Manufacturing Processes (MNG 222) Lecture 2 PDF

Manufacturing Processes (MNG 222) Lecture (2) Dr. Sabry Said Youssef Assistant Professor Mechanical Engineering Dept. Faculty of Engineering, Fayoum University 1  Theory of Metal Machining Theory of Chip Formation in Metal Mac...

Manufacturing Processes (MNG 222) Lecture (2) Dr. Sabry Said Youssef Assistant Professor Mechanical Engineering Dept. Faculty of Engineering, Fayoum University 1  Theory of Metal Machining Theory of Chip Formation in Metal Machining Force Relationships and the Merchant Equation Power and Energy Relationships in Machining Cutting Temperature 2 Theory of Chip Formation in Metal Machining The geometry of most practical machining operations is somewhat complex. A simplified model of machining is available that neglects many of the geometric complexities, yet describes the mechanics of the process quite well. 3 Theory of Chip Formation in Metal Machining Orthogonal Cutting Model : A simplified 2-D model of machining that describes the mechanics of machining fairly accurately Orthogonal cutting: (a) as a three-dimensional process, and (b) how it reduces to two dimensions in the side view. 4  Orthogonal Cutting Model The tool in orthogonal cutting has only two elements of geometry: (1) rake angle and (2) clearance angle. The rake angle (α) determines the direction that the chip flows as it is formed from the workpart. The clearance angle provides a small clearance between the tool flank and the newly generated work surface to Chip Thickness r  Ratio tc where r = chip thickness ratio; to = thickness of the chip prior to chip formation; and tc = chip thickness after separation Chip thickness after cut is always greater than before, so chip ratio is always less than 5 1.0  Shear Plane Angle The geometry of the orthogonal cutting model allows us to establish an important relationship between the chip thickness ratio, the rake angle, and the shear plane angle. Let ls be the length of the shear plane. We can make the to r  to = ls sinØ, and tc = ls cos(Ø-α). substitutions: tc Where r = chip ratio, and α = rake angle 6 Shear Plane Angle 7 Shear Plane Angle 8  Shear Strain in ship formation Shear strain during chip formation: (a) chip formation depicted as a series of parallel plates sliding relative to each other, (b) one of the plates isolated to show shear strain, and (c) shear strain triangle used to derive strain equation 9  Shear Strain in chip formation 𝑑𝑒𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑆 h 𝑒𝑎𝑟 𝑠𝑡𝑟𝑎𝑖𝑛= 𝑙𝑒𝑛𝑔𝑡 h(𝑡 h 𝑖𝑐𝑘𝑛𝑒𝑠𝑠) Shear strain in machining can be computed from the following equation, based on the preceding parallel plate model:  = tan( - ) + cot  where  = shear strain,  = shear plane angle, and  = rake angle of cutting tool 10 Example Orthogonal Cutting mm 11  Actual machining process The shear deformation process does not occur along a plane, but within a zone. If shearing were to take place across a plane of zero thickness, it would imply that the shearing action must occur instantaneously as it passes through the plane, rather than over some finite (although brief) time period. More realistic view of chip formation, showing shear zone rather than shear plane. Also shown is the secondary shear zone resulting from tool ‑chip friction 12  Types of chip The formation of the chip depends on the type of material being machined and the cutting conditions of the operation. Four basic types of chip can be distinguished below: 1. Discontinuous chip 2. Continuous chip 3. Continuous chip with Built-up Edge (BUE) 4. Serrated chip 13  Discontinuous Chip Brittle work materials (e.g., cast irons) Low cutting speeds Large feed and depth of cut High tool‑chip friction 14  Continuous Chip Ductile work materials (e.g., low carbon steel) High cutting speeds Small feeds and depths Sharp cutting edge on the tool Low tool‑chip friction 15  Continuous with BUE Ductile materials Low‑to‑medium cutting speeds Tool-chip friction causes portions of chip to adhere to rake face BUE formation is cyclical; it forms, then breaks off 16  Serrated Chip Semicontinuous - saw-tooth appearance Cyclical chip formation of alternating high shear strain then low shear strain Most closely associated with difficult- to-machine metals at high cutting speeds 17  Forces Acting on Chip Friction force F and Normal force to friction N Shear force F and Normal force to shear F s n Forces F, N, F , and F acting on the chip cannot s n be directly measured Forces in metal cutting: forces acting on the chip in orthogonal cutting 18  The forces applied against the chip by the tool The friction force F is the frictional force resisting the flow of the chip along the rake face of the tool. The normal force to friction N is perpendicular to the friction force. These two components can be used to define the coefficient of friction (μ)between the tool and the chip: F  N The friction force and its normal force can be added vectorially to form a resultant force R, which is oriented at an angle β, called the friction angle. The friction angle is related to the coefficient of friction as:  tan  19 The forces applied against the chip by the The shear force Fs is workpiece the force that causes shear deformation to occur in the shear plane, and The normal force to shear Fn is perpendicular to the shear force. Based on the shear force, we can define the shear stress that acts along the shear plane between the work and the chip: 𝐹𝑠 τ= 𝐴𝑠 where As = area of the shear plane. This shear plane area can be calculated as t ow As  sin  The shear stress represents the level of stress required to perform the machining operation. Therefore, this stress is equal to the shear strength of the work material (τ = S) under the conditions at which 20  Resultant Forces Vector addition of F and N = resultant R Vector addition of Fs and Fn = resultant R ' Forces acting on the chip must be in balance: R ' must be equal in magnitude to R R ' must be opposite in direction to R R ' must be collinear with R 21  Forces Acting on the tool Forces acting on the tool that can be measured: Cutting force Fc and Thrust force Ft The cutting force Fc is in the direction of cutting, the same direction as the cutting speed v, and the thrust force Ft is perpendicular to the cutting force and is associated with the chip thickness before the cut to. Forces in metal cutting: forces acting on the tool that can be measured 22  Forces in Metal Cutting Equations can be derived to relate the forces that cannot be measured to the forces that can be measured: F = Fc sin + Ft cos N = Fc cos ‑ Ft sin Fs = Fc cos ‑ Ft sin Fn = Fc sin + Ft cos Based on these calculated force, shear stress and coefficient of friction can be determined 23 Forces in Metal Cutting 24  Need of forces Analysis Analysis of cutting forces is helpful as : Determination of power consumption [ estimation of cutting power consumption, which enables selection of the power source(s)(motor selection) during design of machine tool]. Knowing cutting forces is helpful in designing the machine in regard the stiffness and damping. To obtain maximum productivity[if you know forces acting on cutting tool we can easily predict life of the tool so we can obtain balance between life of the tool and rate of cutting in order to obtain maximum productivity]. 25 Example: Shear Stress in Machining 26 Example: Shear Stress in Machining 27  The Merchant Equation Merchant started with the definition of shear stress expressed in the form of the following relationship derived by combining Eqs Of all the possible angles at which shear deformation could occur, the work material will select a shear plane angle  which minimizes energy, given by    45   2 2 Derived by Eugene Merchant Based on orthogonal cutting, but validity extends to 3-D machining 28  What the Merchant Equation Tells us?   To increase shear plane angle  45   2 2 Increase the rake angle Reduce the friction angle (or coefficient of friction) Rake angle can be increased by proper tool design, and friction angle can be reduced by using a lubricant cutting fluid. 29 Why we need to increase shear plane angle? Higher shear plane angle means smaller shear plane which means lower shear force Result: lower cutting forces, power, temperature, all of which mean easier machining Effect of shear plane angle : (a) higher  with a resulting lower shear plane area; (b) smaller  with a corresponding larger shear plane area. Note that the rake angle is larger in (a), which tends to increase shear angle according to the Merchant equation 30 Approximation of Turning by Orthogonal Cuttin Approximation of turning by the orthogonal model: (a) turning; and (b) the corresponding orthogonal cutting. 31 Approximation of Turning by Orthogonal Cuttin 32  Power and Energy Relationships A machining operation requires power The power to perform machining can be computed from: P c = Fc v where Pc = cutting power; Fc = cutting force; and v = cutting speed In U.S. customary units, power is traditional expressed as horsepower (dividing ft‑lb/min by 33,000) Fcv HPc  33,000 where HPc = cutting horsepower, hp 33  Power and Energy Relationships The gross power required to operate the machine tool is greater than the power delivered to the cutting process because of mechanical losses in the motor and drive train in the machine. Gross power to operate the machine tool Pg or HPg is given by OR or Pc HPc Pg  HPg  E E Where E = mechanical efficiency of machine tool Typical E for machine tools =  90% 34  Unit Power in Machining It is useful to convert power into power per unit volume rate of metal cut This Called the unit power, Pu or unit horsepower, P HPu HPc c Pu  HPu  MRR MRR OR Where MRR = material removal rate MRR = v fd where v = cutting speed; f = feed; d = depth of cut U P  Pc  Fcv  Fc u MRR vtow t ow Unit power is also known as the specific energy Units for specific energy are typically N‑m/mm or J/mm (in‑lb/in ) 3 3 3 U 35  Unit Power in Machining Example 36 Unit Power in Machining 37  Unit ThePower values in Machining in Table 21.2) Sharp cutting to 0.25 mm tool (0.010 in). For worn tools, the power required to perform the cut is greater, and this is reflected in higher specific energy and unit horsepower values.  For tools in a finishing operation that are nearly worn out, the factor is around 1.10.  For tools in a roughing operation that are nearly worn out, the factor is 1.25. 38  Unit Power in Machining The U and Hpu values in Table 21.2 can still be used to estimate horsepower and energy for situations in which to is not equal to 0.25 mm (0.010 in) by applying a correction factor to account for any difference in chip thickness before the cut. The unit horsepower and specific energy values in Table 21.2 should be multiplied by the appropriate correction factor when to is different Other0.25mm from factors (0.010in). include rake angle, cutting speed, and cutting fluid affect the specific energy and unit horsepower. As rake angle or cutting speed are increased, or when Correction factor for unit horsepower and specific energy when values of cutting fluid is added, the chip thickness before the cut to are 39  Cutting Temperature Approximately 98% of the energy in machining is converted into heat This can cause temperatures to be very high at the tool‑chip The remaining energy (about 2%) is retained as elastic energy in the chip Cutting temperatures are important because high temperatures (1) reduce tool life, (2) produce hot chips that pose safety hazards to the machine operator, (3) can cause inaccuracies in workpart dimensions due to thermal expansion of the work material. 40  Cutting Temperature Several analytical methods to calculate cutting temperature Method by N. Cook derived from dimensional analysis using experimental data for various work materials 0.333 0.4U  vt o  T    C  K  where T = temperature rise at tool‑chip interface; U = specific energy; v = cutting speed; to = chip thickness before cut; C = volumetric specific heat of work material; K = thermal diffusivity of the work material 41  Cutting Temperature Example 42 Measurement of Cutting Temperature Experimental methods can be used to measure temperatures in machining Most frequently used technique is the tool‑chip thermocouple Using this method, K. Trigger determined the speed‑temperature relationship to be of the form: T = K v ͫ where T = measured tool‑chip interface temperature and v = cutting speed. The parameters K and m depend on cutting conditions (other than v) and work material. 43  Measurement of Cutting Temperature Similar relationship exists between cutting temperature and feed; however, the effect of feed on temperature is not as strong as cutting speed. Experimentally measured cutting temperatures plotted against speed for three work materials 44 The End Thanks 45