Based on Kogut and Etsion’s model (KE model), a statistical method is used to establish a model of normal contact stiffness of fixed joint surface during unloading after first loading. Simulation results show that, for the elastoplastic contact, normal contact stiffness of joint surface is the nonlinear function of mean surface separation during loading and unloading and decreases as the separation increases. For different plasticity indexes, the normal contact stiffness of joint surface varies differently following the change of mean surface separation during loading and unloading.

The machine tool is the mother of manufacturing industry, which is assembled by various components. There are some parts that contact each other, namely joint surface. Among them, the fixed joint surface is one of the widely existing joint surfaces. Research showed that [

At present, many scholars at home and abroad have studied the loading and unloading model of fixed joint surfaces. In 2002, Lin and Yui [

Because of this, based on the finite element contact model of Kogut and Etsion [

Figure

Contact deformation diagram of a single asperity with a rigid plane.

The critical deformation of a single asperity

When

Therefore, the critical contact load of a single asperity

According to equation (

When

Similarly, the normal contact stiffness of a single asperity during this loading is obtained as follows:

When

According to [

When

When

Schematic diagram of a deformed asperity before and after loading and unloading.

According to [

The residual deformation

By substituting equations (

In the same way, the plastically deformable asperity does not recover. There is no contact stiffness during unloading.

In [

Based on Greenwood and Williamson’s model (GW model), this paper assumes that there is no interaction between asperities, and all deformation is limited to the contacting asperities. So, the fixed joint surface is equivalent to the contact between a rough surface and a smooth rigid plane, as shown in Figure

Schematic diagram of contact between a rough surface and a smooth rigid surface.

The relation of the ratio

Assuming that there are

The distribution function

The dimensionless distance

The random dimensionless interference of a single asperity can be expressed as follows:

In this paper, the plastic index form proposed by GW is adopted:

According to equation (

The dimensionless form of equation (

The normal contact stiffness of joint surface during unloading can be expressed as

The dimensionless form of the above equation is

It can be seen from equation (

Dimensionless surface roughness parameters [

Number | ||
---|---|---|

1 | 0.0339 | |

2 | 0.0476 | |

3 | 0.0541 | |

4 | 0.0601 |

Influence of

It can be seen from Figure

In order to verify the effectiveness of the normal unloading contact stiffness model of joint surface established in this paper, a comparative analysis is made between the model in this paper and the model in [

A comparison between the unloading model in this paper and that in [

In this paper, a statistical model of the normal contact stiffness of fixed joint surface during unloading after the first load is established, and a simulation analysis is carried out on the model to study the influence of the mean surface separation on the normal contact stiffness. The findings are as follows:

Dimensionless loading and unloading normal contact stiffness decreases with the increase of the dimensionless mean surface separation for different plastic indexes.

The smaller the plastic index is, the less obvious the difference between loading and unloading caused by plastic deformation would be. Therefore, the normal contact stiffness curve during unloading is close to that during loading. On the contrary, with the increase of plastic index, the normal contact stiffness during unloading is obviously less than that during loading.

However, the larger the plastic index is, the slower the loading normal contact stiffness decreases, while the faster the unloading normal contact stiffness decreases.

Unfortunately, our paper did have some limitations and shortcomings, which will be verified by supplementary experiments in the future.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by Shanxi Provincial Natural Science Foundation of China (Grant no. 201901D111248), Shanxi Provincial “1331” Engineering Key Discipline Construction Project of China, and Shanxi Provincial Graduate Education Innovation Project of China (Grant No. 2020BY112).