cfs no. 45

Rxintek Canada Corp.

PROJECT No. 87-li2-15K-022

CFS No. 45

THE EFFECT OF TENSIONING STRESSES ON BANDSAW PERFORMANCE

by-

J . Taylor Research S c i e n t i s t

Lumber Manufacturing Dept. Forintek Canada Corp.

S.G Button Associate Professor

Mechanical Engineering Dept. U n i v e r s i t y of B r i t i s h Columbia

March 1988

This project was financially supported by the Canadian Forestry Service under the Contribution Agreement existing between the

Government of Canada and Forintek Canada Corp.

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One of the most important f a c t o r s in bandsaw performance i s the r o l l tensioning operation c a r r i e d out during the preparation of the blade. The procedure introduces r e s i d u a l stresses into the blade of unknown magnitude and d i s t r i b u t i o n . From the point of view of understanding, modelling and p r e d i c t i n g performance these stresses are of major importance.

The objectives of t h i s project were to Investigate the e f f e c t of r o l l tensioning on bandsaw performance, to determine the degree of r o l l tensioning s t r e s s In a well r o l l tensioned blade, and to conduct a review of fatigue and f r a c t u r e associated with bandsaw blades.

The scope of the work conducted included:

Laboratory t e s t s , c a r r i e d out i n co-operation with the Mechanical Engineering Department at UBC, to determine the optimum c u t t i n g performance of a bandmill with untensioned blades.

F i e l d t r i a l s to e s t a b l i s h the performance c a p a b i l i t i e s of untensioned blades in a m i l l environment.

A comparison of r o l l tensioning stress magnitudes determined by the l i g h t gap technique with those obtained using f i n i t e element analysis methods.

A review of relevant fatigue and f r a c t u r e l i t e r a t u r e and an assessment of the present state of the a r t with respect to the f a t i g u e a n a l y s i s of bandsaw blades.

The c u t t i n g t e s t s show that t h i n untensioned blades at high s t r a i n s are capable of providing excellent c u t t i n g accuracy, the boards produced had a standard, w i t h i n board, d e v i a t i o n of 7 to 13 thou. The f i e l d t r i a l s were most encouraging and showed Improvements i n c u t t i n g accuracy of 30 to 40% and reductions i n blade thickness of one gauge.

The review covers t r a d i t i o n a l methods of estimating the blade fatigue l i f e ( A l l e n , 1985), the r o l e of l i n e a r e l a s t i c f r a c t u r e mechanics in c a l c u l a t i n g blade fatigue l i f e , and the s t r a i n based approach to determining the crack i n i t i a t i o n period.

From the r e s u l t s of the laboratory t e s t s and f i e l d t r i a l s i t i s apparent that s i g n i f i c a n t improvements In recovery can be achieved with t h i n , untensioned, blades operating at high s t r a i n s . However, i t i s important that the m i l l s have reasonably modern, well maintained, bandmills and f i l i n g room equlpnent, good q u a l i t y c o n t r o l procedures and enthusiastic personnel.

The review of fatigue and f r a c t u r e highlighted the f a c t that a d d i t i o n a l material s t r e s s - s t r a i n properties and material constants are required before l i n e a r e l a s t i c f r a c t u r e mechanics, or the s t r a i n based approach to estimating crack i n i t i a t i o n , can be used to improve current fatigue l i f e p r e d i c t i o n s .

Summary

Table of Contents

L i s t of Tables

L i s t of Figures

1.0 OBJECTIVE AND SCOPE

2.0 INTRODDCTIQN

3.0 BACKGROUND

4.0 STAFF

5.0 MATERIALS AND METHODS

5.1 LABORATORY EQUIPMENT AND INSTRUMENTATION 5.2 SAWBLADES 5.3 OPERATING CONDITIONS 5.4 CUTTING TESTS 5.5 FIELD TRIALS 5.6 BLADE STRESS ANALYSIS

6.0 RESULTS

6.1 TRACKING STABILITY 6.2 LABORATORY CUTTING TESTS 6.3 FIELD TRIALS 6.4 BLADE STRESS ANALYSIS

7.0 REV1£H OF FATIGUE AND FRACTUBE

7.1 CURRENT METHODS OF ESTIMATING FATIGUE LIFE 7.2 LINEAR ELASTIC FRACTURE MECHANICS AND FATIGUE 7.3 THE CRACK INITIATION PERIOD

8.0 DISCDSSKmS

8.1 TRACKING STABILITY 8.2 CUTTING TESTS 8.3 FIELD TRIALS 8.4 BLADE STRESS CALCULATIONS 8.5 FATIGUE AND FRACTURE

8.5.1 8.5.2

S i m p l i f i e d Approach Linear E l a s t i c Fracture Mechanics and Fatigue Crack I n i t i a t i o n 8.5.3

9.0 CONCXDSIONS

9.1 LABORATORY TESTS AND FIELD TRIALS 9.2 BLADE STRESS ANALYSIS 9.3 FATIGUE AND FRACTURE

9.3.1 S i m p l i f i e d (Goodman Diagram) Approach 9.3.2 LEFM and Fatigue

9.3.3 Crack I n i t i a t i o n

10.0 ACKNOWLEDGEMENTS

11.0 REFERENCES

APPENDICES

APPENDIX I - BOARD MEASUREMENT DATA AND METHOD OF CALCULATING CUTTING VARIATION

APPENDIX II - METHOD OF DETERMINING ENDURANCE STRENGTH OF BANDSAW STEEL FOR 5 HR. OPERATING LIFE

LIST OF TABLES

TABLE I - RESULTS OF LABORATORY CUTTING TESTS WITH UNTENSIONED BLADES

TABLE II - CUTTING ACCURACY OF UNTENSIONED BLADES FROM FIELD TRIALS

TABLE III - CUTTING ACCURACY OF TENSIONED BLADES ( i . e . PRIOR TO FIELD TRIALS)

TABLE IV - CURRENT FATIGUE BASED METHOD OF DETERMINING BANDMILL STRAIN FOR A 5 FT. BANDMILL

TABLE V - METHOD OF DETERMINING BANDMILL STRAINS FOR THE EXPERIMENTAL 5-FT. BANDMILL WITH 8-in. AND 10-in. BY 18-G.A. UNTENSIONED SAWBLADES

LIST OF FIGDKBS

FIGURE 1 - BENT BANDSAW BLADE AND TRANSVERSE DEFLECTED SHAPE FIGURE 2 - INFLUENCE OF PRESSURE FORCES ON TRACKING STABILITY FIGURE 3 - DETAILS OF WHEEL GROOVE PATTERNS FIGURE 4 - INSTRUMENT ARRANGEMENT FIGURE 5 - DETAILS OF THE CUTTING AREA FIGURE 6 - DISPLACEMENT OF 8-in. BLADE IN 8-in. DEEP CUT WITH CANT

AND KNOT LOCATIONS FIGURE 7 - DISPLACEMENT OF 8-in. BLADE IN 12-in. DEEP CUT FIGURE 8 - DISPLACEMENT OF 10-in. BLADE IN 8-in. DEEP CUT FIGURE 9 - DISPLACEMENT OF 10-in. BLADE IN 12-in. DEEP CUT FIGURE 10 - ROLL TENSIONING STRESS AND NODAL STRESS VALUES FIGURE 11 - LONG PLATE BUCKLING 10-FT. PARABOLIC STRESS FIGURE 12 - LONG PLATE BUCKLING 10-FT. PARABOLIC STRESS FIGURE 13 - LONG PLATE BUCKLING 10-FT. PARABOLIC STRESS FIGURE 14 - LONG PLATE BUCKLING 10-FT. PARABOLIC STRESS FIGURE 15 - MODIFIED GOODMAN DIAGRAM FIGURE 16 - TYPICAL S-N DIAGRAMS FIGURE 17 - EFFECT OF MEAN STRESS FIGURE 18 - RELEASED LOADING FATIGUE TESTS FIGURE 19 - MODIFIED GOODMAN DIAGRAM RELATING STRESS & STRENGTH FIGURE 20 - CALCULATION OF MEAN STRESS FIGURE 21 - STRESSES IN A ROTATING SAWBLADE FIGURE 22 - Ki FOR COMMON CONFIGURATIONS FIGURE 23 - FIGURE CRACK LENGTH VERSUS APPLIED CYCLES FIGURE 24 - SCHEMATIC SIGMOIDAL BEHAVIOUR OF FATIGUE CRACK

GROWTH RATE FIGURE 25 - STRAIN-LIFE CURVES

1.0 O B J E C T I V E A N D S C O P E

The o v e r a l l objective of t h i s work i s to be able to model and p r e d i c t the behaviour of handsaws.

The objectives of t h i s s p e c i f i c project were to investigate the e f f e c t of r o l l tensioning on bandsaw performance, to determine the degree of r o l l tensioning s t r e s s i n a well r o l l tensioned blade, and to conduct a review of fatigue and f r a c t u r e associated with bandsaw blades. The scope of the work conducted Included:

a) Laboratory t e s t s , c a r r i e d out i n co-operation with the Mechanical Engineering Department at UBC, to determine the optimum cu t t i n g performance of a bandmill with untensioned blades.

b) F i e l d t r i a l s to e s t a b l i s h the performance c a p a b i l i t i e s of untensioned blades i n a m i l l environment.

c) A comparison of r o l l tensioning stress magnitudes determined by the l i g h t gap technique with those obtained using f i n i t e element analysis methods.

d) A review of relevant fatigue and f r a c t u r e l i t e r a t u r e and an assessment of the present state of the a r t with respect t o the fatigue analysis of bandsaw blades.

2.0 I N T R O D D C T I O N

In a previous report to the Canadian Forestry Service Taylor and Button, (1987) completed an extensive review of the l i t e r a t u r e associated with bandsaws, conducted preliminary experiments to determine the e f f e c t of r o l l tensioning on blade l a t e r a l s t i f f n e s s and c u t t i n g performance, and examined guide induced s t r e s s and blade motion during washboarding. This report concluded that a d d i t i o n a l work should be undertaken to e s t a b l i s h the r e l a t i v e b e n e f i t s of tensioned versus untensioned blades.

Blade preparation Is considered to be a major factor a f f e c t i n g bandsaw performance and involves s e l e c t i n g the correct blade geometry, r o l l tensioning, l e v e l l i n g and tooth preparation. The most important of these f a c t o r s Is r o l l tensioning, a r o l l i n g process that introduces r e s i d u a l stresses into the blade which are compressive i n the centre and t e n s i l e towards the edges. This process Increases the s t i f f n e s s of the edges of the blade and Improves performance. However, the process requires a considerable amount of s k i l l and the effectiveness of a bandsaw may depend s o l e l y on t h i s one operation.

This report examines the e f f e c t of r o l l tensioning s t r e s s on bandsaw performance through laboratory c u t t i n g t e s t s and f i e l d t r i a l s . I t compares methods of estimating r o l l tensioning s t r e s s , developed by

Foschi (1975) and A l l e n (1985), with those obtained through f i n i t e element a n a l y s i s techniques using c e n t r a l region buckling as the l i m i t i n g value of s t r e s s . It also reviews fatigue and f r a c t u r e associated with handsaws.

The l i t e r a t u r e review covers t r a d i t i o n a l methods of estimating the blade fatigue l i f e ( A l l e n , 1985), the role of l i n e a r e l a s t i c f r a c t u r e mechanics i n c a l c u l a t i n g blade f a t i g u e l i f e , (Pook, 1983; Broeck, 1986) and the s t r a i n based approach t o determining the crack I n i t i a t i o n period (Fuchs and Stephens, 1980; Duggen and Byrne, 1977).

3.0 BACKGRODND

A number of d i f f e r e n t e f f e c t s contribute to the stresses that e x i s t i n an operating sawblade. Some of the stresses can be described as i n i t i a l or residual and are caused by r o l l i n g , shearing, tooth formation, r o l l tensioning and heat treatment and some are Introduced during operation by bandmill s t r a i n , bending, c u t t i n g , t i l t angle and v i b r a t i o n .

The r o l l tensioning operation i s considered to be one of the most important f a c t o r s i n obtaining good bandsaw performance. The deformations Introduced into the blade by r o l l tensioning cause the bandmill s t r a i n to be highest towards the edges of the blade. This increases the edge s t i f f n e s s of the blade and improves performance, but i t also increases the stress i n an area where stress i s already high, due to the tooth g u l l e t s .

Blade s t i f f n e s s i s an important factor i n obtaining good c u t t i n g accuracy and one of the best methods of increasing blade s t i f f n e s s Is to increase bandmill s t r a i n . The use of t h i n , untensioned, blades enables the s t r a i n to be increased without decreasing service l i f e . This i s possible because the use of thinner blades reduces the stress due to bending the blade over the wheels, and minimising r o l l tensioning minimises the related stresses, the saving i n str e s s can then be re-introduced by increasing bandmill s t r a i n .

Modern high s t r a i n bandmills are capable of providing more load than the blade can handle and a balance between the r o l l tensioning s t r e s s and s t r e s s from bandmill s t r a i n . Is important. If the combined stresses become too large f a t i g u e - r e l a t e d g u l l e t cracking i s l i k e l y to occur. The optimum r e l a t i o n s h i p between r o l l tensioning s t r e s s and bandmill s t r a i n has yet to be determined.

Methods of determining the amount of r o l l tensioning s t r e s s have been examined by Foschi (1975) and A l l e n (1985). R o l l tensioning stress i s estimated by bending the blade to a s p e c i f i c radius and measuring the transverse curvature (Figure 1): t h i s i s c a l l e d the light-gap technique. For good performance the r o l l tensioning stress must vary minimally along the length of the blade. This requires considerable s k i l l i n blade preparation, e s p e c i a l l y i f the blades are damaged.

Fig. 1 Bent bandsaw blade and traverse deflected sliape called 'Light Gap'

Laboratory t e s t s and f i e l d t r i a l s (Button, Lehmann and Taylor, 1986) indi c a t e that s i g n i f i c a n t Improvements in bandsaw performance are possible when thinner blades are used i n conjunction with higher bandmill s t r a i n s . These higher s t r a i n s Improve the o v e r a l l s t i f f n e s s of the blade, and hence the c u t t i n g accuracy. However, la r g e r bandmill s t r a i n s decrease the fatigue l i f e of the blade, and as bandmills are us u a l l y operated f o r periods approaching the blade fatigue l i f e l i m i t , understanding blade f a t i g u e l i f e c h a r a c t e r i s t i c s - together with the a b i l i t y to estimate operating l i f e t i m e s - may become an important fa c t o r i n performance optimization.

The r o l l tensioning stress i s a l s o a f a c t o r i n blade tracking s t a b i l i t y as are the e f f e c t s of crowned wheels and wheel t i l t i n g (Suglhara, 1977). The crown on the wheel causes the blade to track i n a c e n t r a l equilibrium p o s i t i o n which can be adjusted with the wheel t i l t angle to provide the c o r r e c t amount of blade overhang on the c u t t i n g s i d e . R o l l tensioning accentuates the e f f e c t of the wheel crown i n providing a greater r e s t o r i n g moment when the blade moves away from Its equilibrium p o s i t i o n (Figure 2) and helps p o s i t i o n i n g of the blade on the wheels.

There are advantages to using both tensioned and untensioned blades. When comparing the two types i t i s Important to remember that the p r i n c i p l e purpose of the untensioned system i s to allow the bandmill s t r a i n to be increased. The following presents some of the p r i n c i p l e advantages and disadvantages of each type:

a) Tensioning Increases the s t i f f n e s s of the blade at the edges and reduces i t i n the centre while Increasing the bandmill s t r a i n improves the o v e r a l l blade s t i f f n e s s .

b) Tensioned blades are e a s i l y positioned where required on the wheel whereas untensioned blades require a reasonably precise t i l t angle and tend to operate with a larger overhang.

c) The actual stress d i s t r i b u t i o n from r o l l tensioning i s not known and an optimum p r o f i l e has yet to be determined.

d) Exc e p t i o n a l l y s k i l l e d personnel are required to prepare a well r o l l tensioned blade.

e) Generally untensioned blades require l e s s s a w f l l l n g than tensioned blades of the same gauge.

f ) R o l l tensioning Introduces severe stresses i n the blade and aggravates fatigue cracking at the g u l l e t .

g) Alignment of the bandmill i s c r i t i c a l to the successful operation of untensioned blades.

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h) Due to the inaccuracies and unknowns associated with r o l l tensioning i t i s often d i f f i c u l t to i s o l a t e f a c t o r s that are causing problems, or even to determine whether they are due to r o l l tensioning or some other f a c t o r .

i ) R o l l tensioning s t r e s s can be a l t e r e d during operation i n d i c a t i n g that parts of the blade are operating close to, and sometimes exceed, the y i e l d s t r e s s of the m a t e r i a l .

j ) Wheel wear i s reduced by 50 t o 75% with untensioned blades.

4.0 STAFF

J . Taylor Research S c i e n t i s t Lumber Manufacturing Dept.

S.G. Button Associate Professor Mechanical Engineering Dept. Un i v e r s i t y of B r i t i s h Columbia.

5.0 MATERIALS AND METHODS

5.1 LABORATORY EQUIPMENT AND INSTRUMENTATION

The experiments were conducted i n the Wood Sawing Research Laboratory of the Department of Mechanical Engineering at the U n i v e r s i t y of B r i t i s h Columbia. The experimental bandmill had f i v e - f o o t dleuneter s t e e l wheels and was equipped with an hydraulic s t r a i n i n g system and a seven stage setworks. The wheels used had been fa b r i c a t e d f or the previous project and had the groove c o n f i g u r a t i o n shown i n Figure 3a. The s t r a i n i n g system had been modified to provide up to 34,000 l b . of s t r a i n . The saw was driven h y d r a u l i c a l l y v i a a swash p l a t e type hydraulic pump and 100 hp e l e c t r i c motor. The blade speed could be varied from zero to 11,000 fpn. Standard guide blocks were used with a support frame f a b r i c a t e d so the guides could be adjusted. In approximately 2-ln. Increments, from the standard span of 30-in. down to 12-in. A span length of 20.25-ln. was used throughout the experiments.

The ca r r i a g e , running on p r e c i s i o n aligned r a i l s , was driven by cable and drum v i a a second hydraulic system and the feed speed could be varied from zero to 480 fpm.

The Instrumentation and data a c q u i s i t i o n equipment used f o r t h i s p roject are shown schematically i n Figure 4. Up to four non-contacting displacement probes, positioned just above the surface of the lumber, were used to record blade displacement. During the c u t t i n g t e s t s the s i g n a l s from the probes were fed through a Neff high speed data

b. pattern developed during mill trials

Fig. 3 - Details of wheel groove patterns

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The speed of the carriage was recorded by a tachometer mounted on the cable drum of the carriage d r i v e . The probe and tachometer s i g n a l s were c o l l e c t e d by a multi-channel data a c q u i s i t i o n system connected to and driven by the computer.

5.2 SAWBLADES

Two 18-ga. (0.049-ln.) blades were used for the laboratory experiments, one 8-in. wide and the other 10-in. wide. The remaining blade s p e c i f i c a t i o n s were as follows:

tooth p i t c h 1.75-in. g u l l e t depth 0.65-in. g u l l e t area 0.66-sq. i n . swage width 0.117-ln. no back crown ( l i g h t r o l l i n g where necessary to o f f s e t the curve induced when the teeth were punched) no tensioning (zero l i g h t gap)

5.3 OPERATING CONDITIONS -

A guide to the l e v e l of bandmill s t r a i n s to be used were estimated using fatigue theory (see Table V ) and the maximum calculated values for the 8-in. and 10-ln. blades were 27,330 l b . and 34,376 l b . r e s p e c t i v e l y .

For the blade s t a b i l i t y t e s t s the applied bandmill s t r a i n was set at 24,500 l b . with wheel speeds ranging from 50 rpm. to 100 rpm. (790 fpm. to 1570 fjxn.) For c u t t i n g t e s t s with the 8-ln. blade the s t r a i n was set at 24,500 l b . and 30,000 l b . f o r the 8-in and 12-in. deep cuts, r e s p e c t i v e l y . For the 10-ln. blade c u t t i n g t e s t s the s t r a i n was set at 30,000 l b . and 34,000 l b . f o r the 8-ln. and 12-in. ^ e p cuts, again r e s p e c t i v e l y .

The c o n f i g u r a t i o n of the guides i s shown i n Figure 5. The guides were set to provide 100 l b . of guide pressure, which, f o r a s t r a i n of 25,000 l b . , tr a n s l a t e d into a guide o f f s e t of 0.25-in. Accurate alignment i s e s s e n t i a l f o r accurate c u t t i n g , the faces of the guides were aligned i n a v e r t i c a l plane, p a r a l l e l with the l i n e o f carriage motion, to within 0.001-ln.

Fig. 5 - Details of the cutting area

Four sets of c u t t i n g t e s t s were completed. Each blade cut two seven-board samples, one at a g u l l e t feed index (GFI) of 0.6 from an 8-in. deep cant of dry knotty hemlock and one at a GFI of 0.7 from a 12-in. deep cant of c l e a r green hemlock. From A l l e n (1984) a GFI value of 0.7 corresponds to the maximum b i t e recommended for accurate c u t t i n g with bandsaws. A GFI of 0.6 corresponds to a b i t e of 0.05-in.

The guide span was set at 20.25-in; small enough for reasonable accuracy while s t i l l being representative of m i l l conditions.

System performance was assessed by measuring board dimensions with d i g i t a l c a l i p e r s at s i x - i n c h i n t e r v a l s along the top and bottom edges. The data were used f o r c a l c u l a t i n g the within board, between board and t o t a l deviation, as per methods i n Appendix I.

Ad d i t i o n a l information was obtained from the non-contacting displacement probes located just above the cut which recorded the motion of the blade while c u t t i n g .

Also the p o s i t i o n of the untensioned blades on the grooved wheels and the e f f e c t of the wheel t i l t was recorded p r i o r to conducting the c u t t i n g t e s t .

5.5 FIELD TRIALS

The f i e l d t r i a l s were conducted at West Eraser's m i l l at Chetwynd, B.C. The m i l l has four, f i v e foot, high s t r a i n , CanCar bandmills with 150 hp motors. Normal m i l l p r a c t i c e u t i l i z e s both 16-ga. and 17-ga. blades depending on the depth of cut. The bandmill s t r a i n s were 14,000 l b . and the rim speed was 11200 fpm.

For the f i e l d t r i a l s , the wheels on one of the bandmills were grooved (as shown in Figure 3a) f o r use with t h i n untensioned blades at high s t r a i n s . The blades were 16-and 18-ga. by 10-ln. with a kerf of 0.140 and 0.120-in. r e s p e c t i v e l y . The tooth p i t c h was the same on a l l blades, but the tooth shape d i f f e r e d s l i g h t l y from that used i n the laboratory experiments.

5.6 BLADE STRESS ANALYSIS

A well r o l l tensioned blade i s considered to be on the point of buckling due to the compressive stresses in the c e n t r a l region. Two methods of estimating these stresses were used and compared. One method used the methods of A l l e n (1985), and the second u t i l i z e d f i n i t e element analysis techniques.

Estimated r o l l tensioning stresses were assessed for a v a r i e t y of blade widths and thicknesses ( A l l e n , 1985) which assxmes a parabolic stress p r o f i l e across the blade.

For the finite-element work the same parabolic s t r e s s d i s t r i b u t i o n was used and the blade was modelled as a 10-ft. long section with boundary conditions that enforced zero displacement at the edges and zero r o t a t i o n at the ends. The parabolic, r o l l tensioning s t r e s s was Introduced into the model as a v a r i a b l e nodal s t r e s s . A buckling an a l y s i s was then completed to e s t a b l i s h the f i r s t four buckled mode shapes and the corresponding magnitude of the stress required to cause buckling.

6.0 KBSDLTS

6.1 TRACKING STABILITY

Laboratory experiments were conducted to e s t a b l i s h the stable region of operation for the two experimental blades and to s e l e c t operating p o s i t i o n s f or the c u t t i n g t e s t s . The s t a b i l i t y t e s t s involved running the blades on the wheels at a low (50 to 100) rpm. and adjusting the blade p o s i t i o n with the wheel t i l t as required.

The stable region for the 8-in. blade was found to extend from a g u l l e t overhang of 0.75-in. to an overhang of 1.4-in., where the l i m i t i n g f a c t o r was the proximity of the guard. The selected blade p o s i t i o n f or the c u t t i n g t e s t s was with an overhang of 0.875-ln. This gave a wheel t i l t of approximately 0.1 degrees. The overhang was reduced to 0.125-in. at the guides by r e p o s i t i o n i n g the guide blocks.

The stable region for the 10-in. blade extended from a g u l l e t overhang of 0.6-in. to an overhang of 1.4-in. where again the l i m i t i n g f a c t o r was the proximity of the guard. The selected blade p o s i t i o n f o r the c u t t i n g t e s t s was with an overhang of 0.75-in., a wheel t i l t of approximately 0.1 degrees and the blade overhang at the guides was set to 0.44-in.

6.2 LABORATpRY CUTTING TESTS

The purpose of the laboratory c u t t i n g t e s t s was to determine the c u t t i n g accuracy that could be obtained with an untensioned blade under high s t r a i n . Each blade was used to cut two seven-board samples, one from an 8-in. deep cant and one from a 12-In. deep cant. T y p i c a l examples of the blade displacements, measured with the displacement probes, are presented g r a p h i c a l l y in Figures 6 to 9. The blade motion in Figure 6 i s composed of a small high frequency component superimposed on a large low frequency o s c i l l a t i o n . The large low frequency content Indicates that i t i s the blade s t a t i c s t i f f n e s s that i s of primary importance In c o n t r o l l i n g motion while the high frequencies are due to e x c i t a t i o n of the natural frequencies of the blade. The e f f e c t s on blade displacement of the large knots i n the 8-in. deep lumber are c l e a r l y v i s i b l e . The blade motion i n Figure 7 was sampled at a much higher rate than that i n Figure 6 (20,000 vs 1800 samples per second), A much cl e a r e r trace of the high frequency motion was obtained, a l b e i t corresponding to s u b s t a n t i a l l y smaller portion of the c u t t i n g period.

-0.8-^

— 1 1- 1 — I , , , ^

0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

TIME (seconds )

Fig. 6 - Displacement of 8" blade In 8" deep cut with cant and knot location

-0.7

-0.8 H

-0.9 H

-1.0 ^ Ul S UI O < s i - 1 . H

-1.2-^

- 1 . 3 H

Note: High frequency sampling rate covers 6.8 in. of cut only

Blade convolution (butt weid)

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20

TIME (seconds )

Fig. 7 - Displacement of 8" blade in 12" deep cut

OA

Beginning of cot End of cut

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

TIME ( seconds )

Fig. 8 • Displacementof 10"blade in6"deep cut

-0.40

Fig. 9 • Displacementof 10" blade in12" deep cut

Data s i m i l a r to those i n Figure 6, were obtained f o r the 10-in. blade c u t t i n g 8- and 10-in. thick cants (Figures 8 and 9). The c u t t i n g r e s u l t s f o r each seven-board sample are presented i n Table I. A sample of a completed data sheet and the method of obtaining the standard deviations are presented i n Appendix I.

TABLE I; Results of Laboratory Cutting Tests

BLADE WIDTH ( i n . )

BANDMILL STRAIN ( l b . )

CUT DEPTH ( i n . )

LUMBER CONDITION G.F.I.

Standard within

board (Sw) (inxlOOO)

Deviation Total (Sb)

(inxlOOO)

8 24500 8 Dry,Knotty 0.6 11 13

8 30000 12 Clear,Green 0.7 13 14

10 30000 8 Dry,Knotty 0.6 11 13

10 34000 12 Clear,Green 0.7 7 8

6.3 FIELD TRIALS

The purpose of the f i e l d t r i a l s was to compare the performance of the system using untensioned blades to that of a conventional system, under f i e l d operating conditions.

Following preliminary c u t t i n g t e s t s - including overfeeding t e s t s i n which the untensioned blade system showed excellent blade s t a b i l i t y r e l a t i v e to the wheels and suffered l e s s snaking than the conventional system tested at the same time - the bandmill was returned to normal operation.

Af t e r a period of adjustment the s t r a i n was set at 28,000 l b . and the guide o f f s e t (Figure 5) was set at 0.25-in. These were both adjusted p e r i o d i c a l l y to investigate the e f f e c t on performance. At the time of wr i t i n g they were set at 26,000 l b . and 0.25-in. r e s p e c t i v e l y .

The i n i t i a l groove pattern used (Figure 3a) was found to be too coarse. The blades formed permanent d e f l e c t i o n s , corresponding to the groove p o s i t i o n s , and f i n e adjustment of the blade p o s i t i o n became impossible. The blade would only move one complete p i t c h (1.6-in.) which res u l t e d i n too large an overhang. The pattern was l a t e r changed to that shown i n Figure 3b. The f i n e r groove layout enabled the blade to be c o r r e c t l y located and also p e r i o d i c a l l y adjusted to compensate f o r resharpening l o s s e s .

The Q u a l i t y Control Section at the m i l l monitored performance on a long term basis. Table II shows the accuracy f i g u r e s a f t e r four

months of operation. The o r i g i n a l performance f i g u r e s p r i o r to the changeover are shown i n Table I I I .

Table I I ; Cutting Accuracy of Untensioned Blades, from F i e l d T r i a l s

Standard Deviation LUMBER CONDITION

SAW GAUGE

Within board (Sw) (InxlOOO)

Unfrozen 18 14

Unfrozen 16 11

Part Frozen 18 not acceptable

Part Frozen 16 12

Table I I I : Cutting Accuracy of Tensioned Blades ( i . e . P r i o r to F i e l d T r i a l s )

LUMBER CONDITION

Unfrozen

Unfrozen

Standard Deviation SAW within board (Sw)

GAUGE (InxlOOO)

16 23

17 21

For cut depths up to 10-in. the standard wlthin-board deviation had improved by 40% using 18-ga. blades and 50% using 16-ga. blades. For cut depths up to 24-ln. the improvement was 30% and 50% r e s p e c t i v e l y .


The purpose of t h i s s e c t i o n of the work was to compare the magnitude of r o l l tensioning s t r e s s i n a we l l prepared blade as determined from the l i g h t gap technique with that obtained using a f i n i t e element.buckling a n a l y s i s .

The r o l l tensioning stresses determined from A l l e n (1985) are shown i n Figure 10, and are the nodal st r e s s values used i n the buckling a n a l y s i s . The magnification f a c t o r (the amount by which the stresses were m u l t i p l i e d ) to cause buckling and the f i r s t four buckled mode shapes are shown i n Figures 11 to 14.

Tensile stress

Compressive stress (-ve)

Position Nodal Stress

(psi)

0 1 2 3 4

-6.759.48 -5.492.08 -1.689.87 +4.647.14

+13,518.96

Fig. 10 - Roll-tensioning stresses and nodal stress values

Long Plate Buckling (10 ft.) Parabolic Stress

Buckling Mode Shape

Mode Number 1 Factor: 2.16E + 00

Magnification

32.404 In.

Fig. 11


Buckling Mode Shape

Mode Number 2 Factor; 2.15 + 00

Magnification Factor: 10.00

32.404 In.

Fig. 12


Buckling Mode Shape

Mode Number 3 Factor: 2.16E + 00

Magnification Factor: 10.00

32.404 in.

Fig. 13

Long PJale Buckling (10 It) Parabolic Stress

Suckling Mode Shape

Mode Number 4 'factor: 2.19E + 00

'Magnification Factor: 10.00

32.404 In.

Fig. 14

The 'Factor' on each f i g u r e i s the amount by which the i n i t i a l nodal stresses had to be m u l t i p l i e d to cause buckling and i s between 2.15 and 2.19. As the i n i t i a l nodal stresses were the r o l l - t e n s i o n i n g stresses c a l c u l a t e d from A l l e n (1985) the two methods d i f f e r by a f a c t o r greater than 2.

The "Magnification Factor' of 10 on each f i g u r e i s the amount by which the displacements have been m u l t i p l i e d f o r greater c l a r i t y .

7.0 REVIEW OF FATIGUE AKD FRACTDRE

The current methods of estimating blade fatigue l i f e are reviewed i n d e t a i l . A d d i t i o n a l l y , the review covers methods of estimating crack propagation rates using Linear E l a s t i c Fracture Mechanics (LEFM), and methods of estimating crack i n i t i a t i o n rates using a strain-based approach.

7.1 CURRENT METHODS OF ESTIMATING FATIGUE LIFE

Most of the work associated with estimating the fatigue l i f e of bandsaws has been based on the s i m p l i f i e d approach using s t r e s s - l i f e (S-N) curves of the bandsaw m a t e r i a l . The r e s u l t s have enabled modified Goodman diagrams to be constructed and estimates of the allowable bandmill s t r a i n to be determined. A modified Goodman diagram Is shown in Figure 15 and i s constructed from the ultimate strength, y i e l d strength and endurance strength of the m a t e r i a l . The ultimate strength and y i e l d strength f o r the material are obtained from t e n s i l e t e s t data. The endurance strength i s obtained from fatigue endurance t e s t s , where the material Is subjected to repeated forces of s p e c i f i e d magnitude while the cycles are counted to f a i l u r e . The r e s u l t s of these t e s t s are u s u a l l y presented i n an S-N diagram (Figure 16), where S represents the c y c l i c stress and N represents the number of cycles to f a i l u r e .

To use the modified Goodman diagram i t Is necessary to c a l c u l a t e the f l u c t u a t i n g s t r e s s range (7^, from which the maximum mean s t r e s s , (Tj^, Is determined, and the bandmill s t r a i n obtained. The s t r a i g h t l i n e on the diagram from the endurance l i m i t Sg t o the ultimate strength Is Goodman's approximation to the data and i s quite conservative.

Figure 17 presents the non-dimensional r e s u l t s of a s e r i e s of endurance t e s t s f o r s t e e l s . The s t r a i g h t l i n e i s the modified Goodman l i n e and the majority of the data points associated with t e n s i l e f a t i g u e t e s t s f a l l above t h i s l i n e .

To use the Goodman diagram shown i n Figure 15, the mean and f l u c t u a t i n g stresses i n the blade must be c a l c u l a t e d . Blade stresses can be separated into two categories: permanent st r e s s Introduced during f a b r i c a t i o n by r o l l i n g , shearing, tooth formation, r o l l - t e n s i o n i n g and heat treatment; and temporary stress Introduced during operation by bandmill s t r a i n , t i l t angle, v e l o c i t y , v i b r a t i o n .

Fig. 17 - Effect of mean stress on alternating fatigue strength at iong life, steels based on -10^ cycles

bending and c u t t i n g . Femanent stresses Included In t h i s a n alysis are those due to r o l l tensioning, whereas temporary stresses are those associated with bandmill s t r a i n , t i l t angle, v e l o c i t y , and bending. V i b r a t i o n and c u t t i n g stresses are not included, because of t h e i r r e l a t i v e l y small magnitude and l o c a t i o n away from the p o s i t i o n of maximum s t r e s s .

The stresses induced In an i d l i n g bandsaw have been examined previously (Eschler 1982, P a h l l t z s c h and Puttkammer 1972, Porter 1971) and the stresses due to bandmill s t r a i n , t i l t angle and bending are r e a d i l y c a l c u l a t e d . The stresses associated with r o l l tensioning are not so e a s i l y obtained. The r o l l i n g process introduces r e s i d u a l stresses into the blade which are compressive i n the centre and t e n s i l e towards the edges. Foschi (1975) has analyzed the e f f e c t of several in-plane st r e s s d i s t r i b u t i o n s on the transverse curvature and A l l e n (1975), using t h i s work and assuming the d i s t r i b u t i o n to be parabolic, has developed methods of estimating the magnitude of the s t r e s s from the transverse curvature. No other relevant studies were encountered in the l i t e r a t u r e .

Thus, with e i t h e r measured, ca l c u l a t e d or estimated values f o r blade operating stresses a v a i l a b l e , and the ultimate strength, y i e l d strength and endurance strengths of the blade material on hand to construct the Goodman diagram, i t i s possible to obtain estimates of the bandsaw fatigue l i f e f o r given operating conditions. An example of the fatigue l i f e c a l c u l a t i o n s f o r a bandmill with f i v e foot diameter wheels and a 16-ga. blade are as follows:

The endurance strength, a , was obtained from the data provided by Sandvlk for a notched specimen (Figure 18). The f i g u r e presents the r e s u l t s of endurance strength t e s t s f o r bandsaw material of varying ultimate strength. For a material with an ultimate t e n s i l e strength of 200 k s i . the applied c y c l i c loading was from zero to 58.66 k s i . and the mean str e s s was 29.33 k s i . These test data are used to provide one point on the Goodman diagram (for bandsaw s t e e l with an ultimate strength of 200 k s i . ) where the mean stress i s 29.33 k s i . and the range ( c y c l i c ) s t r e s s i s from zero to 58.66 k s i . (see Figure 19). The second point i s obtained from the ultimate s t r e s s . The Goodman l i n e connecting the two points Is terminated at the y i e l d s t r e s s value for the m a t e r i a l .

Once the Goodman diagram for the sawblade s t e e l has been established, the values of the f l u c t u a t i n g s t r e s s , (T^, w i l l determine what mean str e s s can be t o l e r a t e d . The bandmill s t r a i n i s obtained from t h i s value a f t e r the other mean stress components (due to r o l l - t e n s l o n i n g , backcrown and v e l o c i t y ) have been deducted.

The method of determining the bandmill s t r a i n ( A l l e n , 1985) f o r a 5 - f t . bandmill with an 8-in. by 16-ga. blade i s presented i n Table IV.

±60

Notched Specimen

± 2 0

180 190 200 210 220

Ultimate strength - lb/in x 1000 (oounesy oJ Sandvir Feb. 1871)

Fig. 18 - Released loading fatigue tests

Fig. 19 - Modified Goodman diagram relating stress and strength

Table IV

Method of Determining the Bandmill S t r a i n f o r a 5 - f t . Bandmill with a 16-ga. by 8-in. Wide Blade (Allen, 1985)

Oj, (bending stress) - 38,393 psi

0„ = (centrifugal stress) - 2,918 psi

(roll-tensioning stress) •> 23,488 psi

Oj, (backcrown stress) - 2500 psi

(ultimate tensile strength) - 200,000 psi

S, (endurance strength) - 34,367 psi

O, (stress amplitude) - 1/2 (38393) •= 1/20 ,

The only f l u c t u a t i n g s t r e s s i s that associated with the blade bending around the wheels (Gj^) , which corresponds to twice the str e s s amplitude, (O^) , on the Goodman diagram (Figure 20). The mean str e s s , iO^), i s l i n e a r l y r e l a t e d to the stress amplitude, (O^), and i s determined from Figure 15 by the fo l l o w i n g r e l a t i o n s h i p :

(^^ S ^ ) " p s i

The mean s t r e s s i s composed of the t o t a l s t a t i c load plus h a l f the f l u c t u a t i n g load (Figure 21):

c m = + a , + a,, + o^, + a ,

88,285 = + 2,918 + 23,488 + 2,500 + 19,197 = s t r e s s due to bandmill s t r a i n

However, a safety f a c t o r of 1.4 (obtained empirically) i s incorporated i n t o the s o l u t i o n to account f o r v a r i a t i o n s i n operating conditions, blade preparation, etc.

88,285 1.4

Os

S t r a i n

S t r a i n

Os + 48.103

14,967 p s i

2 X c r o s s - s e c t i o n a l area x 2 X (8.0 X .065) X 14,967 15,567 l b .

34.370 • g. ^ 34.370 - O, Tan.a-Tana ' 0.17185

Fig. 20 - Calculation of mean stress - G,

CO

CO

Time

Fig. 21 - Stress in a rotating sawblade

The bandmill s t r a i n of 15,567 p s i i s quite close to the bandmill s t r a i n s used i n industry today. However, some discrepancies e x i s t between the predicted fatigue l i f e and those found i n p r a c t i c e . The p r e d i c t i o n i s based on the endurance strength,(S^) of the m a t e r i a l , implying I n f i n i t e l i f e . In f a c t , the t y p i c a l operating l i f e of a bandsaw blade i s four hours. Thus the p r e d i c t i o n , i f c o r r e c t , should contain a very large f a c t o r of safety. However, the blade preparation and bandmill operating conditions are such that t h i s four hour period i s often c l o s e to the fatigue l i m i t of the blade In as much as small increases i n r o l l tensioning s t r e s s or bandmill s t r a i n can produce g u l l e t cracking.

If the Goodman diagram Is reconstructed based on a f i v e hour operating period, the resultant bandmill s t r a i n becomes u n r e a l i s t i c a l l y high. For the bandmill example given i n t h i s section using a modified f i v e hour endurance l i m i t (S'^) , the estimated s t r a i n becomes 42,750 l b . From previous experimental work at high s t r a i n s i t can be stated that a blade would not l a s t f o r very long at t h i s s t r a i n , i n d i c a t i n g problems with the a n a l y s i s .

The c a l c u l a t i o n s pertaining to a five-hour operating l i f e are reproduced i n Appendix I I . The bandmill s t r a i n s f o r the laboratory experiments were c a l c u l a t e d using a s l i g h t l y d i f f e r e n t method which i s presented i n Table V.

Method of Detertaining Bandmill S t r a i n f o r the Experimental 5 - f t . Bandmill with 8-in. and 10-in. by 18-ga. Untensioned Blades

This method was used to obtain estimates of bandmill s t r a i n s f o r the laboratory experiments. It d i f f e r s from the method used i n Table IV i n that the endurance strength (S^) i s determined from the ultimate strength (S^) and the strength m o d i f i c a t i o n f a c t o r s described i n Shigley (1977). The method described i n Table could not be used f o r t h i n untensioned blades as i t l e d to u n r e a l i s t i c a l l y high bandmill s t r a i n values.

Se = Kf S', S'g = 0.5 S ^ = 0.5 X 200 K s i = 100 K s i

= .5 Surface f i n i s h poor around g u l l e t area Kj, = .814 99 percent material r e l i a b i l i t y Kg = .453 Stress concentration

S, = 18.44 K s i ENDURANCE STRENGTH

(O^) (bending stress) = 26,923 p s i (O^) ( v e l o c i t y stress) = 2,605 p s i (O^^) ( r o l l t e n s i o n i n g stress) = 812 p s i (nominal amount) (Ojj^) (backcrown stress) = 0 (C^^) ( t i l t angle stress) = 0

Where,

Sy = ultimate strength (200 Ksi) Sy = y i e l d strength (178 Ksi) Sg = modified endurance l i m i t (18.44 Ksi) Oj. •= f l u c t u a t i n g s t r e s s (bending s t r e s s i n our case) ( 26 .923 Ksi)

= v e l o c i t y s t r e s s = s t r e s s due to bandmill s t r a i n

CT = s t r e s s amplitude = 1/2C^

From the Goodman diagram (Figure 15) = S^d-CJ^/Sg)

Allowable bandmill s t r a i n i s obtained by deducting the constant s t r e s s values and the s t r e s s amplitude from the mean s t r e s s .

Bandmill s t r a i n = ^str ^ blade c r o s s - s e c t i o n a l area.

S u b s t i t u t i n g the values f o r the 10-in. experimental blade (with a c r o s s - s e c t i o n a l area at the g u l l e t of 0.049-in. x 9.45-in.):

= 200(1-13.462/18.44) = 53.997 K s i

" s t r ' m " a " r t

Gj^j. = 53997 - 2605 - 13461 - 812 = 37119 p s i S t r a i n = G^^j. x c r o s s - s e c t i o n a l area = 37119 x 2 (0.049 x 9.45) S t r a i n = 34376 l b .

A s i m i l a r exercise f o r an 8-in. x 18-ga. blade using the same str e s s values and a c r o s s - s e c t i o n a l area of 0.049-in. x 7.513-in. leads t o :

^str = 37,119 p s i S t r a i n = 37,119 x 2(.049 x 7.513) S t r a i n = 27,330 l b .

Note that the endurance strength (S^) i s based on the surface f i n i s h of the blade around the g u l l e t and on a chosen r e l i a b i l i t y f o r material p r o p e r t i e s . This method b u i l d s a f a c t o r of safety i n t o the endurance strength value used i n the Goodman diagram and explains the d i f f e r e n c e i n the report value (18.44 Ksi) and that used by A l l e n (34.37 K s i ) , where the f a c t o r of safety i s applied to the mean str e s s value ( 0 „ ) .

Another problem with the current method of estimating f a t i g u e l i f e i s that i t cannot determine the f a t i g u e l i f e of a part with a c r a c k - l i k e defect.

7.2 LINEAR ELASTIC FRACTURE MECHANICS AND FATIGUE

In the f a t i g u e l i f e of a material, two p r i n c i p l e mechanisms are associated with fatigue cracking, these are crack i n i t i a t i o n and crack propagation. LEFM ( l i n e a r e l a s t i c f r a c t u r e mechanics) has been used extensively to describe the behaviour of crack propagation and can be used to determine the l i f e to f r a c t u r e provided the crack length, st r e s s magnitude and f r a c t u r e resistance of the material are known.

The Important r e l a t i o n s h i p i n p r e d i c t i n g f a tigue l i f e of a material i s the rate of crack growth with an applied loading. This r e l a t i o n s h i p i s presented as da/dN vs AK, where:

a = crack length. N = number of c y c l e s . A K = range of stress i n t e n s i t y .

The stresses at the crack t i p are dependent on K which i s c a l l e d the Stress Intensity Factor and i s a fundamental r e l a t i o n s h i p associated with LEFM. General expressions f o r K are i n the form:

K = aJTlT y(a/w)

where 0 i s the stress away from the crack t i p and Y i s a f a c t o r associated with the geometry of the crack length 'a' and body width 'W. The values of K depend on body co n f i g u r a t i o n , loading, crack shape, and mode of crack displacement. Values of K are given i n many texts f o r s p e c i f i c configurations (Broeck, 1986). An example of the normalised data for an edge cracked plate i s presented in Figure 22.

The e f f e c t of constant amplitude loading on crack growth for several st r e s s ranges (A O), produces the type of curves shown i n Figure 23.

P l o t t i n g the logarithm of the slope of each curve f o r a given crack length (da/dN) against the logarithm of the range of the s t r e s s i n t e n s i t y (A K) produces the sigmoldal curve shown in Figure 24. Of Importance i s the f a c t that these curves reduce to a s i n g l e curve for a given material and set of t e s t conditions, providing a convenient r e l a t i o n s h i p f o r fatigue a n a l y s i s .

Estimates of crack propagation rates f o r bandsaw blades require constant amplitude data as shown i n Figure 23, including the e f f e c t s of mean s t r e s s . To date t h i s information has not been located.

,1 I I I I I I 0 0.1 0.2 0.3 0.4 0.5 0.6

a/W

Fig. 22 • K, for common configurations. Single edge oracle in tension

Time

Applied Cycles N

Fig. 23 - Fatigue cracic length versus applied cycles. Fracture is indicated by9

U in

I re CC

O U o

Stress Intensity Factor Range AK log scale

Fig. 2 4 - Schematic sigmoidal behavior of fatigue craci< growth rate versus A K

7.3 THE CRftCK INITIATION PERIOD

T h e LEFM approach enables reasonable p r e d i c t i o n of crack propagation rates once a crack e x i s t s . The p r e d i c t i o n of crack i n i t i a t i o n i s much more d i f f i c u l t . A d d i t i o n a l information i s required about t h e s t r e s s and s t r a i n c h a r a c t e r i s t i c s of the material under consideration and u n c e r t a i n t i e s associated with the data e x i s t . This, along with the f a c t that a d d i t i o n a l data are required, aggravates the uncertainty of crack i n i t i a t i o n p r e d i c t i o n .

In fatigue a n a l y s i s , when the parts under consideration contain notches, the behaviour of the material i s best considered i n terms of s t r a i n . The s t r a i n i s more e a s i l y c a l c u l a t e d than the s t r e s s and t h i s has led to a f i n i t e fatigue l i f e theory based on r e l a t i n g the fatigue l i f e of notched parts to the l i f e of small unnotched specimens that are cycled to the same s t r a i n s as the material at the notch root. When the determination of fatigue l i f e to crack i n i t i a t i o n i s required, t h e s t r a i n based approach i s often most appropriate. Reasonable f a t i g u e l i f e estimates (to the formation of small cracks) can be obtained once the s t r a i n - l i f e h i s t o r y of the material has been determined. S t r a i n - l i f e f a t i g ue data can be presented i n the form shown i n Figure 25 and are log-log p l o t s of s t r a i n vs cycles to f a i l u r e . The data are obtained from small, polished, unnotched specimens and the f a i l u r e point i s often taken at the appearance of a small crack of 0.25- to 5-mm. i n depth. The e l a s t i c and p l a s t i c components of the s t r a i n magnitude are obtained fron the steady state hysteresis loops that predominate throughout most of the fatigue l i f e .

A s i m i l a r s i t u a t i o n e x i s t s to that described i n the previous s e c t i o n . Estimates of crack i n i t i a t i o n rates for bandsaw blades require the data shown in Figure 25, including the e f f e c t s of mean s t r e s s . To date t h i s information has not been located.

8.0 DISCOSSIOM

8.1 TRACKING STABILITY

The blades appeared quite stable when the back edge of the blade was in s i d e the wheel l i n e . T i l t i n g the wheel forward moved the blade forward to a new stable p o s i t i o n and the blade showed no tendency to run o f f the front edge of the wheels. However, when moving the blade back on the wheels a l i m i t i n s t a b i l i t y was reached and, once beyond t h i s l i m i t , the blade moved r a p i d l y backwards u n t i l there was a large overhang at the back and the teeth were ins i d e the wheel l i n e .

Normally the optimum blade p o s i t i o n was with 0.25- to 0.5-in. of g u l l e t overhang. Unfortunately, the stable l i m i t , f o r both experimental blades, was with a g u l l e t overhang of 0.75- to 0.875-in. However, t h i s value may depend on the width of the band wheel grooves.

n

O) £ E

< c

53

Reversals to Failure (log scale)

Fig. 25 - Strain-life curves sliowing total elastic and plastic strain components

The experimental blades were not stable when centred on the wheels. A small amount of t i l t along with 0.75- to 0.875-in. of overhang was needed f o r s t a b i l i t y . I t would seem that the blade climbed up the t i l t e d wheel to a point where i t was balanced by the forward p u l l of the overhang.

8.2 CUTTING TESTS

Both blades showed the same accuracy i n c u t t i n g i n the 8-in. dry knotty hemlock but a s i g n i f i c a n t d i f f e r e n c e was apparent i n the 12-ln. c l e a r green hemlock. This was due to a washboarding problem experienced with the 8-in. blade, which was not t o t a l l y eliminated.

For the 10-in. blade the washboarding problem was eliminated and the measured r e s u l t s r e f l e c t the true accuracy c a p a b i l i t i e s of the system. Without the washboarding, which seems to be more prevalent i n thinner blades at higher s t r a i n s , the accuracy of the 8-in. wide blade i s expected to be s i m i l a r to the 10-in. blade.

The d i f f e r e n c e i n accuracy between the 8-in. and 12-in. deep cuts for the 10-ln. blade was considered due to the condition of the 8-in. deep lumber. The wood was very dry and had three large knots i n i t , two at one t h i r d the way along the c u t t i n g distance and one at two t h i r d s . The blade deviation at the knots was quite v i s i b l e . Figure 6 shows the blade motion i n t h i s cut r e l a t i v e to the knots.

8.3 FIELD TRIALS

The performance of the untensioned blade system i n a production environment has been encouraging and gains i n lumber recovery of 1% t o 2% are considered p o s s i b l e . Long term evaluation i s c u r r e n t l y i n progress.

I n i t i a l l y , 18-ga. blades were used for the f i e l d t r i a l s . However, problems encountered with these blades have been g u l l e t cracking, washboarding and poor performance i n frozen wood:

G u l l e t cracking was l a r g e l y overcome by c a r e f u l balancing of the bandmill s t r a i n s with the guide pressure.

The washboarding problem was never completely eliminated and would have made reductions i n target s i z e impossible.

The 18-ga. blades would not perform s a t i s f a c t o r i l y i n frozen lumber and, as 17-ga. blades were not a v a i l a b l e at that time, 16-ga. blades were used. The improvement was remarkable, the accuracy in frozen wood became comparable to that f o r unfrozen wood. Later, 17-ga. blades were found to work well and the sawmill i s now using 17-ga. blades f o r both summer and winter use.

The use of heavier 17-ga. and 16-ga. blades improved the accuracy of the system, eliminated the washboarding problem and also made the

s a w f i l i n g work eas i e r . Considerable care was required with the 18-ga. blades to obtain good performance, e s p e c i a l l y with the swaging operation. An automatic swaging and side grinding machine would have been an asset.

The untensioned saws did not s u f f e r from s t r e t c h i n g of the f r o n t edge l i k e a tensioned saw and the s a w f i l i n g work was l i m i t e d to a small amount of l e v e l l i n g , checking the back crown swaging and sharpening.

Recent experiments have Indicated that 5/16-in. groove widths i n the band wheels may provide better o v e r a l l s t a b i l i t y , performance and p o s i t i o n i n g than the 1/4-in. grooves, e s p e c i a l l y f o r 16-ga. and 17-ga. blades.

8.4 BLADE STRESS CALCULATIONS

The magnitude of buckling stresses was twice as large as that estimated from the l i g h t gap technique. The parabolic shape, assumed for the r o l l tensioning s t r e s s d i s t r i b u t i o n , i s thought to be i n error . Currently, work i s in progress to determine the s t r e s s d i s t r i b u t i o n introduced i n t o the blade by r o l l tensioning.

8.5 FATIGUE AND FRACTURE

8.5.1 S i m p l i f i e d Approach

This method requires minimal information regarding the fatigue l i f e p roperties of the s t e e l and i n consequence the r e s u l t s are not p a r t i c u l a r l y accurate. The example presented included an e m p i r i c a l l y obtained safety f a c t o r that enabled the method to p r e d i c t bandmill s t r a i n s close to Industry operating standards. I t should be recognised that the o r i g i n a l analysis was developed to enable estimates of operating s t r a i n s to be obtained and, f o r a l i m i t e d range of conditions, t h i s has been s u c c e s s f u l . When the fatigue l i f e data were converted to match the actual operating l i f e of a t y p i c a l sawblade, by replacing the i n f i n i t e l i f e endurance strength (S^) with a f i v e hour endurance strength (S'^) the r e s u l t i n g bandmill s t r a i n s increased by a fa c t o r of three.

8.5.2 Linear E l a s t i c Fracture Mechanics and Fatigue

The l i n e a r e l a s t i c approach i s re l a t e d to the state of s t r e s s at the crack t i p and i s capable of providing accurate estimates of f a t i g u e crack propagation rates. The problem with using t h i s method i s that s u i t a b l e material s t r e s s - s t r a i n properties for bandsaw s t e e l are c u r r e n t l y not a v a i l a b l e and, u n t i l these have been determined, any p r e d i c t i o n s of f a t i g u e crack growth rates w i l l have to be performed with estimates of material p r o p e r t i e s .


The s t r a i n based approach examines the c y c l i c behaviour of cracked components by r e l a t i n g the actual s t r a i n s at the crack t i p to the behaviour of smooth t e s t specimens with the same s t r a i n s .

Fatigue t e s t s are conducted using constant amplitude f u l l y reversed cycles of s t r a i n . Steady state h y s t e r e s i s loops can predcsnlnate through most of the fatigue l i f e and these are examined i n terms of t h e i r r e l a t i v e e l a s t i c and p l a s t i c s t r a i n ranges. These t e s t s provide s t r a i n - l i f e curves that can be used, i n a s i m i l a r fashion to S-K curves, to p r e d i c t cycles to crack i n i t i a t i o n .

M a t e r i a l constants are obtained, from both the h y s t e r e s i s loop data and the s t r a i n l i f e curves, that enable estimates of crack i n i t i a t i o n f a t i g u e l i f e f o r notched parts manufactured from the same material to be obtained.

Similar problems to those f o r the LEFM portion of the analysis e x i s t for the crack i n i t i a t i o n p r e d i c t i o n s . Suitable information on the s t r e s s - s t r a i n r e l a t i o n s h i p s of bandsaw s t e e l ( for c y c l i c f a t i g ue and c y c l i c s t r e s s - s t r a i n behaviour) are c u r r e n t l y not a v a i l a b l e . With present techniques p r e d i c t i o n s f o r fatigue crack i n i t i a t i o n cannot be performed without t h i s information.

9.0 CCMCLDSIONS

9.1 LABORATORY TESTS AKD FIELD TRIALS

a) Untensioned blades, operating at maximum feed rates, can provide excellent c u t t i n g accuracy.

b) Conversion of e x i s t i n g bandmills to the untensioned blade, grooved wheel, system i s a r e l a t i v e l y simple process.

c) The system performed s u c c e s s f u l l y i n f i e l d t r i a l s and has achieved s i g n i f i c a n t improvements i n accuracy and reductions i n kerf widths.

d) The system performs well i n both frozen and unfrozen lumber.

e) Accurate alignment of the p r i n c i p l e components of the bandmill and feed system i s e s s e n t i a l , e s p e c i a l l y i f the thinner blades are to be used s u c c e s s f u l l y .

£) The blades are stable i n operation with no v i s i b l e movement r e l a t i v e to the wheels.

g) The thinner (18-ga.) blades have a tendency to washboard i n the deeper cuts and do not perform well i n frozen lumber.

h) Further t e s t s are required to determine the optimum groove width on the band wheels, f o r each gauge of blade.


Further work i s required to e s t a b l i s h an accurate p r o f i l e of the stresses due to r o l l tensioning.

9.3 FATIGUE AND FRACTURE

9.3.1 S i m p l i f i e d (Goodman Diagram) Approach

a) Although the method requires minimal information and Is quick and easy to use, empirical adjustments f or the a c t u a l conditions of operation are necessary to obtain r e a l i s t i c data.

b) Modifications to the fatigue strength values to account f o r the actual operating l i f e of a bandsaw (5 hr.) resulted i n overestimates of the bandmill s t r a i n by a fa c t o r of three.

c) Fatigue l i f e p r e d i c t i o n s for pre-cracked material are not po s s i b l e .

9.3.2 LEFM and Fatigue

Before LEFM can be used to pr e d i c t crack propagation rates In bandsaw s t e e l a d d i t i o n a l material s t r e s s - s t r a i n properties are required, such as:

the sigmoidal curve data i n Figure 24. the e f f e c t of mean s t r e s s i n the sigmoidal curve data. v e r i f i c a t i o n of the stress i n t e n s i t y factor at y i e l d .


To obtain meaningful crack i n i t i a t i o n l i f e p r e d i c t i o n , a d d i t i o n a l material c y c l i c s t r a i n properties are required:

10.0 ACKNONLEDGMENTS

The authors would l i k e to thank West Fraser M i l l s Ltd. f o r the time and e f f o r t they put in t o the f i e l d t r i a l s and Mr. Ed A l l e n f o r h i s ac t i v e i n t e r e s t and advice throughout the p r o j e c t .

11.0 REFERENCES

A l l e n , F.E., 'High s t r a i n theory and a p p l i c a t i o n ' . Proceedings of the 8th Wood Machining Seminar, U n i v e r s i t y of C a l i f o r n i a , Forest Products Lab., Richmond, CA. Oct. 1985.

A l l e n , F.E., 'Bandsaw Tooth and G u l l e t Design'. Kockums CanCar Inc., Surrey, B.C. 1984.

A l l e n , F.E., 'High-Strain/Thin K e r f . Proceedings of F i r s t North American Sawmill C l i n i c , Portland, OR. Feb. 1973.

Broeck, D., 'Elementary Engineering Fracture Mechanics'. N i j h o f f , Dordrecht, 1986.

Duggan,T.V. and J.Byrne, 'Fatigue As A Design C r i t e r i o n * . Macmillan, London, England 1977.

Eschler, A., 'Stresses and Vibrations i n Bandsaw Blades'. M.A.Sc. Thesis, Dept. of Mechanical Engineering, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, 1982.

Foschi, R.O., 'The l i g h t gap technique as a t o o l f o r measuring r e s i d u a l stresses i n bandsaw blades'. Wood Science and Technology, V o l . 9 p.243-255, 1975

Fuchs, H.O. and R.I. Stephens, 'Metal Fatigue i n Engineering'. Wiley, Toronto, Ontario, 1980.

Button, S.G., Lehmann, B.F and J . Taylor, 'Laboratory Testing of a Bandmill with Grooved Wheels'. Res. Rep. Forintek Canada Corp., Vancouver, B.C., 21p., 1986

Pah l l t z s c h , G. and K. Puttkammer, 'The loading of bandsaw blades: stresses and strength f a c t o r s ' . [Translated from Holz a l s Roh-und Werkstoff, May 1972, No.5, 165-174].

Pook, L.P., 'The Role of Crack Growth In Metal Fatigue'. The Metals Society, London, England 1983.

Porter, A.W., 'Some engineering considerations of h i g h - s t r a i n band saws'. For. Prod. J . , 21(4):24-32, 1971.

Shigley, J.E., Mechanical Engineering Design. 3rd. Ed. McGraw-Hill, New York, NY, pp.177-206. 1977.

Sugihara, H., "Theory of Running S t a b i l i t y of Bandsaw Blades". 5th. Wood Machining Seminar, U n i v e r s i t y of C a l i f o r n i a , Forest Products Lab., Richmond, CA. 99p, 1977.

Taylor, J . 'The Dynamics and Stresses of Bandsaw Blades*. M.A.Sc. Thesis, Dep. of Mechanical Engineering, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C. 1986.

Taylor, J . and S.G. Button, ' M i l l T r i a l s and Performance Optimization of a Bandmill with Grooved Wheels". Res. Rep., Forintek Canada Corp., Vancouver, B.C., 26 p., 1987.

APPENDIX I

BOARD MEASUREMENT DATA AND METHOD OF

CALCULATING CUTTING VARIATION

APPENDIX I

BOARD MEASUREMENT DATA AND METHOD OF CALCULATING CUTTING VARIATION

Fonnulae

n = # samples per board N - # boards

1 ^ 3Cj = — E Xij = mean thickness of board j

1 ^ 1 ^ "

X = 5Cj = Xij = grand mean thickness

2 S. 2 1 / " \2 = board v a r i a t i o n of board j

(n-1)

2 1 N 2 S = -TT i S = within-board v a r i a t i o n w N j . l j

2 N 2 1 / N \ ^

(N-1) = v a r i a t i o n of the mean board thickness

2 N n 2 l / N n \2

= t o t a l v a r i a t i o n T j - l L - l a Nn L-1 ~ l j

(Nn-1)

_(Top) _(Bottom) Taper - ^ -

APPENDIX I

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APPENDIX I I

METHOD OF DETERMIKIKG ENDURANCE STRENGTH

OF BANDSAW STEEL FOR A 5 HR. OPERATING LIFE

APPENDIX II

METHOD OF DETERMINING ENDURANCE STRENGTH

OF BANDSAW STEEL FOR A 5 HR. OPERATING LIFE

S'f = modified endurance l i m i t

l ogS'j s -mlogN + b

where

N = number of cycles m = slope of S-N curve b = o f f s e t

m = (l/3)log(.9Su/Se')

b = log (.9Sy)2/s<^

where

Sy = ultimate strength = 200,000 p s i .

S'g = endurance l i m i t = 34,370 p s i .

The f i v e hour f a i l u r e s t r e s s at zero mean str e s s f o r a notched specimen, using the above i s :

N = 10,000 F t ^ X Rev X 60 Min x 5hr x 1 eye = 190,986 cycles Min PI X 5 f t Hr Rev

m = 0.2397 b = 5.9744 logS'j •= 4.7085

cfs no. 45

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