Chapter 20 Fundamentals of Machining/Orthogonal Machining (Review) EIN 3390 Manufacturing Processes Spring, 2011 1

20.2 Fundamentals Variables in Processes of Metal Cutting: Machine tool selected to perform the processes Cutting tool (geometry and material) Properties and parameters of workpiece Cutting parameters (speed, feed, depth of cut) Workpiece holding devices (fixture or jigs)

FIGURE 20-1 The fundamental inputs and outputs to machining processes.

20.2 Fundamentals 7 basic chip formation processes: shaping, turning, milling, drilling, sawing, broaching, grinding (abrasive)

FIGURE 20-2 The seven basic machining processes used in chip formation.

20.2 Fundamentals Responsibilities of Engineers Design (with Material) engineer: determine geometry and materials of products to meet functional requirements Manufacturing engineer based on material decision: select machine tool select cutting-tool materials select workholder parameters, select cutting parameters

20.2 Fundamentals Cutting Parameters Speed (V): the primary cutting motion, which relates the velocity of the cutting tool relative to the workpiece. For turning: V = p(D1 Ns) / 12 where, V – feet per min, Ns – revolution per min (rpm), D1 diameter of surface of workpiece, in. Feed (fr): amount of material removed per revolution or per pass of the tool over the workpiece. In turning, feed is in inches per revolution, and the tool feeds parallel to the rotational axis of the workpiece. Depth of Cut (DOC): in turning, it is the distance that the tool is plunged into the surface. DOC = 0.5(D1 – D2) = d

FIGURE 20-3 Turning a cylindrical workpiece on a lathe requires you to select the cutting speed, feed, and depth of cut.

20.2 Fundamentals Cutting Tool is a most critical component used to cut the work piece selected before actual values for speed and feeds are determined. Figure 20-4 gives starting values of cutting speed, feed for a given depth of cut, a given work material, and a given process (turning). Speed decreases as DOC or feed increase Cutting speed increases with carbide and coated- carbide tool material.

FIGURE 20-4 Examples of a table for selection of speed and feed for turning. (Source: Metcut’s Machinability Data Handbook.)

20.2 Fundamentals To process different metals, the input parameters to the machine tools must be determined. For the lathe, the input parameters are DOC, feed, and the rpm value of the spindle. Ns = 12V / (p D1) = ~ 3.8 V/ D1 Most tables are arranged according to the process being used, the material being machined, the hardness, and the cutting-tool material. The table in Figure 20-4 is used only for solving turning problems in the book.

20.2 Fundamentals DOC is determined by the amount of metal removed per pass. Roughing cuts are heavier than finishing cuts in terms of DOC and feed and are run at a lower surface speed. Once cutting speed V has been selected, the next step is to determine the spindle rpm, Ns. Use V, fr and DOC to estimate the metal removal rate for the process, or MRR. MRR = ~ 12V fr d where d is DOC (depth of cutt). MRR value is ranged from 0.1 to 600 in3/min.

20.2 Fundamentals MRR can be used to estimate horsepower needed to perform cut. Another form of MRR is the ratio between the volume of metal removed and the time needed to remove it. MRR = (volume of cut)/Tm Where Tm – cutting time in min. For turning, Tm = (L + allowance)/ fr Ns where L – length of the cut. An allowance is usually added to L to allow the tool to enter and exit the cut. MRR and Tm are commonly referred to as shop equations and are fundamental as the processes.

20.2 Fundamentals One of the most common is turning: workpiece is rotated and cutting tool removes material as it moves to the left after setting a depth of cut. A chip is produced which moves up the face of the tool.

FIGURE 20-5 Relationship of speed, feed, and depth of cut in turning, boring, facing, and cutoff operations typically done on a lathe.

20.2 Fundamentals Milling: A multiple-tooth process. Two feeds: the amount of metal an individual tooth removes, called the feed per tooth ft, and the rate at which the table translates pass the rotating tool, called the table feed rate fm in inch per min. fm = ft n Ns where n – the number of teeth in a cutter, Ns – the rpm value of the cutter. Standard tables of speeds and feeds for milling provide values for the recommended cutting speeds and feeds and feeds per tooth, fr.

FIGURE 20-6 Basics of milling processes (slab, face, and end milling) including equations for cutting time and metal removal rate (MRR).

FIGURE 20-7 Basics of the drilling (hole-making) processes, including equations for cutting time and metal removal rate (MRR).

FIGURE 20-9 (a) Basics of the shaping process, including equations for cutting time (Tm ) and metal removal rate (MRR). (b) The relationship of the crank rpm Ns to the cutting velocity V.

FIGURE 20-10 Operations and machines used for machining cylindrical surfaces.

FIGURE 20-10 Operations and machines used for machining cylindrical surfaces.

FIGURE 20-11 Operations and machines used to generate flat surfaces.

20.3 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 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 Oblique machining has three measurable components of forces acting on the tool. The forces vary with speed, depth of cut, and feed.

FIGURE 20-12 Oblique machining has three measurable components of forces acting on the tool. The forces vary with speed, depth of cut, and feed.

Cutting Forces and Power 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 Power Specific 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 Power Primary 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 Power Considering 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)

20.6 Mechanics of Machining (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 (b - a)

FIGURE 20-20 Free-body diagram of orthogonal chip formation process, showing equilibrium condition between resultant forces R and R.

20.6 Mechanics of Machining (statics) Friction force F and normal force are: F = Fc sina + Ft cosa , N = Fc cosa + Ft sina, and b = tan-1 m = 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 = Fc cosf - Ft sinf , and Fn = Fc sinf + Ft cosf, Where Fs is used to compute the shear stress on the shear plane

20.6 Mechanics of Machining (statics) Shear stress: 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 = (Fcsinf cosf - 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.

20.7 Shear Strain g & Shear Front Angle f 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 f Use 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.

20.8 Mechanics of Machining (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 Machining dynamics is a closed-loop interactive process that creates a force-displacement response.

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) 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) 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)

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 the 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.

20.8 Mechanics of Machining (Dynamics) Factors Influencing Chatter: Cutting stiffness Ks Speed FEED DOC: The primary cause and control of chatter. Total width of chip Back rack angle Clearance angle Size (nose radius), shape (diamond, triangular, square, round) and lead angle of insert

Effects of Temperature 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.

FIGURE 20-31 Distribution of 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 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 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 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.