1 Introduction Grinding is a widely used precision machining method. In the study of grinding, due to the limited understanding of the processing mechanism, the actual adjustment of the grinding process is mostly based on trial and error (ie, based on a large amount of experience accumulated by the operator), especially The grinding temperature analysis model is mostly obtained through single factors. With the ever-increasing performance of computers, the application of simulation technology in the industry has become more and more extensive, and new ideas have been brought to the research of grinding theory, making it possible to overcome the limitations of traditional research methods and to study the grinding process in depth. The change of the grinding temperature in the system establishes a theoretical model of the grinding temperature field. Simulation is to realize and predict the performance and characteristics (dynamic and static) of a product under real-world conditions in a simulation environment. It includes a series of steps from modeling, applying loads and constraints, and predicting the product's response under real conditions. By observing and estimating the simulation test process, the simulated output parameters and basic characteristics of the simulated system are obtained, from which the real parameters and real performance of the actual system are estimated and inferred. Simulation technology With the aid of a computer, it is possible to obtain various changes of the grinding temperature field under different input parameters in a complex grinding process, thus creating conditions for further research on the grinding machining mechanism. 2 Establish a mathematical model of the grinding temperature field The finite element method is used to establish a mathematical model of the grinding temperature field. Since the entire grinding temperature field satisfies the law of conservation of energy, the heat transfer equation for the grinding temperature field is:
PC ∂q - ∂ (kx ∂q )- ∂ (ky ∂q )- ∂ (kz ∂q )-rQ=0 ∂t ∂x ∂x ∂y ∂y ∂z ∂z (in W) where W is The entire domain, which consists of three types of boundary conditions, namely: q=q( l,t) (on the l1 boundary) kx ∂q nx+ky ∂q ny+kz ∂q nz=q ∂x ∂y ∂z ( On the G2 boundary) kx ∂q nx+ky ∂q ny+kz ∂q nz=a(qa -q) ∂x ∂y ∂z (at the G3 boundary) According to the principle of discretization of the finite element method, the workpiece is divided Into a limited number of units, the thermal load during the grinding process is added to the unit on the boundary, that is, the overall temperature load is discreted into a node load equivalent to the actual load, and the grinding temperature field is obtained by substituting the above three types of boundary conditions. The finite element model. The field function temperature of the grinding temperature field is both a function of the spatial domain W and a function of the time domain t. In the simulation model, the cyclical iteration method is used to discretize the loading process of the thermal load into a finite number of extremely short processes (the time domain and the spatial domain are considered to be coupled in a single process). Take dry-grinding as an example, load a fixed heat flow in a certain grinding zone in a very short time, move to another zone and load a fixed heat source in the next time, and use the result obtained from the last time as the initial of this analysis. In this very short period of time, the temperature of the field function is considered to be related to time and space, but the two are not coupled, so that a mathematical model of the grinding temperature field as follows can be derived using a partial discretization method:
Where: r - material density c - material specific heat t - time kx, ky, kz - material thermal conductivity in the x, y, z direction q - given temperature on the G1 boundary, q = q (G,t) q—a given heat flux at the boundary of G2, q=q(G,t) a—convective heat transfer coefficient qa—is the ambient temperature under natural convection conditions; the forced convection condition Next, the temperature of the insulation wall for the boundary layer. Qa=qa(l,t) The above formula divides the partial differential equations in the time domain and space domain into the initial value problem of the ordinary differential equations with temperature q(t) in the spatial domain. Solving the n linear ordinary differential equations, and obtaining the node temperature array, the temperature distribution of the entire workpiece can be obtained. This formula is suitable for both dry and wet grinding conditions. 3 Simulation process and results of grinding temperature field Taking the surface grinding temperature field as an example, a simulation model of the grinding temperature field is established. As shown in Fig. 1, assume that the grinding contact arc zone is ABB'A', and the surface heat source length l≈(dsap) is 1â„2 parallel to the direction of workpiece motion.
Fig.1 Heat source diagram of workpiece surface
Figure 3 Simulation process of grinding temperature field
Fig.2 Schematic diagram of grinding temperature field of TC4 workpiece during dry grinding
Fig. 4 Comparison of dry and wet grinding simulation and test results at different depths under the surface layer
Enter each grinding process parameter, and finally obtain the three-dimensional isotherm map of the grinding temperature field through the operation of the simulation model. By changing the size of each parameter to compare the changes in the output temperature field, you can clearly understand the influence of the parameter change on the temperature field. For dry grinding of difficult-to-machine materials TC4 titanium alloy workpieces, the grinding amounts are as follows: wheel speed ns=143r/min, wheel diameter ds=245.2mm, wheel speed vs=18.46m/s, workpiece speed vw=14m/ Min=23.33cm/s, grinding depth ap=0.01mm, cut into grinding. The test piece width b = 10mm, length l = 170mm. The average tangential grinding force Ft=66.001N. The temperature field of the workpiece is shown in Figure 2. Similarly, a schematic diagram of the wet grinding temperature field can be obtained after the boundary conditions of the convection heat transfer are loaded, and the error is within 10% after the comparison with the measured temperature. Fig. 3 is a schematic diagram of the simulation process of the grinding temperature field. Fig. 4 is a comparison of the dry grinding and wet grinding simulation and test results at different depths under the surface layer. It can be seen from Figure 4 that under the same grinding conditions, the maximum temperature difference between dry and wet grinding is very large (usually between 200 and 300 °C), especially when the surface temperature gradient of the workpiece is large, and the dry grinding It is easy to cause burns, and the temperature during wet grinding is much lower than the burn temperature of the workpiece. The results obtained by using the simulation model are not significantly different from the measured values, and the error is within 10% (the results obtained from the simulation analysis are approximately 10% higher than the measured values). This is because the temperature test specimen itself has errors, and the measured temperature is a certain depth from the surface layer of the workpiece, so the simulation results are closer to the actual temperature value of the workpiece. 4 Conclusions In the study of grinding temperature field, computer simulation technology can accurately obtain the overall grinding temperature distribution map, thereby reducing the error caused by the use of test instruments. The resulting isothermal map is more simple and intuitive. At the same time, due to the complexity of the grinding temperature field, it is easier to analyze the effect of different machining parameters on the temperature of the grinding arc region by using the simulation model, and thus find out the variation law of the grinding temperature field. The application of simulation technology can also optimize the grinding temperature field: under the conditions of changing the processing parameters, the temperature of the grinding temperature field tends to be reasonable, thereby reducing the generation of grinding burns. The computer simulation technology of the grinding temperature field not only applies to various popular high-performance grinding technologies, but also lays a good foundation for the simulation of the whole grinding process.
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