Chapter 20Chapter 20

Fundamentals of Fundamentals of Machining/Orthogonal Machining/Orthogonal

MachiningMachining(Part 2 Review)(Part 2 Review)

EIN 3390 Manufacturing ProcessesEIN 3390 Manufacturing ProcessesFall, 2010 Fall, 2010

20.3 Energy and Power in Machining20.3 Energy and Power in Machining

Power requirements are important for proper machine tool selection.Cutting force data is used to:

properly design machine tools to maintain desired tolerances.determine if the workpiece can withstand cutting forces without distortion.

Cutting Forces and PowerCutting Forces and Power Primary cutting force Fc: acts in the direction of the cutting

velocity vector. Generally the largest force and accounts for 99% of the power required by the process.

Feed Force Ff :acts in the direction of tool feed. The force is usually about 50% of Fc but accounts for only a small percentage of the power required because feed rates are small compared to cutting rate.

Radial or Thrust Force Fr :acts perpendicular to the machined surface. in the direction of tool feed. The force is typically about 50% of Ff and contributes very little to the power required because velocity in the radial direction is negligible.

FIGURE 20-12 Obliquemachining has three measurablecomponents of forces acting onthe tool. The forces vary withspeed, depth of cut, and feed.

FIGURE 20-12 Obliquemachining has three measurablecomponents of forces acting onthe tool. The forces vary withspeed, depth of cut, and feed.

Cutting Forces and PowerCutting Forces and PowerPower = Force x Velocity

P = Fc . V (ft-lb/min)

Horsepower at spindle of machine is:hp = (FcV) / 33,000

Unit, or specific, horsepower HPs: HPs = hp / (MRR) (hp/in.3/min)

In turning, MRR =~ 12VFrd, thenHPs = Fc / 396,000Frd

This is approximate power needed at the spindle to remove a cubic inch of metal per minute.

Cutting Forces and PowerCutting Forces and PowerSpecific Power

Used to estimate motor horsepower required to perform a machining operation for a given material.

Motor horsepower HPm

HPm = [HPs . MRR . (CF)]/EWhere E – about 0.8, efficiency of machine to overcome friction

and inertia in machine and drive moving parts; MRR – maximum value is usually used; CF – about 1.25, correction factor, used to account for variation in cutting speed, feed, and rake angle.

Cutting Forces and PowerCutting Forces and PowerPrimary cutting force Fc:

Fc =~ [HPs . MRR . 33,000]/VUsed in analysis of deflection and vibration problems in machining and in design of workholding devices.

In general, increasing the speed, feed, depth of cut, will increase power required.

In general, increasing the speed doesn’t increase the cutting force Fc. Speed has strong effect on tool life.

Cutting Forces and PowerCutting Forces and PowerConsidering MRR =~ 12Vfrd, then

dmax =~ (HPm . E)/[12 . HPs V Fr (CF)]

Total specific energy (cutting stiffness) U: U = (FcV)/(V fr d) = Fc/(fr

. d) =Ks (turning)

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 20-14 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 20-17 Schematicrepresentation of the materialflow, that is, the chip-formingshear process. f defines theonset of shear or lower boundary.c defines the direction of slipdue to dislocation movement.

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: c = t / tc = (AB sin cos( - )], or

tan c cos/(1 - c,sin

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,

c = 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 are:

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

Where force F and 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

for a given metal, shear stress is not sensitive to variations in cutting parameters, tool meterial, or cutting environment.

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 and is linearly related to speed

20.8 Mechanics of Machining (Dynamics)20.8 Mechanics of Machining (Dynamics)Self-excited vibration is the periodic response to 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.

20.8 Mechanics of Machining (Dynamics)20.8 Mechanics of Machining (Dynamics)Factors affecting on the stability of machining

Cutting stiffness of workpiece material (machinability), KsCutting –process parameters (speed, feed, DOC, total width of chip)Cutter geometry (rake asd clearance angles, insert size and shape)Dynamic characteristics of the machining process (tooling, machining tool, fixture, and workpiece)

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

20.8 Mechanics of Machining (Dynamics)20.8 Mechanics of Machining (Dynamics)Factors Influencing Chatter:

Cutting stiffness KsSpeedFEEDDocTotal width of chipBack rack angleClearance angleSize (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 region.◦ 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

◦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.

Homework for Chapter 20Homework for Chapter 20Review Questions:3, 5, 15, and 24 (pages 557 – 558, 5 points for each

question )

Problems:1. a, b, c, d (5 points for each)3. (10 points)

7. for extra credit: 20 pointsAfter your calculation, please compare your HPs and s with HPs values in table 20-3, and s values in Figure 20-22.