# Mathematical statistics and machining pre quantity of distortion law in gear manufacturing process

#### 1. Statistics of distortion data

The distortion of batch gear production has statistical characteristics. In the mass production of gears, the distortion data is counted as normal distribution curve. There are two distribution forms in the figure, distribution 1 is more dispersed than distribution 2. The above measures are adopted to control the dispersion of gear distortion to the smallest possible range, as shown in the distribution of curve 2 in the figure.

#### 2. Adjustment of gear processing size

After all kinds of measures are taken to control the gear distortion fluctuation to a certain extent, the machining dimension adjustment before heat treatment, i.e. the reservation of machining allowance, can be implemented in gear production through the statistics of distortion data. Master the distortion rule of heat treatment and adjust the size of gear before heat treatment to compensate the distortion of heat treatment. This is a common method for mass production of gears.

50 gears are commonly used in production for cold processing and heat treatment under certain conditions. After measuring the geometric parameters of the gears before and after heat treatment, and statistical processing of the data, according to the distortion law, then move the tolerance zone position, and determine the machining dimension tolerance before heat treatment according to the following formula:

The upper limit value of some parameters before heat treatment = the upper limit value of the tolerance of the finished gear – the maximum size distortion that may be caused by heat treatment;

The lower limit value of some parameters before heat treatment = the lower limit value of the tolerance of the finished gear – the minimum size distortion that may be caused by heat treatment;

By subtracting the above two formulas, we can get:

Tolerance range of finished gear = tolerance range of gear before heat treatment + tolerance range of heat treatment distortion.

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