The cutting formulas are a pivotal part of CNC (Computer Numerical Control) machining processes and so is understanding and mastering them. Crucial CNC parameters like cutting speed, feed rate, and spindle speed all stem from these formulas and are directly impacted by the precision, efficiency and tool life of the machining. This article is designed to provide the reader with an extensive coverage of the factors and methods of CNC calculation. The aim of this blog is to provide guidance towards improving the readers crafting skills through powerful and realistic examples and technical explanations.
In What Ways Does a Machine Impact the Calculation of Cuts?
A machine impacts the cutting calculations based on the machine’s strength, energy, and precision. The available cutting limits can also be controlled by the spindle horsepower, maximum RPM, and the axis feed rate. Moreover, the vibrations and chatter during machining are influenced by machine stability, which can severely limit both accuracy and tool longevity. Many modern CNC machines have computer-controlled systems with built-in software that automatically modify cutting parameters, therefore improving the speed and quality of machining.
Understanding the Machine
Influence: Heavier cuts and harder materials are easier to machine with higher horsepower.
Typical Range: Standard milling machines are 10-50 HP.
Influence: Working on small features or soft materials becomes easier with high precision at higher RPMs.
Typical Range: Varies with the type of machine from 6,000-30,000 RPM.
Influence: Productivity, especially with high-speed machining operations, improves with a higher feed rate.
Typical Range: 200-1,500 IPM (Inches per minute)
Influence: The range of tolerance is directly proportional to the accuracy of components that are completed.
Typical Tolerance Range: ±0.001” to ±0.0001”
Influence: A more rigid machine reduces excessive vibration which improves surface finish and increases tool life.
Measurement Parameter: Frequency in Hz or micrometers displacement.
Through this information, one can understand how specific characteristics of machines affect the performance and the cut results. Choosing a machine with the right specifications is vital for maximizing operations while maintaining quality results.
The Role of Cutting Speed in Machining
Machining efficiency, tool life, and surface finish all depend on the cutting speed. Having a higher cutting speed will, in most cases, result in a more efficient machining process, in less time. However, if too much speed is put into use, it can lead to excessive tool wear and failure. Cutting speed adjustment according to the material properties, as well as the desired tool type and finish, guarantees both productivity and tool life.
Calculating Efficiently with Your Machine
There are multiple critical variables that contour the precise and effective calculation of cutting speed, some of which are:
6Different materials have specific cutting speeds. For example:
Aluminum is easily machinable and cutting speeds of between 300 to 600 feet per minute (FPM) surface feet is needed for optimal cutting.
Steel is moderately machinable and needs moderate speeds of 100 to 300 FPM depending on hardness.
Titanium alloys are much more difficult to machine so lower speeds of 50 to 200 FPM is more beneficial.
The Material of the Tool affects the speed range:
High-Speed Steel (HSS) tools are not as efficient and have a spindle speed range of 20-40% lower than carbide tools.
Carbide Tools have higher range, depending on application it is possible to exceed the speed of HSS by 5X.
Not all machines can reach optimal cutting speeds as they have limits on the spindle speed. For example:
A lathe with a 2,000 RPM maximum spindle speed will not be able to reach optimal cutting speeds with materials that need high revolutions.
Calculated speeds are affected by the depth of cut, cooling method, and type of machining operation, turning, milling or drilling. Dry cutting needs lower speeds while coolant cutting allows for higher speeds.
The cutting speed (V) can be expressed as V = (π × D × N)/12 for Imperial units’ surface feet per minute (SFM), or V = (π × D × N)/1000 for Metric units in meters per minute (m/min).
V = ( π * tool or workpiece diameter (D) * Spindle speed (N) ) / 12 ( Imperial Unit )
V = ( π * tool or workpiece diameter (D) * Spindle speed (N) ) / 1000 ( Metric Unit )
D = Tool or workpiece diameter ( inches or millimeters )
N = Spindle speed (RPM)
To calculate the machining speed for a steel workpiece with a 2-inch diameter tool at a spindle speed of 500 RPM:
V = (π × 2 × 500) / 12 ≈ 261.8 SFM.
What is the Importance of Machining Time in Cutting Calculations?
Defining Machining Time
In manufacturing, machining time is of utmost importance because it affects productivity, the expense incurred, and the duration of a given project. Simply put, machining time is the length of time spent in the process of removing material from a workpiece. The importance of accurately calculating machining time lies in it’s positive impacts on optimal machine use, minimized downtime, and effective operation. Machining time is influenced by the following: cutting speed, feed rate, tool diameter, and length of cut. When appropriate cutting parameters that minimize machining time are selected, output increases while quality standards remain unaltered.
How to Calculate Machining Time
To calculate machining time, use the following formula:
Machining Time (T) = Length of the Cut (L) ÷ (Cutting Speed (V) multiplied by Feed Rate (F))
Length of the Cut (L) is the distance traveled by the cutting tool throughout the material it needs to cut through, usually expressed in mm or inches.
Cutting Speed (V) is the movement rate of the cutting tool in relation to the workpiece. It is given in meters per minute (m/min) or feet per minute (ft/min).
Feed Rate (F) is the distance a machine tool moves in relation to the workpiece in a given time interval, either during a single rotation (revolution) or a minute’s time. It is measured in millimeters per revolution (mm/rev) or inches per revolution (in/rev).
Estimating machining times accurately requires precise measure of these parameters. The values of cutting speed and feed rate are usually obtained from material properties, tool features, and recommended cutting conditions. Nevertheless, reliable estimates also need to consider tool changes and setup variations.
Factors Affecting Machining Time
Cutting Speed – The tool’s engagement with an object has a specific velocity that facilitate its machining. Choosing the most effective cutting speed ensures efficiency and integrity of the material.
Feed Rate – The tool advancement per single turn determines over a defined period the amount of material the tool is able to remove, which affects the speed and accuracy.
Depth of Cut – The depth range of a layer removed during a single pass determines the total number of cuts and leads to defining the time required to perform the entire operation.
Material Properties – Machining speed of harder materials should be lower, while softer materials can be processed more quickly.
Tool Condition – Compared to cutting tools with wider edges, sharp, well-maintained tools, improve efficiency and reduce the total time needed for machining.
How to Determine the Right Cutting Speed?
Ways to Measure Cutting Speed
When determining a cutting speed, there are multiple factors to consider and a few calculations to make. The cutting speed (V) is most often determined by the following equations:
- V = (π × D × N) / 12 (imperial)
- V = π × D × N / 1000 (metric)
- V is the cutting speed in surface feet per minute (SFM) or meters per minute (m/min).
- D refers to the workpiece or cutting tool’s (in inches/millimeters) diameter.
- N is the spindle speed in revolutions per minute (RPM).
Always look up the manufacturer’s recommendations or cutting speed charts corresponding to the material in question and the tool material. These days, there are cutting edge dynamic cutting speed calculators or software tools that help greatly by taking into account many issues such as tool wear, material changeability, and machine constraints.
Cutting Speed and the Role of a Calculator
To compute cutting speed with a calculator, use the following equations:
- Cutting Speed (V) = π × D × N ÷ 12(for inches)
- Cutting Speed (V) = π × D × N ÷ 1000 (for millimeters)
- In this instance equations, V is the cutting speed.
- D is the diameter of the work piece or the cutting tool.
- N is the spindle speed.
Check that the units are accurate and check with the manufacturer or material data for speed value accuracy.
The Relationship between Cutting Speed and Machining Process Time
Machining process time is influenced by cutting speed because of the correlation between cutting speed, the amount of material being removed, and time. In most cases, more material being cut translates to less time spent machining. Higher cutting speed actively decreases machining time provided the heat generated by the tool and the wear and tear on the tool itself are within acceptable boundaries. Boldly high cutting speeds, however, can lead to reduced tool lifespan and poor quality of the work piece. Finding a balanced approach that observes the attributes of the material in question and tooling recommendations is essential.
How to Calculate the Depth of Cut?
Understanding Depth of Cut
The depth of cut refers to the thickness of the layer of material that is being cut off in one stroke of the cutting tool. It is one of the important factors in machining operation because it affects the speed of machining and the cutting force. The depth of cut can be estimated from the following equation:
Depth of Cut (DOC) = (Initial Workpiece Diameter – Final Workpiece Diameter) / 2
This formula is valid for covering linear processes like milling or turning and assures correct estimation of the material layer being cut off. Tool stiffness, machine capability, and workpiece material also need to be considered when determining DOC because if set too high, it may shorten tool lifespan, create vibration, and yield bad surface quality. In general, recommended depth of cut values can be found on tooling charts of vendors in many cases.
Strategies and Instruments Done to Compute Depth of Cut
For the meticulous measurement of cut depth, the application of precise tools and techniques is required. The following illustrates some of the primary tools to achieve this goal.
Most people use Calipers measuring the first and the last diameters of the workpiece since it has a high level of accuracy. The digital variant of these devices has the best readings of up to ±0.001 inches which improves measurement confidence.
To achieve more accurate readings, especially with smaller changes in diameter, micrometers prove to be useful tools. These devices are more precise, allowing an accuracy value of ±0.0001 inches making them suitable for high precision machining processes.
With the advancement of modern technology, most CNC machines today come with integrated probing systems and these automated systems determine and check the depth of cut done. This mitigates the chance for human error and assists in guaranteeing accuracy during operations.
Let us take this example to discuss further:
Initial Diameter of the workpiece = 100 mm
Final Diameter of the workpiece = 80 mm
Using previous stated data,
Depth of Cut (DOC) = (100 mm – 80 mm) / 2 = 10 mm
Optimizing Depth of Cut for Efficiency
When optimizing the Depth of Cut (DOC), it is important to keep in mind the material properties, tool shape, and even the sturdiness of the machine. An optimal DOC is usually recommended for harder materials in order to keep the tool from excessively wearing and ensure dimensional accuracy. Softer materials, on the other hand, may be able to withstand a deeper DOC which is beneficial in terms of efficiency. Furthermore, more suitable cutting speeds and feed rates which are in accordance with the prescribed DOC, can enhance tool life as well as the quality of the surface finish. Now, advanced CAM software provide real-time recommendations by simulating toolpath and stress analysis to set optimal DOC values without the need for trial and error, expediting machining workflows.
What is the Process to Calculate Cutting Force?
The Significance of Cutting Force in Machining Processes
The cutting force is perhaps the most important factor during machining processes. This is because it is directly responsible for tool wear, energy consumption, and quality of the final workpiece. The cutting force can be determined with the following formula:
Cutting Force (Fc) = Specific Cutting Force (kc) x Chip Cross-sectional Area (A)
Specific Cutting force (kc): This is a constant value that is dependent on the material and is normally expressed in N/mm². It changes with the level of hardness and machinability of the workpiece material.
Chip Cross-Sectional Area (A): It can be calculated using the formula:
A = Depth of cut (ap) x Feed per tooth (fz) x Number of teeth (z)
Example of Calculation:
Let’s consider machining of a steel workpiece using the following parameters:
Material-specific cutting force (kc) = 2,100 N/mm2
Depth of cut (ap) = 2 mm
Feed per tooth (fz) = 0.1 mm
Number of active teeth (z) = 5
Now replace the variables in the chip cross sectional area equation:
A = 2 mm x 0.1 mm x 5 = 1 mm2
Now compute the final cutting force:
Fc = 2,100 N/mm2 x 1 mm2 = 2,100 N
Cutting power (Pc) is computed using the following relation:
- Pc = Fc x vc / 60,000
- Fc = Cutting force (N)
- vc = Cutting speed (m/min)
- Using the next parameters:
- Cutting force: Fc = 2100 N
- Cutting speed: vc = 150 m/min
- Putting the values into the equation:
- Pc = 2,100 x 150 / 60,000 = 5.25 kW
Applications of Cutting Force Calculations in Machining
Cutting force calculations are of utmost importance for some of the machining processes, for example those related to tool design, machine selection, process optimization, etc. The separate calculations of these forces are very important for the efficient operation of the machine tool.
When establishing the cutting force (Fc), engineers are able to evaluate if the cutting tool material and design are compatible, meaning they can efficiently sustain the forces during machining processes.
A high Fc, for instance, would require the use of carbide tools rather than high-speed steel if tool wear and breakage are to be prevented.
Cutting force (Fc): 3,000 N
Tool material tensile strength requirement >3,500 N/mm²
The power needed for a particular cutting operation is calculated through Pc computation to determine if a specific tooling machine will suffice without causing an overload. The machine power rating should be greater than the calculated Pc for the machine to operate efficiently.
Cutting power (Pc): 7.5 kW
Machine’s installed power capacity ≥ 10 kW
Surface Roughness and Tolerance
The optimization of cutting forces makes vibration control better, and this leads to improvements in surface finish and dimensional accuracy of the final product. Choosing the right parameters through lower cutting force helps improve tool deflection and surface defacement.
Feed per tooth (fz): 0.08 mm
Cutting speed (vc): 120 m/min
Achieved surface roughness Ra ≤ 1.5 µm
Proper derivation of cutting forces leads to economical cutting conditions, which results in lower energy expenditure, prolonged tool life, and reduced cost incurred.
Reduced energy expenditure by 15 percent when optimized Pc = 6 kW
Increased tool life from 60 minutes to 80 minutes per tool due to decreased Fc = 2,500 N.
Frequently Asked Questions (FAQs)
Q: What is the importance of using a formula in CNC machining?
A: In CNC machining, formulas are important since they are used to measure cutting speed, feed rate, and machining time. These measurements facilitate accurate calculations for efficiency, precision, and safety in the cutting process. This guarantees the CNC machine operates optimally while producing high-quality workpieces.
Q: How do you calculate the feed per tooth in CNC milling?
A: Feed per tooth in CNC milling is calculated with the formula: Feed per Tooth = Feed Rate per Minute / (Number of Teeth on the Cutting Tool x Rotational Speed). This measurement is essential in knowing how much material is removed by each tooth of the cutting tool, assisting with the efficiency of removing material during the cutting process.
Q: What is the role of speed and feed in CNC machining?
A: Speed and feed having a dependable role in CNC machining because they determine the cutting speed and feed rate respectively, needed to calculate the surface speed{s} and material removal rate{m}. When these parameters are correctly adjusted, there is improvement in the performance of the machine tool, decrease tool wear, and an enhanced surface quality of the workpieces.
Q: How is cutting speed determined from the spindle speed?
A: To determine the cutting speed from the spindle speed, the formula Cutting speed = (π x Diameter of the Workpiece x Spindle Speed) / 1000 can be applied. The operator estimate the tool engagement speed with the work piece, enabling efficient cutting process. In this setting, cutting speed is defined as the tool engagement speed with the workpiece.
Q: How is table feed significant in CNC milling?
A: Table feed defines the position of the work piece in relation to the motion of the cutting tool and it is very important to make sure that the required dimensions and surface are met. Accurate estimation of table feed enables balance between efficiency in material removal and the life cycle of the tool.
Q: What is the method of calculating feed per revolution on the CNC lathe turning machine?
A: In CNC turning, the feed per revolution is calculated using the equation: feed per revolution = feed rate/spindle speed. This calculation is essential for determining the quantity of material that is processed during each spindle revolution, which is fundamental in attaining the desired accuracy in turned workpieces.
Q: What is the formula for calculating machining time in CNC operations?
A: The time allocated for machining can be determined using the equation maching time: Machining time = ( length of cut / feed rate per minute). This formula is necessary for calculating the time sought for the tool to perform a cut’s pass over the surface of the workpiece which contributes to effective CNC operations’ time management.
Q: What are the consequences of implementing constant surface speed in CNC machining?
A: Constant surface speed is a characteristic of CNC machining in which the spindle speed is adjusted throughout the operation so that there is a set speed at which the material is cut as the diameter changes. This helps in ensuring that the workpiece is machined efficiently for material removal as well as for achieving desired surface finish which considerably increases effectiveness and quality of the cutting process.
Q: How are rotational speed and cutting speed related to each other in CNC machines?
A: Rotational speed and cutting speed are connected in CNC machines since the cutting speed relies on the spindle’s rotational speed and the workpiece’s diameter. Using the correct formula, machinists can find the cutting speed to make the cutting process more efficient, thus increasing the effectiveness and precision of machining tasks.
Reference Sources
- Direct calculation of Johnson-Cook constitutive material parameters for oblique cutting operations
- Authors: Nam Nguyen, A. Hosseini
- Journal: Journal of Manufacturing Processes
- Publication Date: April 1, 2023
- Citation: (Nguyen & Hosseini, 2023)
- Summary: This study presents a method for directly calculating the Johnson-Cook material parameters specifically for oblique cutting operations. The authors focus on the significance of accurately determining these parameters to improve the predictive capabilities of cutting models. The methodology involves experimental validation and computational simulations to derive the parameters effectively.
- Calculation and analysis of quasi-dynamic cutting force and specific cutting energy in micro-milling Ti6Al4V
- Authors: Yabo Zhang et al.
- Journal: The International Journal of Advanced Manufacturing Technology
- Publication Date: April 5, 2022
- Citation: (Zhang et al., 2022, pp. 6067–6078)
- Summary: This paper investigates the quasi-dynamic cutting forces and specific cutting energy during the micro-milling of Ti6Al4V. The authors employ a combination of experimental and analytical methods to derive cutting force models that account for the unique characteristics of micro-milling processes. The findings highlight the influence of cutting parameters on force and energy consumption, providing insights for optimizing micro-milling operations.
- Optimal calculation and experimental study on cutting force of hypoid gear processed by generating method
- Authors: Chuang Jiang et al.
- Journal: The International Journal of Advanced Manufacturing Technology
- Publication Date: February 9, 2021
- Citation: (Jiang et al., 2021, pp. 1615–1635)
- Summary: This research focuses on the cutting force calculations for hypoid gears processed using generating methods. The authors present both theoretical calculations and experimental validations to optimize the cutting process. The study emphasizes the importance of accurate cutting force predictions in enhancing the efficiency and quality of gear manufacturing.
