Determination of machining allowance after quenching of outer ring of carburized steel bearing
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**Determination of Machining Allowance After Quenching of the Outer Ring of a Carburized Steel Bearing**
Home > Bearing Knowledge > Determination of Machining Allowance After Quenching of the Outer Ring of a Carburized Steel Bearing
Source: China Bearing Network | Time: 2013-02-03
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After carburizing and quenching, the outer ring of a steel bearing often experiences a phenomenon known as "elastic retraction." This refers to the slight shortening of the part after it is removed from the mold. Elastic retraction is a critical factor that must be considered in machining processes, especially when determining the remaining material for grinding.
This article discusses the calculation of elastic retraction for the outer ring of a carburized steel double-row tapered roller bearing. It also covers how to determine the remaining machining allowance after turning, estimate the theoretical grinding amount post-quenching, and provides an example for better understanding.
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### 1. Calculation of Elastic Retraction
From production theory, the amount of elastic retraction is influenced by the wall thickness and diameter of the workpiece. An empirical formula has been established:
$$ d = \frac{26B^4}{D^3} \quad (1) $$
Where:
- $ B $: Maximum wall thickness of the workpiece
- $ D $: Outer diameter of the bearing ring
- 26: A coefficient derived from repeated theoretical analysis under rotary quenching conditions
This formula applies to workpieces with an outer diameter between 200 and 300 mm.
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### 2. Determining the Remaining Material After Turning
The machining allowance after turning is affected by the elastic retraction. The greater the retraction, the more material needs to be left for subsequent grinding. Based on theoretical analysis, the remaining allowance after turning ($ H?D_1 $) is proportional to the thickness-to-diameter ratio of the workpiece:
$$ H?D_1 = 0.042 \times \frac{D}{B} \quad (2) $$
Here, the coefficient 0.042 is derived from extensive theoretical studies.
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### 3. Estimating the Theoretical Grinding Amount After Quenching
The theoretical grinding amount after quenching is calculated by adding the remaining machining allowance after turning to the elastic retraction value:
$$ H?D_2 = H?D_1 + d \quad (3) $$
This ensures that sufficient material is left for final grinding, even after the part shrinks during quenching.
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### 4. Example Calculation
Let’s take the outer ring of a 197726 bearing as an example:
- Maximum wall thickness $ B = 18.85 \, \text{mm} $
- Outer diameter $ D = 230.9 \, \text{mm} $
- Machining allowance after turning $ \Delta D_1 = 0.65 \, \text{mm} $
Using the formulas:
- **Elastic retraction**:
$ d = \frac{26 \times (18.85)^4}{(230.9)^3} = 0.266 \, \text{mm} $
- **Remaining allowance after turning**:
$ H?D_1 = 0.042 \times \frac{230.9}{18.85} = 0.514 \, \text{mm} $
- **Theoretical grinding amount**:
$ H?D_2 = 0.266 + 0.514 = 0.78 \, \text{mm} $
However, the original value of $ \Delta D_1 = 0.65 \, \text{mm} $ did not match the actual measured grinding amount of 0.9 mm. After adjusting $ \Delta D_1 $ to 0.5 mm, the calculated value (0.78 mm) closely matched the measured result (0.76 mm), proving the revised value is more accurate.
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It is important to ensure that the size of the quenching die matches the turning diagram. Theory shows that the shrinkage caused by quenching is sufficient to achieve the desired shape, making precise machining allowances essential for quality control.
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