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### Chapter 20Fundamentals of Machining/Orthogonal Machining(Part 2 Review)EIN 3390 Manufacturing ProcessesFall, 2010

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.

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% ofFf and contributes very little to the power required because velocity in the radial direction is negligible.

machining has three measurable

components of forces acting on

the tool. The forces vary with

speed, depth of cut, and feed.

machining has three measurable

components of forces acting on

the tool. The forces vary with

speed, depth of cut, and feed.

Power = 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, then

HPs = Fc / 396,000Frd

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

Cutting 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)]/E

Where 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 PowerPrimary cutting force Fc:

Fc =~ [HPs. MRR . 33,000]/V

Used 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 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)

Cutting Forces and PowerIn Orthogonal Machining (OM), tool geometry is simplified from 3-dimrnsional (oblique) geometry

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

the orthogonal plate machining

setups. (a) End view of table,

quick-stop device (QSD), and

plate being machined for OPM.

(b) Front view of horizontal

milling machine. (c) Orthogonal

plate machining with fixed tool,

moving plate. The feed

mechanism of the mill is used to

produce low cutting speeds. The

feed of the tool is t and the DOC

is w, the width of the plate.

tube turning (OTT) produces a

two-force cutting operation at

speeds equivalent to those used

in most oblique machining

operations. The slight difference

in cutting speed between the

inside and outside edge of the

chip can be neglected.

representation of the material

flow, that is, the chip-forming

shear process. f defines the

onset of shear or lower boundary.

c defines the direction of slip

due to dislocation movement.

Assume 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:

gc = t / tc = (AB sin f)/[ABcos(f - a)], or

tan f = (gccosa)/(1 - gc,sina)

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

20.5 Merchant’s Modelgc = t / tc = (sin f)/[cos(f - a)] = Vc./V, and

Vs / V = (cosa)/[cos(f - a)]

Where V – velocity for workpiecepasing tool, Vc – chip moving velocity, Vs – shearing velocity, f – onset of shear angle, a - rake angle

.

20.5 Merchant’s ModelAssume 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 (b - a)

20.6 Mechanics of Machining (statics)FIGURE 20-20 Free-body diagram of orthogonal chip

formation process, showing equilibrium condition

between 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.

Friction force F and normal force are:

F = Fcsina + Ftcosa,

N = Fccosa + Ftsina, and

b = tan-1m = tan-1 (F/N),

Where m - force F and friction coefficient, and b – the angle between normal force N and resultant R. If a = 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 + Ft2 ),

Fs = Fccosf - Ftsinf, and

Fn = Fcsinf + Ftcosf,

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

20.6 Mechanics of Machining (statics)ts= Fs/As,

Where As - area of the shear plane,

As = (t w)/sinf

Where t – uncut ship thickness and w – width of workpiece.

ts= (Fcsinfcosf - Ft sin2f )/(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.

20.6 Mechanics of Machining (statics)FIGURE 20-22 Shear stress ts variation with the Brinell hardness number for a group of

steels and aerospace alloys. Data of some selected fcc metals are

also included. (Adapted with permission from S. Ramalingham and K. J. Trigger, Advances in

Machine Tool Design and

Research, 1971, Pergamon Press.)

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:

g= cosa/[sin(f + y) cos(f + y -a)]

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

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

Us = t .g

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

- d(Us)/dy = 0,
- Solving the equation above,
- y = 450 - y + a/2, and
- g= 2cosa/(1 + sina),
- It shows the shear strain is dependent only on the rake angle a.

FIGURE 20-23 The Black–Huang “stack-of-cards” model for calculating shear strain in metal

cutting is based on Merchant’s bubble model for chip formation, shown on the left.

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.

20.8 Mechanics of Machining (Dynamics)dynamics is a closed-loop

interactive process that creates

a force-displacement response.

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)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.

20.8 Mechanics of Machining (Dynamics)types of vibration in machining.

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 asd 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.

overlapping cuts get out of

phase with each other, a variable

chip thickness is produced,

resulting in a change in Fc on the

tool or workpiece.

- Cutting stiffness Ks
- Speed
- FEED
- Doc
- Total width of chip
- Back rack angle
- Clearance angle
- 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.

analysis of the cutting process

produces a stability lobe

diagram, which defines speeds

that produce stable and unstable

cutting conditions.

Energy 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.

heat generated in machining to

the chip, tool, and workpiece.

Heat going to the environment

is not shown. Figure based on

the work of A. O. Schmidt.

heat generated in machining to

the chip, tool, and workpiece.

Heat going to the environment

is not shown. Figure based on

the 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.

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.

Review 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 points

After your calculation, please compare your HPs and ts with HPs values in table 20-3, and ts values in Figure 20-22.

Homework for Chapter 20
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