# Mathematical model for predicting the torque during tapping using FEM simulation

### Significance Statement

Tapping, a machining operation, is normally used for a majority of areas of application and materials. This process represent the last stage for a component production. Tool breakage normally happens due to excessive torque and may lead to costly wastage of materials. The tapping process is complicated with high requirements on tool producers. Unfortunately, it is one of the least understood machining methods. For this reason, forecasting tool performance by simulation appears to be of utmost research interest.

The finite element machining simulation is fundamental in the improvement and optimization of production processes, tools, and work pieces. Implementing the Finite Element Method can help predict several basic values including tensions, process forces, strains, wear and surface attributes. To apply the predictive models for industrial applications effectively, these variable values should be correlated with the force measurements for the power.

Ekrem Oezkaya and Dirk Biermann at the Institute of Machining Technology in Germany developed an approach, which is suitable to predict the relative torque during the design phases. In this way, it was possible to simulate the tapping process in a reasonable computing time for the first time and thus contribute to the research effort of moving forward the 2-D to 3-D simulation development. Their research work is published in International Journal of Mechanical Sciences.

The researchers used different tapping tools with M8 and 1.25 pitch in a bid to establish the torque. To compute a realistic torque out of the dynamic cutting forces, the authors considered the entire chamfer length, which is a function of lead angle.

The 3-D finite element simulation of the tapping process requires a long computing time, resulting from the especially high complexity of tool and workpiece geometries. The authors presented the development of a 3-D finite element tap simulation model for computing time reduction and a mathematical model for the evaluation with experimental results.

A computing time reducing segmentation of the 3D model was carried out. The authors achieved the best results when they used the developed segmented model 4. In their study this model was simulated in the length of a chamfer, implementing a workpiece with a volume circle segment of 15°. The resulting simulated torque course consisted of local maximum torques peaks originating from the discontinuous contact between tool and workpiece, due to the modified model geometry.

With the deployment of the mathematical model, the mean torque of the local maximum partial torques was accumulated to a global maximum torques. Comparing the results of segmented model 4 with the basic evaluation indicated excellent outcomes with only a few marginal variations.

The resulting method of their study was applied in the developed finite element-based software system named ToolSimulation and created the possibility of simulating the 3D tapping process and predicting the relative torque before the production of tool prototypes. The proposed method by Oezkaya and Biermann offers a reliable tool for estimating the relative torque and will be fundamental for design engineers to save energy, resources, and cost.

### About the author

Dr.-Ing. Ekrem Oezkaya has been a research assistant at the Institute of Machining Technology at the TU-Dortmund since 2011. His main research fields are in the development of an FEM-based software system, the development of a simulative model for the influence analysis of cooling lubricant in the field of tool development and optimization using CAD, FEM and CFD simulation and the 3D simulation of the thread drilling process.

### About the author

Prof. Dr.-Ing. Dirk Biermann is director of the Institute for Machining Technology at the TU-Dortmund. His research areas cover all relevant machining processes and the information technology environment in machining. In addition, various modeling concepts, as well as optimization in production technology are the focus of his scientific work, which are elaborated in direct cooperation with partners from the industry.

### Reference

Ekrem Oezkaya and Dirk Biermann. Segmented and mathematical model for 3D FEM tapping simulation to predict the relative torque before tool production. International Journal of Mechanical Sciences, volume 128–129 (2017), pages 695–708.