What is the formula for calculate cutting speed in CNC Machining?

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What is the formula for calculate cutting speed in CNC Machining?

  • 1: Cutting line speed: V=πDN/1000N=rpm (spindle revolutions) D=¢mm (cutting diameter) V=M/minπ=3.14
  • 2: Cutting power: KW=(Ks×V×d×f)÷(6000×λ) W=Kw (cutting power) f=feed amount (mm/rev) d=cutting depth (mm)λ=0.7~0.85 (Mechanical efficiency)
  • 3: Cutting resistance: P=Ks×q P=KG Ks=kg/square mm q=f×d [cutting area [square mm]]
  • 4: Cutting torque: T=P×(D/2) T=kg-mD=¢mm (cutting diameter)
  • 5: Feed speed and feed amount: Vf=N×fVf=feed speed (mm/min)N=rpm (spindle revolutions) f=feed amount (mm/rev)
  • 6: Drilling time: T=L/Nf=πDL/1000VfT=Drilling time (min) D=¢mm (drill diameter) L=Drilling depth (mm) V=M/minf=feed amount (mm/rev )
  • 7: Tool nose arc radius compensation: Z=r(1-tanθ/2)X=ZtanθZ=Z compensation value X=X compensation value r=tool nose arc radius θ=inclined angle
  • 8: Worktable feed: Vf=fz×Z×nVf=worktable feed (mm/min)fz=feed per tooth (mm/t)Z=number of teeth of milling cutter n=number of revolutions of milling cutter

The relationship between cutting speed, cutting amount and feed rate

The relationship between cutting speed, cutting amount and feed rate

The relationship between cutting speed, cutting amount and feed rate is a key factor in determining the efficiency of a milling machine. When the feed rate is too low, the cutting speed will be too high to produce any chips. The chips will not be cut off and they will accumulate at the end of the cut.

1. Selection criteria for cutting amount

During rough machining, the main focus is to improve the productivity, but economy and processing cost should also be considered; during semi-finishing and finishing, cutting power, economy and processing cost should be taken into account under the premise of ensuring machining quality. The detailed value should be determined according to the machine tool manual, cutting quantity manual, and experience.

Starting from the durability of the tool, the selection sequence of the cutting amount is: first confirm the amount of back-feeding knife, secondly confirm the feed amount, and finally confirm the cutting speed.

1. Selection criteria for cutting amount

2. Confirmation of the amount of knives eaten on the back

The amount of back cutting is determined by the stiffness of the machine tool, workpiece and tool. Under the conditions of rigidity, the amount of back cutting should be as much as possible equal to the machining allowance of the workpiece, which can reduce the number of passes and improve production efficiency.

Criteria for confirming the amount of knives eaten on the back:

(1) When the surface roughness value of the workpiece is required to be Ra12.5μm ~ 25μm, if the machining allowance of CNC machining is less than 5mm ~ 6mm, the rough machining can meet the requirements with one feed. However, when the allowance is large, the rigidity of the process system is poor or the power of the machine tool is lacking, it can be completed by multiple feeds.

(2) When the surface roughness value of the workpiece is required to be Ra3.2μm ~ 12.5μm, it can be divided into two steps of roughing and semi-finishing. The selection of the amount of back cutting during roughing is the same as before. Leave 0.5mm to 1.0mm allowance after rough machining, and cut it off during semi-finishing.

(3) When the surface roughness value of the workpiece is required to be Ra0.8μm ~ 3.2μm, it can be divided into three steps: roughing, semi-finishing and finishing. For semi-finishing, the back-feeding knife measures 1.5mm to 2mm. When finishing, the back-feeding knife measure is 0.3mm~0.5mm.

3. Confirmation of feed amount

The feed rate is mainly based on the machining accuracy and surface roughness requirements of the parts, as well as the material selection of the tool and workpiece. The maximum feed rate is limited by the stiffness of the machine tool and the capabilities of the feed system.

Criteria for confirming the feed rate:

1) When the quality requirements of the workpiece can be ensured, in order to improve the production efficiency, a higher feed rate can be selected. Generally selected in the range of 100 ~ 200m/min.

2) When cutting, machining deep holes or machining with high-speed steel tools, a lower feed speed should be selected, generally within the range of 20-50m/min.

3) When the machining accuracy and surface roughness requirements are high, the feed speed should be selected to be smaller, generally within the range of 20 ~ 50m/min.

4) When the tool is idling, especially when it is “returning to zero” at a long distance, the maximum feed rate set by the CNC system of the machine tool can be selected.

3. Confirmation of feed amount

4. Confirmation of spindle speed

The spindle speed should be selected according to the allowed cutting speed and workpiece (or tool) diameter. Its calculation formula is:

n=1000v/πD

v—-cutting speed, the unit is m/min, which is determined by the durability of the tool;

n—-spindle speed, the unit is r/min;

D—-workpiece diameter or tool diameter, in mm.

The calculated spindle speed n should finally be selected according to the machine tool manual or the speed that is closer to the machine tool.

In short, the detailed value of the cutting amount should be confirmed by analogy according to the machine tool function, related manuals and practical experience. At the same time, the spindle speed, cutting depth and feed speed can be used to each other to form the best cutting amount.

Formula:

(1) The amount of cutting knife (cutting depth) “ap”

The vertical distance between the machined surface of the workpiece and the surface to be machined is called the back-cut amount. The back cut is measured through the base point of the cutting edge and in the direction perpendicular to the working plane. It is the depth of the turning tool cutting into the workpiece at each feed, so it is also called the cutting depth. The amount of back knife can be calculated as follows:

a p = ( d w — d m ) /2

In the formula, a p——the amount of knife on the back (mm);

dw ——The diameter of the workpiece to be machined (mm);

dm ——The machined outer diameter of the workpiece (mm).

(2) Feed amount “f”

The relative displacement of the tool and the workpiece in the direction of the feed movement when the workpiece or the tool makes one revolution.

According to the different feeding directions, it is divided into longitudinal feed and lateral feed. Feed rate.

(Note) The feed speed v f refers to the instantaneous speed of the feed movement of the selected point on the cutting edge relative to the workpiece.

v f=fn

where v f ——feed rate (mm/s);

n ——Spindle speed (r/s);

f ——feed rate (mm/s).

(3) Cutting speed “vc”

The instantaneous velocity of the selected point on the cutting edge relative to the main motion of the workpiece. The calculation formula is as follows

v c=( π d w n)/1000

where v c — cutting speed (m/min);

dw – the diameter of the workpiece to be machined (mm);

n —— workpiece speed (r/min).

Cutting amount

1. The amount of back knife ap(mm) ap=(dw – dm) / 2 (mm)

2. Feed f(mm/r)

3. Cutting speed vc(m/min)Vc=∏dn/1000(m/min)

n=1000vc/∏d(r/min)

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Author: Mose Li

Author: Mose Li

Director of Project Engineering at 3Q Machining

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