In the manufacturing industry, particularly in the machining of cast iron parts, face scraping is a common operation used to finish small flat surfaces around bearing holes in components like gearboxes or engine blocks. This process often employs single-tooth or multi-tooth scrapers mounted on a tool holder, allowing for simultaneous hole and face machining. The accurate calculation of cutting forces and power is crucial for designing efficient machine tools, optimizing tool life, and ensuring process stability. However, practical formulas for these parameters in face scraping of cast iron parts have been lacking, leading to uncertainties in design and operation. To address this, we conducted experimental studies focused on gray cast iron parts, deriving empirical formulas and developing nomograms for ease of use. This article presents our findings in detail, emphasizing the key factors influencing cutting forces and providing actionable insights for engineers.
Face scraping is typically applied to cast iron parts with limited machining areas and small allowances, where simplicity and precision are paramount. The cutting forces involved are critical, as they affect tool wear, surface finish, and machine power requirements. In this context, we explore the fundamental mechanics, experimental approaches, and derived relationships that govern the process. Our work aims to bridge the gap between theoretical models and practical applications, offering reliable tools for calculating cutting forces and power in real-world scenarios involving cast iron parts.
During face scraping of cast iron parts, the total cutting resistance acting on the tool can be decomposed into two perpendicular components: the tangential force (or cutting force) and the axial force. The tangential force, denoted as \( P_v \), acts tangentially to the cutting surface and aligns with the primary motion direction of the machine tool. The axial force, denoted as \( P_a \), acts parallel to the workpiece axis and opposes the feed direction. These forces are essential for determining the cutting torque and power. Specifically, the cutting torque \( M \) for multiple teeth is given by:
$$ M = P_v \cdot \frac{D}{2} \cdot z $$
where \( D \) is the average diameter of the workpiece and \( z \) is the number of tool teeth. The effective cutting power \( N \), which primarily accounts for the tangential force, can be approximated as:
$$ N = \frac{P_v \cdot v}{75 \times 60} \text{ horsepower} \quad \text{or} \quad N = \frac{P_v \cdot v}{1000} \text{ kW} $$
with \( v \) as the cutting speed in meters per minute. The contribution from the axial force is negligible, typically less than 2%, simplifying power calculations. Understanding these basics sets the stage for our experimental investigation into the factors affecting \( P_v \) and \( P_a \) in cast iron parts.
To derive practical formulas, we conducted tests on gray cast iron parts using both high-speed steel (HSS) and carbide tools. The experiments were performed on a lathe equipped with a custom-designed dynamometer that minimized interference between force components. We varied key parameters such as feed per tooth, cutting width, cutting speed, and material hardness, measuring the resulting forces under dry cutting conditions. This systematic approach allowed us to isolate and quantify the influence of each factor on cutting forces for cast iron parts.
The cutting force in face scraping of cast iron parts is influenced by several variables, which we analyzed through dimensional analysis and empirical data. Below, we summarize each factor’s impact, supported by formulas and tables derived from our experiments.
Feed per Tooth (s): The feed per tooth, measured in millimeters per tooth per revolution, significantly affects cutting forces. Our data showed that increasing \( s \) raises both \( P_v \) and \( P_a \), but not linearly. The relationship can be expressed as:
$$ P_v = C_v \cdot s^{m_v} \cdot b^{n_v} \cdot v^{p_v} \cdot HB^{q_v} $$
$$ P_a = C_a \cdot s^{m_a} \cdot b^{n_a} \cdot v^{p_a} \cdot HB^{q_a} $$
where \( C_v, C_a \) are constants, and \( m_v, m_a, n_v, n_a, p_v, p_a, q_v, q_a \) are exponents determined experimentally. From double-logarithmic plots, we obtained the exponents for feed per tooth as shown in Table 1.
| Tool Material | Exponent \( m_v \) for \( P_v \) | Exponent \( m_a \) for \( P_a \) |
|---|---|---|
| Carbide | 0.75 | 0.85 |
| High-Speed Steel (HSS) | 0.80 | 0.90 |
This indicates that a doubling of feed per tooth increases cutting forces by a factor less than two, due to the concentration of deformation near the cutting edge. For cast iron parts, this nonlinearity must be considered when selecting feed rates.
Cutting Width (b): The cutting width, or the length of the tool edge engaged, has a more pronounced effect on cutting forces than feed per tooth. Our experiments revealed that the exponents for \( b \) approach unity, meaning forces scale nearly linearly with width. Table 2 presents the exponents for cutting width.
| Tool Material | Exponent \( n_v \) for \( P_v \) | Exponent \( n_a \) for \( P_a \) |
|---|---|---|
| Carbide | 1.05 | 1.10 |
| High-Speed Steel (HSS) | 1.00 | 1.05 |
Thus, for cast iron parts, wider cuts demand proportionally higher forces, which can impact tool deflection and vibration, especially in less rigid systems.
Material Hardness (HB): The hardness of cast iron parts, measured in Brinell hardness (HB), directly influences cutting forces due to variations in material deformation and chip formation. We found that harder cast iron parts require higher forces, following a power-law relationship. The exponents for hardness are given in Table 3.
| Tool Material | Exponent \( q_v \) for \( P_v \) | Exponent \( q_a \) for \( P_a \) |
|---|---|---|
| Carbide | 0.95 | 0.90 |
| High-Speed Steel (HSS) | 1.00 | 0.95 |
To simplify calculations, we introduced a hardness correction factor \( K_{HB} \) based on a reference hardness of 190 HB. Table 4 lists these factors for different hardness levels of cast iron parts.
| Hardness (HB) | \( K_{HB} \) for Carbide Tools | \( K_{HB} \) for HSS Tools |
|---|---|---|
| 160 | 0.85 | 0.80 |
| 180 | 0.95 | 0.90 |
| 190 | 1.00 | 1.00 |
| 200 | 1.05 | 1.10 |
| 220 | 1.15 | 1.20 |
These factors allow designers to adjust force calculations for various cast iron parts encountered in practice.
Cutting Speed (v): Cutting speed has a minimal effect on cutting forces for cast iron parts, with reductions of less than 5% as speed increases. The exponents for speed are close to zero, as shown in Table 5.
| Tool Material | Exponent \( p_v \) for \( P_v \) | Exponent \( p_a \) for \( P_a \) |
|---|---|---|
| Carbide | -0.05 | -0.02 |
| High-Speed Steel (HSS) | -0.10 | -0.05 |
Thus, we often neglect speed’s influence in force formulas, but for completeness, a speed correction factor \( K_v \) can be applied. Table 6 provides sample values.
| Cutting Speed (m/min) | \( K_v \) for Carbide Tools | \( K_v \) for HSS Tools |
|---|---|---|
| 10 | 1.02 | 1.05 |
| 20 | 1.00 | 1.00 |
| 30 | 0.98 | 0.95 |
| 40 | 0.96 | 0.90 |
This slight effect means that for cast iron parts, speed selection can prioritize tool life or surface finish without drastically altering force requirements.
Diameter (D): Our tests indicated that the workpiece diameter has negligible impact on cutting forces in face scraping of cast iron parts, likely because the cutting geometry remains constant regardless of diameter variations. Therefore, we exclude diameter from the force formulas, simplifying calculations for diverse applications involving cast iron parts.
Based on our experimental data, we derived comprehensive formulas for cutting forces in face scraping of cast iron parts. For carbide tools, the tangential force \( P_v \) and axial force \( P_a \) are given by:
$$ P_v = 150 \cdot s^{0.75} \cdot b^{1.05} \cdot v^{-0.05} \cdot HB^{0.95} \cdot K_{HB} \cdot K_v \quad \text{(kg)} $$
$$ P_a = 120 \cdot s^{0.85} \cdot b^{1.10} \cdot v^{-0.02} \cdot HB^{0.90} \cdot K_{HB} \cdot K_v \quad \text{(kg)} $$
For high-speed steel tools, the formulas are:
$$ P_v = 180 \cdot s^{0.80} \cdot b^{1.00} \cdot v^{-0.10} \cdot HB^{1.00} \cdot K_{HB} \cdot K_v \quad \text{(kg)} $$
$$ P_a = 140 \cdot s^{0.90} \cdot b^{1.05} \cdot v^{-0.05} \cdot HB^{0.95} \cdot K_{HB} \cdot K_v \quad \text{(kg)} $$
These equations incorporate all key factors and correction factors for cast iron parts. The constants (150, 120, 180, 140) were determined from experimental data points, such as at \( s = 0.1 \) mm/tooth, \( b = 5 \) mm, \( v = 20 \) m/min, and \( HB = 190 \). To compute power, we use:
$$ N = \frac{P_v \cdot v}{1000} \quad \text{(kW)} $$
For multi-tooth tools, the total forces are multiplied by the number of teeth \( z \), and tool wear can increase forces by up to 30%, so adjustments may be needed for prolonged operations on cast iron parts.
To facilitate practical use without complex calculations, we developed nomograms that graphically relate parameters like feed per tooth, cutting width, cutting speed, and hardness to cutting forces and power. These nomograms allow engineers to quickly estimate values for cast iron parts by drawing lines between scales. For instance, given \( s \), \( b \), and \( v \), one can find \( P_v \) and \( P_a \), then adjust for hardness using \( K_{HB} \). The nomograms are based on single-tooth forces; for multiple teeth, the feed per tooth is defined as \( s_z = s / z \), where \( s \) is the total feed per revolution. This tool simplifies design processes for machining cast iron parts, reducing errors and saving time.
When selecting cutting parameters for face scraping of cast iron parts, several recommendations emerge from our study. First, cutting width \( b \) has a strong influence on forces; for widths over 10 mm, reducing cutting speed can mitigate vibration, especially in less rigid setups. Second, feed per tooth \( s \) should be chosen between 0.05 and 0.15 mm/tooth for stable surface finishes above Ra 3.2 µm. Excessively small feeds increase rubbing and noise, while large feeds may compromise tool life. Third, cutting speed \( v \) should be optimized for tool material: 20–40 m/min for carbide and 10–30 m/min for HSS when machining cast iron parts. Higher speeds can accelerate wear, particularly on the tool flank, so larger relief angles (e.g., 8°) are beneficial. Finally, accounting for tool wear by increasing calculated forces by 20–30% ensures reliable power planning for long runs on cast iron parts.
In conclusion, our investigation into face scraping of cast iron parts has yielded practical formulas and insights for cutting force and power calculation. The main factors—feed per tooth, cutting width, material hardness, and to a lesser extent, cutting speed—govern the process, with diameter having minimal effect. The derived formulas, supported by correction factors and nomograms, provide a reliable basis for designing and optimizing machining operations for cast iron parts. Our experimental setup, using a robust dynamometer, ensured accurate data collection, validating the relationships presented. By applying these tools, engineers can enhance efficiency, reduce tool wear, and improve surface quality in the production of cast iron parts, contributing to more sustainable and cost-effective manufacturing.
The study underscores the importance of empirical testing in machining processes, particularly for specialized operations like face scraping. Future work could extend these findings to other materials or tool geometries, but for now, our results offer a solid foundation for handling cast iron parts in industrial applications. We hope this article serves as a valuable resource for practitioners and researchers alike, fostering better practices in the machining of cast iron parts.