Fundamentals of Orthg Cutting

8/3/2019 Fundamentals of Orthg Cutting

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Fundam entals of M achining/Orthogonal Cutting

Machining is the process of removing unwanted material from a work piece in the form of chips. If

the work piece is metal, the process is often called metal cutting or metal removal.

Fundamentals

The process of metal cutting is complexbecause it has such a wide

variety inputs which are listed in figure. These variables are:1.Themachine tool selected to perform the process.2.The cutting tool selected [geometry & material].3.Theproperties and parameters of the work piece.4.The cutting parameters selected [speed, feed & depth of cut]5.The work piece holding devices or fixtures or jigs.

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There are seven basic chip formation processes (see Figure): turning, milling, drilling,

sawing, broaching, shaping (planing), and grinding (abrasive machining).

Usually the workpiece material is determined by the design engineer to meet the

functional requirements of the part in service. The manufacturing engineer will often

have to select cutting tool parameters, and work holder parameters and then cutting

parameters based on that work material decision.

Let us begin with the assumption that the workpiece material has been selected and you have

decided to use a high-speed steel cutting tool for a turning operation.

For all metal-cutting processes, it is necessary to distinguish between

speed, feed, and depth of cut. The turning process will be used to

introduce these terms. See Figure. In general, speed (V) is the primarycutting motion, which relates the velocity of the cutting tool relative to

the workpiece. It is generally given in units of meters per minute

(m/min) or meters per second (m/s). Speed (V)is shown with the heavy

dark arrow. Feed (fr) is the amount of material removed per revolutionor per pass of the tool over the workpiece. In turning, feed is in

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mm/rev, and the tool feeds parallel to the rotational axis of the

workpiece. Depending on the process, feed units are mm /rev, mm/

cycle, mm /minute, mm / tooth. Feed is shown with dashed arrows.

The depth of cut (DOC) represents third dimension. In turning, it is thedistance the tool is plunged into the surface. It is the difference in the

diameter D1, the initial diameter, and D2, the final diameter:

DOC = D1-D2/2 = d mm

The selection of the cutting speed Vdetermines the surface speed of

the rotating part that is related to the outer diameter of the workpiece.

V= D1Ns/1000Where D1is in mm, Vis speed in surface mm per minute, and N is the

revolutions minute (rpm) of the workpiece. The input to the lathe will

be in revolutions per minute of the spindle.

s

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Cutting speed, feed, and DOC selection depend on many factors, and a great deal of

experience and experimentation are required to find the best combinations. A good

place to begin is by consulting tables of recommended values as shown in Figure21-4. Most tables are arranged according to the process being used, the materialbeing machined, the hardness, and the cutting tool material.

The table in figure 21-4 is for turning processes only. The amount ofmetal removed per pass determines the DOC. In practice, roughing cuts are

heavier than finishing cuts in terms of feed and DOC and are run at

a lower surface speed.

Once cutting speed V has been selected, Equation Ns = 1000 V/ D1 is used to

determine the spindle rpm, Ns. The speed and feed can be used with the DOC to

estimate the metal removal rate for the process, or MRR. For turning, the MRR is

MRR = 1000 V frd [mm3/min]

This is an approximate equation for MRR. For turning, MRR values can range from 2.5

to 15240 mm3/min. The MRR can be used to estimate the power needed to perform a

cut, as will be shown later. For most processes, the MRR equation can be viewed as

the volume of metal removed divided by the time needed to remove it.

MRR = volume of cut / Tm

Where: Tmis the cutting time in minutes. For turning, the cutting time depends upon

the length of cut L divided by the rate of traverse of the cutting tool past the rotatingworkpiece frNsas shown in Figure. Therefore, Tm = L + allowance / fr Ns [min]

An allowance is usually added to the L term to allow for the tool to enter and exit the

cut.

Turning is an example of a single-point tool process, as is shaping. Milling and drilling are

examples ofmultiple-point tool processes. Figures 21-5 through 21-9

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For many of the basic processes, the equations for Tmand MRR are given. Theseequations are commonly referred to as shop equationsand are as fundamental asthe processes themselves, so the student should be as familiar with them as with thebasic processes.

The process of milling requires two figures because it takes different forms de-

pending upon the selection of the machine tool and the cutting tool. Milling, amultiple tooth process, has two feeds: the amount of metal an individual

tooth removes, called the feed per tooth ft(mm/tooth),and the rate atwhich the table translates past the rotating tool, called the table feedrate fm in mm per minute. It is calculated from fm = ftn Ns

Where n is the number of teeth in a cutter and Ns is the rpm value of the

cutter. Just as was shown for turning, standard tables of speeds and feeds formilling provide values for the recommended cutting speeds and feeds pertooth, ft.

Figure 21-10 and Table 21-2 provide a summary of the basic machining processes in terms oftypical machine tools which can perform the process, the typical sizes (min-max), theproduction rates (part/hour), tolerances (precision or repeatability) and surface finish(roughness). Milling has pretty much replaced shaping and planning although gear shaping isstill a viable process.

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ENERGY AND POWER IN MACHINING

All of the processes described to this point are examples of oblique, or three-force, cutting and were shown in Figure 21-2. The cutting force system in aconventional, oblique-chip formation process is shown schematically in Figure21-11. Oblique cutting has three components:1. Fc:Primary cutting force acting in the direction of the cutting velocity vector.This force is generally the largest force and accounts for 99% of the powerrequired by the process.

2. Ff:Feed force acting in the direction of the tool feed. This force is usuallyabout 50% of Fc but accounts for only a small percentage of the powerrequired because feed rates are usually small compared to cutting speeds.

3. Fr:Radial or thrust force acting perpendicular to the machined surface. Thisforce is typically about 50% of Ff and contributes very little to powerrequirements because velocity in the radial direction is negligible.

The oblique cutting geometry shown in Figures 21-1 and 21-3 is repeated in Figure 21-11:

which shows the general relationship between these forces and speed, feed, and depth cut.Note that these figures cannot be used to determine forces for a specific process.

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The power required for cutting (power at spindle)Pc= FcV / 60 Watt [N.m/s]

In metal cutting a very useful parameter is called unit, or specific power,which is defined as: u = Pc x 60,000/ MRR [N/mm

2]

In turning, for example, where MRR= 1000V fr dTherefore, u= 60 Fc / fr d

Values for specific power u, which is also called unit power, are given in Table 21-3.

These values are obtained through orthogonal metal-cutting experiments described

later in this chapter.

Specific power is related to and correlates well with shear stress s for a given metal,

which will be derived later. Unit power is sensitive to material properties (e.g.,

hardness), rake angle, depth of cut, and feed, whereas s is sensitive to material

properties only.

Specific power can be used in a number of ways. First, it can beused to estimate the motor power required to perform a machining

operation for a given material. u values from the table are

multiplied by the approximate MRR for the process. The motor

power, Pmotor is then

Pmotor = u x MRR x CF / E

Where Eis the efficiency of the machine. The Efactor accounts for thepower needed to overcome friction and inertia in the machine anddrive moving parts. Usually, 80% is used. Correction factors (CFs)mayalso be used to account for variations in cutting speed, feed, and rakeangle. There is usually a tool wear correction factor of 1.25 used toaccount for the fact that dull tools use more power than sharp tools.

The primary cutting force Fccan be roughly estimated according to

Fc = u x MRR / V

This type of estimate of the major force Fc is useful in analysis of deflectionand vibrationproblems in machining and in the proper design of work holdingdevices, because these devices must be able to resist movement anddeflection of the part during the process.

In general, increasing the speed, the feed, or the depth of cut will

increase the power requirement.

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Doubling the speed doubles the power directly.Doubling the feed orthe depth of cut doubles the cutting force Fc. In general, increasing thespeed does not increase the cutting force Fca surprising experimentalresult.However, speed has a strong effect on tool life because most of the

input energy is converted into heat, which raises the temperature ofthe chip, the work, and the tool, to the latter's detriment.

The above equation can be used to estimate the maximum depth of cut, d, for aprocess as limited by the available power.

dmax = Pmx E / u x V x fr (CF)

Another handbook value useful in chatter or vibration

calculations is cutting stiffness Ks. In this text, the

term specific energy Uwill be used interchangeably with

cutting stiffness Ks. It is interesting to compute the

total specific energy in the process and determinehow it

is distributed between the primary shear and the

secondary shear that occurs at the interface between the

chip and the tool.It is safe to assume that the majority

of the input energy is consumed by these two regions.

Therefore, U = Us + UfWhere specific energy [also called cutting stiffness] is

U = Fc V / V fr d = Fc / fr d = Ks [turning]

The specific shear energy

Us = Fs Vs / V fr d

Where Vs is the shear velocity and Fs is the shear force.

The specific friction energy

Uf = F Vc / V fr d = F rc / fr d

Where Vc is the chip velocity, F is the friction force and

rc is the chip thickness ratio [explained next page]

Usually, 30 to 40% of the total energy goes into friction and 60 to 70% into

the shear process. Typical values for U are given in Table 21-3. This isexperimental data developed by the orthogonal machining experiment described in the

next section.

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ORTHOGONAL MACHINING (Two FORCE)

In order to understand the complex process of oblique cutting, the tool geometry is simplified from the three-

dimensional (oblique) geometry, which typifies most processes, to a two-dimensional (orthogonal) geometry.

Low speed orthogonal plate machining as shown in Figure 21-12 uses a flat plate setup in a milling machine.

The workpiece is moving past the tool at velocity V.

Schematic illustration of a two- dimensional cutting process, also called orthogonal cutting.Note that the tool shape and its angles, depth of cut, to, and the cutting speed, V, are all

independent variables.

The feed of the tool is now called t

o,the uncut chip thickness. The DOC is the widthof the plate w. The cutting edge of the tool is perpendicular to the direction of

motion V. The angle that the tool makes with respect to a vertical from theworkpiece is called the back rake angle.

A positive angle is shown in the schematic. The chip is formed by shearing. The

onset of shear occurs at an angle with respect to the horizontal. This model issufficient to allow us to consider the behaviour of the work material during chipformation, the influence of the most critical elements of the tool geometry (the

edge radius of the cutting tool and the back rake angle ),and the interactionsthat occur between the tool and the freshly generated surfaces of the chip againstthe rake face and the new surface as rubbed by the flank of the tool.

Basically, the chip is formed by a localized shear process that takes placeover a very narrow zone. This large-strain, high-strain-rate, plasticdeformation evolves out of a radial compression zone that travelsahead of the tool as it passes over the workpiece. This radialcompression zone has, like all plastic deformations, an elasticcompression region that changes into a plastic compression regionwhen the yield strength of the material is exceeded.

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The applied stress level increases as the material approaches the tool where the material has no recourse but to shear. The onset of theshear process takes place along the lower boundary of the shear zone

defined by the shear angle . The shear lamellas (microscopic shear

planes) lie at the angle to the shear plane.

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MERCHANT'S MODEL

For the purpose of modelling chip formation, assume that the shearprocess takes place on a single narrow plane rather than on the set ofshear fronts that actually comprise a narrow shear zone. Further, assumethat the tool's cutting edge is perfectly sharp and no contact is beingmade between the flank of the tool and the new surface.The workpiecepasses the tool with velocity V, the cutting speed. The uncut chipthickness is t0. Ignoring the plastic compression, chips having thickness tcare formed by the shear process. The chip has velocity Vc. The shearprocess then has velocity Vsand occurs at the onset of shear angle . Thetool geometry is given by the back rake angle and the clearance angle.

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F = tan = Where = the coefficient of friction

N

r = to where, r = the chip thickness ratio

tc

to= AB sin tc = AB cos ( - )

r = AB sin = sin

AB cos ( - ) cos cos + sin sin

r cos cos + r sin sin = sin sin r cos cos + r sin sin = 1 r cos = 1- r sin

sin sin tan

tan = r cos

1- r sin

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The velocities are also important, and can be calculated for later use in power calculations. The

Velocity diagram below can also be drawn to find cutting velocities.

Where,

V = cutting velocity (m/min.) - as set or measured on the machine

Vs = shearing velocity

Vc = chip velocityUsing the sine rule,

Vs = V

sin(90- ) sin(90+ - )

Vs= V sin(90- ) = V cos

sin (90+ - ) cos ( - )

Also Vc = V sin

cos (-)

Since mass continuity has to be maintained: Vto = Vctc or Vc = Vr

Hence: Vc = V sin

cos ( - )

The velocity relationships are:

V = Vs = Vc

cos ( - ) cos sin

TYPES OF CHIP [refer text book]

MECHANICS OF MACHINING (STATICS)

Orthogonal machining has been defined as a two-force system.Consider Figure 21-19, which shows a free-body diagram of a chip thathas been separated at a shear plane. It is assumed that the resultantforce R acting on the back of the chip is equal and opposite to theresultant force R' acting on the shear plane. The resultant R is

composed of the friction force Fand the normal force Nacting on thetool chip interface contact area.

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Figure 21-19: Free body diagram of orthogonal chip formation process,

showing equilibrium condition between resultant forces R and R/.

The resultant force R'is composed of a shear force Fand normal force

F

s

s

c

s

F

nacting on the shear plane area A . Since neither of these two sets of

forces can usually be measured, a third set is needed, which can be

measured using a dynamometer (force transducer) mounted either in

the work holder or the tool holder. Note that this set has resultant R,

which is equal in magnitude to all the other resultant forces in the

diagram. The resultant force Ris composed of a utting force Fcand a

tangential (normal) force Ft.Now it is necessary to express the desired

forces (F , F n, F, N) in terms of the measured dynamometer

components, Fcand t, and appropriate angles.

To do this, a circular force diagram is developed in

which all six forces are collected in the same force

circle (Figure 21-20). The only symbol in this figure as

yet undefined is , which is the angle between the normalforce Nand the resultant R. It is called friction angle

and is used to describe the friction coefficient onthe tool-chip interface area, which is defined as F/ N.

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MECHANICS OF MACHINING (DYNAMICS)

Machining is a dynamic process of large strain and high strain rates.All the process variables are dependent variables. The process isintrinsically a closed-loop interactive process as shown in Figure 21-23.

Remember that plastic deformation is always preceded by elastic deformation, which

behaves like a big spring. The mechanism by which a process dissipates energy is

called chatter or vibration.In machining, it has long been observed in practice that rotationalspeed may greatly influence process stability and chatter. Experienced operators commonly listen to

machining noise and interactively modify the speed when optimizing a specific application. In

addition, experience demonstrates that the performance of a particular tool may vary significantly

based on the machine tool employed and other characteristics such as the workpiece, fixture holder,

and the like. Today more than ever, the manufacturing industry is more competitive and responsive,

characterized by both high volume and small batch production seeking economies of scale. High

productivity is achieved by increased machine and tooling capabilities along with the elimination ofall non-value-added activities. Few companies can afford lengthy trial-and-error approaches to

machining-process optimization or additional processes to treat the effect of chatter.

In metal cutting, chatter is a self-excited vibration that is caused by the closed loop

force-displacement response of the machining process. The process-induced

variations in the cutting force may be caused by changes in the cutting velocity, chip

cross section (area), tool/chip interface friction, built-up edge, workpiece variation, or

most commonly, process modulation resulting in regeneration of vibration.

The proper classification of the type of vibration is the first step inidentifying and solving the cause of unwanted vibration (see Figure 21-24).

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Figure 21-24: There are three types of vibration in machining.

Free Vibration is the response to any initial condition or sudden

change. The amplitude of the vibration decreases with time and

occurs at the natural frequency of the system. Interrupted

machining is an example that often appears as lines or shadows

following a surface discontinuity.

Forced Vibrationis the response to a periodic (repeating with time)

input. The response and input occur at the same frequency. Theamplitude of the vibration remains constant for set input conditions

and is linearly related to speed. Unbalance, misalignment, tooth

impacts, and resonance of rotation systems are the most common

examples.

Self-Excited Vibration is the periodic response of the system to a

constant input. The vibration may grow in amplitude (become

unstable) and occurs near the natural frequency of the system

regardless of the input. Chatter due to the regeneration of waviness

in the machined surface is the most common metal cutting example.

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How do we know chatter exists? Listen and look! Chatter is

c harac terized by the following:

1. The sud den onset of vib ra tion (a sc ree c h or buzz) tha t rap id ly

increases in amplitude until a maximum threshold (saturation) is

reached.

2. The frequenc y of c ha tter rema ins very c lose to a na tura l freq uenc y

(critical frequency) of the machining system and changes little with

va ria tion of p roc ess parameters. The largest forc e-d isp lac em ent

response occurs at resonance and therefore the greatest energy

dissipation.

3. Chatter often results in unacceptable surface finish exhibited by a

helical or angular pattern (pearled or fish scaled) superimposed over

norma l feed ma rks.

4. Visible surface undulations are found in the feed direction andc orrespond ing wavy or serra ted c hips with va riab le thickness.

Figure 21-25 shows some typical examples of chatter visible in the surface finish marks.

There are several important factors that influence the stability of a machining process:

. Cutting stiffness of the workpiece material (related to the machinability), Ks

. Cutting-process parameters (speed, feed, DOC, total width of chip)

. Cutter geometry (rake and clearance angles, edge prep, insert size and shape)

. Dynamic characteristics of the machining process (tooling, machine tool, fixture, and

workpiece).

Ks, cutting stiffness, is closely aligned with flow stress but simpler to calculate in that isnot used. Like flow stress, cutting stiffness can be viewed as a material property of the

workpiece, dependent on hardness.

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In machining, the chip is formed due to the shearing of

the workpiece material over the chip area (A = thickness

x width = t x w), which results in a cutting force Fc.

The magnitude of the resulting cutting force is

predominantly determined by the material cutting

stiffness Ksand the chip area such that Fc= Ksx t x w.

The direction of the cutting force Fc is influencedmainly by the geometries of the rake and clearance

angles as well as the edge prep.

HEAT AND TEMPERATURE IN METAL CUTTING

In metal cutting, the power put into the process (Fc V) is largely

converted to heat, elevating the temperatures of the chip, the

wo rkp iec e, and the too l.

These three elements of the p roc ess, along with the environment(whic h inc lud es the c utting fluid ), ac t a s the hea t sinks.

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Figure 21-30 shows the distribution of the heat to these

three sinks as a function of cutting speed. As speed

increases, a greater percentage of the heat ends up in

the chip to the point where the chips can be cherry red

or even burn at high cutting speeds.

There are three main sources of heat. Listed in order of their heat-generating capacity, they are shown in Figure 21-31.

1. The shear front itself, where plastic deformation results in the major heatsource. Most of this heat stays in the chip.

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2. The tool/chip interface contact region, where additional plasticdeformation takes place in the chip, and considerable heat is generated due tosliding friction.3. The flank of the tool, where the freshly produced workpiece surface rubs

the tool.

Documents

Fundamentals of Orthg Cutting