Proceedings of the Institution of Mechanical Engineers

When the cutting speed or feed of a metal cutting tool is increased, the most striking effect is on the rate of tool wear, but there are other changes which take place at the same time. These are changes in the geometry of the chip, tool forces, and tool build-up and surface finish. An attempt is made in this paper to form a logical theory to explain these variations in the mechanics of the process. The problem of tool wear is not attempted.

A series of tests has been conducted on mild steel and copper, over a wide range of speed, feed, and tool angle; and a theory has been developed. The results arrived at are:—

(1) That local temperature in the chip plays an important part in affecting the friction at the chip tool interface.

(2) For many purposes effects due to speed and feed can be treated as functions of the product of speed and feed.

(3) Temperature does not affect the shear strength of the metal directly.

(4) The extent of built-up edge prevailing can be put as a function of the product of speed and feed.

A full geometrical analysis of a cutting tool edge is made, in which an effective rake of universal application is defined in terms of the primary rake and the angle of obliquity of the edge. The fundamental angles are related in an easy manner to the traditional workshop terms, and may readily be applied to any cutting tool. A law of chip flow is given and its effects on the resulting chip shape are analysed. The effect of unit cube passing through the shear plane is also analysed and a method is given of finding the direction cosines of the axes of the ellipsoid of stress.

The flow law is used to find the directions ofthe cutting force between chip and tool and its various components. An examination of velocity and force diagrams for oblique cutting in Merchant's shear theory leads to a debatable result at variance with his fundamental machining equation.

Although predominantly theoretical, the paper has a practical background.

New mechanical and semi-mechanical devices put into practice in the foundry between 1942 and 1949 are described. They include in the mass-production shop, the moulding machine, brake block production and a modern knocking-out station, sand preparation and reconditioning and a multiple-belt storage hopper. Mechanization in the jobbing foundry is also discussed.

An earlier investigation has been continued on the protection of a rising water main against the consequences of a sudden interruption in the supply. In place of the air bottle previously tried, an automatic air-inlet valve was placed at the lower end of the pipe-line. Experiments on a laboratory scale showed that the cushion of air thus introduced brought the returning water column to rest without sound or shock. Theoretical calculations of maximum pressure and of air drawn in were verified. The lift of the pipe-line being small compared with its length, it was found that, over the range of velocity usually employed, the maximum pressure set up by the returning column diminished as the initial velocity of the interrupted supply was increased.

With no protective device in use, a series of violent impacts took place owing to the column striking and rebounding from the closed valve at the lower end of the pipe-line. An electronic gauge, having a very high natural frequency, was used to measure the magnitude and duration of the shock pressures. Its indications were generally in accord with an analysis based on the usual theory of pressure waves, but the maximum pressures actually recorded somewhat exceeded the theoretical estimates, owing to the existence of additional pressure fluctuations caused by reflections from bends, sockets, and other discontinuities in the pipe-line. The insertion of a spring-loaded relief valve only slightly reduced the shock pressures.

After describing the operation of a typical hydraulic ram installation, the paper reviews the fundamentals of the water hammer as a prerequisite to the proper understanding of the limitations of this hydraulic machine. The historical development is discussed in some detail with the object of ascertaining what research work remained to be done. The author presents his own theory based on the application of general laws of mechanics to the study of a specially designed experimental hydraulic ram. By means of a theory developed, which agrees satisfactorily with experiment, it is possible to forecast the behaviour of any automatic hydraulic ram, provided that the following four properties of a given installation have been determined separately by experiment: (a) loss of head in the drive pipe; (b) loss of head due to the impulse valve; (c) drag coefficient of the impulse valve; and (d) head lost during the period of retardation.

As a result of extensive investigation of water flow formulae and test data on water mains and experimental test pipes, four new formulae for water flow in pipes have been evolved. These apply to pipes in new condition using water at normal temperatures, and cover all classes and sizes of pipes and a very wide range of velocities. The constants in the formulae do not require to be varied to suit the condition or the size of pipe. It is only necessary to choose the appropriate formula to suit the material of which the internal surface of the pipe is made. These four formulae are:—

(1)

For smooth non-ferrous pipes: V = 47m***^0·71i^0·57.

An approximate estimate of the conditions arising when fluids other than water are used can be obtained by plotting these formulae on a Reynolds number diagram, and taking the value of F at the appropriate Reynolds number, but this is not recommended, since these formulae have not been compared with practical test results for fluids other than water.

The use of these formulae will give the discharge to be expected from any class and size of pipe to an error of not more than about ±10 per cent. Such accuracy is adequate for all ordinary water flow calculations, and is better, over the whole range of pipe surfaces, sizes, and velocities, than has been previously possible by the use of any other formula.

Significant developments in the theory of turbulent flow in smooth and rough pipes are reviewed to establish a rational basis for the commonly accepted logarithmic laws for pipe friction. The Prandtl (1932)‡ smooth-pipe law, , where f is the friction coefficient in the formula , agrees with measured results on smooth pipes up to Reynolds numbers of at least 3 × 10⁶. With rough pipe walls and sufficiently high Reynolds numbers, viscosity (and hence Reynolds number) ceases to have any direct effect and the friction coefficient depends on wall roughness and pipe size only. Almost all practical cases of water flow in commercial pipes lie between these two extremes of completely smooth and fully rough conditions, where the friction coefficient varies with both Reynolds number and roughness.

Exponential flow formulae of the Manning type—V = ***Am₁xiy—can be rearranged into a more rational form f = B(Re)p(k/d)q*** relating f to Reynolds number and relative roughness for a given class of pipe carrying a fluid of given viscosity. A detailed study is made of published test data on wrought-iron and steel pipes which generally operate in the transition zone, and an exponential formula is derived which agrees with these results. This is found to be similar to that given by Blair for this class of pipe.

The relative merits of these exponential formulae, and of the Colebrook-White transition function, are discussed and it is concluded that, for most practical cases of water flow in pipes, the simple formulae are no less reliable.

The fatigue strength under reversed direct stress was ascertained for specimens of various diameters in the range from 0·19 inch to 2·4 inches, the largest diameter being determined by the capacity of the machines available. Two steels were used in this investigation—a 25-ton mild steel and a 65-ton, per cent nickel-chromium steel. The specimens were either plain or notched (transverse hole) and, as far as possible, geometrical similarity was preserved with regard to the transition radii and the diameter of the transverse hole. A few fatigue tests on other types of notch, such as a circumferential V-groove and a shoulder, were also carried out.

No intrinsic size effect with either material was observed with the plain specimens.

With transverse-hole specimens in mild steel, the fatigue limit was ±8·4 tons per sq. in. for specimens of 0·33 inch diameter, and 6·1 tons per sq. in. for specimens of 1·7 inches diameter, thus showing that an appreciable size effect was present. A similar size effect was found with the alloy steel specimens containing a transverse hole, and fatigue limits of ±17·1 and ±13·9 tons per sq. in. respectively were obtained for these two sizes of specimen.

It is suggested that the low values of fatigue-strength reduction factors usually associated with mild steel as a result of laboratory tests do not apply to the larger sections of this material commonly employed in engineering practice.

This paper describes fatigue tests, under pulsating direct stress, of aluminium-alloy and mild-steel panels, with and without central holes, approximately 0·1 inch in thickness and up to 12 inches in maximum width.

Comparison of the results of tests on panels of similar shapes but of different sizes shows that larger panels are relatively weaker.

The influence on the fatigue strength of varying the size of a drilled hole in a wide panel has been explored over a range of hole-diameters from to of the net width. While, in general, the presence of a hole causes a marked reduction in fatigue strength, the smallest holes result in only a slight reduction.

It is known that a spot weld is a much more rigid connexion between two sheets than a rivet, and that this is likely to have some bearing on the relative strengths of the two types of joint. A recent test has emphasized this point. A spot-welded box, identical with a riveted box except that spot welds replaced rivets, failed at about two-thirds of tie failing load of the riveted box in spite of the fact that the shear strength of an individual spot weld was nearly twice that of a rivet, as determined by tests.

In this paper the problem is examined theoretically on the basis of experimentally obtained stress-strain curves for riveted and spot-welded joints in shear. The theoretical treatment takes account of the plastic, as well as the elastic, part of the stress-strain curves, and examples are given of the relative behaviour of the two types of joint in certain simple structural elements.

A multi-row lap joint is the first example chosen, and the second is a stringer reinforced panel in which there is appreciable shear-lag. In each example the riveted specimen gives the higher failing load (assuming the fastenings fail and not the connected members), although the experimental failing load of the individual rivet is less than half that of the spot weld. For lower loads, curves are shown which indicate the radical change that takes place in the distribution of shear among the rivets and welds, as more and more of them are loaded beyond their yield points. While such changes are of only incidental interest so far as the ultimate failing load of the structure is concerned, they are of paramount interest when assessing the life of the structure under repeated loading at loads that may be small compared with the ultimate load, for the distribution of shear among the fastenings is then clearly an important consideration.

The shear-lag case is of interest as showing how the difference between rivet and weld shear flexibility tends to be masked by that of the sheet panel connecting the booms and stringers. It is therefore a useful example for emphasizing that the character of the structure must be taken into account, as well as the individual properties of the fastenings, when comparing the likely behaviour of rivets and welds.

Intuition and personal opinion, rather than theoretical investigation, have often been the main guides in the determination of design stresses for fillet weld connexions. Excessive safety at the expense of accuracy and economy have resulted in weld connexions which, although they did not fail under working conditions, were not always economical.

In the case of eccentrically loaded joints the stress f_torsion under a torque T has been determined by using the polar moment of inertia J of the weld throats: f_torsion = Tr/J, where r is the distance of the extreme fibre from the centroid of the weld throat. This method, though accurate enough for closed weld arrangements, resulted in uneconomical sizes for other arrangements. This paper suggests a means of determining the working loads of eccentrically loaded fillet welded joints by working out the stresses in the plastic state prevailing immediately before failure occurs. From this calculation the value of the failing load is obtained, which is divided by a certain load factor, the result being taken as the permissible load. If the results are represented in the form of graphs the time spent on calculation is considerably reduced. Practical experiments gave results which were in close agreement with the result of these calculations.

In the second part of the paper, the two differing opinions on the best arrangement of fillet weld connexions joining rolled angle sections to gusset plates are investigated, so far as their effect upon the strength of the assembly is concerned, and no difference is found with regard to the static strength of the assembly, while stress peaks at the end of the welds may indicate a weakness of one arrangement under fatigue loading conditions. Further research in this direction is suggested.

This paper gives the results of calculations which were undertaken, in the first instance, to determine the increase in operating range of a disk coupling with skew misalignment which would be obtained by tapering the disks. The results of later investigations concerning the stresses due to “umbrella” deflexions, the vibration frequencies of tapered disks, and the torque buckling of disks of constant thickness, are also presented.

All the results have been obtained by integration of the general differential equation for disk bending.

In this paper the problem of transverse impact on a uniform beam is considered theoretically. Two examples which can be taken as representing a wide range of impacts which occur in practice are referred to particularly: (1) the beam struck transversely by a uniform square-ended rod travelling perpendicularly to it; (2) the same problem for the striker having a spherical end.

In these examples it is shown that the ability of the beam to deflect in shear as well as in bending plays a dominant part in what takes place, and that, as far as the force between striker and beam is concerned, the length of the beam is usually without importance, as there is not time during the impact for an elastic wave to travel to the ends of the beam and return.

It is shown that in regard to example (2) the theory presented is in good agreement with Arnold's experimental results obtained some years previously, and curves are given from which the maximum force between beam and striker can be obtained in terms of three parameters, representing respectively the velocity, the mass, and the radius of the striker, each dependent on the ratio of shear stiffness to bending stiffness for the beam.

In the simple plastic theory commonly used for mild steel it is assumed that after yielding has occurred in either tension or compression, straining can continue indefinitely at constant stress. Such an assumption has been found satisfactory for low carbon steels having a plastic range corresponding to eight to ten times the strain at yield, but for steels of greater strength this range is often considerably shorter, and it becomes necessary to take into account the strain-hardening range beyond.

To obtain experimental data, four steels were selected, varying in carbon content from 0·28 to 0·89 per cent, and having widely different stress-strain relations. For each steel a number of simply supported beams of square section were subjected to a symmetrical two-point loading; tension specimens were prepared from the unyielded ends of these beams and tested in a spring-loaded autographic testing machine to determine upper and lower yield stresses. In addition, two tension specimens from each steel were tested in a lever type of machine, and the stress-strain relations through the plastic range and the initial stages of the strain-hardening range were obtained with the aid of a “Gerard” extensometer***. This information gave good support to the theoretical work, whereby the behaviour of these steels in flexure can be correlated with the tensile properties.

Part I gives an account of an experimental investigation of the forces, work and strains involved, and the conditions for successful drawing of a cylindrical shell from a flat circular blank. It is claimed that the results are sufficiently accurate to provide a basis of reference for theoretical treatments of cup-drawing, as well as an empirical basis of comparison between different drawing conditions.

The work was carried out in an experimental crank-press of 50 tons nominal capacity, and was based on a cup diameter of 4 inches. Blank thicknesses from 0·025 to 0·060 inch were used, and although most of the work was carried out on a low-carbon rimming steel, comparative tests were made with aluminium, brass, and copper, of different tempers.

The conditions examined included methods of blank-holding, drawing ratio, punch and die profile radii, punch-die clearance, and blank thickness.

Although this part has no theoretical pretensions, it includes a descriptive account of stresses and strains in the deep-drawing process, based on plastic theory.

In cup-drawing, an element of metal whose initial diameter exceeds the mean cup diameter is under conditions of true radial drawing, which is combined with plastic bending under radial tension when it reaches the die profile, whereas other elements will be subject to stretch-forming under biaxial tension, which will be combined with bending under tension if they fall within the punch profile.

In this part an analysis of the stresses and strains in the region of true drawing is attempted, taking into consideration the effects of bending, thickness changes, strain-hardening, blank-holding force, die-profile friction, and tool geometry, but not of anisotropy in the material. Theoretical punch load-travel diagrams, process work, maximum punch loads and strains are compared with recorded experimental results over a wide range of tool design, operating conditions, and materials.

It is suggested that the theory can be applied with confidence in predicting punch loads and strokes and in prescribing power and strength ratings for deep-drawing presses.

This paper is concerned with the factors involved in the selection of the most suitable designs of pumping installations, particularly of the larger sizes, and, in the first place, discusses the effects of the different types of pump on the construction of the pumping station. It goes on to demonstrate the relative advantages of different designs over the wide range of specific speeds available.

Methods of determining the most suitable hydraulic characteristics in three typical cases are examined and the effects of these factors on the first cost and running and maintenance costs are considered. As most selections are usually a compromise between the ideal hydraulic characteristics and those available from the pump and prime mover, the relative merits of constant-speed, variable-speed, and variable-pitch impellers are discussed. Certain aspects of the methods in use for priming pumps are considered and the chief causes of pressure surges in pipe-lines are briefly outlined.

The paper concludes with a discussion of the various factors which may decide whether it is desirable that the plant shall be automatically operated, centrally controlled, or individually controlled.

The connexion between aircraft, land, and marine hydraulics is emphasized, especially in regard to the working fluid and the sealing problems. The ideal fluid which would suit all cases does not, as yet, exist. The properties, advantages, and disadvantages of a number of well known, and a few lesser known, fluids are discussed. The fluids include those based on petroleum, castor, water-glycol, halogenated, and synthetic compounds.

The properties covered include viscosity and density, and their variation with temperature and pressure; chemical and toxic effects; bulk modulus or compressibility; water miscibility, and the significance of cloud, pour, and boiling points.

The fire hazard, and its difficulties of assessment in relation to the usual recorded properties and conditions, is noted.

Thermal conductivity, dielectric strength and storage conditions are also considered.

Some of the information, of which much hitherto has been widely scattered, has been derived from recent research, and an attempt has been made to arrange the data in rational form.

In tests on low-pressure oil seals the technique of designing a synthetic rubber lip type of rotary seal so that it is “run-in” on the shaft was applied to finishing the lip of a seal for reciprocating duty. The performance of a seal so treated is shown to be greatly superior to that of untreated seals. A new method of measuring the inward load was devised and is described in detail. Interesting data on friction were noted and are shown graphically.