Fatigue failures of welded conveyor drums

Engineering FailureAnalysis, Vol 2, No. i pp. 59-69, 1995

Pergamon

Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 1350-6307/95 $9.50 + 0.00

1350-6307(95)00002-X

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. I N T RO D U CT IO N 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 u n i t s o f this t y p e w e r e i n s t a l l e d as p a r t o f a l a r g e n e w p l a n t f o 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 e d b y f a t i g u e . T h e f a i l u r e s highlighted a fundamental design problem with the drums, which ultimately required 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 h e e n t i r e p l a n 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 progressively 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

'

~

~"""'~. O ~

"

"~

~

~

"

' T

e

n

s

drum i

I.O) 1

o

l,iO I

~ n

~',

drum

Snub drum *-'~0 drum Discharge

Weight Tail drum Fig. 1. Schematic diagram of the conveyor. 59

"1 ko I

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 c a r b o n - m a n 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 Self-aligning bearing plate C

Boss

. . . . .

~Shaft

¢

p

.D.

q

Fig. 2. Cross-sectionthrough a conveyor drum.

\

Fatigue failures of welded conveyor drums

61

Table 1. Dimensions of conveyor drums (mm) Unit

D r u m type

a

b

c

t

p

q

1, 2

Drive Snub Be nd Tension Tail

500 250 250 300 300

210 130 130 130 130

110 70 70 70 70

30 20 20 20 20

900 990 920 920 920

1300 1300 1250 1250 1250

3

Drive Snub Be nd Tension Tail

500 250 250 300 300

210 130 130 150 150

110 70 70 85 85

30 20 20 25 25

900 990 920 920 920

1300 1300 1250 1250 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 Omax 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

-.

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°°°° I".':

•

.\ ." ....I° ,'.° -.:.,\ ..': :.-.. : ..: -.;\ •° : °- - -, . ' ; . : ° \ t _. "_- .'_.-'..:

~

Fracture paths

Fig. 3. Mode of failure of the drums.

62

D.R.H.

JONES P

(-)

F

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 m a x i m u m bending stress and the adverse effect of the weld on the fatigue strength of the steel. The n u m b e r 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 m o m e n t s for the shaft we have

F(q - p) = MA + MB.

(1)

Table 2. N u m b e r of fatigue cycles N (million) Unit

Drum type

1,2,3

Drive Snub Bend Tension Tail

N ( 1 week)

N (4 weeks)

0.6 [.2 1.2 I.() 1.0

2.4 4.6 4.6 3.9 3.9

(a)

4

q

(b) F

~M B

oB~--zQ ,

~

F

~.M B

.~-

F

Simply supported plate

Clamped plate

Fig. 5. Forces and m o m e n t s acting on: (a) the shaft, and (b) the end plate.

Fatigue failures of welded conveyor drums

63

T h e s t a n d a r d result [1] gives

OB- MAp, E1

(2)

where ?[C 4

I -

(3) 4

T h e deflection of the end plate can be treated as a t r u n n i o n loading p r o b l e m . T h e s t a n d a r d results [1] give

Oma x

fl MB , at 2

--

(4)

and 0B -

0IMB

(5)

Et 3

a~ and fl are dimensionless p a r a m e t e r s which are separate functions of (b/a). Values are available [1] for the cases w h e r e the o u t e r circumference o f the plate is: (i) simply s u p p o r t e d , and (ii) clamped. C o m b i n i n g E q n s ( 1 ) - ( 5 ) gives

flFp(q - p)t O'ma x

~--"

=

a( 0~7TC4

kF.

(6)

pt3)

Table 3 lists values of O'max calculated for F = 1000 kgf. In practice, the p e r i p h e r y of the end plate is neither simply s u p p o r t e d n o r clamped, and the average value of O'max has b e e n taken as a reasonable r e p r e s e n t a t i o n of the real situation.

2.3.

Operational loadings

In practice, the value of O'max in each d r u m is d e t e r m i n e d by the force F which is delivered to the shaft by the boss. Referring 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 d r u m , and M is the c o m b i n e d mass o f the shell, end plates and bosses. Thus

F = 0.5(P + Mg).

(7)

e = 2Tsin(V/2),

(8)

W e note that w h e r e V is the angle of wrap. T h e 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

1, 2

Drive Snub Bend Tension Tail Drive Snub Bend Tension Tail

3

o:(i)

fl(i)

Omax(i)

tr(ii)

fl(ii)

0.275 0.152 0.152 0.261 0.261 0.275 0.152 0.152 0.169 0.169

1.95 1.41 1.41 1.89 1.89 1.95 1.41 1.41 i .49 1.49

7.39 31.5 32.9 30.6 30.6 7.39 31.5 32.9 17.4 17.4

0.150 0.072 0.072 0.141 0.141 0.150 0.072 0.072 0.081 0.081

1.61 1.07 1.07 1.55 1.55 1.61 1.07 1.07 1.15 1.15

Omax(ii) (average) 8.21 27.8 29.2 30.7 30.7 8.21 27.8 29.2 16.1 16.1

7.80 29.7 31.1 30.7 30.7 7.80 29.7 31.1 16.8 16.8

D. R. H. J O N E S

64

T

~T Fig. 6. Forces acting at the bosses.

Table 4. Values of the bearing reaction force F T (kgf)

~g (°)

M (kg)

F (kgf)

q~ (°)

Drive Snub Bend Tension Tail

400(1

210 30 90 180 180

2250 500 500 800 800

3735 1279 3010 3600 3950

-2 -78 -48 90 4

Drive Snub Bend Tension Tail

6600

210 30 90 180 180

2250 500 500 1000 1000

6181 1952 4846 6100 6532

5 -77 - 47 90 6

Unit

D r u m type

1, 2

3

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 superposition, together with standard results [1] for end slopes, we have

OB - mgp3 6EI~/

P I MB + mg( ~ - p)2 E1 t 4~ Combining Eqns (4), (5) and (9) gives -_

[Jmgpt

Omax(sw)

(

t - + pt 3)

a(~

p-~ 61:

rag(q- p ) ~ . 2 J

(9)

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

(10)

Now

= 2zrc2~p,

m

• ~

q

....

Fig. 7. Forces, m o m e n t s and deflections produced by the self-weight of the shaft.

(11)

Fatigue failures of welded conveyor drums

65

where p is the density of the shaft material. Combining Eqns (6), (10) and (11) we find Ormax(sw , _ ~c2pg [p2 ( 2 - p)2 + ~(q _ p)~. (12) O'max F(--q~ p) ~ 3 2 J Values of the ratio 100Omax~sw)/amax 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 amax 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. W E L D F A T I G U E 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)/tTmaxfor a density of 7.8 ×

10-6 kgmm -3

Unit

Drum type

e (mm)

1, 2

Drive Snub Bend Tension Tail

1440 1400 1350 1350 1350

13.9 20.5 7.7 6.4 5.9

3

Drive Snub Bend Tension Tail

1440 1400 1350 1350 1350

8.4 13.4 4.8 5.6 3.5

100Omax(sw)/amax

Table 6. Operational history of conveyor drums amax (MPa)

Aa (MPa)

Drive Snub Bend Tension Tail

29 46 98 103 121

58 92 196 206 242

1.0-3.9 1.0-3.9

2

Drive Snub Bend Tension Tail

29 46 98 103 121

58 92 196 206 242

1.0-3.9

3

Drive Snub Bend Tension Tail

48 66 155 96 110

96 132 310 192 220

,-Unit 1

Drum type

Nf (million) 1.2-4.6

1.2-4.6 1.2-4.6 (1)

D. R. H. JONES

66

Curves for 97.7% survival

300 ~

I

200 150 100

30 20 15

" ~ " -,. ~ "~

105

106

107

I08

l09

Number of cycles 300 200 150

~

Curves for 50% survival ~

..-..: -

09 s0

-

3o

-

40 r~

-

20 15 -I0

'~

"~ ...~

--

.,.,,.,,. '.,.".

l L I l iii{l

05

-

',.:

i { i l HI{

106

107

i { {} lilli

108

"-

l I I l~l~

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 w e l d e d c o n v e y o r drums Details on surface of member

67

Details on end connections of member

Grinding direction

))))!)))))))',

I

t

~2

C/D

DIE

C

\ Grind all edges

i

300 401

Fig. 9. Classes o f w e l d s for use with Fig, 8.

200 150

100

60 50 ~

C o n s t a n t At~ in clean dry air m m--

30

~6~/e .d o, i ,

15

,9 .% ~ ~"~o "" n + 2

lO

i

10

lO 6

10 7

t

%., ~tl %,,

10 8

10 9

/"

.

"~atr

Nf Fig. 10. W e l d fatigue data a b o v e 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. JONES 300

--

~

--1 B e n d - - - - ~ - 1 Bend -2Tail ~ 1 Tail ~.1 T e n , o n ------4,-2 Tension

"

200,s0

4Bend

I Snub D. 1 D r i v e .,.. ~ I Snub ~ 1 Snub

100 _

60 50 40

----

30

--

~

~

~-~

2 Drive .. "-.

20 --

" "~

15 --

"..

10 --

".. I

i llilli[

8105

I

106

i lllJJli

I

107

i Illllil

i

] lllllll

108

'~"

109

Nf Fig, H,

Mean-line

curve

for

the

Class

F2 detail

with the

(Ao, N)

values for the

drums

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. D E S I G N I M P L I C A T I O N S A reasonable design life for the conveyor drums is 20 years of continuous operation, equivalent to ~ 1 0 9 revolutions. If a fatigue limit operates, the design curve in Fig. 8 shows that A o must be less than ~ 34 MPa, i.e. Omax~< 17 MPa. As shown in Table 6, the values of Omax 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 Omax 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 Omax 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 d r u m s

69

25 -

v

10

5

0

I

I

I

I

I

I

10

20

30

40

50

60

t (mm) Fig. 12. Variation of O'maxwith plate thickness for a drive d r u m operating at F = 3735 kgf with a reduced shaft overhang (q - p ) of 310 m m .

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.

R E FE RE N CE S 1. W. C. Y o u n g , 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: " C o d e of Practice for Fatigue".