The relationship and formula between cutting speed, depth of cut, and feed rate

In CNC programming, programmers must determine the cutting parameters for each operation and write them into the program as instructions. Cutting parameters include cutting speed, depth of cut, and feed rate. Different cutting parameters are required for different machining methods.

1Principles for Selecting Cutting Parameters
During rough machining, the priority is generally to improve productivity, but economic efficiency and processing costs should also be considered; during semi-finishing and finishing, cutting efficiency, economic efficiency, and processing costs should be balanced while ensuring processing quality. Specific values should be determined according to the machine tool manual, cutting parameter manual, and experience.
From the perspective of tool durability, the order of selecting cutting parameters is: first determine the depth of cut, then the feed rate, and finally the cutting speed.

2Determining the Depth of Cut
The depth of cut is determined by the rigidity of the machine tool, workpiece, and tool. Under the condition that rigidity allows, the depth of cut should be as close as possible to the machining allowance of the workpiece, which can reduce the number of passes and improve production efficiency.
Principles for Determining Depth of Cut:
（1）When the surface roughness requirement isRa12.5μm～25μmif the machining allowance of CNC machining is less than5mm~6mmrough machining can achieve the requirement with one feed. However, if the allowance is large, the rigidity of the process system is poor, or the machine tool power is insufficient, it can be completed in multiple feeds.
（2）When the surface roughness requirement isRa3.2μm～12.5μmrough machining and semi-finishing can be performed in two steps. The depth of cut for rough machining is selected as before. An allowance is left after rough machining and removed during semi-finishing.0.5mm～1.0mmallowance,
（3）When the surface roughness requirement isRa0.8μm～3.2μmrough machining, semi-finishing, and finishing can be performed in three steps. The depth of cut for semi-finishing is selected as1.5mm～2mm。The depth of cut for finishing is selected as0.3mm～0.5mm。
3Determining the Feed Rate
The feed rate is mainly determined by the machining accuracy and surface roughness requirements of the part, as well as the materials of the tool and workpiece. The maximum feed rate is limited by the rigidity of the machine tool and the performance of the feed system.
Principles for Determining Feed Rate:
1）When the quality requirements of the workpiece can be guaranteed, a higher feed rate can be selected to improve production efficiency. Generally selected within the range of100～200m/min范围内选取。
2）When cutting, machining deep holes, or using high-speed steel tools, a lower feed rate should be selected, generally within the range of20～50m/min范围内选取。
3）When high machining accuracy and surface roughness are required, the feed rate should be smaller, generally within the range of20～50m/min范围内选取。
4）When the tool is in idle travel, especially long-distance“return to zero”the highest feed rate set by the machine tool's CNC system can be selected.
4Determining the Spindle Speed　　
The spindle speed should be selected according to the allowable cutting speed and the diameter of the workpiece (or tool). The calculation formula is: 
n=1000v/πD
v----Cutting speed, unit ism/min，determined by tool durability
n-- -Spindle speed, unit isr/min
D----Workpiece diameter or tool diameter, unit ismm　　
The calculated spindle speednFinally, select the available or closest speed from the machine tool manual.

In summary, the specific values of cutting parameters should be determined based on the machine tool performance, relevant manuals, and practical experience using the analogy method. At the same time, the spindle speed, cutting depth, and feed rate should be mutually adaptable to form the optimal cutting parameters.

Reference Formula:

1) Depth of Cutap

The vertical distance between the machined surface and the surface to be machined of the workpiece is called the depth of cut. The depth of cut is the amount of cut measured at the cutting edge base point and perpendicular to the working plane. It is the depth to which the cutting tool cuts into the workpiece during each feed, so it is also called the cutting depth. According to this definition, when turning the outer circle longitudinally, the depth of cut can be calculated by the following formula:
a p =(d w-d m)/2

Wherea p——Depth of cut(mm)

d w ——Diameter of the workpiece surface to be machined(mm)
dm ——Diameter of the machined surface of the workpiece(mm)

Example 1: The diameter of the workpiece surface to be machined is known to beΦ95mm；Now, feed to a diameter ofΦ90mmCalculate the depth of cut.

Solution:a p =(d w-d m)/2=(95-90)/2=2.5mm

2) Feed Ratef 
The relative displacement between the tool and the workpiece in the feed direction for each revolution of the workpiece or tool.

According to the different feed directions, it is divided into longitudinal feed rate and transverse feed rate. The longitudinal feed rate refers to the feed rate along the direction of the lathe bed guide rail, and the transverse feed rate refers to the feed rate perpendicular to the direction of the lathe bed guide rail.

(Note) Feed speedv fRefers to the instantaneous speed of a selected point on the cutting edge relative to the workpiece feed movement. 
v f=fn 
Wherev f —Feed speed(mm/s)
n —Spindle speed(r/s)
f —Feed rate(mm/s)

3) Cutting speedv c 
The instantaneous speed of a selected point on the cutting edge relative to the main movement of the workpiece. The calculation formula is as follows:
v c=(π d w n )/1000 
Wherev c —Cutting speed(m/min)
dw —Diameter of the workpiece surface to be machined(mm)
n —Workpiece speed(r/min) 
When calculating, the maximum cutting speed should be used as a reference. For example, when turning, the value of the diameter of the surface to be processed is used for calculation, because the speed is the highest here and the tool wears the fastest.

Example 2: Turning a workpiece with a diameter ofΦ60mmThe selected lathe spindle speed is600r/min，求vc.

Solution:v c=(π d w n)/1000 = 3.14x60x600/1000 = 113 m/min

In actual production, the workpiece diameter is often known. According to factors such as workpiece material, tool material and processing requirements, the cutting speed is selected, and then the cutting speed is converted into the lathe spindle speed to adjust the lathe, resulting in the following formula:

n=(1000v c)/ π d w

Example 3: On aCA6140type horizontal lathe turningΦ260mmpulley outer circle, choosevcas90m/min，求n。

Solution:n=(1000v c)/ π d w=(1000x90)/ (3.14x260)=110r/min

After calculating the lathe spindle speed, the value close to that on the nameplate should be selected, that is, selectn=100r/minas the actual speed of the lathe.

3. Summary:

Cutting parameters

1.Depth of cutap(mm) ap=(dw-dm)/ 2 (mm)

2.Feed ratef(mm/r)

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

n=1000vc/∏d(r/min)