Pergamon Engineering Failure Analysis, Vol 2, No. i pp. 59-69, 1995

Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved

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FATIGUE FAILURES OF WELDED CONVEYOR DRUMS

D. R. H. JONES

Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, U.K.

(Received 1 January 1995)

Abstract--This paper analyses the fatigue failure of a number of welded steel drums which were key components in a large new conveyor system for handling minerals. Each drum consisted of a cylindrical shell carried on a solid circular shaft. The shaft projected beyond both ends of the shell, and was supported in self-aligning bearings. The shell was attached to the shaft by fixing a pair of annular plates between the shaft and the ends of the shell. The outer circumference of each plate was welded to the shell, and the inner circumference was welded to a boss which was keyed to the shaft. The drums rotated in service at 0.5-1 s -1. Failures occurred after 1-4 weeks of commissioning trials, corresponding to 0.6-4.6 million revolutions of the drums. Fatigue cracks initiated at the toes of the welds between the plates and the bosses, and propagated through the plates until the shell became detached from the shaft. An elastic analysis showed that high cyclic bending stresses were produced at the plate-boss welds when the drums were loaded by the tension in the conveyor belt. The stress ranges in the failed drums were comparable to the fatigue strengths of welds in structural steel, as given in BS5400:Part10:1980. As a consequence a total of ~-140 drums were condemned throughout the whole of the plant, with major cost implications.

1. INTRODUCTION

1.1. Background

F i g u r e 1 is a s c h e m a t i c d i a g r a m o f t h e c o n v e y o r . T h r e e un i t s o f th is t y p e w e r e

i n s t a l l ed as p a r t o f a l a rge n e w p l a n t fo r t h e t r a n s p o r t a t i o n o f m i n e r a l s . D u r i n g t h e

c o m m i s s i o n i n g o f t h e t h r e e c o n v e y o r s , six o f t h e d r u m s f a i l ed by f a t i gue . T h e f a i lu re s

h i g h l i g h t e d a f u n d a m e n t a l d e s i g n p r o b l e m w i t h t h e d r u m s , w h i c h u l t i m a t e l y r e q u i r e d

t h e r e p l a c e m e n t o f ~ 140 d r u m s t h r o u g h o u t t he e n t i r e p l an t .

1.2. Conveyor design

In order to stop the conveyor belt sagging between the support rollers it must be kept under tension. This is achieved by hanging a weight on the tension drum, as shown in Fig. 1. The conveyor is driven by coupling an electric motor to the shaft of the drive drum via a reduction gearbox and an overload clutch. Even when the conveyor is empty, the tension T in the belt varies from one location to another. The tension is a minimum where the belt exits from the drive drum, increases progress- ively on going clockwise around the system, and reaches a maximum where the belt enters the drive drum. The difference in tension across the drive drum is generated by

~ g V ' ~ " "~ ~ " I .O ) 1 l , iO I "1 ko I ~', d rum

/ " ~ ~' - ~ " " " ' ~ . - ' drum ~ Snub drum *-'~0 ~ ( . O ~ ~ T e n s i o n drum Discharge

Weight

Tail drum

Fig. 1. Schematic diagram of the conveyor.

59

60 D.R.H. JONES

friction in the rest of the system (e.g. losses in the belt and bearings). When the conveyor is carrying material the tension at the entry to the drive drum increases significantly in order to balance the downhill pull of the charge. The difference in belt tension across the drive drum must not exceed the limiting frictional force between the belt and the drive drum, otherwise the conveyor belt will come to a halt. The purpose of the snub drum (see Fig. 1) is to increase the angle of wrap of the belt around the drive drum, which is an effective way of increasing the maximum driving torque. During the commissioning period the conveyors were running almost empty. In order to carry out the failure analysis we have neglected losses in the system, and have assumed a constant belt tension.

The relevant design parameters for the three conveyors are as follows:

Load capacity = 4000 tonne h- [. Belt velocity = 3 ms -1. Inclination of slope = 10 °. Angle of wrap at drive drum = 210 °. Idling tension: T -- 4000 kgf (units 1 and 2) and 6600 kgf (unit 3). Motor rating -- 250 kW (units 1 and 2) and 350 kW (unit 3). Belt section -- 2 m wide x 11 mm thick. Overall length of unit = 80 m (units 1 and 2) and 120 m (units 3).

1.3. Drum design

Figure 2 is a cross-section through a conveyor drum. The drum consists of a cylindrical shell carried on a solid circular shaft. The shaft projects beyond both ends of the shell, and is supported by self-aligning roller bearings. The shell is attached to the shaft by fixing a pair of annular end plates between the shaft and the shell. The outer circumference of each end plate is welded inside the shell, and the inner circumference is welded to a turned boss which is keyed onto the shaft. The shells, end plates and bosses were made from weldable structural steel to BS 4360, Grade 43A (~< 0.25 C, ~< 1.60 Mn, ~< 0.50 Si). The shafts were made from carbon-man- ganese steel to BS 970,080M40. The dimensions of the drums are given in Table 1.

1.4. Details of failures

After periods of between 1 and 4 weeks of continuous operation the following drums had failed: unit 1--snub, tension, tail; unit 2--tail; unit 3--snub, one bend. However, it was not possible to establish the precise time to failure for individual

¢

C

. . . . .

p .D.

Self-aligning bearing

B o s s \

~ S h a f t

q

Fig. 2. Cross-section through a conveyor drum.

plate

Fatigue failures of welded conveyor drums

Table 1. Dimensions of conveyor drums (mm)

61

Unit Drum type a b c t p q

1, 2 Drive 500 210 110 30 900 1300 Snub 250 130 70 20 990 1300 Bend 250 130 70 20 920 1250 Tension 300 130 70 20 920 1250 Tail 300 130 70 20 920 1250

3 Drive 500 210 110 30 900 1300 Snub 250 130 70 20 990 1300 Bend 250 130 70 20 920 1250 Tension 300 150 85 25 920 1250 Tail 300 150 85 25 920 1250

drums within this timeframe. Figure 3 shows the mode of failure which was observed in every drum. The end plate had cracked where it was welded to the boss. Multiple cracking had initiated in the surface of the plate at the toe of the weld. The initial defects had subsequently merged to produce a crack which ran around the entire length of the weld toe. In fully developed failures a circumferential crack formed at both the inner and outer surfaces of the plate. The two cracks then propagated towards one another, meeting at the centre of the plate. As a result, the boss became detached from the end plate. The through cracking generally took a smooth path across the thickness of the plate. However, in some instances the two cracks ran inwards at right angles to the plate surface, with the final separation taking place along the plate centre-line by delamination.

2. FATIGUE STRESSES

2.1. Background

Figure 4 is a schematic illustration of the deflections which occur in a loaded drum. Provided the self-weight of the drum can be neglected, the force applied by the belt is balanced by the reactions at the shaft bearings. Both the shaft and the end plates deflect, and a bending stress field is created through the thickness of the end plates. The maximum bending stress Oma x occurs at the plate surface next to the boss, and cycles from tensile (+) to compressive ( - ) to tensile (+) with each revolution of the drum. The multiple initiation of cracking is consistent with a fatigue mechanism, and

.J, S °°°° -. I " . ' : •

. I° ,'.° . \ ." ... - . : . , \ ..': :.-.. : ..: -.;\ • ° : °- - -, . ' ; . : ° \

t _. "_- .'_.-'..:

Fracture ~ paths

Fig. 3. Mode of failure of the drums.

62 D . R . H . JONES

(-)

F

P

F

Fig. 4. Schematic illustration ol the deflections in a loaded drum.

the location of the initiation sites at the weld toe is consistent with both the position of maximum bending stress and the adverse effect of the weld on the fatigue strength of the steel. The number of fatigue cycles N experienced in service can be estimated for each drum since both the shell diameter and belt speed are known. Values for N are given in Table 2.

2.2. Stress analysis

Figure 5 shows the forces and moments acting on: (a) the shaft, and (b) the end plate. Equating moments for the shaft we have

F(q - p) = MA + MB. (1)

Table 2. Number of fatigue cycles N (million)

Unit Drum type N ( 1 week) N (4 weeks)

1 , 2 , 3 Drive 0.6 2.4 Snub [.2 4.6 Bend 1.2 4.6 Tension I.() 3.9 Tail 1.0 3.9

(a)

4 q ~

(b) F

~ M B

oB~--zQ , . ~ -

Simply suppor ted plate

F

~ . M B

F

Clamped plate

Fig. 5. Forces and moments acting on: (a) the shaft, and (b) the end plate.

Fatigue failures of welded conveyor drums 63

The s tandard result [1] gives

where

OB- MAp, (2) E1

?[C 4 I - (3)

4

The deflection of the end plate can be t reated as a t runnion loading problem. The s tandard results [1] give

fl MB O m a x - - , (4)

at 2

and

0IMB 0B - (5 )

Et 3

a~ and fl are dimensionless pa ramete r s which are separate functions of (b/a). Values are available [1] for the cases where the ou te r c i rcumference o f the plate is: (i) simply suppor ted , and (ii) c lamped. Combin ing Eqns (1 ) - (5 ) gives

flFp(q - p)t O ' m a x ~--" = kF. (6)

a( 0~7TC4 pt3)

Table 3 lists values of O'ma x calculated for F = 1000 kgf. In practice, the per iphery of the end plate is ne i ther simply suppor ted nor c lamped, and the average value of O'ma x has been taken as a reasonable representa t ion of the real situation.

2.3. Operational loadings

In practice, the value of O'max in each d rum is de te rmined by the force F which is del ivered to the shaft by the boss. Refer r ing to Fig. 6, we see that the resultant force acting on the shaft is P + Mg. P is the force which the belt applies to the drum, and M is the combined mass o f the shell, end plates and bosses. Thus

F = 0.5(P + Mg). (7)

We note that e = 2Tsin(V/2), (8)

where V is the angle of wrap. The values o f F are specified in Table 4.

Table 3. Values of the maximum bending stress O'max (in MPa) for F = 1000 kgf

O'ma x

Unit Drum type o:(i) fl(i) Omax(i) tr(ii) fl(ii) Omax(ii) (average)

1, 2 Drive 0.275 1.95 7.39 0.150 1.61 8.21 7.80 Snub 0.152 1.41 31.5 0.072 1.07 27.8 29.7 Bend 0.152 1.41 32.9 0.072 1.07 29.2 31.1 Tension 0.261 1.89 30.6 0.141 1.55 30.7 30.7 Tail 0.261 1.89 30.6 0.141 1.55 30.7 30.7

3 Drive 0.275 1.95 7.39 0.150 1.61 8.21 7.80 Snub 0.152 1.41 31.5 0.072 1.07 27.8 29.7 Bend 0.152 1.41 32.9 0.072 1.07 29.2 31.1 Tension 0.169 i .49 17.4 0.081 1.15 16.1 16.8 Tail 0.169 1.49 17.4 0.081 1.15 16.1 16.8

64 D. R. H. JONES

T

~ T

Fig. 6. Forces acting at the bosses.

Table 4. Values of the bearing reaction force F

T ~g M F q~ Unit Drum type (kgf) (°) (kg) (kgf) (°)

1, 2 Drive 400(1 210 2250 3735 - 2 Snub 30 500 1279 - 7 8 Bend 90 500 3010 - 4 8 Tension 180 800 3600 90 Tail 180 800 3950 4

3 Drive 6600 210 2250 6181 5 Snub 30 500 1952 - 7 7 Bend 90 500 4846 - 47 Tension 180 1000 6100 90 Tail 180 1000 6532 6

2.4. Self-weight stresses"

As shown in Fig. 7, the weight of the shaft tends to make it sag between the bearings. This generates a bending stress Omax(~w) in the end plates. Using superpos- ition, together with standard results [1] for end slopes, we have

OB - mgp3 P I MB + mg( ~ - p)2 rag (q - p ) ~ . (9) 6EI~/ E1 t 4~ 2 J

Combining Eqns (4), (5) and (9) gives

-_ [Jmgpt ( Omax(sw)

t a ( ~ - + pt 3)

N o w

p-~ 61:

(t 7? )2, + (q 2- p)}'

m = 2zrc2~p,

(10)

(11)

• ~ q . . . .

Fig. 7. Forces, moments and deflections produced by the self-weight of the shaft.

Fatigue failures of welded conveyor drums 65

where p is the density of the shaft material. Combining Eqns (6), (10) and (11) we find

O r m a x ( s w , _ ~c2pg [p2 ( 2 - p)2 + ~(q _ p)~. (12)

O'ma x F(--q ~ p) ~ 3 2 J Values of the ratio 100Omax~sw)/ama x are given in Table 5: the maximum self-weight stress is between 4 and 21% of the maximum stress generated by the applied force F. In the case of the snub drums, F acts almost vertically downwards: to first order we add Omax and am~x~sw~ to arrive at the maximum stress in the end plate. In the case of the tension drums, F acts vertically upwards: we therefore subtract amax~sw ) from ama x tO find the maximum stress. With the bend drums, F acts down at an angle of ~ 45°: to first order we add 0.5Omax~sw~ to Omax. With the drive and tail drums, F is almost horizontal: to first order the self-weight stresses can be neglected.

2.5. Summary

The maximum bending stresses in service are collected in Table 6. Table 6 also gives data for the maximum bending stress range Ao = 2tYmax, and the number of stress cycles to failure, Nf.

3. WELD FATI GUE STRENGTHS

3.1. Use of the weld fatigue curves

Figure 8 gives fatigue curves for welds in structural steel, taken from the British Standard code for the design of bridges [2]. Because the fatigue strength of a weld is

Table 5. Values of lOOamax(sw)/tTmax for a density of 7.8 × 10 -6 kgmm -3

e Unit Drum type (mm) 100Omax(sw)/amax

1, 2 Drive 1440 13.9 Snub 1400 20.5 Bend 1350 7.7 Tension 1350 6.4 Tail 1350 5.9

3 Drive 1440 8.4 Snub 1400 13.4 Bend 1350 4.8 Tension 1350 5.6 Tail 1350 3.5

Table 6. Operational history of conveyor drums

1 Drive 29 58 Snub 46 92 1.2-4.6 Bend 98 196 Tension 103 206 1.0-3.9 Tail 121 242 1.0-3.9

2 Drive 29 58 Snub 46 92 Bend 98 196 Tension 103 206 Tail 121 242 1.0-3.9

3 Drive 48 96 Snub 66 132 1.2-4.6 Bend 155 310 1.2-4.6 (1) Tension 96 192 Tail 110 220

amax A a Nf ,-Unit Drum type (MPa) (MPa) (million)

66 D. R. H. JONES

09

r ~

Curves for 97.7% survival 300 ~ I 200 150

100

30 - " ~ 20 " -,. 15 ~ "~

105 106 107 I08 l09

Number of cycles

Curves for 50% survival 300 ~ ~ 200 150

. .-..: - s 0 - - -

40 '~ 3o - ',.:

20 " ~ 15 -- ...~ ., . , , . , , . I0 -- '.,.". "-

l L I l iii{l i { i l HI{ i { {} lilli l I I l~l~

05 106 107 108 109

Number of cycles

Fig. 8. Fatigue curves for welds in structural steel [2].

sensitive to the geometry, the code divides the common types of welds into a number of weld classes, each of which has its own fatigue curve. The geometries of the main classes of weld are shown in Fig. 9. Two sets of fatigue curves are given in the code: the "mean-line curves" give the stress levels at which the weld has a 50% chance of survival; the "design curves" give the stress levels at which the weld has a 97.7% chance of survival. The mean-line curves are usually used in failure analysis (where the welds have already cracked), whereas the design curves are used for design (where cracking is to be avoided). Naturally, for a given life, the stress required to give a 97.7% probability of survival is less than that required to give a 50% probability of survival.

Fatigue data for uncracked components are traditionally obtained under conditions of zero mean stress. When the mean stress is not zero, Goodman's rule indicates that the fatigue strength must be corrected by a factor which depends on the value of the mean stress. No such correction is needed for welds: their fatigue strength is assumed to depend only on the applied stress range A o . This assumption derives from the fact that welds generally contain tensile residual stresses of yield magnitude. Thus, if the weld is subjected to a tensile load during the first quarter of the fatigue cycle, it will yield in tension and will shake down. All subsequent deformation will be elastic, with the maximum cyclic stress in the weld being equal to the yield stress in tension. The fatigue strength of the weld is therefore not affected by the extent to which the applied stress cycle is tensile.

B e l o w 107 cycles the fatigue curves are based on experimental data for actual welds. However, care is needed when using the curves above 107 cycles. The situation is summarised in Fig. 10. Provided the stress range of the fatigue cycle is constant and the environment is clean, dry air a fatigue limit operates: the welds will survive indefinitely as long as the stress range is less than the stress range at 107 cycles. But if the environment is aggressive there may be no fatigue limit: unless fatigue data are available in the specific environment the conservative approach is to extrapolate the curve following the dashed line in Fig. 10.

Fatigue failures o f we lded conveyor drums 67

Details on surface of member Details on end connections of member

))))!)))))))', C/D

Grinding direction

~ 2 DIE C \ Grind

all edges

I t i

Fig. 9. Classes o f we lds for use with Fig, 8. 300 200 150

100

60 Cons tan t At~ in clean dry air 50 ~ m m - - 401 30 ~6~/e .d o, i ,

,9 .% ~ /" . 15 ~"~o "" n + 2 "~atr

% . , lO i t ~tl %,,

10 lO 6 10 7 10 8 10 9

N f

Fig . 10. W e l d fatigue data above 10 7 cycles.

Random overloads can trigger the growth of defects that would be stable at the normal value of the stress range. The code allows for this by reducing the slope of the fatigue curve above 10 7 cycles as shown in Fig. 10. The extent of this reduction depends on the class of weld. The slope of the fatigue curve below 10 7 cycles is defined as 1In (over one decade of stress range the number of cycles goes through n decades), n = 3 for Classes D - W , but rises to 3.5 for Class C and 4 for Class B. Above 10 7 cycles the slope of the fatigue curve is set equal to 1/(n + 2).

3.2. Failure analysis

The welds between the plate and the boss are responsible for transferring a direct load between the two components and are classified as "details on end connection of member" in Fig. 9. We classify the weld detail as F2 because: (a) the welded joint between the plate and the boss has only partial penetration, and (b) the cracks initiated at the weld toes and ran into the member itself. Figure 11 shows the

68 D. R . H . J O N E S

300 -- ~ --1 Bend- - - -~- 1 Bend - 2 T a i l ~ 1 Tail

" ~.1 Ten ,on ------4,-2 Tension 200,s0 4Bend I Snub

100 D. 1 Dr ive _ .,.. ~ I Snub ~ 1 Snub -

60 -- ~ ~ ~ - ~ 2 Drive 50 -- .. 40 -- "-

30 -- -.

20 -- " "~

15 -- " . .

10 -- " . . I i l l i l l i [ I i l l l J J l i I i I l l l l i l i ] l l l l l l l '~"

8105 106 107 108 109

Nf

Fig , H , M e a n - l i n e c u r v e for the C l a s s F2 d e t a i l w i t h t he ( A o , N ) v a l u e s fo r the d r u m s superimposed.

mean-line curve for the Class F2 detail with the (Ao, N) points for the drums superimposed.

The locations of the (Ao, N) points for the drive and snub drums in relation to the F2 curve are consistent with the observations that: (a) the three drive drums remained intact, and (b) of the three snub drums, two failed and one remained intact. However, the bend, tension and tail drums should all have failed at less than half of the calculated Ao. It is not clear why, out of these 12 drums, only four failed in service; nor is it clear why it took so long for cracking to occur in the drums which did fail. Errors in the stated service times and tensioning weights are probably at the root of such discrepancies.

4. DESIGN IMPLICATIONS

A reasonable design life for the conveyor drums is 20 years of continuous operation, equivalent to ~ 10 9 revolutions. If a fatigue limit operates, the design curve in Fig. 8 shows that Ao must be less than ~ 34 MPa, i.e. Omax ~< 17 MPa. As shown in Table 6, the values of Oma x calculated for the drums ranged from 29 to 155 MPa, which emphasises the extent of the design problem. Referring to Eqn (6), we see that the most potent way of reducing Omax is to increase the shaft radius c. This is because the flexural rigidity of the shaft increases as c4: the stiffer the shaft, the less the flexure of the end plates. It is therefore not surprising to find that the lowest stress of 29 MPa is found in the drums with the thickest shafts, i.e. the drive drums.

As an example of how Oma x can be reduced to an acceptable level using the existing design philosophy, we consider a drive drum from unit 1 operating under idling conditions (F = 3735 kgf). An obvious first step in decreasing Oma x is to reduce the overhang of the shaft from the 400 mm specified to the value of 310 mm found in a snub drum. The next step is to vary the thickness of the end plate. Figure 12 plots Omax as a function of plate thickness: the graph shows that the specified thickness of 30 mm is actually very close to the thickness which gives a maximum value of stress. The stress can be reduced either by increasing or decreasing the plate thickness. Setting t -- 15 mm brings am, x down to the required level of 17 MPa whilst achieving improved economy and ease of welding. However, a drive drum modified in this way would not be able to function safely when the conveyor is transporting a charge (because of the large increase in belt tension at entry to the drive drum). It might be possible to offset the additional belt loadings by reducing the plate thickness still further, but the design appears to be marginal. Arguably the best way out of the design problem is to select the lightest shaft consistent with avoiding the failure of the

Fatigue failures of welded conveyor drums 69

25 -

v

10

5

I I I I I I 0 10 20 30 40 50 60

t (mm)

Fig. 12. Variation of O'max with plate thickness for a drive d rum operating at F = 3735 kgf with a reduced shaft overhang (q - p ) of 310 mm.

shaft itself, and to couple the end plates to the bosses with an articulated joint which permits flexural movement between the two components. Bending stresses are thereby eliminated, and the risk of fatigue cracking is removed.

REFERENCES

1. W. C. Young, Roark's Formulas for Stress and Strain (6th edn), McGraw-Hill , New York (1989). 2. British Standards Institution, BS 5400: 1980: "Steel, Concrete and Composite Bridges": Part 10: "Code

of Practice for Fat igue".