20.4 Orthogonal Machining (Two Forces)

Chapter 20Chapter 20

Fundamentals of Fundamentals of Machining/Orthogonal Machining/Orthogonal

MachiningMachining(Part 2)(Part 2)

EIN 3390 Manufacturing ProcessesEIN 3390 Manufacturing ProcessesFall, 2011 Fall, 2011

20.4 Orthogonal Machining (Two 20.4 Orthogonal Machining (Two Forces)Forces)In Orthogonal Machining (OM), tool geometry is simplified from 3-dimrnsional (oblique) geometry

Three basic orthogonal machining setup1.Orthogonal Plate Machining a plate in a milling machine (low-speed cutting)2.Orthogonal Tube Turning end-cutting a tube wall in a turning setup – medium-speed ranges.3.Orthogonal Disk Machining end-cutting a plate feeding in a facing direction – high-speed cutting.

FIGURE 20-13 Three ways to performorthogonal machining. (a) Orthogonal platemachining on a horizontal milling machine, goodfor low-speed cutting. (b) Orthogonal tube turningon a lathe; high-speed cutting (see Figure 20-16).(c) Orthogonal disk machining on a lathe;very high-speed machining with tool feeding (ipr)in the facing direction

FIGURE 20-14 Schematics ofthe orthogonal plate machiningsetups. (a) End view of table,quick-stop device (QSD), andplate being machined for OPM.(b) Front view of horizontalmilling machine. (c) Orthogonalplate machining with fixed tool,moving plate. The feedmechanism of the mill is used toproduce low cutting speeds. Thefeed of the tool is t and the DOCis w, the width of the plate.

FIGURE 20-15 Orthogonaltube turning (OTT) produces atwo-force cutting operation atspeeds equivalent to those usedin most oblique machiningoperations. The slight differencein cutting speed between theinside and outside edge of thechip can be neglected.

FIGURE 20-16 Videographmade from the orthogonal platemachining process.

FIGURE 20-17 Schematicrepresentation of the materialflow, that is, the chip-formingshear process. defines theonset of shear or lower boundary. defines the direction of slipdue to dislocation movement.

FIGURE 20-18 Three characteristic types of chips.(Left to right) Discontinuous, continuous, and continuous with built-up edge. Chip samples produced by quick-stop technique. (Courtesy of Eugene Merchant (deceased) at Cincinnati Milacron, Inc., Ohio.)

20.5 Merchant’s Model20.5 Merchant’s ModelAssume that 1) the shear process takes place on a single narrow plane as A-B in figure 20- 19. 2) tools cutting edge is perfectly sharp and no contact is being made between the flank of the tool and the new surface.

Chip thickness ratio: rc = t / tc = (AB sin cos( - )], or

tan rc cos/(1 - rcsin

Where AB – length of the shear plane from the tool tip to the free surface.

20.5 Merchant’s Model20.5 Merchant’s Model For consistency of volume,

rc = t / tc = (sin cos( - )] = Vc./V, and Vs / V = (cos cos( - )]

Where V – velocity for workpiece pasing tool, Vc – chip moving velocity, Vs – shearing velocity, – onset of shear angle, rake angle

.

FIGURE 20-19 Velocitydiagram associated withMerchant’s orthogonalmachining model.

20.6 Mechanics of Machining 20.6 Mechanics of Machining (statics)(statics)Assume that the result force R acting on the back of the chip is equal and opposite to the resultant force R’ acting on the shear plane.

R is composed of friction force F and normal force N acting on tool-chip interface contact area.

R’ is composed of a shear force Fs and normal force Fn acting on the shear plane area As.

R is also composed of cutting force Fc and tangential (normal) force Ft acting on tool-chip interface contact area. Ft = R sin ( - )

FIGURE 20-20 Free-body diagram of orthogonal chipformation process, showing equilibrium conditionbetween resultant forces R and R.

FIGURE 20-21 Merchant’s circular force diagram used to derive equations for Fs , Fr , Ft , and N as functions of Fc, Fr , f, a, and b.

20.6 Mechanics of Machining 20.6 Mechanics of Machining (statics)(statics) Friction force F and normal force N are:

F = Fc sin + Ft cos , N = Fc cos - Ft sin and= tan-1 = tan-1 (F/N),

Where friction coefficient, and – the angle between normal force N and resultant R. If = 0, then F = Ft , and N = Fc . in this case, the friction force and its normal can be directly measured by dynamometer.

R = SQRT (Fc2 + Ft

2 ),Fs = Fc cos - Ft sin , andFn = Fc sin + Ft cos

Where Fs is used to compute the shear stress on the shear plane

20.6 Mechanics of Machining 20.6 Mechanics of Machining (statics)(statics)Shear stress:

s = Fs/As,

Where As - area of the shear plane,

As = (t w)/sinWhere t – uncut ship thickness and w – width of workpiece.

s = (Fcsin cos - Ft sin2 )/(tw) psi

In metal cutting shear stress is a material constant. For a given metal, shear stress is not sensitive to variations in cutting parameters, tool material, or cutting environment. Once this value is known for a metal, it can be used in basic engineering calculations for machining statics (forces and deflection) and dynamics (vibration and chatter).

Fig. 20-22 shows some typical values for flow stress for a variety of metals, plotted against hardness.

FIGURE 20-22 Shear stress ts variation with the Brinell hardness number for a group ofsteels and aerospace alloys. Data of some selected fcc metals arealso included. (Adapted with permission from S. Ramalingham and K. J. Trigger, Advances inMachine Tool Design andResearch, 1971, Pergamon Press.)

20.7 Shear Strain 20.7 Shear Strain & Shear Front & Shear Front

Angle Angle Use Merchant’s chip formation model, a new “stack-of-cards” model as shown in fig. 20-23 is developed. From the model, strain is:

= cossin( + ) cos( + )]

where the angle of the onset of the shear plane, and - the shear front angle.

The special shear energy (shear energy/volume) equals shear stress x shear strain:

Us =

20.7 Shear Strain 20.7 Shear Strain & Shear Front Angle & Shear Front Angle Use minimum energy principle, where will take on value (shear direction) to reduce shear energy to a minimum:

d(Us)/d = 0, Solving the equation above,

= 450 - + , and = 2cossin),

It shows the shear strain is dependent only on the rake angle

FIGURE 20-23 The Black–Huang “stack-of-cards” model for calculating shear strain in metalcutting is based on Merchant’s bubble model for chip formation, shown on the left.

20.8 Mechanics of Machining 20.8 Mechanics of Machining

(Dynamics)(Dynamics)Machining is a dynamic process of large strain

and high strain rate.

The process is a closed loop interactive

processes as shown on fig. 20-24.

FIGURE 20-24 Machiningdynamics is a closed-loopinteractive process that createsa force-displacement response.

20.8 Mechanics of Machining (Dynamics)20.8 Mechanics of Machining (Dynamics)

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.

Forced vibration is the response to a periodic (repeating

with time) input. The response and input occur at the

same frequency. The amplitude of the vibration remains

constant for set input condition.


Self-excited vibration is the periodic response of the

system to a constant input. The vibration may grow in

amplitude and occurs near natural frequency of the

system regardless of the input. Chatter due to the

regeneration of waviness in the machining surface is the

most common metal cutting example.

FIGURE 20-25 There are threetypes of vibration in machining.

FIGURE 20-26 Someexamples of chatter that arevisible on the surfaces of theworkpiece.


Factors affecting on the stability of machining

•Cutting stiffness of workpiece material

(machinability), Ks

•Cutting –process parameters (speed, feed, DOC,

total width of chip)

•Cutter geometry (rake and clearance angles, insert

size and shape)

•Dynamic characteristics of the machining process

(tooling, machining tool, fixture, and workpiece)


Chip formation and regenerative Chatter

In machining, chip is formed due to shearing of

workpiece material over chip area (A = t x w), which

results in a cutting force.

Magnitude of the resulting cutting force is predominantly

determined by the material cutting stiffness Ks and the

chip area such that F c = Ks t w.

The direction of the cutting force Fc in influenced mainly

by the geometries of rack and clearance angles and

edge prep.

FIGURE 20-27 When theoverlapping cuts get out ofphase with each other, a variablechip thickness is produced,resulting in a change in Fc on thetool or workpiece.

FIGURE 20-28 Regenerativechatter in turning and millingproduced by variable uncut chipthickness.


Factors Influencing Chatter:Cutting stiffness Ks (Machinability): The larger stiffness, the larger

cutting force, and the less machining stability.

Speed: At slow speed (relative to the vibration frequency), as speed

increases, chatter gets more significant.

Feed: does not greatly influence stability, but control amplitude of

vibration.

DOC: The primary cause and control of chatter.

Total width of chip: DOC times number of cutting edges in cutting.

Increase number of engaged cutting edges will result in chatter.


Factors Influencing Chatter:

Back rake angle: increasing it will reduce magnitude of

cutting force, and increase process stability.

Clearance angle: reducing it will increase frictional

contact between tool and workpiece, and may produce

process damping.

Size (nose radius), shape (diamond, triangular,

square, round) and lead angle of insert.

FIGURE 20-29 Milling and boring operations can be made more stable by correct selection of insert geometry.

FIGURE 20-30 Dynamicanalysis of the cutting processproduces a stability lobediagram, which defines speedsthat produce stable and unstablecutting conditions.

Effects of TemperatureEffects of TemperatureEnergy dissipated in cutting is converted to heat,

elevating temperature of chip, workpiece, and tool.

As speed increases, a greater percentage of the heat ends up in the chip.

Three sources of heat:◦ Shear front.◦ Tool-chip interface contact regiion.◦ Flank of the tool.

FIGURE 20-31 Distribution ofheat generated in machining tothe chip, tool, and workpiece.Heat going to the environmentis not shown. Figure based onthe work of A. O. Schmidt.

FIGURE 20-31 Distribution ofheat generated in machining tothe chip, tool, and workpiece.Heat going to the environmentis not shown. Figure based onthe work of A. O. Schmidt.

FIGURE 20-32 There are three main sources of heat in metal cutting. (1) Primary shear zone. (2) Secondary shear zone tool–chip (T–C) interface. (3) Tool flank. The peak temperature occurs at the center of the interface, in the shaded region.

FIGURE 20-32 There are three main sources of heat in metal cutting. (1) Primary shear zone. (2) Secondary shear zone tool–chip (T–C) interface. (3) Tool flank. The peak temperature occurs at the center of the interface, in the shaded region.

Effects of TemperatureEffects of Temperature

Excessive temperature affects◦strength, hardness and wear resistance of cutting

tool.◦dimensional stability of the part being machined.◦machined surface properties due to thermal

damage◦the machine tool, if too excessive.

FIGURE 20-33 The typical relationship of temperature at the tool–chip interface to cutting speed shows a rapid increase. Correspondingly, the tool wears at the interface rapidly with increased temperature, often created by increased speed.

SummarySummaryHigh-strength materials produce larger cutting forces than

materials of lower strength, causing greater tool and work deflection; increased friction, heat generation, operation temperature.

Work hardness prior to machining controls the onset of shear.Highly ductile materials generate extensive plastic deformation

of the chip, which increases heat, temperature, and longer, continuous chips.

A variation of the continuous chip, often encountered in machining ductile materials, is associated a bill-up-edge (BLE) formation on the cutting tool. BLEs are not stable and will break off periodically. BUE formation can be minimized by reducing depth of cut, altering cutting speed, using positive rake tools, applying a coolant, or changing cutting-tool materials.

HW for Chapter 20HW for Chapter 20

Review Questions:15, and 24 (pages 557 – 558)

Problem 7. After your calculation, please compare your

HPs and s with HPs values in table 20-3, and s values in Figure 20-22.

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20.4 Orthogonal Machining (Two Forces)