Content Menu
● Coordinate transformation formula
● Arc calculation formula
● Cutting speed and feed rate calculation
● Trigonometric formulas
● Tool geometry
● Thread machining formula
● Processing time calculation
● Turning formula
● Milling Processing Formula
● Drilling Process Formula
● Grinding formula
● Sawing Processing Formula
● Feed speed calculation
● Cutting force and power calculation
● Temperature and heat calculations
Formulas in CNC programming play a vital role. They are the basis for accurate calculations and help us write programs that can control the machining process. They are crucial to continuously improving production efficiency and machining accuracy. This article carefully summarizes 80 core formulas commonly used in the field of CNC programming, aiming to provide convenience and support for the work of colleagues.
Coordinate transformation formula
1.x' = x + Δx (Cartesian coordinate system conversion)
Note: This is a basic translation transformation formula, which can adjust the position of a point in the rectangular coordinate system by a displacement of Δx along the x-axis.
Example: There is a point whose original coordinate position is (3, 5). Now, if we move two two nits in the x direction (Δx = 2), its new x coordinate is the original 3 plus 2, which is 5. Therefore, the new coordinate of this point becomes (5, 5), where the y coordinate remains unchanged.
2.y' = y + Δy (Cartesian coordinate system conversion)
Note: This is a basic translation transformation formula, which is used to change the position of a point in the y-axis direction in the rectangular coordinate system so that it moves a distance of Δy.
Example: There is a point whose initial coordinates are set to (3, 5). If the point moves three units in the y-axis direction (i.e., Δy = 3), its new y-coordinate is the original coordinate 5 plus 3, which is 8. Therefore, the new coordinates of the point after movement become (3, 8), where the x-coordinate remains unchanged at 3.
3.z' = z + Δz (Cartesian coordinate system conversion)
Note: This is a basic spatial translation formula that can realize the position change of a point in the rectangular coordinate system in the z-axis direction. The specific movement distance is Δz.
Example: We have a point in 3D space, and its initial coordinates are (3, 5, 7). Suppose this point moves four units in the z-axis direction that is, Δz = 4. To find the new z coordinate of this point after it moves, we need to add the original z coordinate 7 to the value of Δz 4. In this way, the new z coordinate z' is 7 + 4 = 11. Therefore, the new coordinates of this point after it moves become (3, 5, 11), where the x coordinate and y coordinate remain unchanged, still 3 and 5.
4.x' = x cos θ - y sin θ (rotation matrix)
Note: This is a two-dimensional rotation coordinate transformation formula, which can help us calculate the new x-coordinate value of a point after rotating an angle θ around the origin in a rectangular coordinate system.
Example: If the original coordinates of a point are (3, 5) and θ is 30 degrees, then the new x coordinate is: x′=3 cos 30° - 5 sin 30°≈ 0.098. Therefore, the nelatestoint coordinates are approximately at (0.098, y′), and y′ needs to be calculated using the corresponding rotation formula.
5.y' = x sin θ + y cos θ (rotation matrix)
Description: This is a two-dimensional rotation coordinate transformation formula used to determine the new y coordinate value of a point after rotating by an angle θ around the origin in a rectangular coordinate system.
Example: If the original coordinates of a point are (3, 5) and θ is 30 degrees, then the new y coordinate is: y′=3 sin 30° + 5 cos 30°≈ 5.83. Therefore, the latest point coordinates are approximately at (x′, 5.83), and x′ needs to be calculated using the corresponding rotation formula.
6.x = r cos θ (polar coordinate conversion)
Note: This is the conversion formula for converting the coordinates (r, θ) in the polar coordinate system to the x coordinate in the rectangular coordinate system.
Example: If a point's polar coordinates are (5, 60°), then the corresponding x coordinate is: x=5 cos 60°=2.5. Therefore, the new point coordinates are (2.5, y), where y needs to be calculated using the corresponding polar coordinate conversion formula.
7.y = r sin θ (polar coordinate conversion)
Note: This is the calculation formula for transforming polar coordinates (r, θ) into y coordinates in a rectangular coordinate system.
Example: f the polar coordinates of a point are (5, 60°), then the corresponding y coordinate is: y=5 sin 60°=4.33. Therefore, the new point coordinates are (x, 4.33), where x needs to be calculated using the corresponding polar coordinate conversion formula.
8.r = √(x^2 + y^2) (polar coordinate conversion)
Explanation: This is the formula for converting the coordinate point (x, y) in the rectangular coordinate system to the value r from the origin in the polar coordinate system.
Example:: If a point's rectangular coordinates are (3, 4), then the corresponding r value is: r = √(3^2 + 4^2) = √25 = 5. Therefore, the new polar coordinates are (5, θ), where θ needs to be calculated using the corresponding polar coordinate conversion formula.
9.θ = tan^(-1)(y / x) (polar coordinate conversion)
Explanation: This is the formula for converting a point (x, y) in a rectangular coordinate system to an angle θ in a polar coordinate system.
Example: If the rectangular coordinates of a point are (3, 4), then the corresponding angle θ is: θ=tan^(-1)(4 / 3)≈53.13°. Therefore, the new polar coordinates are approximately at (r, 53.13°), where r needs to be calculated using the corresponding polar coordinate conversion formula.
Arc calculation formula
10. (x - h)^2 + (y - k)^2 = r^2 (equation of a circle)
Explanation: This is a standard mathematical expression for describing a circle, where the circle's center is given by the coordinates (h, k), and r represents the length of the circle's radius.
Example: Given a circle with its center at coordinates (2, 3) and a radius of 5, we can write the equation of this circle using the standard equation of a circle. Specifically, substitute the x-value of 2 and y-value of 3 for the circle's center and the radius of 5 into the equation (x - h)2 = r2 + (y - 3)2.
11.L = r θ (arc length calculation)
Note: This is a formula for calculating the length of an arc, where L represents the arc length, r is the circle's radius, and θ is the central angle of the circle, and the angle is measured in radians.
Example: If the radius of a circle is 4fourand, the central angle is 60°, or π/3 radians, then the arc length is: L = 4 * (π/3) = (4π/3).
12. C = 2 π r (circumference)
Note: This is a formula for calculating the circumference of a circle. C represents the circle's circumference, and r is the circle's radius.
Example: We have a circle with a radius of 7. To calculate the circumference of this circle, we substitute the known radius 7seveninto the formula: C = 2 × π × 7 = 14π
13.A = π r^2 (area of a circle)
Note: This is a mathematical formula for calculating the area of a circle. A represents the area of the circle, and r represents the circle's radius.
Example: We have a circle with a radius of 5. To calculate the area of this circle, we can use the formula A = π times the radius squared. Substituting the radius of 5 into the formula, we get that the area A iequalsπ times 5 squared, which is 25π.
14.A = (1/2) r^2 θ (area of the sector)
Note: This is a calculation formula for the area of a sector. A represents the area of the industry, r is the circle's radius, θ is the central angle of the circle, and this angle is measured in radians.
Example: If the radius of a circle is 6sixand the central angle is 45° or π/4 radians, then the area of the sector is: A = (1/2) * 6^2 * (π/4) = 9π/2.
Cutting speed and feed rate calculation
15. Vc = π D n / 1000 (cutting speed) Explanation: This is a formula for solving the cutting speed, where Vc represents the cutting speed, the tool diameter is recorded as D, and the spindle speed is represented by n. Example: If the tool diameter is 50 mm and the spindle speed is 1200 rpm, the cutting speed is Vc = π * 50 * 1200 / 1000 = 188.4 m/min.
16. F = fz zn (feed rate) Explanation This formula is used to calculate the feed rate, where F represents the feed rate, fz represents the feed per tooth, z is the number of teeth on the tool, and n is the spindle speed. Example: If the feed per tooth is 0.1 mm, the number of teeth on the tool is 4, and the spindle speed is 1200 rpm, then the feed rate is F = 0.1 * 4 * 1200 = 480 mm/min.
17.n = (1000 Vc) / (π D) (Spindle speed) Explanation: This is a formula for solving for spindle speed, where n represents the spindle speed, Vc is the cutting speed, and D is the diameter of the tool. Example: if the cutting speed is 150 m/min and the tool diameter is 50 mm, then the spindle speed is n (1000 * 150) / (π * 50) = 954 rpm.
18.fz = F / (zn) (Feed per tooth) Explanation: This is a formula for calculating the feed per tooth, where fz represents the feed per tooth, F is the feed rate, z is the number of teeth on the tool, and n is the spindle speed. Example: If the feed rate is 500 mm/min, the number of teeth on the tool is 4, and the spindle speed is 1000 rpm, then the feed per tooth is fz = 500 / (4 * 1000) = 0.125 mm.
19. f = F / n (feed per revolution) Explanation This is a formula to determine the feed per revolution, where f represents the feed per revolution, F is the feed rate, and n is the spindle speed. Example: If the feed rate is 480 mm/min and the spindle speed is 1200 rpm, then the feed per revolution is f = 480 / 1200 = 0.4 mm.
20. t = L / F (feed time) Explanation: This is a formula to solve for the feed time, where t represents the time required for feeding, L is the length of the machine, and F is the feed rate. Example: We have a length that needs to be machined, which is 100 mm. At the same time, there is a feed rate, which represents the distance the tool moves per minute, and the feed rate here is 500 mm/min. To know how long it takes to machine this length, we substitute the known values into the formula: t = 100 mm ÷ 500 mm/min = 0.2 minutes. Therefore, it takes 0.2 minutes to process this 100 mm length.
Trigonometric formulas
21. a/sin A = b/sin B = c/sin C (Law of Sines)
Explanation: The law of sines is a theorem about triangles. It states that in any triangle, the ratio of the lengths of any two sides is equal to the ratio of the sines of their corresponding angles.
Example: If the sides of a triangle are a=6, b=8, and angles A and B are 30° and 45° respectively, then the law of sines shows that 6/sin 30° = 8/sin 45°.
22. c^2 = a^2 + b^2 - 2ab cos C (Law of Cosines)
Description The law of cosines is a theorem about triangles. It states that in any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of the cosines of those two sides and the angle between them.
Example If the side lengths of a triangle are a=5, b=7, and the included angle C is 60°, then the side length c can be calculated as: c^2=5^2 + 7^2 - 257*cos 60°.
23. sin θ = opposite side / hypotenuse (sine)
Note: The definition of sine is that in a right triangle, for a given angle θ, its sine value is equal to the ratio of the length of the opposite side corresponding to the angle to the length of the hypotenuse.
Example: If the opposite side of a right triangle is three threes, the hypotenuse is 5, then the sine of angle θ is sin θ = 3 / 5 = 0.6.
24. cos θ = adjacent side/hypotenuses (cosine)
Note: The definition of cosine is that in a right triangle, for a given angle θ, its cosine value is equal to the ratio of the length of the adjacent side corresponding to the angle to the length of the hypotenuse.
Example: If the adjacent side of a right triangle is 4fourand, the hypotenuse is 5, then the cosine of the angle θ is cos θ = 4 / 5 = 0.8.
25. tan θ = opposite side / adjacent side (tangent)
Not: The definition of tangent is that in a right triangle, for a given angle θ, its tangent value is equal to the ratio of the length of the opposite side corresponding to the angle to the length of the adjacent side.
Example: If the opposite side of a right triangle is three and the adjacent side is 4, then the tangent of angle θ is tan θ = 3 / 4 = 0.75.
26.cot θ = 1 / tan θ (cotangent)
Note: The definition of cotangent is that in a right triangle, for a given angle θ, the cotangent is equal to the reciprocal of the tangent of the angle, that is, equal to the ratio of the length of the adjacent side to the length of the opposite side.
Example: If a right triangle's tangent is 0.75, then the cotangent of angle θ is: cot θ = 1 / 0.75 = 1.33.
27.sec θ = 1 / cos θ (secant)
Note: The definition of secant is that in a right triangle, for a given angle θ, its secant value is equal to the reciprocal of the cosine of the angle, that is, equal to the ratio of the length of the hypotenuse to the length of the adjacent side.
Example: f the cosine of a right triangle is 0.8, then the secant of the angle θ is: sec θ = 1 / 0.8 = 1.25.
28.csc θ = 1 / sin θ (cosecant)
Note: Te definition of cosecant is that in a right triangle, for a given angle θ, the cosecant value is equal to the reciprocal of the sine of the angle, that is, equal to the ratio of the length of the hypotenuse to the length of the opposite side.
Example: If the sine of a right triangle is 0.6, then the cosecant of the angle θ is: csc θ = 1 / 0.6 = 1.67.
Tool geometry
29.γ = α - β (tool rake angle)
Description: This is a formula for solving the tool rake angle, where γ represents the tool rake angle, α is the tool clearance angle, and β is the tool wedge angle.
Example, If the tool clearance angle α is 15° and the tool wedge angle β is 30°, then the tool rake angle is: γ=15° - 30°=-15°.
30.α = γ + β (tool clearance angle)
Note: This is a formula for calculating the tool back angle, where α represents the tool back angle, γ is the tool rake angle, and β is the tool wedge angle.
Example: If the tool rake angle γ is 10° and the tool wedge angle β is 20°, then the tool clearance angle is: α=10° + 20°=30°.
31.β = 90° - α - γ (tool wedge angle)
Note: This is a formula for solving the tool wedge angle, where β represents the tool wedge angle, α is the tool back angle, and γ is the tool rake angle.
Example: If the tool clearance angle α is 25° and the tool rake angle γ is 10°, then the tool wedge angle is: β = 90° - 25° - 10° = 55°.
32.ap = D - d (cutting depth)
Note: this is a calculation formula for cutting depth, where ap represents the cutting depth, D is the diameter of the workpiece, and d is the diameter after processing.
Example: If the workpiece diameter D is 50 mm and the processed diameter d is 45 mm, then the cutting depth is ap=50 - 45=5 mm.
33.b = f sin φ (cutting width)
Note: This is a calculation formula for cutting width, where b represents cutting width, f is feed rate, and φ is cutting angle.
Example: If the feed f is 0.2 mm and the cutting angle φ is 30°, the cutting width is b=0.2 * sin 30°=0.1 mm.
34.h = f cos φ (cutting thickness)
Note: This is a calculation formula for cutting thickness, where h represents the cutting thickness, f is the feed rate, and φ is the angle formed during cutting.
Example: If the feed rate f is 0.2 mm and the cutting angle φ is 30°, then the cutting thickness is: h=0.2 * cos 30°=0.173 mm.
Thread machining formula
35.D = d + 2P (outer diameter)
Note: This is a formula for calculating the outside diameter, where D represents the outside diameter, d is the inside diameter, and P is the thread pitch.
Example: If the inner diameter d is 8 mm and the pitch P is 1 mm, the outer diameter is D=8 + 2*1=10 mm.
36.d = D - 2P (inner diameter)
Note: This is a formula for calculating the inner diameter, where d represents the inner diameter, D is the outer diameter, and P is the pitch.
Example: If the outer diameter D is 10 mm and the pitch P is 1 mm, the inner diameter is d=10 - 2*1=8 mm.
37.Dm = D - 1.5P (median diameter)
Note: This is a formula for solving the mean diameter, where Dm represents the mean diameter, D is the outer diameter, and P is the pitch.
Example: If the outer diameter D is 10 mm and the pitch P is 1 mm, then the median diameter is m=10 - 1.5*1=8.5 mm.
38.P = 1 / n (pitch)
Note: This is a formula for calculating the pitch, where P represents the pitch and n is the number of teeth per inch (or the number of threads).
Example: If the number of threads per inch n is 8, then itch is P = 1 / 8 = 0.125 inches.
39.t an α = P / (π Dm) (pitch angle)
Note: This is a calculation formula for the pitch angle, where α represents the pitch angle, P is the pitch, and Dm is the median diameter.
Example: If the pitch P is 1 mm and the median diameter Dm is 8 mm, the pitch angle is tan α=1 / (π * 8)=0.0398.
Processing time calculation
40.t = L / F (one-way processing time)
Note: This is a formula for calculating the one-way processing time, where t represents the time required for one-way processing, L is the processing length, and F is the feed rate.
Example: If the machining length L is 100 mm and the feed rate F is 200 mm/min, the machining time for one pass is t100 / 200=0.5 min.
41.t = n L / F (multi-pass processing time)
Note: This is a calculation formula for multi-pass processing time, where t represents the total time required for multi-pass processing, n is the number of processing times, L is the processing length each time, and F is the feed rate.
Example: If the number of machining times n is 3, the machining length L of each machining is 100 mm, and the feed rate F is 200 mm/min, then the multi-pass machining time is: t=3 100 / 200=1.5 minutes.
42. t Total = t Preparation + t Processing (total processing time)
Note : This is a formula for calculating the total processing time, where total represents the total processing time, preparation represents the time required for the preparation stage, and processing represents the actual processing time.
Example: if the preparation time preparation is 10 minutes and the actual processing time processing is 20 minutes, then the total processing time is: total = 10 + 20 = 30 minutes.
43.t preparation = t positioning + t clamping + t tool setting (preparation time)
Note: This is a calculation formula for preparation time, where preparation represents the time required for the entire preparation stage, positioning is the time needed for positioning, clamping is the time required for clamping the workpiece, and tool set is the time needed for tool setting.
Example: If the positioning time positioning is 2 minutes, the clamping time clamping is 3 minutes, and the tool setting time setup is 1 minute, then the preparation time is tpreparation=2+3+1=6 minutes.
44.t clamping = n * t each clamping (clamping time)
Note: This is a calculation formula for clamping time, where clamping represents the total clamping time, n represents the number of clamping times, and teach-clamping represents the time required for each clamping.
Example: If the number of clamping times n is 4, and the time required for each clamping t is 5 minutes, then the total clamping time is t = 4 * 5 = 20 minutes.
Turning formula
45.Vc = π D n / 1000 (turning cutting speed)
Note: This is a formula for calculating the cutting speed during turning, where Vc represents the cutting speed, D is the diameter of the workpiece, and n is the spindle speed.
Example: f the workpiece diameter D is 50 mm, and the spindle speed n is 1200 rpm, then the turning cutting speed is Vc = π * 50 * 1200 / 1000 = 188.4 m/min.
46.f = z fz (turning feed rate)
Note: This is a calculation formula for turning feed rate, where f represents the feed rate, z represents the number of teeth of the tool, and fzFzs the feed amount per tooth.
Example: If the number of teeth z of the tool is 2twoand the feed per tooth fz is 0.1 mm, then the turning feed rate is f=2 * 0.1=0.2 mm per revolution.
47.ap = (D - d) / 2 (cutting depth)
Note: This is a formula for calculating the cutting depth of turning, where ap represents the cutting depth, D represents the diameter of the workpiece, and d represents the diameter after machining.
Example : If the workpiece diameter D is 50 mm and the processed diameter d is 45 mm, the turning cutting depth is ap=(50 - 45) / 2=2.5 mm.
48.t = L / F (turning time)
Note: This is a calculation formula for turning processing time, where t represents the time required for processing, L represents the processing length, and F is the feed rate.
For example, if the machining length L is 100 mm and the feed rate F is 0.2 mm per revolution, the turning machining time is: =100 / 0.2=500 revolutions.
49.Q = Vc ap f (turning material removal rate)
Note: This is a formula for calculating the material removal rate during turning, where Q represents the material removal rate, Vc represents the cutting speed, ap represents the cutting depth, and f represents the feed rate.
Example If the cutting speed Vc is 150 m/min, the cutting depth ap is 2 mm, and the feed rate f is 0.2 mm/rev, the turning material removal rate is Q = 150 * 2 * 0.2 = 60 mm3/min.
Milling Processing Formula
50.Vc = π D n / 1000 (milling cutting speed)
Note: This is a calculation formula for milling cutting speed, where Vc represents the cutting speed, D represents the diameter of the milling cutter, and n represents the spindle speed.
Example: If the milling cutter diameter D is 50 mm and the spindle speed n is 1200 rpm, the milling cutting speed is Vc = π * 50 * 1200 / 1000 = 188.4 m/min.
51.f = z fz (milling feed rate)
Note: This is a formula for calculating the milling feed rate, where f represents the feed rate, z represents the number of teeth on the tool, and fz represents the feed per tooth.
For example, If the number of teeth z of the tool is four and the feed per tooth fz is 0.1 mm, then the milling feed rate is f=4 * 0.1=0.4 mm per revolution.
52.ap = (D - d) / 2 (milling cutting depth)
Note: This is a calculation formula for milling cutting depth, where ap represents the cutting depth, D represents the original diameter of the workpiece, and d represents the diameter after processing.
Example: If the original workpiece diameter D is 50 mm and the processed diameter d is 45 mm, the milling cutting depth is: a=(50 - 45) / 2=2.5 mm.
53.b = W (milling width)
Note: This is a formula for calculating the milling width, where b represents the milling width and W represents the width of the workpiece.
Example: If the workpiece width W is 20 mm, the telling width is b=20 mm.
54.t = L / F (milling time)
Note: This is a calculation formula for milling time, where t represents the time required for milling, L represents the processing length, and F represents the feed rate.
Example: If the machining length L is 100 mm and the feed rate F is 0.4 mm per revolution, the milling time is t100 / 0.4=250 revolutions.
55.Q = Vc ap f (milling material removal rate)
Note: This is a formula used to calculate the material removal rate during milling, where Q represents the material removal rate, Vc represents the cutting speed, ap represents the cutting depth, and f represents the feed rate during milling.
Example: If the cutting speed Vc is 150 m/min, the cutting depth ap is 2 mm, and the feed rate f is 0.4 mm/rev, then the milling material removal rate is Q = 150 * 2 * 0.4 = 120 mm3/min.
Drilling Process Formula
56.Vc = π D n / 1000 (drilling cutting speed)
Note: This is a calculation formula for drilling cutting speed, where Vc represents the cutting speed, D represents the diameter of the drill bit, and n represents the spindle speed.
Example: If the drill diameter D is 20 mm and the spindle speed n is 1500 rpm, the drilling cutting speed is Vc = π * 20 * 1500 / 1000 = 94.2 m/min.
57.f = fz z (drilling feed rate)
Note: This is a calculation formula for drilling feed rate, where f represents the feed rate, fz represents the feed per tooth, and z represents the number of teeth on the drill.
Example: If the feed per tooth fz is 0.05 mm and the number of drill teeth z is 2, the drilling feed rate is f = 0.05 * 2 = 0.1 mm per revolution.
58.ap = L (drilling depth)
Note: This is a calculation formula for drilling depth, where ap represents the drilling depth, and L represents the total drilling length.
Example: If the drilling length L is 50 mm, the depth is ap=50 mm.
59.t = L / F (drilling time)
Note: This is a formula for calculating drilling time, where t represents the time required for drilling, L represents the drilling length, and F represents the feed rate.
Example: If the drilling length L is 50 mm and the feed rate F is 0.1 mm per revolution, the drilling time is t=50 / 0.1=500 revolutions.
60.Q = Vc ap f (drilling material removal rate)
Note: This is a calculation formula for drilling material removal rate, where Q represents the material removal rate, Vc represents the cutting speed, ap represents the drilling depth, and f represents the feed rate.
Example: I the cutting speed Vc is 100 m/min, the drilling depth ap is 50 mm, and the feed rate f is 0.1 mm/rev, then the drilling material removal rate is Q = 100 * 50 * 0.1 = 500 mm3/min.
Grinding formula
61.Vc = π D n / 1000 (grinding cutting speed)
Note: This is a formula for calculating grinding cutting speed, where Vc represents the cutting speed, D represents the diameter of the grinding wheel, and n represents the spindle speed.
Example: If the grinding wheel diameter D is 200 mm and the spindle speed n is 3000 rpm, the grinding cutting speed is Vc = π * 200 * 3000 / 1000 = 1884 m/min.
62.f = fz z (grinding feed rate)
Note: This is a calculation formula for grinding feed rate, where f represents the feed rate, fz represents the feed per tooth, and z represents the number of teeth on the grinding wheel or the distribution density of the abrasive particles.
Example: If the feed per tooth fz is 0.01 mm and the number of teeth z of the grinding wheel is 50, then the grinding feed rate i: f= 0.01 * 50 = 0.5 mm per revolution.
63.ap = L (grinding cutting depth)
Not : This is a calculation formula for grinding cutting depth, where ap represents the grinding depth an L represents the grinding length.
Example: If the grinding length L is 5 mm, the grinding cutting depth is ap=5 mm.
64.b = W (grinding width)
No: This is a formula for calculating the grinding width, where b represents the grinding width and W represents the width of the workpiece.
Example: If the workpiece width W is 20 mm, the grinding width is b=20 mm.
65.t = L / F (grinding time)
Not: This is a calculation formula for grinding time, where t represents the time required for grinding, L represents the grinding length, and F represents the feed rate or the moving speed during the grinding process.
Example: If the grinding length L is 100 mm and the feed rate F is 0.5 mm per revolution, the grinding time is t=100 / 0.5=200 revolutions.
66.Q = Vc ap f (grinding material removal rate)
Note: This is a calculation formula for grinding material removal rate, where Q represents the amount of material removed per unit time, Vc represents the cutting speed, ap represents the grinding depth, and f represents the feed rate.
Example:I f the cutting speed Vc is 500 m/min, the grinding depth ap is 0.05 mm, and the feed rate f is 0.5 mm/rev, then the grinding material removal rate is Q = 500 * 0.05 * 0.5 = 12.5 mm3/min.
Sawing Processing Formula
67.Vc = π D n / 1000 (sawing cutting speed)
Note: This is a calculation formula for sawing cutting speed, where Vc is the cutting speed, D represents the diameter of the saw blade, and n is the spindle speed.
Example: If the saw blade diameter D is 150 mm and the spindle speed n is 1800 rpm, the sawing cutting speed is Vc = π * 150 * 1800 / 1000 = 848.2 m/min.
68.f = fz z (sawing feed rate)
Note: This is a calculation formula for sawing feed rate, where f represents the feed rate, fz is the feed per tooth, and z represents the number of teeth on the saw blade.
Example: If the feed per tooth fz is 0.02 mm and the number of teeth z on the saw blade is 100, the sawing feed rate is f = 0.02 * 100 = 2 mm per revolution.
69.ap = L (sawing cutting depth)
Note: This is a calculation formula for sawing cutting depth, where ap represents the sawing dept , and L represents the total length of the sawing or the length of the cutting path.
Example: If the sawing length L is 50 mm, the sawing cutting depth is ap=50 mm.
70.b = W (sawing width)
Note: This is a calculation formula for sawing width, where b represents the cutting width during sawing, and W represents the width of the workpiece being sawed.
Example: If the workpiece width W is 10 mm, the sawing width is b=10 mm.
71.t = L / F (sawing time)
Note: This is a formula to calculate the time required for sawing, where t represents the sawing time, L represents the sawing length, and F represents the feed rate, that is, the speed at which the saw blade moves.
Example: If the sawing length L is 100 mm and the feed rate F is 2 mm per revolution, the sawing time is t=100 / 2=50 revolutions.
72.Q = Vc ap f (sawing material removal rate)
Note: This is a calculation formula for sawing material removal rate, where Q represents the amount of material removed per unit time, Vc represents the cutting speed, ap represents the sawing depth, and f represents the feed speed or the movement rate of the saw blade.
Example: If the cutting speed Vc is 800 m/min, the sawing depth ap is 50 mm, and the feed rate f is 2 mm/rev, the sawing material removal rate is Q = 800 * 50 * 2 = 80,000 cubic mm per minute.
Feed speed calculation
73.Vf = fn (linear feed rate)
Note: This is a calculation formula for the linear feed speed, where Vf represents the linear feed speed, f represents the feed amount per revolution, and n represents the spindle speed.
Example: If the feed per revolution f is 0.2 mm and the spindle speed n is 1500 rpm, then the linear feed rate is: f = 0.2 * 1500 = 300 mm per minute.
74.Vc = π D n (circumferential feed speed)
Note: This is a calculation formula for the circular feed speed, where Vc represents the circular feed speed, D represents the diameter of the workpiece or tool, and n represents the rotation speed of the spindle.
Example: If the workpiece diameter D is 100 mm and the spindle speed n is 1200 rpm, then the peripheral feed rate is c = π * 100 * 1200 = 376991.12 mm per minute.
75.Vs. = Fn (spindle feed speed)
Note: This is a calculation formula for the spindle feed speed, where Vs represents the spindle feed speed, F represents the feed rate, that is, the feed amount per unit time, and n represents the spindle speed.
Example: If the feed rate F is 0.1 mm/rev and the spindle speed n is 1000 rev/min, then the spindle feed rate is Vs=0.1 * 1000=100 mm/min.
Cutting force and power calculation
76.Fc = kc A (cutting force)
Note: This is a formula for calculating cutting force, where Fc represents the force generated during the cutting process, kc is a coefficient related to the cutting conditions, and A represents the area of the cutting area.
Example: If the cutting force coefficient kc is 2000 N/mm² and the cutting area A is 2 mm², the cutting force is: Fc=2000 * 2=4000 N.
77.Pc = Fc Vc (cutting power)
Note: This is a calculation formula for cutting power, where Pc represents the power consumed during the cutting process, Fc represents the cutting force, and Vc represents the cutting speed.
Example: If the cutting force Fc is 4000 N and the cutting speed Vc is 2 m/s, the cutting power is Pc=4000 * 2=8000 W.
78.Ps = Pc / η (spindle power)
Note: This is a calculation formula for the spindle power, where Ps represents the total power output of the spindle, Pc represents the power consumed during the cutting process, and η represents the efficiency of the transmission system.
Example: If the cutting power Pc is 8000 W and the transmission efficiency η is 0.8, then the spindle power is Ps=8000 / 0.8=10000 W.
Temperature and heat calculations
79.Tc = T0 + Kc (Pc / A) (cutting temperature)
Note: This is a calculation formula for cutting temperature, where Tc represents the temperature generated during the cutting process, T0 represents the initial temperature, Kc is a temperature coefficient related to the cutting conditions, Pc represents the cutting power, and A represents the area of the cutting area.
Example: We have an initial temperature of T0, which is 20°C. Now, there is a temperature-dependent coefficient Kc, whose value is 0.02°C/W, which means that for every 1W increase in power, the temperature rises by 0.02°C (under certain conditions). At the same time, we have a cutting process whose power Pc is 8000W, and the cutting area A is 2 square millimeters. Now, we substitute the known values into the formula: Tc = 20°C + 0.02°C/W × (8000W / 2mm²) = 100°C So, the temperature during the cutting process is 100°C.
80.Q = mc ΔT (heat transfer)
Note: This is a calculation formula for heat transfer, where Q represents the amount of heat transferred, m represents the mass of the object, and c represents the specific heat capacity of the substance, that is, the amount of heat absorbed or released when the temperature of a unit mass of the substance increases or decreases by 1 °C, and ΔT represents the temperature change
Example: Consider an object with a mass of 5 kg and a specific heat capacity of 0.9 kJ/kg/°C. When the temperature of this object changes by 30°C, we can calculate the amount of heat it absorbs or releases. Specifically, we use the formula Q = m × c × ΔT to calculate the amount of heat, where Q is the amount of heat, m is the mass, c is the specific heat capacity, and ΔT is the temperature change. Substituting the known mass of 5 kg, the specific heat capacity of 0.9 kJ/ kg /°C, and the temperature change of 30°C into the formula, we get Q = 5 × 0.9 × 30 = 135 kJ, so the object transferred 135 kJ of heat during the temperature change.
It is inevitable to encounter difficulties and challenges in the learning journey, but these challenges shape our skills and push our professional level forward. Simply understanding the formula is only the starting point of learning. To truly master and apply it flexibly, we must constantly practice and practice in actual operations.
Post time: Jan-07-2025