Interaction of process and machine in grinding of hard and brittle materials such as cemented carbide may cause dynamic instability of the machining process resulting in machining errors and a decrease in productivity. Commonly, the process and machine tools were dealt with separately, which does not take into consideration the mutual interaction between the two subsystems and thus cannot represent the real cutting operations. This paper proposes a method of modeling and simulation to understand well the process-machine interaction in grinding process of cemented carbide indexable inserts. First, a virtual grinding wheel model is built by considering the random nature of abrasive grains and a kinematic-geometrical simulation is adopted to describe the grinding process. Then, a wheel-spindle model is simulated by means of the finite element method to represent the machine structure. The characteristic equation of the closed-loop dynamic grinding system is derived to provide a mathematic description of the process-machine interaction. Furthermore, a coupling simulation of grinding wheel-spindle deformations and grinding process force by combining both the process and machine model is developed to investigate the interaction between process and machine. This paper provides an integrated grinding model combining the machine and process models, which can be used to predict process-machine interactions in grinding process.
High performance cutting tools play an important role in modern manufacturing. To some extent, the performance of a cutting tool determines the cutting behavior and the process capability. With recent developments in aerospace and automobile industries, there are increasing demands for high-quality parts [
Due to the hardness of cemented carbide cutting tools are mainly manufactured by grinding process. Grinding is one of the most common material removal processes to achieve desired surface integrity, dimensional tolerance, and form tolerance. It is used as a typical finishing process as well as for high material removal rates. In the grinding process, the machine tools and process constitute a closed loop machining system. The generated cutting forces and temperature cause elastic deformations in the machine tool system which change the instantaneous chip area which in turn has an influence on the cutting forces.
During precision machining, the dynamic interactions between machining process and grinding machine structure, for example, vibrations, deflections, or thermal deformations, result in poor quality of produced parts, short life of machine components and tools [
In order to meet requirements of high accuracy and productivity in grinding of cemented carbide cutting tools, it is essential to understand well the interaction between the process and the machine tool system linked with the force and the deformation. The interaction between process and machine is usually hard to predict due to its complexity, and extensive experiments are laborious and expensive. In many cases, predictions can only be made by means of complex simulations [
The prediction of process-machine interactions requires models of machine and process. To predict the interactions these models have to be built and then coupled and simulated. Due to the large number of abrasive grains with unknown time-dependent geometry and distribution, grinding is a complex material-removal process [
The simulation of cutting processes under consideration of process and machine properties can be carried out along with different methods. The coupled simulation was a relatively new approach which permits simultaneous usage of two different simulation environments with data exchange by means of a suitable interface [
In this paper, the interaction of process and machine in cemented carbide insert grinding is studied. The authors propose a geometric-kinematical simulation and a wheel-spindle model based on finite element method. Furthermore, a couple simulation approach which treats the grinding process and machine tool structure in an integrated manner is presented. Also, an investigation of the results of process-machine interaction is described.
A kinematic-geometrical simulation model (KSIM) is adopted in this research work, which was first developed by Warnecke and Zitt [
To gain realistic simulation results the grinding wheel topography has to be modeled precisely. The topography of a diamond wheel in a stationary wear state was measured by using a KEYENCE VHX-5000 3D-measuring system. Figure
Topographies of grinding wheel.
In order to avoid the overlapping between abrasive grains in the binder, a virtual grid approach is used to account for the random nature of the grinding wheel. Assuming abrasive grains are distributed in a square area of the grinding wheel and each grain is restrained in an imaginary grid, see Figure
Virtual grids of abrasive grains distribution.
The major components of the topography of grinding wheel are abrasive grains and bonds. Since only the grains participate in actual cutting process, the influence of binds is neglected in modeling. For modeling the grinding, a real diamond 12A2T grinding wheel in stationary wear state with a dimension of Φ400 × 4.8 mm was used as archetype; see Figure
Virtual grinding wheel archetype.
Random position coordinates of grains.
Modeled grinding wheel section.
With the grinding wheel model at hand, simulations for different combinations of the input grinding parameters can be conducted. In the simulation, ideal cutting is assumed neglecting ploughing and friction effects; therefore the process force at a given time depends linearly on the cutting depth based on Kienzle approach:
Cemented carbide cutting insert grinding.
The exemplary parameter combination of cutting speed 42 m/s, depth of cut 0.02 mm, and feed rate 300 mm/min was chosen to show and explain the results of simulation. In Figure
Simulated process force.
For an exact simulation of the mutual interaction between grinding process and machine, the machine structure has to be modeled accurately. Therefore the machine model has to be able to respond to excitations coming from the grinding process and to create an output which again has an influence on the calculated grinding process. Since the modeling of a complete machine is usually very complex and time consuming, if some of the machine components react to an excitation by the grinding process, a selective model can be adopted [
Material properties of spindle and wheel hub.
Steel | 40Cr | |
---|---|---|
Density [kg/m3] | 7890 | 7870 |
Young modulus [GPa] | 209 | 211 |
Poisson’s ratio | 0.269 | 0.277 |
Wheel-spindle FE model.
Point contact.
For parameterising the wheel-spindle model, static and dynamic behavior of the real machine must be measured and characterized accurately. A modal experiment was conducted by using an impact hammer instrumented with a piezoelectric transducer and an accelerometer. Then the measured eigenfrequencies were compared with the results of the modal analysis by using commercial FEA software to verify and validate the related FE model. All eigenfrequencies extracted from FE simulations are well matched to the experimental data; see Table
Eigenmodes 1–5 extracted from experimental data and FE simulations.
Mode | Experiment [Hz] | FE model [Hz] | Difference [%] |
---|---|---|---|
1 | 220 | 215.62 | 1.99% |
2 | 330 | 353.64 | 7.16% |
3 | 780 | 753.23 | 3.43% |
4 | 950 | 929.53 | 2.16% |
5 | 1050 | 1019 | 2.95% |
Assuming the dynamic displacements of machining system under excitation of grinding process forces at a given time will be
In order to simulate the interaction of grinding process and machine structure, a coupling simulation method is adopted in this work. In coupling simulation, both simulations run simultaneously in different simulation environments and communicated to each another in synchronized cycles [
Coupling simulation of process-machine interaction.
A simulation cycle is developed in a coupling simulation. First, a simulated force signal generated by the process model starts as input data for the machine model. The machine model delivers displacements related to the contact zone for one wheel revolution, which again constitutes input data for the process model. Equation (
Data exchange and convergence for iteration process.
Iteration convergence behavior.
A fast Fourier transform of the force signal in Figure
FFT-transform of force signal.
Considering the force and deformation in one wheel revolution, the coupling simulation between grinding wheel and process is performed in a set of harmonic grinding depths with a fixed amplitude of 20
Effective force and displacement.
Initial force and effective force.
In this paper, a method of modeling and simulation for process-machine interaction in grinding of cemented carbide indexable inserts was presented.
A center coordinate adjusting method and a virtual grid method were adopted to model the topographies of grinding wheel. The methods proposed in this work take account of the random nature of abrasive grains and were able to avoid overlapping between abrasive grains in the binder in modeling. With the grinding wheel model at hand, a process model base on KSIM was able to generate forces as input data in process-machine interaction. A wheel-spindle structure was selected and modeled by means of finite element method. The dynamic characteristic of the model was then verified by experimental modal analysis, which proves to match well with the experimental results.
The characteristic equation of the closed-loop dynamic grinding system was derived to account for the inner-relation of process and machine. A coupling simulation with an iteration algorithm was proposed to investigate the process and machine interaction. In the coupling approach, process and machine structure were dealt with in an integrated manner and interacted in synchronized cycles. Dynamic interaction of grinding forces and grinding wheel deformations were then investigated based on the proposed simulation method. It shows that the grinding wheel deformations have an influence on the cutting forces. The coupling method serves as a useful tool to understand well the interaction phenomenon in grinding of cemented carbide indexable inserts.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was financially supported by the Science and Technology Innovation Project of Shannxi Province under Grant no. 2014KTDZ01-04, and the Science and Technology Major Special Project of China under Grant no. 2011ZX04003-021.