements of the wrist pin (or rod-eye) bushing for acceptable nuclear standby service.

9. Perform a metallurgical examination of fractured connecting rods in FaAA possession.

10. Complete final report.

1, AJ B-2

l l

l REVIEW TDI ANALYSIS:

1.

Review any TDI stress analyses or strain gage testing of connecting rods. 1 1

INFORMATION REQUIRED:

1. Connecting rod, wrist pin bearing and cap bolt drawings.

2.

Engine operating parameters (i.e., speed, firing pressure time history, etc.).

3.

Component physical parameters (piston weight, connecting rod recipro-cating and rotating weights, etc.).

4. TDI specified rod cap bolt torques and installation procedures.

5.

TDI failure history of DSR-48 and DSRV connecting rods.

6. Bushing and connecting rod material specifications.

O(~~h s

i B-3

.- - . -