Determining the minimum cooling rate required for quenchants

An old-school method can be used to either select a new oil for a new process, or to determine if an existing oil is adequate to heat treat a new part.


In this column, I will illustrate a method to determine if a cooling rate from a cooling curve is adequate to achieve required properties.


When looking at an application for a quenchant, there are many factors to consider, including achieving the desired properties, cost, ease of cleaning, disposal, and distortion or residual stresses. Arguably, the most important of these factors is whether the existing oil or a prospective oil is adequate to meet the required properties needed. In this short article, I will try to demonstrate one quick method of determining the adequacy of a quenchant.

The first thing to determine is the required properties at the center of surface of the part. Often, for a given part configuration the hardness is given a proscribed depth, such as at the center, surface, or someplace in between. For instance, in AMS 2759 [1], there is a requirement in paragraph under Quench System Monitoring that a 1.5-inch (381 mm) diameter bar that is 4.5” (1,143 mm) long, shall have a hardness of HRC 44 minimum at the center, and at the ¾ radius position, have a hardness of HRC 50 minimum.

Concept of Equivalent Round

Knowing that this specimen is round vastly simplifies things. However, parts are rarely round bars, and often complex shapes. A method is needed to simplify the shape to determine a simple shape for calculations. One such method is that of an Equivalent Round. This method takes an arbitrary shape and determines a round bar dimension that would have similar thermal properties. This is useful, not only for determining the equivalent round for estimating quenching properties, but also useful for determining soaking time during austenitizing and tempering.

The Jominy curve for the alloy (in this case SAE 4140) is obtained. For SAE 4140H, the Jominy curve is shown in Figure 1.

Figure 1: Jominy curve for SAE 4140H from [3].

From AMS 2759, the required hardness at the center of the bar is HRC 44, and at the ¾ radius, the hardness required is HRC 50 minimum. Looking at the curve for the hardness at the minimum values on the Jominy curve, we see that the hardness of 50 HRC corresponds to a distance from the quenched end of 6/16”, and the center hardness of 44 HRC corresponds to 9/16” from the quenched end.

Once the center and 3/4¾radius Jominy End Quench positions have been determined, it is necessary to determine the equivalent round. Using the chart in Figure 2, we can determine the equivalent round of our part. Since our test piece is already specified as 1.5” in diameter, we can skip this step.

Figure 2: Equivalent round for simple shapes. For plates where the length is less than the thickness T, the section is a plate of L thickness. And the equivalent round size is 1.5L, otherwise, the equivalent round is 1.5T. For tubes of any section that are open at both ends, when the length is less than the diameter, then the thickness is a plate of T thickness. If the length is less than the thickness T, the section is a plate of L thickness. For restricted tubes of any section that are restricted or closed at one end, when the diameter is less than 2.5” (635 mm), the equivalent round is 2.5 the thickness. If the diameter is greater than 2.5” (635 mm), then the equivalent round size is 3.5 times the thickness T (after [4]).
Figure 3: Lamont chart correlating quench rate required (H-value), Jominy End Quench distance, and bar diameter (from [3]).

The next step is to consult the Lamont charts [2]. The charts from the original paper can be used, or those found in other publications, such as the Timken Practical Guide for Metallurgists [3]. This booklet is very useful, and available for free from their website. A consolidated Lamont chart is shown in Figure 3.

From this chart, at a 1.5” diameter, the H-Value that corresponds to a center Jominy distance of 9/16” is an H-value of 0.35. For the 3/4” radius, the H-value required to obtain hardness at a 5/16” Jominy distance would be an H-value of 0.5. Since 0.5 is the fastest quench rate required, this is the value we will use.

Determination of H-Value from Cooling Curve

In a previous column [5], I discussed the determination of H-Value from cooling curve data. I refer you to that article for a more detailed explanation of the determination of Grossman [6] H-Value. Simply put, the H-value is a value that correlates to the rate of heat extraction of different quenchants, and it has been classically defined as:

where h is the heat transfer coefficient at the surface of the part (usually defined at 705°C or 1,300°F), k is the thermal conductivity of the steel. Since the thermal conductivity of steels does not change appreciably over temperature, or from one alloy grade to another, the Grossman H-Value is approximately proportional to the heat transfer coefficient.

To make things easier, I have calculated the effect of cooling rate at 705°C on H-Value for a wide range of cooling rates. This is shown in Figure 4. From this graph, the determination of the H-Value from the cooling curve can be determined directly.

Figure 4: Correlation of the cooling rate at 1,300°F and the Grossman H-Value [5].

For the example at hand, the 1.5” diameter SAE 4140 steel bar needs at least an H-value of 0.5 at the 3/4 radius. Looking at Figure 4, and drawing a horizontal line from an H-value of 0.5 to where it intersects the curve, and then drawing a line vertically, the required cooling rate is approximately 90°F/s (50°C/s) at 1,300°F. Table 1 shows typical cooling rates for several different oil-based products.

Table 1: Cooling rates at 705°C for a slow, medium, and fast quench oil, compared to water, without agitation. Oils were tested at 60°C, while water was tested at ambient temperature.

For this application to meet the required 3/4 radius hardness requirement required an H-value of 0.5. This corresponds to a cooling rate at 1,300°F of 95°F/s (52.7°C/s).

Examining Table 1, the slowest oil that achieves this quench rate is Houghto™-Quench G. Remember that cooling curves for oils
are measured without agitation. Agitation speeds up the heat extraction rate and the H-value. It is possible, with adequate agitation, that a slower oil could be used to achieve the necessary hardness. However, this estimate is conservative, and should meet requirements readily.


In this column, I have described an old-school method to determine the cooling rate necessary to achieve the desired hardness in a heat-treated part. A method was described to simplify a complex geometry, and to estimate the needed cooling rate of an oil. This method can be used to either select a new oil for a new process, or to determine if an existing oil is adequate to heat treat a new part.


  1. SAE International, AMS 2759G, Heat Treatment of Steel Parts, General Requirements, Warrendale, PA: SAE International, 2018.
  2. J. L. Lamont, “How to Estimate Hardening Depth in Bars,” Iron Age, no. 10, pp. 64-70, 1943.
  3. Timken Company, Timken Practical Guide for Metallurgists, 14th ed., Canton, OH: Timken Company, 2015.
  4. Department of Defense, MIL-H-6875H, Heat Treatment of Steel, Process For, 1989.
  5. D. S. MacKenzie, “Determining Grossman H-Value from cooling curve data,” Thermal Processing, no. February, pp. 21-23, 2020.
  6. M. A. Grossman, M. Asimov and M. F. Urban, “Hardenability, Its Relationship to Quenching and Some Quantitative Data,” ASM Transactions, pp. 124-190, 1939.