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Eugeniusz Rusiński Wrocław University of Technology, Wrocław, Poland

NUMERICAL-EXPERIMENTAL INVESTIGATION OF REASONS OF FATIGUE CRACKS OF MACHINES ELEMENTS

1. Introduction Machines used in underground mining, such as: derricks, roof bolting machines, loaders,

transportation vehicles as well as others are generally used for ore exploitation, loading and transportation, i.e. basic mining tasks [1]. Construction design practice, exploitation and tests prove that such machines as well as their sub-components are subject to requirements radically different from machines operating on the surface. In general exploitations conditions are much heavier. Considering their specific application, they are subject to adverse operating conditions, variable operating conditions and are often subject to percussive loads (fig. 1).

Fig. 1. SWB (Self-propelled roof ripping vehicles) during operation at an underground

mine Design of mining machines requires from the constructor to use quick and accurate

calculation methods. The design should result in a reliable construction, withstanding the required loads, whilst also being economical [2]. This can be achieved through the use of modern integrated CAD/FEM systems. Other approaches can be also used for the designing purpose and in order to achieve loads coming from operational conditions [3, 4].

Among the vast number of machines operating in underground mines, we would like to concentrate on loaders. A common fault, which is found in machines of this type is damage to the scoop bucket and the cutting blade. There are also cases related to damage of the frame or the loading jib. During exploitation of one of such machines in an underground copper mine, the jib suffered damage as shown in fig. 2. This consisted of a cross fracture of the jib boom, causing complete separation of the front part of the jib from the rest of the machine. The fault occurred during unloading of the scoop.

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Fig. 2. Damaged loader boom

Another example is the dumping conveyor’s steerable carriage (fig. 3) broke down

during work in winter conditions. The dumping conveyor’s driving system consists of one steerable and two nonsteerable caterpillar units. The steerable caterpillar unit is made up of two crawler frames, a carriage and a steering frame.

Fig. 3. Breakdown of dumping conveyor’s steerable carriage.

In such machines the half-shafts are usually 3 m long and have a diameter of 500 mm,

decreasing to 300 mm inside the carriage. The resulting mass amounts to about 3.5 tons. This design solution requires, however, solid support and protection against slipping out.

Due to damage of half shaft safetying one half-shaft slipped out and caused breakdown of the machine. The track girder of the dumping conveyor after the breakdown is shown in fig. 4.

After the dumping conveyor’s gantry together with the machine body had been hoisted and the track girder had been removed the damaged end of the half-shaft could be examined. The half-shaft’s damaged end with broken off pieces is shown in fig. 5.

In order to determine the causes of mining machines construction elements damage, a decision was made to verify the design of the machine, using CAD/FEM numerical stress assessment. Furthermore, detailed material analysis was also performed, to check for possible material and technological faults, which could also be plausible causes of this damage.

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Fig. 4. Breakdown of one carriage: results of steerable carriage breakdown

Fig. 5. Damaged half-shaft of steerable carriage

2. Numerical experiment

The digital model of the jib boom is shown in fig.4.

Technical parameters of the loader: boom erection is performed using two hydraulic actuators: • φ of the piston 160 mm • φ of the piston rod 80 mm • total extension s1 = 630 mm • length of the actuator l1 = 1170+ s1 the scoop bucket is also controlled using two hydraulic actuators:

• φ of the piston 140 mm • φ of the piston rod 70 mm • total extension s2 = 470 mm • length of the actuator l2 = 1036 + s2 • weight of the scoop bucket m = 2450 kg • capacity of the scoop bucket V = 3.5m3 • average ore density ρ s = 2000 kg/m3 • hydraulic fluid pressure p = 155 bar The analysis assumed four positions of the jib boom, as shown in fig. 7. Stress analysis

was performed for 18 different cases. Each of these assumed a fixed position of the scoop bucket, with the stress load being generated by the actuators. A simplifications was made, assuming the scoop bucket as an ideally rigid construction, similarly a same assumption was made for its rotation axis [9].

Fig. 6. Discrete model of the jib arm

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Case A Case B

Case C

Fig. 7. Diagrams of jib boom loads The stress calculations for the jib boom were performed using finite element analysis

using the I-DEAS [10] system. Sample stress calculations are presented in fig. 8. The computations provided a

3D representation of the stress levels as well as show the deflection of the jib boom, depending on the load size and geometrical configuration. The most representative case occurs when the scoop bucket was loaded unevenly, causing significant torsion of the jib boom. The highest stress level occurs at the point where the scoop bucket is mounted to the boom, as shown by setup C (fig. 7), when the jib boom and scoop bucket are being lifted. The maximum combined stresses in this case are:

σMAX = 413 MPa Stress concentration is caused at a structural notch at the boom’s actuator mounting

point. At this point there is also a change in the rigidity of the boom’s side strip caused by the bushing for the actuator mechanism’s mounting bolt. This is also the point where the boom cracking was initiated.

The loads acting on the half-shaft, particularly on its end where the slip-out protection is situated, were analyzed. Considerable axial forces produced by the side shearing of soil occur during curvature travel. In unfavourable conditions they and the lateral forces due to the

Fig. 8. Contour lines representing stress levels

in the boom, according to the Huber-Mises theory

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gradient and wind pressure may add up. The protection against half-shaft slip out is shown in fig. 9.

FEM calculations of the half-shaft end were carried out for the most unfavourable case of loading. One should note that because of the very small rounding radius at the bottom of the groove for the protective plates considerable stress concentrations arise under the action of axial forces. The radius is as small as r = 0.2 mm (as measured on microsections of the protection). The half-shafts were made of toughened constructional alloy steel 42CrMoS4

whose yield point is Re = 880 N/mm2 and strength Rm = 1030 N/mm2. The FEM strength calculations of the half-shaft were performed for two values of the axial force acting on the half-shaft protection:

- axial force F = 1393 kN – the axial force at travelling along a curvature with radius R = 60 m with the terrain gradient and wind pressure (HZS (L)) taken into account and with neglected friction on the half-shaft mounting hubs,

- axial force F = 704 kN – the axial force at travelling along a curvature with radius R = 60 m with terrain gradient and wind pressure (HZS (L)) and friction (μ = 0.09) on the half-shaft mounting hubs taken into account.

The first case is rather theoretical since it assumes that total axial force F = 1393 kN acts on the half-shaft’s end. But some of the axial force is taken by friction between the hub and the journal at the places of half-shaft mounting. According to standard [12] the coefficient of friction in this case can be assumed at a level of μ = 0.09-0.22. Assuming the less favourable friction coefficient value (μ = 0.09) and knowing the forces in the bearings, the axial force taken by the half-shaft’s end was determined to be F = 704 kN.

Figure 10 shows the distribution of Huber-Misses stress determined by FEM calculations [13] for radius r = 0.2 mm and r = 4 mm while the maximum Huber-Misses stresses on the groove’s bottom for two values of the axial force transmitted by the half-shaft lug are given in table 1. The rounding radius of 4 mm was adopted for comparison purposes in order to determine its safe (strength wise) value.

Fig. 10. Distribution of Huber-Misses reduced stress in slide-out protection groove

(nonlinear elastoplastic calculations): a) r = 0.2 mm, b) r = 4 mm.

Fig. 9. Halfshaft end - protection against

slip out

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Table 1. Maximum Huber-Misses stresses in analyzed half-shaft end

Calculations

Axial force F [kN]

Rounding radius r [mm]

Reduced stress σ [MPa]

Safety factor δ

4 822 1.07 without friction 1393 0.2 1080 (1780*)) 0.49

4 405 2.17 with friction 704 0.2 880 1.00 *) a theoretical value for material elasticity in the full load range.

The FEM [17] calculations indicate that at the bottom of the groove with radius r = 0.2

mm stresses considerably exceed the yield point. The stresses come down below the yield point at radius r = 4 mm.

3. Macroscopic and fractographic evaluation of the jib arm The fragment of boom supplied for testing was made of a 50 mm metal sheet and had a fracture

running across the entire cross section of the boom. The fracture ran from the edge of the fillet weld (fig. 11) used to attach an additional flat bar with a lubrication groove. The fracture surface was corroded, therefore before fractographic analysis it was chemically cleaned using „Fosol”.

The fractographic analysis concluded that the fracture was an immediate brittle fracture, originating at points marked A and B in fig. 11, located along the S1 weld joint fusion with the boom material. Analyzing the surface topography of the fracture points A and B using a scanning electron microscope showed a smoothed surface, which is characteristic for fracture origination points. The fractures at points A and B probably originated already during or shortly after welding, and ultimately lead to an immediate brittle fracture of the jib boom. It is also probable that the welding fractures lead to a small fatigue zone. However, because of corrosion it is impossible to observe a clear fatigue line, which would confirm the presence of the fatigue zone. Surface morphology observed at point A is shown in fig. 12. The immediate brittle fracture zone is shown in fig. 13.

Fig. 11. Topography of the immediate brittle fracture zone of the jib boom. Spots A and B

mark the fracture origination points, located at the S1 weld joint fusion

Fig.12. Surface morphology of the fracture at point A (fig.4). Zone with smoothed material

grain. SEM image

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Because of corrosion it is impossible to observe a clear fatigue line, which would confirm the presence of the fatigue zone. Macroscopic evaluation of the weld joint was performed at the cross microsection of the S2 fillet weld (fig. 14). The weld surface was etched using Adler’s etching solution (Ma11Fe).

Fig. 13. Morphology of the fracture

surface at the immediate brittle fracture zone

Fig. 14. Weld joint between the flat bar and jib boom. Clearly visible differences in

structure of the welded materials, the weld and the HAZ, along with welding errors in

the form of incomplete weld penetration and trapped gas bubbles. Etched using Mi1Fe,

regular microscope. Observations proved incomplete weld penetration at the root of the fillet weld. Both

welds as well as the weld fusion line also exhibited numerous welding errors in the form of interruptions as well as gas bubbles.

A macroscopic image of the weld joint showing these welding errors is presented in fig. 10. The macrostructure examination of the weld joint also revealed various structures in the flat bar, jib boom and weld joint materials as well as within the HAZ (heat affected zone). The welding errors lead to weakening of the weld joint, however they are not a direct cause of the brittle fracture, which occurred. Occurrence of these errors is caused by improper welding technique.

4. Metallographic examination of half-shaft Metallographic examinations were carried on three elements from the fractured

caterpillar half-shaft. The elements were denoted as 1, 2 and 3 (figs 15 and 16). Naked-eye macroscopic examinations and examinations by means of a stereoscopic microscope at a magnification of 30x were conducted. Also microscopic examinations using a NEOPHOT 32 light microscope and a digital camera were performed.

Fig. 15. Fragments broken off caterpillar half-shaft – element 1 and 2

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Fig. 16. Piece cut out from damaged half-shaft cross section – element 3

The macroscopic examinations showed fractures originating in the caterpillar half-shaft.

The fractographic investigations showed that the fractures had fatigue fracture features, including a temporary coarse-grained brittle zone (figs 17 and 18). In element 1 the fatigue zone area is located near edge AC and it takes up about 2% of the fracture area. The fatigue zone area in element 2 is located near edge EG, occupying about 4% of the fracture area (fig. 16). The fractures were locally coated with corrosion products. The fatigue zones have a lenticular shape, most wide close to the middle of edges AC and EG in the investigated elements [14 and 14]. The places are denoted as S1 and S2 for respectively elements 1 and 2. The fatigue zone in point S1 is about 3 mm wide against the temporary zone width of about 65 mm while in point S2 it is about 6 mm wide against the temporary zone width of about 60 mm (fig. 17). In the case of element 1, the first fatigue zone area is located by edge A and the second one at a distance of about 20 mm from edge C. Similarly in element 2 one fracture fatigue zone area is located directly at edge E while the other at a distance of about 10 mm from edge G. Such a fatigue fracture structure indicates that the largest stresses occur in the medial part of the groove towards points A and C (element 1) and E and G (element 2).

Fig. 17. General view of surface of fracture with marked edges. Symbol S2 marks widest

fracture fatigue zone area

It was found that both fractures had been initiated at the place where the cross section changes. The fatigue zone is located along the undercuts denoted by symbols K1 and K2 in fig. 14. The fracture of element 1 ran parallel to edge AC and at an angle of 45 deg. to the halfshaft’s longitudinal symmetry axis by edge GH. The angle gradually increases to-wards edge EF, reaching 60 deg.. This indicates that in element 1 the fracture of the half-shaft groove resulted from the action of shearing forces and bending moments on it. As a result of damage to element 1 an additional bending moment was produced (as one point of support was removed) whereby the direction of fracture propagation changed in element 2, as evidenced by the clear plastic deformation in point G, which probably occurred in the final stage of fracturing (fig. 18).

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Fig. 18. Element 2. Magnified fragment from fig. 15(visible plastic deformation in point G)

The small area of the fatigue zone in comparison with that of the temporary zone is

evidence of great strain of the half-shaft material. This means that either too low safety factors were adopted or the allowable stress was considerably exceeded during operation. Also improper heat treatment of the element’s structural material could be the cause. The most likely places of fracture initiation are points A and C (element 1) and E and G (element 2) where a local stress concentration might have occurred because of the change in the cross section. The fact that the fracture occurred in the middle section of edges AC and EG may suggest either nonuniform distribution of stresses (surface pressures) in the groove or a manufacturing or structural notch. The nonuniform stress pattern in the half-shaft groove could also be due to the faulty fabrication of the grooves, and also of the plates (e.g. their clamping surfaces not being flat and parallel). The signs of wear on the clamping surfaces indicate that the surface pressures were distributed on the groove’s circumference and not over its whole surface. This distribution of clamping stresses explains the lenticular shape of the fatigue zone: since the clamping forces are uniformly distributed on the circumference, the maximum bending moments produced by them occurred in the groove’s middle part in the region of points S1 and S2. The place from which the specimens were taken is shown in fig. 19.

Fig. 19. Place (determined by macroscopic examinations) where specimens for further

metallographic studies were taken

On both sides of specimen a the radius on the edge of the half-shaft groove for sliding in the protective plates was measured in the place marked N in fig. 19. A transition with curvature radius r=0.2 mm was found. This radius is too small to be a manufacturing radius.

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Fig. 20. Location of half-shaft groove; a) groove edge curvature radius r = 0.2 mm on

specimen’s left side, b) plastic strain zone on groove’s bottom Microscopic examinations were carried out on unetched and etched (with Mi1Fe re-agents)

microsections. The results of the examinations are shown as microphotographs in figs 21-24. In the unetched microsections non-metallic inclusions, mainly in the form of sulphides

uniformly distributed over the whole surface of the specimen along the direction of plastic forming (fig. 20), were found.

After etching with Mi1Fe a pearlitic-ferritic structure (locally in the form of the Widmanstätten structure) was observed (fig 23). Such a microstructure is the result of local inhomogeneity in chemical composition, caused by improper heat treatment and plastic forming and incomplete reforging of the steel because of the considerable thickness of the component. Consequently, the material’s mechanical properties might have deteriorated [15].

The examinations also showed a crack originating from the groove’s edge, running parallel to the cross section change edge at an angle of 45deg to the shaft’s axis and running along the boundaries of ferrite and pearlite grains (fig. 24).

Fig. 21. Non-metallic inclusions uniformly

distributed over whole surface of micro-section along direction of plastic working.

Unetched condition. Light microscopy

Fig. 22. Inhomogeneous pearlitic-ferritic structure. Etched condition. Light micros-

copy

Fig. 23. Etched condition. Light microscopy: a) inhomogeneous pearlitic-ferritic mi-crostructure with features of Widmanstätten structure, b) magnified fragment

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Fig. 24. Edge of lock groove. Light microscopy: a) visible crack initiated in area where

cross section changes – unetched condition, b) magnified fragment of area in etched condition, visible crack running along boundaries of ferrite and pearlite grains

5. Conclusion The main purposes of the paper were to discuss designing problems of machines used in

Polish mining industry. Numerical and experimental approaches were used in order to achieve wider point of view of such accidents, which happens in this type of machines.

Based on the performed boom material tests, evaluation of the fracture, weld joint between the flat bar with the lubrication groove and the jib boom side strip as well as the MES stress analysis, it was found that: the material used for the jib boom has a chemical composition required for S355JR high-strength low alloy structural steel, complying with the harmonized PN-EN 10025:2002 (old name: 18G2 according to PN-86/H-84018). The microscopic evaluation of fragments etched using Mi1Fe, proved that the material of the jib boom outside of the weld has a ferritic-perlite structure showing slight evidence of Widmannstätten structure characteristics. This structure resulted from improper heat treatment and forging, meaning that the metal used for the jib boom was insufficiently rolled and thus has lower mechanical strength. It also makes welding of this material difficult. Calculation of the carbon equivalent according to the Polish standard PN-86/H-84018, based on the chemical composition of this steel determined during testing, is 0,453 % and is close to the allowable value of 0,46 %. However, the evaluated jib boom steel has poor weldability, which should be taken into account before performing any welding repairs;

CE = C + Mn/6 + (Cr+Mo+V)/5 + (Ni+Cu)/15 = 0,22 + 1,40/6 = 0,453 % � 0,46 % The finite element analysis performed for a wide variety of loads proved that the brittle

fracture occurred at a structural notch, causing concentration of stress forces (fig.25). The maximum combined stresses in cases where the jib boom was subjected to torsion forces amounted to: σMAX = 336 ÷ 413 MPa.

The jib boom fracture was inevitable, because the material is defective and has an improper structure. The loader jib boom thus has limited fatigue life.

The FEM analyses of the caterpillar unit and of the half-shaft end showed that the main cause of the breakdown was the way in which the half-shaft had been protected against slipping out. The

Fig. 25. Area of concentrated stress

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fractures in the caterpillar support half-shaft lock are of the fatigue type: the temporary part is brittle and coarse-grained. The fatigue zones were initiated at the place where the cross section changes. They extend from the groove’s edge into the material at an angle of about 45deg to the half-shaft’s symmetry axis and have a lenticular shape which is widest near the middle of the groove’s edge. The fatigue zone area in specimen 1 amounts to 2% and in specimen 2 to about 4%. This fatigue fracture structure suggests that the largest stresses occurred in the groove’s medial part.

Due to the low ratio of fatigue zone area to remaining zone area a considerable effort of the structure or the use of very low safety factors could have been the case. Pearlitic-ferritic structure with locally occurring Widmanstätten structure was observed in the investigated element. These features might have resulted in the deterioration of the material’s mechanical properties. Such a structure indicates that the element was not properly heat treated. Microscopic examinations of element 3 revealed the presence of cracks (fig. 23) indicating the onset of fatigue fracture. The cracks were initiated at the place at the groove’s bottom where the cross section changes and they ex-tend into the material at angle of about 45deg parallel to the whole edge of the specimen taken from the element. The examinations showed that the slip-out protection had not been properly designed and made. The direct cause of the breakdown was the too small rounding radius of the groove’s bottom (r = 0.2), leading to fracture, sliding out of the half-shaft and the breakdown of the dumping conveyor. A fatigue analysis of the groove’s bottom showed that the half-shaft material was in the range of limited fatigue strength (fig. 26). Hence it is concluded that the adopted protection is not good for this system of fixing the half-shafts. A much better solution is an annular protection with a properly large rounding radius of the half-shaft groove. The undercarriage system consisting of two half-shafts is advantageous from the fabrication and weight points of view. An alternative could be a single-shaft design in which the slide-out protection is much simpler (vertical protection in the form of an additional shaft). But this system would be much heavier (hollow shafts could be employed to reduce the weight) and more expensive.

Since many breakdowns of two-shaft undercarriages have been reported it can be concluded that such systems require more care in their design as compared with single-shaft systems. It can be helpful here to run numerical simulations to identify the weak points of the design. This approach was adopted in the present research. Also friction forces at the places where the half-shafts are supported play a significant role. Depending on the kind of friction (static or sliding) they can reach different magnitudes. In many cases,

Fig. 26. Wöhler diagram for steel 40HM with

marked limited fatigue strength region for radius r = 0.2 mm in half-shaft grooves.

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such loads determine the safety of operation of the undercarriage. But the magnitudes of the forces have not been precisely identified yet. Therefore further experimental re-search is needed to make the design of such systems more accurate.

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Mechanical Review (Przegląd Mechaniczny), 1/2004 p. 32. [3] Wszołek G.: Vibration analysis of the excavator model in GRAFSIM program on the basis of a block

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Publishing House, Wrocław 1994. [12] DIN/22261-2 – Bagger Absetzer und Zusatzgeräte in Braunkohlentagebauen, Teil 2:

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Journal of Materials Processing Technology 157-158 (2004) p. 405-409

Jarosław Stryczek Wrocław University of Technology, Wrocław, Poland

DEVELOPMENT OF THE FLUID POWER GEAR MACHINES

ABSTRACT Clarification of the fluid power gear machines is presented in the article. The machine

are divided into four groups, ie. The external gearing involute fluid power machines, the internal gearing involute fluid power machines, the internal gearing cycloidal machines, and the machines featuring a number of gears. Findings of the research carried out by the FPRG from the Technical University of Wroclaw concerning the development of all types of the machines mentioned above have also been presented in the paper. Furthermore, the new types