Understanding the Calculation Methods of Centrifugal Casting

Centrifugal casting is a specialized casting process in which liquid metal is poured into a rotating mold. Throughout the entire process of metal filling and solidification, the mold continues to rotate at a certain speed or with step-wise changes in speed.

The centrifugal force acting on the liquid metal causes it to flow along the wall of the metal mold, resulting in relative slip flow. During this process, gases and impurities generated move towards the central area of the casting, resulting in a denser structure and higher strength.

Due to these process advantages, centrifugal casting is particularly suitable for the production of cylindrical castings in single or batch quantities. Common centrifugal casting products include pipes, liners, sleeves, piston rings, pulleys, and large nuts.

Centrifugal casting can be divided into vertical and horizontal types. In the former, the axis of rotation is aligned with the direction of gravity, while in the latter, the axis of rotation is horizontal and perpendicular to the direction of gravity.

In these two cases, the interaction between gravity and centrifugal force is different, leading to differences in the calculation of centrifugal casting speeds. This needs to be paid special attention to.

The impact of centrifugal casting speed on casting quality:

Centrifugal casting speed directly affects defects such as porosity, inclusion, shrinkage, and segregation in the casting. Additionally, the circularity of the casting and the density of the internal structure are also closely related to the speed.

Due to the nature of rotation itself, the centrifugal force experienced by the outer periphery of the casting is greater than that experienced by the inner portion. Therefore, centrifugal casting products are more prone to segregation. Increasing the speed helps increase the turbulence of the metal liquid, forming a self-stirring effect, partially offsetting the adverse effects of segregation, and promoting uniformity of the crystalline structure, which is beneficial for reducing early-stage “cloud spot” segregation.

In addition, insufficient speed may lead to a phenomenon known as “raindrop,” where the alloy liquid cannot adhere to the surface of the previously poured alloy liquid, resulting in longitudinal cracks on the outer surface.

Of course, the speed should not be too high either, as excessively high speeds pose strict challenges to the manufacture and installation of centrifugal machines. This not only affects machine lifespan but also, if accuracy is insufficient, can even cause violent mold oscillation, resulting in major safety incidents.

Summary of Centrifugal Casting Speed Calculation Methods

There are more than 20 methods for calculating centrifugal casting speeds, most of which are based on mold type, casting size and thickness, alloy type, etc. In this article, we mainly introduce five commonly used calculation formulas.

Method 1: Konstantinov’s Formula

Konstantinov believed that regardless of the type of metal melt, when the “effective gravity” on the inner surface of the casting reaches 3.4×10^6 N/m^3, it ensures the production of centrifugally castings with fine-grained structure. The mold rotation speed is calculated using the following formula.

n: Mold rotation speed (r/min);
R: Inner surface radius of the casting (m);
γ: Alloy gravity (N/m^3);
β: Adjustment coefficient (can be selected according to the table below).

Table 1: Konstantinov Adjustment Coefficient β Quick Reference Table

Type	β
Copper alloy horizontal centrifugal casting bushing component	1.2~1.4
Copper alloy vertical centrifugal casting ring component	1.0~1.6
Cast iron bushing component	1.2~1.5
Cast steel sleeve component	1.0~1.3
Aluminum alloy bushing component	0.9~1.1

Method 2: Bruneau’s Formula Calculation

Bruneau’s formula calculates the centrifugal casting speed using a gravity coefficient.

n: Mold rotation speed (r/min);
R: Inner surface radius of the casting (m);
G: Gravity coefficient, which can be checked according to the table below.

Table 2: Bruneau’s Gravity Coefficient Quick Reference Table

Casting Name	G	Casting Name	G
Hollow Cold Hardened Roll	75~150	Bearing Steel Ring	50~65
Internal Combustion Engine Cylinder Liner	80~110	Cast Iron Pipe (Sand Mold)	65~75
Large Cylinder Liner	50~80	Cast Iron Pipe (Metal Mold)	30~60
Steel-backed Copper Sleeve	50~60	Double-layer Centrifugal Cast Pipe	10~80
Steel Pipe	50~65	Aluminum-silicon Alloy Complete Set	80~120

Note: In theory, a value of 20 for G is sufficient for the formation of cylindrical and tubular castings, but in practice, values much higher than this are used, as shown in the table above.

Method 3: Kamen Formula

n: Mold rotation speed (r/min);
R: Inner surface radius of the casting (m);
C: Comprehensive coefficient, which can be checked according to the table below.

Casting Alloy	Alloy Density (g/cm³)	Casting Name	Centrifugal Casting Method	Comprehensive Coefficient (C)
Cast Iron	7.2	Pipe, Expansion Ring	Horizontal	9000~12500
Cast Steel	7.85	Cylinder Liner	Horizontal	10750~13650
Yellow Brass	8.20	Ring	Horizontal	10000~11000
Brass	8.8	φ90~φ120mm	Horizontal	13500
Lead Bronze	9.5~10.5	Bearing	Horizontal	8500~9500
Babbitt Alloy	7.3~7.5	Bushing	Horizontal, Horizontal	7000~9000
Aluminum Alloy	2.65~3.10	–	–	1300~17500
Bronze	8.4	–	Horizontal	17000

Note: The comprehensive coefficient (C) can be checked according to the table above.

Method 4: Non-metallic Mold Rotation Speed Calculation Formula

n: Mold rotation speed (r/min);
P: Maximum centrifugal pressure that non-metallic molds can withstand (MPa), refer to Table 4 for details;
γ: Alloy density (kg/m^3);
R_outer, R_inner: Outer and inner diameters of the casting (m).

Table 4: Quick Reference Table for Maximum Centrifugal Pressure (P) Values in Non-metallic Mold Rotation Speed Calculation

Mold Type	Core Making Type	Maximum Centrifugal Pressure (P) (MPa)
Sand Mold	Green Sand	0.003~0.004
	Shell Molding	0.004~0.006
Ceramic Mold	–	0.006~0.008

Note: This calculation formula primarily ensures that the mold is not damaged by centrifugal forces, so rotational speeds exceeding the calculated results may pose a risk of mold damage.

Method 5: Calculation of Mold Rotation Speed Based on Upper and Lower Tolerances of Casting Inner Hole

n: Mold rotation speed (r/min);
P: Maximum centrifugal pressure that non-metallic molds can withstand (MPa), refer to Table 4 for details;
γ: Alloy density (kg/m^3);
D, d: Permissible radii of the casting inner hole (m).

In vertical centrifugal casting, the rotation axis is in the vertical direction. Therefore, insufficient rotation speed may result in differences in the diameter of the casting inner hole. The actual rotation speed used should be greater than the calculated rotation speed.

Among the five calculation formulas mentioned above, except for Konstantinov’s formula, which is derived precisely, the other formulas are empirical and have strong applicability constraints. The selection of coefficients also has a considerable range. Typically, it is believed that a deviation in rotation speed of less than 15% will generally not have a significant impact on the quality of the casting during the casting process.

Due to historical reasons, Konstantinov’s formula is more commonly used in China and the former Soviet Union, while Bruneau’s formula and Kamen’s formula are more widely used in Europe and the United States.

Product Details Reference Material To learn more.