Wood Science and Technology Vol. 8 (1974) p. 148--161 �9 by Springer-Verlag 1974

A Review of Residual Stresses and Tensioning in Circular Saws

B y RIC~A~]) SzYMA~I and C. D. Mo~E, J r .*

University of California, Forest Products Laboratory, Richmond, Cal.

Summary

The origin and measurement of residual stresses and their effect on the transverse stability of circular saws are discussed, with emphasis placed on nondestructive stress analyses, their limits of application, and their possible adaptation to the measurement of residual stressesin circular saws. Saw stability variations can be computed once the stress distribution is known. Evaluation of the X-ray diffraction technique and the ultrasonic and magnetic methods were considered for this purpose.

Alternatively, saw stability can be related to resonance and bending stiffness measurements in specific modes. However, the state of stress cannot be inferred from these tests. For saw stability prediction, measurement of the state of stress is more essential than are direct stiff- ness measurements.

Introduction

The s t a t e of s tress in a saw b l ade is known to s ign i f i can t ly inf luence i ts per- fo rmance as a cu t t i ng tool . These stresses ar ise f rom the cu t t i ng process, t he r o t a t i o n a l body force, t he t e m p e r a t u r e d i s t r ibu t ion , and the res idual or in i t i a l stresses. Of these s t resses on ly t he res idua l stresses canno t be c o m p u t e d b y numer i ca l me thods p r e sen t l y ava i l ab le [Mote 1970b]. Because the ent i re s t a t e of s tress mus t be known for mos t ana lyses , i t is necessa ry to focus a t t e n t i o n upon m e a s u r e m e n t and p red i c t i on of t h e res idua l s t ress s ta te .

Res idua l s tresses p resen t in saw b lades can be d iv ided in to two ca tegor ies : un in t en t iona l and in t en t iona l stresses. U n i n t e n t i o n a l stresses a re i n t roduc e d b y the process of saw manufac tu r i ng and usage. The p l a t e s tock is an i so t rop ic as a resu l t of rol l ing. Stresses a rc i n t roduced when the saw b l a n k is r emoved f rom the p la te , and b y subsequent manu:[actur ing opera t ions such as ha rden ing , quenching, temper ing , and t o o t h fo rmat ion . Tens ioning stresses a re i n t roduc e d i n t e n t i o n a l l y

* The authors would like to express their gratitude to Professor R. M. Bragg, Department of Material Science and Engineering, U. C. Berkeley, and to Dr. R. L. Gause and Mr. W. lq. Clotfelter, l~arshall Space Flight Center, Huntsville, Alabama, for valuable suggestions and permissien to use X-ray and ultrasonic equipment. The authors are also grateful for the finan- cial support of the project from the University of California l%rest Products Laboratory; the California Cedar Products Company, Stockton; the California Saw, Knife and Grinding Company, San Francisco; Sun Studs, Roseburg, Oregon; Weyerhaeuser Company, Tacoma, Washington; and McIntire-Stennis Funds.

I~eview of residual stresses and tensioning in circular saws 149

through local plastic deformation of the saw resulting in "permanent" membrane stresses. Recent research has shown tha t the state of membrane stress in the saw determines its relative stabil i ty [Dugdale 1963a, b, c, 1964, 1965, 1966a, b, 1968; Mote 1963, 1964, 1965, 1967, 1970a, b]. Accordingly, opt imal tensioning can be looked upon as a perturbat ion of the membrane stress state which maximizes saw stabil i ty in the operating environment. The residual stress state is, of course, not constant forever, and application of optimal tensioning procedures depends upon knowing the residual stress state at any time.

Some theoretical work has been done on the tensioning process, but there is still no accurate, nondestructive method for measuring residual stresses in saws. The pr imary objectives of this paper are to review existing methods of residual stress measurement in metals, and to discuss bet ter approaches to nondestructive measurement of residual stresses and stabil i ty in saw blades.

Residual stresses in metals and their measurement

The te rm internal or residual stresses is applied to a number of different phenomena. A comprehensive review and classification of internal stresses ihas been presented by Orowan [1948], who defined internal stresses as those existing in bodies upon which no external forces are acting. According to Orowan [1948], these stresses fall into two categories: "First, an external (mechanical, thermal, or chemical) factor may affect different parts of a body differently, even if the material of the body is quite homogeneous ; second, textural inhomogeneities of the material may give rise to internal stresses, even if the external influences acting upon the body are uniform, e.g., a homogeneous stress."

Internal stresses of the first category are usually large and well defined in their distribution, and for this reason they are often called macrostresses or residual stresses of the first kind. The objective of tensioning is to introduce macrostresses, and accordingly they are of principal concern here. The second category describes residual stresses on a smaller scale which are usually randomly distributed. These are called microstresses, or residual stresses of the second kind, because their domain of influence is microscopic. Denton [1966] has suggested the idea of residual stresses of the third kind which focused at tention upon subgrannular stress variations. The nature, origin, and effects of residual stresses have been discussed in depth by Treuting et al. [1952].

Methods of measuring residual stresses have been reviewed by Sachs and Espsey [1941], Hiendelholer [1951], Baldwin [1949], Denton [1966], and Frick et al. [1967]. Residual stress measurement methods are classified as destructive and nondestructive. The former group consists of material removal procedures, and the lat ter group consists of combinations oi X-ray diffraction, optical, ultra- sonic, and magnetic methods. In reviewing the most popular measurement methods in this paper, the authors place particular emphasis on the application and accuracy of nondestructive methods. A detailed review and evaluation of methods for nondestructive measurement of residual stresses, and the potential application of these methods to residual stress measurement in circular saws, can be found in recent reports by Szymani [1972a, b, 1973].

11"

150 R. Szymani and C. D. Mote

Material removal procedures

Material removal is the most widely used technique of residual stress measure- ment. The characteristic feature of these techniques is the removal of test specimen material by machining, grinding, etching, etc. Stresses in the removed material are then determined by measurement of the dimensional changes or strain in the parent material. Major contributors to the material removal methods include Heyn [19141, Sachs [19401, Sachs and Espey [1941], and Rembowski [1958]. Dugdale [1963c] has used procedures of this type in tensioning stress analysis in circular saws; discussion of his work will follow in the subsequent section.

The experimental techniques employed in all of these methods are funda- mentally similar. Major variations in technique usually occur in the procedure by which strain is measured or material is removed. The use of strain gages is convenient and shortens analysis t ime substantially. Strain gages were used by Dugdale [1963c], l%ichards [19451, Mack [19621, Hanslip [1952], Greaves et al. [1945], Palermo [19631, and Riparbelli [19501. Tokareik and Polzin [19521 applied stress coat or brittle lacquer for the strain measurements. The major advantages of material removal techniques relative to nondestructive methods stem from the fact tha t they are generally easier to apply, more economical, and give a relatively complete picture of the residual stress state. Strain gages also give excellent strain resolution and are not sensitive to microstresses. Metal removal techniques are, however, destructive and often prohibit any normal service with the machine element after the stresses have been evaluated. These methods can probably serve only as reference methods in the analysis of residual stresses in circular s a w s .

Stress measurement by X-ray

X-ray determination of stresses is based upon the measurement of lattice strains of specially oriented sets of lattice planes in the region studied. Measure- ment of lattice strains is accomplished by using a collimated X-ray beam of suitable wavelength 2 and recording the high-angle interference lines of specimens by means of a back reflection film camera and diffractometer. Correlation of the lattice strain Ad/d with the strain calculated from the theory of isotropic elasticity is used to determine the elastic stress state.

The X-ray method is discussed in textbooks [Burrer and Massalski 1966; Cullity 1967; Taylor 1961] and has been reviewed by Mareheraueh [1966], Denton [1966], and Christenson [19601. This method is nondestructive, and also permits the study of steep elastic stress gradients and highly localized stresses. The X-ray beam strikes only a small area of a specimen (less than 1 to 2 mm in dia- meter), whereas strain gages measure weighted mean strain over a much larger area and measure both elastic and plastic strains. Since a reference measurement in the stress-free condition is not required, determination of residual stresses by X-rays has a high potential of application.

The X-ray diffractometer method permits fast accumulation of test data. Unfortunately, when using a diffraetometer the investigator is restricted to small, easily moveable specimens having a favorable geometrical shape, and this excludes most saws. However, the back-reflection film camera method is not limited by

l~eview of residual stresses and tensioning in circular saws 151

size and mobility of the specimen, although certain geometric requirements must be satisfied. This method would be applicable to most saws ; also, equipment used with this method can be made completely portable, which offers possibilities for field application. The industrial application for this method is discussed by Schaal [1955], B~lstadt et al. [1963, 1965], and Neff [1960].

The potential of X-ray methods in tensioning stress analysis problems hinges mainly upon resolution of the stress state and the depth or penetration at which stresses are determined. In general, errors in X-ray stress measurements are of the order of ~: 3,000 psi, whether diffraction lines are sharp or dilfuse [Christenson 1960]. However, it is possible tha t with maximum resolution and large tensioning stresses the technique may have some application. Appropriate surface preparation could eliminate local surface stresses which are introduced during the saw manu- facturing process. Additionally in thin saws, as in thin-plate theory, the variation of stress with depth should be less significant.

l~esults from a preliminary stress analysis of the sawblade material [Szymani 1972b] have indicated that accuracy of the X-ray technique was of the order of =~ 2,500 psi. This stress accuracy is not satisfactory for saw tensioning applications where peak tensioning stresses are approximately 20 ksi, and where stresses in the range 2 to 8 ksi are common. Furthermore, the small penetration of X-rays (2 • 10 -3 ram) results in a measure of surface stresses tha t are function of surface preparation.

Because of the limited accuracy and the fact tha t the bulk and not the surface stresses are of interest, it is apparent tha t application of this method to the saw tensioning problem is questionable.

Optical and ultrasonic methods

In principal, any physical property of a material which is modified by stress offers a potential means for investigation of residual stresses, l~iney [1957] was able to apply photoelasticity to the determination of residual stresses in electron tubes. Nisida et al. [19561 utilized the photoelastic properties of cellulose nitrate to study residual stresses in plastically deformed beams and wedges. ~qye [1947] used the birefringence properties of silver chloride crystals to investigate metallo- graphic influences on residual stresses.

Firestone and Frederick [1946] have demonstrated tha t residual stresses can cause changes in the velocity and attenuation of ultrasonic waves. Velocity of the shear wave is independent of the direction of particle motion in isotropie materials, but if isotropy is destroyed by the applied stress, wave velocity varies with the direction of particle motion. I t was found that a plane-polarized ultrasonic shear wave would propagate only if particle motion was either parallel or perpendicular to the applied stress. This technique has been used by Rollins [1959, 1961] and Rollins et al. [1963].

Ultrasonic stress analysis of cold-rolled ainminium using shear wave bire- fringence was first proposed by Gause [1967]. Use of ultrasonic surface waves for residual stress analysis in aluminium has been demonstrated by McKannan [1967], who stated that it is possibl e to resolve the stresses in aluminium to an order of 200 to 400 psi.

152 1% Szymani and C. D. Mote

Benson [1968] describes methods of measuring stresses in various alloys of alumininm using bothshear and surface waves. Techniques developed by him were applied to measurement of residual stresses in aluminium plates containing welds. According to Benson the accuracy of stress measurements obtained ultrasonically compares favorably with conventional destructive test methods.

Of the various ultrasonic methods available for measurement of residual stresses in saw blades where bulk stresses are of interest, the shear wave method seems to have the greatest potential. This approach, however, cannot be applied to relatively thin saws because of the short duration of wave travel time and as- sociated instrument limitations. Using surface waves acoustic analysis of stresses in circular saws [Clotfelter 1972 ; Szymani 1973], two major limitations have been encountered which preclude application of this technique in its present form. One of the limiting factors is a low value for a so-called stress-acoustic coefficient (delay t ime for 1-inch path length of wave travel at 1 ksi) which relates the change in velocity to stress. This factor directly controls the accuracy of this method and in the case of saw-blade material was found to be of the order of 0.1 ns/ksi whereas in the case of alumininm alloys it is much higher and averaging 1.5ns/ksi [Benson 1968]. Thus, the low stress-acoustic coefficient in conjunction with the variation in measurement of t ime delay, which averaged • 1 nsec, results in a :J: 10 ksi error in stress. I t was also found tha t the ultrasonic method is highly sensitive to the directional properties due to initial rollig.

Magnetic method

This method is based on certain magnetic phenomena occurring in ferro- magnetic materials such as steel, cast iron, nickel, and some nickel alloys (the magnetic properties of ferromagnetic materials change significantly with appli- cation of stress). Bagchi and Cullity [1967] described the effect of applied and residual stress on the magaetoresistance of nickel. They studied the distribution of residual microstresses by applied stresses after plastic elongation. The mag- netoresistance was found to decrease with increasing plastic deformation. Using nickel and steel, Abuku and Cullity [1971] developed a magnetic method for the measurement of residual longitudinal stress in the outer portion of cylindrical bars. Their method involves measurement of the reversible effective permeability over the range of frequency of the applied alternating field. They found tha t the reversible effective permeability of nickel and steel in a large biased field increases almost linearly with tensile stress. They also demonstrated tha t a combination of magnetic and X-ray diffraction measurements can provide information about the magnitude of the stress gradient near the surface because of their large differences in penetration depth. This gradient cannot be determined nondestructively by either method alone.

Rolwitz [1969] described the measurement of residual and applied stresses in short-peened compressor blades, and applied stresses in cylindrical rods and rectangular bars by means of magneto-absorption techniques. Using some recent information provided by l~olwitz [1972], a portable instrument has been developed which has potential for using field-type measurements; this method employs the Barkhausen noise concept which is at t r ibuted to the abrupt and discontinuous

l~eview of residual stresses and tensioning in circular saws 153

motion of magnetic domain walls when test material is subjected to a stress field. Investigation of the applicability of this method to residual stress analysis in saw blades is presently underway at the University of California Forest Products Laboratory.

From the foregoing review it is apparent tha t a major drawback of non- destructive methods is their failure to provide acceptable accuracy for stress analysis in saw blades. Since residual stress measurement is saw blades must be practical and nondestructive, such a technique with sufficient accuracy would be used as a reference method in conjunction with other less precise but meaningful methods (such as vibration or bending tests) which allow estimation of tensioning stress influence upon saw stability.

Residual stresses in circular saws

Residual stresses and their eHect on the saw blade stability

Accurate tensioning stress analysis is part icularly impor tan t when highest possible cutting efficiency is desired. This would require reduction of saw thickness to reduce kerr losses and maintenance or increase of saw dynamic stability. Theoretical and experimental investigations of tensioning stresses and their effect on saw stiffness and stabil i ty have been studied by Barz et al. [Barz 1953, 1957, 1960; Barz, Berger 1960; Barz 1962, 1963, 1965; Barz, Miinz 1968]; Berolzheimer and Best [1959]; Dugdale [1963a, b, e, 1964, 1965, 1966a, b, 1968]; Fricbe [1970]; Khasdan [1956]; Mote et al. [Mote 1963, 1964, 1965, 1967, 1970a, b; Mote, Nieh 1971]; Pahlitzseh and Rowinski [1966a, b]; Sugihara [1952]; and Yakunin and Khasdan [1957] among others.

Similar theoretical explanations of the effect of the internal stresses on saw- disc stiffness were presented independently by Dugdale [1963a] and Mote [1964, 1965]. Dugdale [1963a] presented a theoretical discussion of the inclusion of initial stresses in the strain energy of deformation. Saw stiffness variat ion is predictable by evaluation of the strain energy of deformation associated with membrane stresses.

2~r b

Um f f , , ew \2 [ ~ 8w ,2~ : ](rrr[~-r ) q- (Xoo[--;-~-) I h r d r d O 0 a

(1)

where a = inner disc radius b = outer disc radius h = �89 disc thickness w --~ transverse displacement no0 = initial hoop stress arr = initial radial stress

The total strain energy of deformation includes a contribution due to bending, UB, which is independent of the initial stress state, so tha t the to ta l strain energy is

U : U , - t - Urn.

154 R. Szymani and C. D. Mote

If the state of stress is known, Eq. (1) can be approximately evaluated and the corresponding stiffness variation predicted. When the state of stress in the saw- disc is such that strain U increases in a particular mode of deformation, then stiffness in tha t mode also increases.

The transverse displacement, w, of the saw disc at any point can be expanded in a Fourier series

w(r, O) -~ Vo(r ) -{- Vl (r ) sin0 + V~(r) s in20 + V~(r) sin 30 + . . . .

= V o -~ ~ V~sin nO. (3) n ~ l

This series representation reduces the saw-disc deflection into a sum of harmonic modes of vibration. This decomposition is very useful in the analysis of the strain- energy variations. Combining Eqs. (1) and (3) strain energy Um becomes

l aVo/. liar1 t, 1 Um ~--~h art 1 dr ] r d r + f tl dr ] - ~ - ~ aOOV~ r d r +

q

,,_ (rooV~ r d r . . . (4)

b

/ dv"l' "' V:}rdr I(..6.,+7.~ where each integral in Eq. (4) can be interpreted as stiffness in a particular mode of deformation. In some modes it is common for stiffness to increase because of weighting of the initial stress state, whereas in other flexural modes the stiffness decreases.

Dugdale also included stiffness variations caused by a large, normal edge load. Reduction in stiffness for a compressive normal load P is approximately propor- tional to edge load magnitude

K : I~'(1 3 E'b h a p) (5)

where K = numerical stiffness for displacement under transverse load with a radial normal compressive force P

K ' = numerical stiffness coefficient for zero normal load E ' = modified elastic modulus E/(1 -- v ~') h = �89 disc thickness b ~ peripheral radius

This stiffness is approximate because the deformation modes are altered by the introduction of edge load. The result of Eq. (5) is exactly correct only in cases where the deformation mode is unaltered by the load P. A simply-supported beam under tension is such a case. In general the approximate stiffness K (5) is bounded from above by the exact value.

The influence of nearly arbitrary normal and tangential edge loading distribu- tions on the disc membrane stress state and modal stiffness can also be investigated using the finite element procedures outlined by Mote [1970b].

Review of residual stresses and tensioning in circular saws 155

~ o t e [1964] compared the distribution of tensioning stresses in a circular saw blade to those in a composite disc, where radial stresses are everywhere com- pressive and hoop stresses are tensile at radii greater than the tensioning radius and compressive at radii less than the tensioning radius. The location of the tensioning radius is critical, as indicated by Eq. (4). As an alternative to using Eq. (4) for potential energy variations, one can consider using natural frequency variations which have an equivalent interpretation, namely each natural frequency is shifted by in-plane stresses. However, residual stresses introduced in the tensioning process and thermal stresses due to the cutting process have an op- posing effect on the saw's natural frequencies. Thermal stresses f rom peripheral heating reduce critical natural frequencies and proper tensioning increases them; for this reason proper tensioning improves saw stabil i ty in the cutting environ- ment.

More recent studies of Dugdale [1966 b, 1968] have shown tha t the introduction of internal stresses during tensioning leads to a substantial increase in the critical speed of circular saw blades. The critical speed of a circular disc is the rotat ion speed at which the saw executes resvnant oscillations when driven by a moving transverse force of a constant magnitude. In the cutting process the force is s tat ionary in space and the disc is moving. The quant i ty to be maximized for opt imum stabili ty is the critical speed at which the standing-wave resonance occurs. There may be other significant instability mechanisms, but they have not yet been identified. The stabili ty criterion results from the observation tha t the resonant response of the saw disc is composed of two wave-form solutions traveling in opposite angular directions on the disc [Mote 1970 a] ; the situation is analogous to the Doppler effect in sound transmission. The frequency of a sound-pressure source increases as the source moves toward the receiver and decreases as the source moves away from the receiver. In the rotat ing saw disc the resonant frequency associated with the forward-traveling wave increases because of saw rotation, and the resonant frequency associated with the backward-traveling wave is reduced because of the rotation. Thus, the resonant frequencies fi for the two solutions are determined f rom

(egmn + nK2) 2 -~ fi2 for n = 1, 2, 3. . . (6)

where C0mn ~ natural frequency in the operating environment corresponding to m-nodal circles and n-nodM diameters

K2 -= disc rotat ion frequency which is the angular velocity of the moving concentrated load

fl ~ load excitation frequency n ~ number of nodal diameters of the resonance mode.

The critical speed is the lowest rotat ion speed at which resonance is excited in one vibration mode by a constant transverse force.

Y2 crit. = rain ( ~ -) for a l l n = 1, 2, 3. . . (7)

Thus, the shift in critical speed is associated with natural frequency variations.

156 1% Szymani and C. D. Mote

Recent developments by Mote and Nieh [1971] confirmed experimentally tha t the critical speed is a controlling parameter in saw stability. Furthermore, they demonstrated tha t tensioning induces positive variations in natural frequency which result in a significantly higher critical speed (i. e., better saw stability).

Introduction o] tensioning stresses and methods o] their evaluation

There are three principal techniques used to introduce tensioning stresses in circular saw blades. They are : hammering, rolling, or thermal tensioning. Hammer- ing to control and introduce residual stresses has been used at various stages in the manufacture of saws for a hundred years. Tensioning stresses during the hammer- ing process are set up by applying rings of blows to a saw blade with the hammer face oriented eireumferentially or radially, thus causing various nearly axi- symmetric distributions of internal stress. Effects of distribution of these two types of blows were assessed by Dugdale [1966a], whose experimental and theoretical work shows that the circumferential rings of blows produced an in- crease in stiffness in the second and higher harmonic modes of flexure and, accord- ingly, the second and higher nodal diameter modes vibration. Radial blows may be used for restoring stiffness in the axi-symmetric mode in case they should become too reduced. In practice, some combinations of these two types of blows are used in order to meet the operating requirements of the saw blade. Because the process is mainly art, and because it is usually impossible to determine and control tensioning stresses introduced by hammering, this process will probably be used to a lesser degree in the future.

The reliability, reproducibility, and consistency of initial tensioning were substantially improved by introducing tensioning machines [Barz 1963; Berolz- heimer and Best 1959]. Here, tensioning stresses are introduced by two rollers opposing each other on saw-blade surfaces rolled circumferentially under constant load at constant radius; compressive normal load is sufficiently high to induce plastic deformation in the saw under the rollers. Detailed description of the rolling machine has been given by Stakhiev [1965].

The third type of tensioning process as proposed by Mote [1965] is " thermal tensioning". Here the objective is to heat the saw blade and purposely induce appropriate thermal stresses. Thermal tensioning appears to be as effective as tensioning by rolling, with the additional advantage that the state of stress can be calculated and continuously adjusted. As this process is relatively new, problems associated with it have not been widely investigated, but it should be noted that a form of thermal tensioning is always present in the process. Mote and Nieh [1971] have shown that the critical speed can increase 16 per cent because of ther- mal stresses induced from bearing heating alone. In more precision spindles and high tolerance processes, bearing heating can be expected to increase with a notable gain in terms of saw transverse stability. The "packing" technique used by some saw filters today is also a form of thermal tensioning.

A rapid method for measuring internal stresses in thin disks is discussed by Dugdale [1963 c] ; however, this method is destructive because a radial slit is made in the disc and stresses are calculated from displacement of the slit edges. Dugdale found good agreement between these results and those obtained from strain

l~eview of residual stresses and tensioning in circular saws 157

gages. Strain gages have been successfully used for measuring initial tensioning stresses also by Mote [1964] and Pahlitzsch and Rowinski [1966a]. Strain gages are limited to the measurement of the initial tensioning stresses, and this technique cannot be used to determine residual stresses present in the saw blade at any time.

Dugdale [1963b] used the test apparatus in Fig. 1 to measure the stiffness of tensioned and untensioned saw discs. A number of dial gages was used to record displacements at the edge of the centrally clamped disc. Upward and downward loading was applied by means of cables passing over pulleys and at tached to weights. In this method, readings of dial gages were taken at points of loading and at points between the loads; various test disc stiffness coefficients were thus determined experimentally. The four-point loading method in which four equal transverse loads are applied at 90 ~ intervals determine the approximate stiffness of the two-nodal-diameter mode. This vibration mode is often the critical stability mode, or the resonance mode associated with critical speed. Dugdale [1965] later modified the method by changing the loading arrangement, using a relatively soft spring to apply a constant load with load adjusted to give an average deflection of 0.050 in. for tests on discs of 0.125 in. thickness. Disc deflection Was recorded on the dial gages as the disc was rotated.

Using the bending test approach employed by saw tilers for examining saw blade tensioning, Baiz [1953, 1957] developed a testing device which recorded disc elevation contours in the form of a polar diagram. Tensioning was then evaluated from the distances between individual curves obtained from static bending of untensioned and tensioned saw blades. Khasdan [1950] and Meins [1963] evaluated tensioning by recording deflection of the blade subjected to load. Positioning of the load and dial gages was similar in both cases; Fig. 2a shows the method of Meins. Determination of tensioning by the deflection test has been also done by Tverdynina [1966] and Pahlitzseh and Rowinski [1966a]. A review of various methods used for evaluation of tensioning by deflection has been recently presented graphically by Barz and Miinz [1968] and is shown in Fig 2. Tensioning eva- luation in the case of the polar diagram technique (Fig. 2e) is based on the dif- ferences between contours R and D. A more extensive review of various methods

T--q

Fig. 1. Diagram showing the apparatus for the measurement of deflections of a centrally clamped disc. From Dugdale [1963 c]

158 R. Szymani and C. D. Mote

b

C

<)

d

O

Fig. 2. Arrangements for applying 10ad ~nd positioning dial gauges during evaluation of tensioning in saw blades by: a) ~eins [1963]; b) Dugdale [1965]; c) Tverdynina [1966];

d) Pahli~zsch and Rowinski [1966]; e) ]3arz and Mtinz [1968]

for the evaluat ion of tensioning stresses by deflection can be found in a recent paper published by Proke~ [1972].

All these techniques refer to a static bending test in one form or another. Differences between the techniques lie in the methods of load application or deflection measurement . The l imi ta t ion of the techniques is t h a t t hey can be used for determinat ion of stiffness of the saw blade only in a specific mode of deformat ion or under a specific loading configuration. This becomes apparent in Eqs. (1)--(4) where stiffness or s train energy terms are seen to involve the s tate of stress and deformation. Specifically, the stiffness in each mode is the in tegrated p roduc t of the unknown stress s ta te and the unknown deformation. Knowledge of the stress s tate could permit computa t ion of the stiffness in any mode of defor- mation, bu t the converse is no t true. The use of strain gages is l imited to the initial tensioning-stress measurement . Therefore, once the saw blade is tensioned, it is impossible to measure stresses again with strain gages wi thout destroying at least pa r t of the saw.

References

Abuku, .S., Cullity, ]3. D. 1971. A magnetic method for the determination of residual stress. Experimental Mechanics l l (5) : 217--223.

]3agehi, D. K., Cullity, ]3. D. 1967. Effects of applied and residual stress on the magneto- resistance of nickel. J. Appl. Physics 88 (3): 999--1000.

Baldwin, W. M. 1949. Residual stresses in metals. Proceedings, American Society for Testing Materials 49: 539--583.

]3arret, C. S., Massalski, T. V. 1966. Structure of metals. McGraw-Hill Book Co., New York, 466--484.

Review of residual stresses and tensioning in circular saws 159

Barz, E. 1953. Untersuchungen an Kreiss~gen fiir Holz, Fehler- und Spannungspriifverfahren. Forschungsbericht l~r. 51 des Wirtsehafts- undVerkehrsministeriums Nordrhein-Westfalen. KSln und Opladen: Westdeutscher Verlag.

Barz, E. 1957. Fertigungsverfahren und Spannungsverlauf bei Kreiss~gebl~ttern ffir Holz. Forsehungsberichte des Wirtschafts- und Verkehrsministeriums 1Nordrhein-Westfalen l~r. 360. KSln und Opladen: Westdeutseher Verlag.

Barz, E., Berger, A. 1960. Holzbereitungswerkzeuge. Mitteilungen der Deutsehen Gesellsehaft ffir Holzforschung. Heft Nr. 45. Stuttgart DGfH.

Barz, E. 1960. Prfifger~te fiir den Richt- und Spannungszustand yon Kreissageblattern. I-Iolz Rob- Werkstoff 18 (1): 19--25.

Barz, E. 1962. Der Spannungszustand von Kreiss~geblattern und seine Auswirkungen auf das Arbeitsverhalten. Holz Roh- Werkstoff 20 (10): 393--397.

Barz, E. 1963. Vergleichende Untersuchungen fiber das Spannen von Kreissagebl~ttern mit Maschinen und mit Richthammern. ttolz Roh- Werkstoff 21 (4): 135--144.

Barz, E. 1965. Zur Frage der Eigenspannungen in scheiben- nnd bandf5rmigen Werkzeugen. I. Mitteilung: ZerstSrungsfreie Ermittlung yon Eigenspannungen bei scheiben- und band- fSrmigen Trennwerkzeugen. ttolz Roh- Werkstoff 28 (10) : 412--419.

Barz, E., Mfinz, U. 1968. Priifung und Beurteilung des Richt- und Spannungszustandes bei Kreiss~gebl~ittern ffir die Holzbearbeitung. Holz Roh- Werkstoff 26 (5): 170--175.

Benson, R. W. 1968. Development of nondestructive methods for determining residual stresses and fatigue damage in metals. Contract No. NAS 8-20208. Propulsion andVehiele Engineer- ing Laboratory, George C. Marshall Space Flight Center, Huntsville, Alabama.

Berolzheimer, C., Best, C. 1959. Thin circular saw blades. Forest Prod. J. 9 (11): 404--412. Bolstadt, D. A., Davis, R. A., Quist, W. E., Roberts, E. C. 1963. Measuring stress in steel

parts by X-ray diffraction. Metal Progress, 88--92. Bolstadt, D. A., Quist, W. E. 1965. The use of a portable X-ray unit for measuring

residual stresses in aluminum, titanium and steel alloys. Advances in X-ray Analysis 8: 26--37.

Christenson, A. L. (ed.) 1960. Measurement of stress by X-ray. Society of Automotive Engineers Technical Report I~o. 182, SAE, Inc., New York.

Clotfelter, W. ~q. 1972. Marshall Space Flight Cen~er, Huntsville, Alabama. Personal com- munication.

Cullity, B. D. 1967. Element of X-ray diffraction. Addison-Wesley Reading, Mass., 431--451. Denton, A. A. 1966. Determination of residual stresses. Metallurgical Rev. 11 (101): 1--28. Dugdale, D. S. 1963a. Effect of internal stress on elastic stiffness. J. Mech. Phys. Sei. 11-"

41 --47. Dugdale, D. S. 1963b. Effect of internal stress on the flexural stiffness of discs. Int. J. Engi-

neering Sei. 1: 89--100. Dugdale, D. S. 1963c. Measurement of internal stress in discs. Int. J. Engineering Sci. 1"

383--389. Dugdale, D. S. 1964. Indentation of strips with flat dies on a flat anvil. Int. J. Production Res.

3 (2): 141--151. I)ugdale, O. S. 1965. Flexure tests for revealing internal stress in discs. Int. J. Engineering

Sci. 8: 1--8. Dugdale, D. S. 1966a. Theory of circular saw tensioning. Int. J. Production Res. 4 237--248. Dugdale, D. S. 1966b. Stiffness of a spinning disc clamped at its centre, g. Mech. Phys. Solids

14: 349--356. Dugdale, D. S. 1968. Flexure of thin plates containing internal stress. Int. J. Engineering Sci.

6: 239--249. Frick, R. P., Gurtman, G. A., l~r H. D. 1967. Experimental determination of residual

stresses in an orthotropic material. J. of Materials 2 (4) : 719--748. Friebe, E. 1970. Steifheit und Schwingungsverhal~n yon Kreiss~gebl~ttern. Holz Rob- Werk-

stoff 28 (10): 349--357. Firestone, F. A., Frederick, J. R. 1946. Refinements in supersonic reflectoscopy polarized

sound. J. of the Acoustical Soe. of America. 18 (1): 200--211.

160 R. Szymani and C. D. Mote

Gause, R. L. 1967. Ultrasonic analysis of cold-rolled aluminum. Nondestructive testing: Trends and techniques. Proceedings of the Second Technology Status and Trends Symposium, NASA SP-5082: 31 --42.

Greaves, R. W., Kirstowsky, E. C., Lipson, C. 1945. Residual stress study. Proceedings, Society for Experimental Stress Analysis 2 (2) : 44--58.

Hanslip, R. E. 1952. Residual stress in surface-hardened oil field pump rods. Proceedings, Society for Experimental Stress Analysis 10 (1): 97--112.

Heyn, E. 1914. Internal strains in cold wrought metals and some troubles caused thereby. J. of the Institute of Metals 12: 1--37.

Hiendelhofer, K. 1951. Evaluation of residual stresses. McGraw-Hill, Inc. New York. Khasdan, S. M. 1956. Tensioning of circular saws. Deter. Prom. 5 (9): 15--17. Maeherauch, E. 1966. X-ray stress analysis. Experimental Mechanics 6: 140--153. Mack, D. R. 1962. Measurement of residual stresses in disks from turbine-rotor forgings.

Proceedings, Society for Experimental Stress Analysis 19 (1): 155--158. McKannan, E. C. 1967. Ultrasonic measurement of stress in aluminum. Nondestructive

testing: Trends and techniques. Proceedings of the Second Technology Status and Trends Symposium NASA SP-5082: 43--54.

Meins, W. 1963. Ger~uschuntersuchungen an Kreiss~geblattern fiir die Holzbearbeitung. Dissertation. T. H. Braunschweig.

Mote, C. D., Jr. 1963. Effect of inplane stresses on the vibration characteristics of clamped- free discs. Ph.D. Dissertation, Univ. of Calif., Berkeley.

Mote, C. D., Jr. 1964. Circular saw stability. Forest Prod. J. 14 (6) : 244--250. Mote, C. D., Jr. 1965. Free vibration of initially stressed circular disks. Trans. ASME 87 (B) :

258--264. Mote, C. D., Jr. 1967. Natural frequencies in annuli with induced thermal membrane stresses.

Trans. ASME 89 (B): 611--618. Mote, C. D., Jr. 1970a. Stability of circular plates subjected to moving loads. Journal of the

Franklin Inst. 290 (4) : 329--344. Mote, C. D., Jr. 1970b. Discrete element models for the stress and vibration analysis of plates.

University of California Forest Products Laboratory, Service Report No. 35.01.77. Mote, C. D., Jr., Nieh, L. T. 1971. Control of eircnlar disc stability with membrane stresses.

Experimental Mechanics 11 (11): 290--298. Neff, H. 1960. RSntgenographisehe Spannungsmessungen an geh~rteten St~hlen. Sonder-

druek aus ,,ATM", Lieferung 298. Nisida, M., Hond, M., Hasunuma, T. 1956. Studies of plastic deformation by the photo-plastic

method. Proceedings, Sixth Japanese National Congress of Applied Mechanics, 137--140. Nye, J. F. 1947. Discussion on the measurement of internal stresses. Symposium of Internal

Stresses in Metals and Alloys. Institute of Metals, London, 382. Orowan, E. 1948. Classification and nomenclature of internal stresses. Symposium on Internal

Stresses in Metals and Alloys. Institute of Metals, London, 47--59. Pahlitzsch, G., Rowinski, B. 1966a. Uber das Schwingungsverhalten yon Kreiss~geblattern.

Erste Mitteilung: Bestimmung und Auswirkung der geometrischen Form und des Vor- spannungszustandes. Holz Roh- Werkstoff 24 (4): 125--134.

Pahlitzsch, G., Rowinski, B. 1966b. Zweite Mitteilung: Ermittlung und Auswirkungen der kritischen Drehzahlen und Eigenfrequenzen der S~gebl~tter. Holz Rob- Werkstoff 24 (8): 341 --346.

Palermo, P. M. 1963. An evaluation of the hole-relaxation method of determining residual stresses. Report 1742, David Taylor Model Basin, Washington 7, D. C.

Proke~, S. 1972. Comparison of methods for measuring tension of saw disks. Drevo. 27 (7): 181--183.

Rembowski, J. L. 1958. Theory for the calculation of the tangential residual stress distribution in curved beams. Proceedings, Society ~or Experimental Stress Analysis 16 (1) : 195--198.

Richards, D. G. 1945. A study of certain mechanically-induced residual stresses. Proceedings, Society for Experimental Stress Analysis 3 (1) : 40--61.

l~iney, T. D, 1957. Photoelastie determination of the residual stress in the dome of electron tube envelopes. Proceedings, Society for Experimental Stress Analysis 15 (1): 161--170.

Review of residual stresses and tensioning in circular saws 161

Riparbelli, C. 1950. A method for the determination of initial stresses. Proceedings, Society for Experimental Stress Analysis 8 (1) : 173--196.

Rollins, F. R. 1959. Study of methods for nondestructive measurement of residual stresses, Technical l~eport 59--561, Wright Air Development Division, Wright-Patterson Air Force Base, Dayton, Ohio.

Rollins, F. R. 1961. Ultrasonic methods for nondestructive measurement of residual stresses, Technical Report 61 --42, Part I, Wright Air Development Division, Wright-Patterson Air Force Base, Dayton, Ohio.

Rollins, F. R., Kobett, D. 1%., Jones, J. L. 1963. Study of ultrasonic methods for nondestructive measurement of residual stress, Technical Report 61--42, Part II, Wright Air Development Division, Wright-Patterson Air Force Base, Dayton, Ohio.

Rollwitz, W. L. 1969. Magnetoabsorption techniques for measuring material properties. Part II. Measurement of residual and applied stress. Technical Report 66--76, Air Force Materials Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio.

Rollwitz, W. L. 1972. Southwest Research Institute, San Antonio, Texas. Personal com- munication.

Sachs, G. 1940. Practical metallurgy, Amer. Soc. Metals, Cleveland, Ohio. Sachs, G., Espey, G. 1941. The measurement of residual stresses in metals. Iron Age. Sep-

tember 18, 63--71;September 25, 36--42. Schaal, A. 1955. Industrielle AnwendungsmSglichkeiten der rSntgenograph~schen Spannungs-

messung. Archly fiir das Eisenhiittenwesen. 26 (8) : 445--447. Stakhiev, Yu, M. 1965. Rolling machine for circular saws. Derev. Prom. 14 (2) : 28. Sugihara, H. 1952. Some problems of circular saw blades, especially on tensioning. Wood Rcs.

Inst. Kyoto University, 4: 1--32. Szymani, R. 1972a. l~esidual stresses and tensioning of circular saws for wood. University of

California Forest Products Laboratory, Service Report No. 35.01.94, Progress Report No. 1.

Szymani, R. 1972b. Evaluation of X-ray technique for residual stress analysis in circular saws. University of California Forest Products Laboratory Technical Report No. 35.01.94, Progress Report No. 2.

Szymani, R. 1973. Potential of ultrasonic methods for residual stress analysis in circular saws. University of California Forest Products Laboratory. Technical Report No. 35.01.94, Pro- gress Report No. 3.

Taylor, A. 1961. X-ray metallography. John Wiley & Sons, Inc., New York. Tokarcik, A. G., Polzin, M. H. 1952. Quantitative evaluation of residual stresses by the

stresscoat drilling technique. Proceedings, Society for Experimental Stress Analysis 9 (2) : 195--207.

Treuting, R. G., Lynch, J. J., Wishart, H. B., Richards, D. G. 1952. Residual Stress Measure- ments. Amer. Soe. Metals, Cleveland, Ohio.

Tverdynina, M. M. 1966. Tensioning control of the circular saws by the deflection of saw rim. Deter. Prom. 15 (3): 12--14.

Yakunin, Ya, K., Khasdan, S. M. 1957. Stability and vibration of circular saw discs during operation. Derev. Prom. 6 (8): 11--14, 6 (9): 14--15.

(Received March 5, 1973)

R. Szymani, Assistant Specialist University of California Forest Products Laboratory, Richmond, Cal., and Dr. C. D. Mote Jr., Professor Mechanical Engineering and Associate Research Engineer Forest Products Laboratory, University of California, Berkeley; on leave at the Norsk Treteknisk Institut, Oslo, Norway