3. UTILISATION MACHINING EFFECTIVE CUTTING PARAMETERS

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1 The second part of this chapter is more theoretical in approach and discusses the cutting parameters as they actually affect the tool. CUTTIG SPEED (VC) AD SPIDLE SPEED () The cutting speed is entered at the CADM programming stage. It can be modified by path verification software (such as C Simul, Vericut, etc.), by the operator using the control potentiometer on the control desk. It may also fluctuate if the spindle torque or power capacity limit is reached. If optimisation is the aim, it is essential to avoid any spontaneous modification of this parameter (for example, by locking the potentiometers), but rather to ensure that the input cutting speed is valid for each segment. Path verification programs (such as C Simul, Vericut, etc.) are useful tools for identifying hazardous situations (unduly thick chips, collisions at rapid feed rates, machine power limitations, etc.). The speed to be controlled and considered is the actual cutting speed at the tool/material contact point.. Using the effective working diameter At a set spindle speed, the actual cutting speed varies from one point to another on the cutting edge according to its distance from the centreline: Case of annular tool For machining with an annular tool, the tool/material interaction can be represented by the drawing shown on Figure 1. Annular milling cutters have the advantage that there is no cutting edge operating at zero speed. SP300 Machining Effective cutting parameters Page 3. 13

2 Ø t = Ø tool Ø i = Ø insert a p Ø1 = minimum Ø eff Ø1 = Ø t Ø i minimumvc eff = pi.ø1. / 1000 Ø2 = maximum Ø eff Ø2 = Ø t Ø i.(1-cos(arcsin((ø i - a p) / Ø i))) maximum Vc eff = pi.ø2. / 1000 a e Figure 1 : Effective cutting speed and effective cutting diameter in machining with a annular tool. Generally speaking the calculated cutting speed at the nominal diameter of the tool is close to the effective cutting speed. Tables I and II show the relative change in speed at minimum diameter (Ø1) and maximum diameter (Ø2) for information. In the case of a very small axial engagement (a p /Ø i = 0.1) and with an annular milling cutter of small diameter, the actual minimum cutting speed may be 23% below that calculated for nominal diameter. Once the axial engagement or the tool diameter increases, the maximum effective cutting speed approaches the cutting speed at nominal diameter. The difference between the minimum and maximum effective cutting speeds varies from 5 to 40% according to the ratio of the diameters of the tool and the tips. The effective diameter will be taken as the nominal diameter of the tool, except in special cases (small diameter tool). SP300 Machining Effective cutting parameters Page 3. 14

3 Table I : Relative change in maximum effective cutting speed (max. Vc eff ) at maximum effective diameter Ø1) with respect to the cutting speed (Vc) at nominal diameter (Ø t )). Ø2/Ø t or Ø i /Ø t Vc eff maxi/vc 0,4 0,35 0,3 0,25 0,2 0,15 0,1 0,05 0,1 0,77 0,80 0,83 0,86 0,89 0,92 0,94 0,97 0,25 0,86 0,88 0,90 0,92 0,93 0,95 0,97 0,98 0,3 0,89 0,90 0,91 0,93 0,94 0,96 0,97 0,99 a p /Ø i 0,5 0,95 0,95 0,96 0,97 0,97 0,98 0,99 0,99 0,6 0,97 0,97 0,97 0,98 0,98 0,99 0,99 1,00 0,75 0,99 0,99 0,99 0,99 0,99 1,00 1,00 1,00 Table II : Relative change in minimum effective cutting speed (min. Vc eff ) at minimum effective diameter (Ø2) by comparison with cutting speed (Vc) at nominal diameter (Ø t ) Ø1/Ø t ou Ø t (mm) Vceff mini/vc ,60 0,70 0,76 0,80 0,85 0,88 0,91 0,93 0, ,68 0,73 0,80 0,84 0,89 0,91 0,93 Ø i ,60 0,67 0,75 0,80 0,86 0,89 0,91 (mm) ,70 0,76 0,83 0,87 0, ,65 0,72 0,80 0,84 0, ,60 0,68 0,77 0,82 0,85 Determination of spindle speed for an annular tool : Knowing the permitted cutting speed, to calculate the spindle speed () using the relationship : = 1000.Vc/π/Ø i where is the spindle speed in rpm, Vc the cutting speed at the diameter in m/min., and Ø t the nominal diameter of the milling cutter in mm. SP300 Machining Effective cutting parameters Page 3. 15

4 Case of spherical tool For a spherical tool, in addition to the cutting depth (e) and the pitch (p) it is necessary to take the clearance angle into account. Figure 2 shows how the cutting thickness (th) and the clearance angle (α) are used simultaneously to determine the effective cutting diameter. Ø t diameter of milliing cutter Tool advance α clearance angle e Ø1 Ø2 Ø1 = -Ø t.cos ( α+ Arcsin ((Ø t-2.e)/ø t)) Ø2 = Ø t.sin ( α) Diameters positively orientated Diameters negatively orientated Positive orientation of angles Figure 2 : Effective cutting speed and effective diameter of cut in machining with a spherical tool. The formulae shown on Figure 2 are used to calculate the effective diameters of cut at the two extremities of the chip formation zone. By using a sign convention it is possible to use a single formula for all the cases shown. On the figure the fixed object is the milling axis. The angle α varies with the positive direction shown. The advance movement pivots with α. The diameters shown positive are for a cutting extremity to the right of the tool axis and those shown negative correspond to a cutting extremity on the left. There are two possible cases: The two diameters have the same sign: the milling cutter is not operating on the axis, and the two diameters give the values of the minimum and maximum effective working diameters. The two diameters have opposite signs: the tool is working on its axis, the minimum effective diameter is zero, and the maximum effective diameter is the maximum of the two absolute values of the calculated diameters. In this case the cutter operates by down milling on one side of the axis and up milling on the other (the negative diameter, with the cutting zone to the left of the axis, works by down milling if the cutting depth is behind the tool on Figure 2, and up milling if this cutting depth is at the front, see chapters on clearance angle and up milling machining page 3.23). SP300 Machining Effective cutting parameters Page 3. 16

5 Table III : Calculating the ratios of effective cut diameters to the tool diameter (Ø1/Ø t and Ø2/Ø t ) as a function of clearance angle (α) and of the ratio of the cutting depth (e) to the tool diameter (Ø t ). Ø1/Ø t Clearance angle α ,1 0,80 0,50 0,14-0,26-0,60-0,86-0,99 0,2 0,60 0,24-0,14-0,52-0,80-0,97 - e / Ø t 0,3 0,40 0,01-0,37-0,70-0,92-1,00-0,4 0,20-0,20-0,55-0,83-0, ,5 0,00-0,39-0,71-0,93-1, Ø2 / Ø t 1 0,921 0,707 0, ,37-0,71 Table III shows that the effective cut diameters can vary from zero to the value of the tool diameter. It is therefore essential to use the effective cut diameter when calculating the spindle speed as a function of cutting speed. It can also be seen that for extreme clearance angles (positive or negative), and particularly when the cutting depth (e) is low, the tool does not operate on the axis (φ1/φ2 have the same sign). For low clearance angles and high cutting depths (e) the tool operates on the axis with a zero cutting speed. Calculating the spindle speed for a spherical tool : The first step is the calculation fo effective cut diameters : Ø eff Calculate the effective cut diameters Ø1 and Ø2 as a function of tool diameter (Ø t ), clearance angle (α) and cut depth (e), using Table III. If the two diameters Ø1 and Ø2 have the same sign, their absolute values give the minimum and maximum effective cut diameters. If the two diameters Ø1 and Ø2 have opposite sign, the minimum effective cut diameter is zero (tool operating on the axis) and the maximum effective diameter is the maximum value of the absolute values of Ø1 and Ø2 Ø eff = Max (abs(ø 1 ), Abs(Ø 2 )). From the permitted maximum range of cutting speeds (max. Vc eff ), calculate the spindle speed () using the relationship = 1000.Vc/π/Ø eff where is the spindle speed in rpm, Vc is the cutting speed in m/min, and Ø eff is the max effective cut diameter of the milling cutter in mm. c - Case of axial operations In cases of axial operation, with the tool completely engaged in the material, the spindle speed is calculated using the nominal tool diameter (See page 3.9). SP300 Machining Effective cutting parameters Page 3. 17

6 EFFECTIVE CHIP THICKESS (F Z Eff) The parameter entered to control the effective chip thickness is the tooth advance (f z ) which is used for calculating the tool advance rate with respect to the workpiece. Just like the spindle rotation speed (that governs the cutting speed), the table feed rate can be modified either directly in the program or by using the control potentiometer on the C desk. It is essential to avoid any spontaneous adjustment of this parameter (for example, by locking the potentiometers), and to ensure that the input feed rate is valid for each zone. Contour verification programs (C Simul) are useful tools for identifying hazardous situations (excessive feed, collision during rapid feed, machine power limitations, etc.). The feed rate that should be imposed is the one that gives the desired effective chip thickness at the tool/material contact point, a thickness that can become very low (even too low) when the radial engagement (cut depth) or axial engagement (pitch) diminish. Case of annular tools The advance per tooth does not give the effective chip thickness except as regards the tool diameter when the latter is substantially engaged over at least its radius. In all circumstances, the maximum effective chip thickness depends on the advance per tooth fz but also on the radial and axial engagements (See Figure 3). Ø t = Ø tool Ø i = Ø insert a p P2 f zeff = f z.cos(arcsin((ø i-2a p)/ø i)).cos(arcsin((ø t-2a e)/ø t)) if A p < Ø i/2 and a e < Ø i/2 f zeff = f z.cos(arcsin((ø i-2a p)/ø i)) if a p < Ø i/2 and a e > Ø t/2 f zeff = f z.cos(arcsin((ø t-2a e)/ø t)) if a p > Ø i/2 and a e < Ø t/2 f zeff = f z si a p > Ø i/2 et a e > Ø t/2 P1 Effective thickness in the plane P2 a e Figure 3 : Maximum effective chip thickness when machining with an annular tool. SP300 Machining Effective cutting parameters Page 3. 18

7 Table IV can be used for calculating the effective chip thicknesses as a function of tooth advance, diameters of tool and tip and the radial and axial penetration. For low axial and radial penetration, the effective chip thickness can be reduced to one-third of the advance per tooth. It is therefore important to calculate the ratio of maximum effective thickness to advance per tooth (f z eff/f z ) before setting the advance per tooth (f z ) and to calculate the tool advance speed with respect to the workpiece. For roughing operations with a carbide tool, certain tool manufacturers recommend a f z eff > 0.1 mm. However the user should consult the tool manufacturer s recommendations in each particular case. Table IV : Calculating the maximum effective chip thickness (f z eff) as a function of the advance per tooth f z and of the ratio of axial penetration (a p ) to the diameter of the insert (Ø i ) and the ratio of the radial penetration (a e ) to the tool diameter (Ø t ). f z eff/ f z a e /Ø t 0,1 0,15 0,2 0,3 0,4 0,5 0,75 1 0,1 0,36 0,43 0,48 0,55 0,59 0,60 0,60 0,60 0,2 0,48 0,57 0,64 0,73 0,78 0,80 0,80 0,80 a e /Ø i 0,3 0,55 0,65 0,73 0,84 0,90 0,92 0,92 0,92 0,4 0,59 0,70 0,78 0,90 0,96 0,98 0,98 0,98 0,5 0,60 0,71 0,80 0,92 0,98 1,00 1,00 1,00 0,75 0,60 0,71 0,80 0,92 0,98 1,00 1,00 1,00 Case of spherical tool In the case of a spherical tool, the maximum effective chip thickness depends on the cutting depth (e), the pitch (p) and the advance per tooth (f z ). (See drawing on Figure 4). (See next page). SP300 Machining Effective cutting parameters Page 3. 19

8 Ø t diameter of milling cutter P2 Tool advance p e Maximum effective thickness in P1 Maximum effective thickness in P1 P1 f zeff = f z.cos(arcsin((ø o-2e)/ø t)).cos(arcsin((ø t-2p)/ø t)) if e < Ø t/2 and p < Ø t/2 f zeff = f z.cos(arcsin((ø t-2e)/ø i)) if e < Ø t/2 and p > Ø t/2 f zeff = f z.cos(arcsin((ø t-2p)/ø t)) if e > Ø i/2 and p < Ø t/2 f zeff = f z if e > Ø i/2 et p > Ø t/2 Figure 4 : Maximum effective chip thickness in machining with a spherical tool. Table V can be used to calculate the maximum effective chip thicknesses as a function of the advance per tooth, the tool diameter, the cutting depth and the pitch. The difference between the advance per tooth and maximum effective chip thickness can be considerable (three to one). It is therefore important to take account of the maximum effective thickness in order to validate the advance per tooth before calculating the tool advance speed with respect to the workpiece. In fact a value of f z eff of the order of the edge preparation radius would result in machining with a clearly negative cut, liable to mark the surface. SP300 Machining Effective cutting parameters Page 3. 20

9 Table V : Calculation of the maximum effective chip thickness (f z eff) with respect to f z as a function of the ratio of the cut depth (e) to the tool diameter (Ø t ) and the ratio of the pitch (p) to the tool diameter (Ø t ). f z eff/ f z p/ø t 0,1 0,15 0,2 0,3 0,4 0,5 0,75 1 0,1 0,36 0,43 0,48 0,55 0,59 0,60 0,60 0,60 0,2 0,48 0,57 0,64 0,73 0,78 0,80 0,80 0,80 E / Ø t 0,3 0,55 0,65 0,73 0,84 0,90 0,92 0,92 0,92 0,4 0,59 0,70 0,78 0,90 0,96 0,98 0,98 0,98 0,5 0,60 0,71 0,80 0,92 0,98 1,00 1,00 1,00 DETERMIATIO OF THE RESIDUAL ROUGHESS RELATED TO "e" OR "a p " Careful consideration of the tool/workpiece interaction permits a quick calculation of the roughness of a machined surface. The values of da p or d e can easily be calculated using Figure 5 and Table VI. Ø i (Ø t ) da p = 0,5.Ø i.cos(arcsin(f z /Ø i )) d e = 0,5.Ø t.cos(arcsin(p/ø t )) da p (d e ) Figure 5 : Roughness related to the axial penetration (or cutting depth) and to the advance per tooth (or the scanning pitch). Table VI : Calculation of the maximum roughness related to the axial penetration (or cut depth) and to the advance per tooth (or the pitch) as a function of the tip diameter Ø i (or Ø t of the tool) in milling with an annular tool (or a spherical tool). da p (de) f z /Ø i (p/ø t ) (mm) 0,1 0,2 0,3 0,4 0,5 0,6 5 0,013 0,051 0,115 0,209 0,335 0,500 Ø i 10 0,025 0,101 0,230 0,417 0,670 1,000 (Ø t ) 15 0,038 0,152 0,345 0,626 1,005 1,500 (mm) 20 0,050 0,202 0,461 0,835 1,340 2, ,063 0,253 0,576 1,044 1,675 2,500 SP300 Machining Effective cutting parameters Page 3. 21

10 RADIAL PEETRATIO (a e ) Just like the axial penetration, the radial penetration is introduced in the CADM programming. The value entered initially can be changed so as to adapt the number of passes to the cut depth. It is therefore prudent to verify the minimum and maximum programmed values along the tool trajectory (angles, corners, etc.). In particular the user should look at convexities where the milling cutter may penetrate to its entire diameter. The radial penetration can also vary significantly when concave areas are being machined. Figure 6 and Table VII show how a local concave zone can modify the radial penetration. β a e eff (p e ff) a e : radial penetration (pitch : pa) Ø t : tool diameter a e eff/a e = 0,5.Ø t /a e.(1-sin(β+arcsin(1-2a e /Ø t ))) Figure 6 : Variation in radial penetration (a e ) of the milling cutter in a concave zone of angle β. Table VII : Calculating the ratio between the effective radial penetration (a e eff) and the radial penetration (a e ) as the cutter passes along the centreline of a concave zone of angle β. a e eff/a e β( ) , , ,1 8,000 6,241 4,293 2,453 1,000 0,2 4,500 3,774 2,854 1,880 1,000 0,3 3,194 2,823 2,275 1,635 1,000 a e /Ø t 0,4 2,475 2,286 1,939 1,488 1,000 0,5 2,000 1,924 1,707 1,383 1,000 0,6 1,650 1,651 1,529 1,300 1,000 0,8 1,125 1,230 1,244 1,163 1, ,500 0,691 0,854 0,962 1,000 The radial penetration can also be very considerably affected by a concave trajectory curve, as much for an annular tool as a spherical one. This problem can be avoided by modifying the tool trajectory. In any event it is essential to maintain the maximum effective radial penetration for calculating the maximum useful power necessary. SP300 Machining Effective cutting parameters Page 3. 22

11 THE CLEARACE AGLE (α) The clearance can be adjusted deliberately but in most cases it has a fixed value owing to the inclination of certain walls of the mould. Clearance has a beneficial effect when it enables the tool to work away from its point where the cutting speed is zero (See Cutting speed and spindle speed page 3.13). The clearance also has an effect on the way the tool works : up or down machining (See next chapter below). In order to control the clearance at all points of the tool trajectory a fourth axis is needed and there must be no problems related to the space taken up by the spindle. Since by definition plastic injection moulds can be removed, and in view of the space problems that are difficult to resolve in a cavity, machining is carried out mostly using the machine s principal three axes, or possibly with a quasi-fourth axis (adjustment of the clearance and then working along three axes), since continuous adjustment of the clearance along the tool trajectory is usually reserved for machining complex shapes such as turbine blades, aircraft parts, and so on. Therefore clearance is more often endured than controlled. However it is important to understand its influence on the effective cutting conditions : on the effective cutting speed (See chapter on cutting speed and spindle speed page 3.13 on the working mode (up/down machining) : See next section. UP-DOW MACHIIG From the standpoint of chip formation, down machining is highly preferable (See Figure 7) to up machining. Chip formation is clean and the process facilitates ejection of the chip from the cutting zone. With up machining, the chip is formed after a minimum thickness is reached, resulting in tool-workpiece rubbing before cutting as such begins. In addition the chip is more difficult to eject. Chip discharged away from the cutting zone Vf Chip cleanly cut as soon as it comes into contact with the tooth Down milling Chip of narrow section, crushed and then cut Vf Up milling Chip discharged in front of the tool : danger of recycling chips Figure 7 : Machining with an annular tool, down and up. SP300 Machining Effective cutting parameters Page 3. 23

12 Down machining is possible only on machines where the feed mechanism has zero play (which applies to the very great majority of machines now in service). For annular tools, the working method of the tool is easy to determine: the radial penetration is simply placed at one side of the milling cutter or the other. In full width working there are the drawbacks of up machining as regards chip formation, but not as concerns its ejection which takes place in the same way as in down machining. Generally speaking except for lead-ins (ramps or helical work) it is preferable not to work deep in the material. As regards ball-type milling cutters, the boundary between up and down working is more fuzzy, especially when the milling cutter is working on its axis. Figure 8 shows a number of machining approaches using a spherical cutter with clearance angle, pushing or pulling. MACHIIG WITH CLEARACE AGLE (PULLIG) MACHIIG WITH CLEARACE AGLE (PUSHIG) "PUSH" MACHIIG WITH HIGH CLEARACE AGLE AD LOW DEPTH OF CUT A V f A A A A A V f V f A-A case 1 A-A case 1 A-A case 1 Cutting zone in down milling Cutting zone in up milling Cutting zone in down milling Cutting zone in up milling Cutting zone in up milling A-A case 2 A-A case 2 A-A case 2 Cutting zone in down milling Cutting zone in down milling Cutting zone in up milling Figure x8 : Milling with a spherical tool with clearance angle showing the different zones in up or down machining. Down machining is more favourable to good chip formation. It is difficult to apply with a spherical tool, but very easily controllable with an annular tool. This argument obviously favours annular tools that should be used as soon as the other machining constraints permit (shape of workpiece, values of radii, final roughness, and so on) SP300 Machining Effective cutting parameters Page 3. 24

13 VALIDATIG MACHIE PARAMETERS I MILLIG The effective cutting parameters can be used to validate the selected cutting conditions (adequate available power, and so on) and for calculating the corresponding machine parameters (spindle speed, feed rate, etc.). Calculating the feed rate and useful power The maximum feed rate is easy to calculate from the maximum effective cutting conditions. Knowing the specific cutting power for the material being machined, it is possible to determine the maximum cutting power necessary for the proposed process. a Specific cutting power for SP300 The specific cutting power is the power (in watts) necessary to remove material at a rate of 1 cm³/min. Knowing the maximum material removal rate (calculated from the maximum effective cutting parameters) this power value is used to predict the necessary cutting power. This is usually regarded as constant for a given material but in fact it does vary according to the tool, its degree of wear, and the cutting parameters. Figure 1 page gives an example of how the specific cutting power varies as a function of cutting speed and tool wear. Similar measurements show that it falls slightly as the advance per tooth, axial penetration and radial penetration increase. For a mould steel of 300 HB, the values given in the tables of specific cutting powers will be around W/cm³/min. The cutting conditions, the tool and the material being worked are not usually specified. Also the determination of power in milling is a delicate matter the accuracy of which is difficult to determine. This may explain the range of values encountered. For SP300 the following ranges will be used : from 50 to 60 W/cm³/min. for a new tool, from 65 to 80 W/cm³/min. for a tool at the end of its life In estimating the power necessary for the spindle, with a concern for safety causing us to consider the most unfavourable situation, we shall systematically use the highest value: Wc = 80 W/cm 3 /min. SP300 Machining Effective cutting parameters Page 3. 25

14 b - Calculating the maximum feed and power necessary For roughing operations (or possibly coarse semi-finishing) it will be necessary to calculate the feed rate in order to ensure that the machine has adequate discharge capacity. The feed rate is calculated as follows : ❶ With a spherical tool the maximum feed rate Q (cm 3 /min) is : Q = Vf. ap. a e eff max/ 1000 Vf is the relative advance of the tool with respect to the workpiece in mm/min so that Vf = xzxf z is the spindle speed calculated from the cutting rate (Vc in m/min) and the effective cutting diameter (φeff in mm: nominal diameter for an annular tool). = 1000xVc / Π / Øeff (See chapter Cutting speed and spindle speed page 3.13) z = number of teeth on the tool f z = advance per tooth validated using the minimum effective chip thickness criteria. a e eff max and a p in (mm) are the maximum penetrations along the trajectory (a e eff max = Ø if the tool is working fully in the material, otherwise see the calculation of a e eff max See chapter Radial penetration page 3.22). ❶ With an annular tool the maximum feed rate Q (cm 3 /min) is : Q = Vf. e. a e eff max eff max/ 1000 Vf is the relative advance of the tool with respect to the workpiece in mm/min such that Vf = xzxf z is the spindle speed calculated from the cutting speed (Vc in m/min) and the effective cut diameter (φeff in mm: nominal diameter for an annular tool) = 1000xVc / Π / Øeff (See chapter Cutting speed and spindle speed page 3.13) z = number of teeth on the tool (z = 2 for most spherical tools) f z is the advance per tooth validated as a function of the minimum effective chip thickness criteria. a e eff max and a p in (mm) are the maximum penetration along the trajectory (a e eff max = Ø if the tool is working fully in the material, otherwise see the calculation of a e eff max See chapter Radial penetration page 3.22)) SP300 Machining Effective cutting parameters Page 3. 26

15 c - Calculation and validation of the necessary spindle power Using the material feed rate it is possible to calculate the necessary cutting power. This requires knowledge of the specific cutting power for the material considered : for SP300 use Wc = 80 W/cm³/min (See page 3.25). The necessary power is calculated as follows: P useful = Q.Wc Q is the material removal rate in cm³/min calculated as above Wc is the specific power for SP300 : 80 W/cm³/min. This value of P useful should be less than the available power, which is the total power available at the spindle at the speed in question (P ()) less the off-load power (P off-load) : P useful < (P () P off-load). SP300 Machining Effective cutting parameters Page 3. 27

16 Table for validating machine parameters with an annular tool References of the selected tool Mark : Reference o : Diameter Øo (mm) : b of teeth z : Diameter of inserts Ø i (mm) : Minimum chip thickness f z min (mm) : Selected machine ame : Availability of curve showing power against spindle speed : Off-load spindle power P off-load (W): Max. feed rate ensuring correct path : Maximum chip removal rate Qchip max. (cm 3 /min) : Cutting conditions Cutting speed Vc (m/min) Advance per tool f z (mm/tooth) Axial penetration a p (mm) Radial penetration a e (mm) SP300 Machining Effective cutting parameters Page 3. 28

17 Effective cutting conditions and validation of chosen parameters (annular tool)) Calculation of spindle speed Calculation of spindle speed: (rpm) = Vc/(pi.Øeffmax) Validation of f z Calculation of a e /Ø t Calculation of a p /Ø i Determination of f z eff / f z (table IV, page 3.19) Calculation of f z eff (mm) : f z eff/f z. f z Is f z eff adequate in terms of f z min at cutting edge? Calculation of feed rate Vf (mm/min) Calculation of Vf (mm/min) = = f z (mm).z.(rev/min) Is Vf compatible with the maximum feed rate of the machine Vf max mach? Roughness related to axial penetration : Maximum axial penetration a p along trajectory (mm) : Calculation of f z /Ø i Calculation of a p /Ø t Determination of da p /ad p (Table VI, page 3.21) =Does the da p allow the desired roughness to be achieved? Determination of maximum radial penetration a e (mm : Is the situation giving maximum radial penetration known? If not, take a e max = Øeff maxi If it is, value of=β Calculation of a e /Ø t Determination of a e eff/a e (table VII, page 3.22) Calculation of a e maxi (mm): a e eff/a e.a e Calculation of chip removal rate Q (cm 3 /min) : Q (cm 3 /min) = Vf (mm/min). ap (mm). a e maxi (mm) / 1000 Is this rate compatible with the maximum machine rate Qchip max? Validation of spindle speed Total power (W) at speed (rpm) P () Power available (W) : P() Poff-load Calculation of usable power: P (W) = Q (cm 3 /min).80 (W/cm 3 /min) Is the usable power compatible with the available power? SP300 Machining Effective cutting parameters Page 3. 29

18 Table to validate machine parameters with a spherical tool References of the selected tool Mark : reference : diameter Ø t (mm) : b of teeth z : Minimum chip thickness f z min (mm) : Selected machine ame : Availability of curve showing power against spindle frequency : Off-load spindle power P off-load (W) : Maximum feed rate Vf max. mach : Maximum chip removal rate Qchip max. (cm³/min) : Cutting conditions : Cutting speed Vc (m/min) Advance per tooth f z (mm/tooth) Cut depth e (mm) Scanning pitch p (mm) Minimum and maximum clearance angle α min and α max ( ) SP300 Machining Effective cutting parameters Page 3. 30

19 Effective cutting conditions and validation of chosen parameters (spherical tool) Calculation of spindle speed Value of clearance angle α ( ) giving maximum effective cut diameter Calculation of e/ø t Determination of Ø1/Ø t (table III page 3.17) Determination of Ø2/Øt (table III page 3.17) Calculation of maximum effective diameter Øeff max (mm) = Ø t.(max(abs(ø1/ø t ),abs(ø2/ø t ))) Calculation of spindle speed : (rpm) = Vc/(pi.Øeffmax) Validation of f z Calculation of p/ø t Calculation of e/ø t Determination of f z eff / f z (table IV page 3.19) Calculation of f z eff (mm) : f z eff/f z. f z Is f z eff sufficient with respect to minimum f z at cutting edge? Calculating feed rate Vf (mm/min) Calculation of Vf (mm.min) = f z (mm). z.(rpm) Is Vf compatible with the maximum feed rate of the machine Vf max mach? Roughness related to axial penetration: Maximum axial penetration A p along trajectory (mm) : Calculation of p/ø t Calculation of e/ø t Determination of δe (table VI page 3.21) =Does the δe allow the desired roughness to be achieved? Determination of maximum radial penetration (mm): Is the situation lading to maximum radial penetration known? If not, take a e max = Øeff maxi If it is, value of=β Calculation of p/ø t Determination of a e eff/a e (table VII page 3.22) Calculation of a e maxi (mm): a e eff/a e.a e Calculation of chip removal rate Q (cm 3 /min) : Q (cm 3 /min)=vf (mm/min). e (mm). a e maxi (mm)/1000 Is this rate compatible with the maximum machine work rate Qcop max? Validation of spindle speed Speed available at the spindle? Total power (W) at speed (rpm) P() Power available (W): P() Poff-load Calculation of usable power : P (W) = Q (cm 3 /min).80 (W/cm 3 /min) Is the usable power compatible with the available power? SP300 Machining Effective cutting parameters Page 3. 31