Study of vertical milling machine layout in terms of rigidity

This work presents a new concept of automatic compensation of the ram deformation during its in-cantilever horizontal motion of the milling machines that feature a ram slide (headstock) on the column side. During the ram horizontal motion that is a CNC controlled axis of the machine, there is a permanent modification of the ram gravity center that makes the reaction forces in the guideways to permanently change their rates as well. Thus, an elastic variable deformation occurs on the ram supports along with the elastic deformation of the guideways and the elastic deformation of the ram slide. The new concept of automatic compensation of the elastic deformation presented in this work takes its compensation force from the feed kinematic linkage of the ram, having interdependence between the ram motion length and the rate of the compensation force. The rate of the compensation force taken over from the kinematical linkage is very low, then it is mechanically multiplied (>100 times), until the value needed for the quasi-total compensation of the elastic deformations is reached. The experimental application of this new concept has been done on a milling machine model BFK 1000 CNC, where an increase by 90% of the ram geometrical accuracy while going out in cantilever has been obtained, compared to the case when such a compensation device would be missing.

Statement of the problem. The analysis of the deplanation hypothesis for linear and angular deformations in reinforced concrete in bending with torsion has been carried out. Results. A simple new method from the method of grids has been developed for complex functions under the combined action of bending and torsion. Diagrams of linear and angular deformities and a new hypotheses have been analyzed. Complex functions have been found to determine the linear and angular deformations, bending and torque moments in the compressed area of concrete. The author has found the projection coefficients of linear and angular deformations using diagrams of compressed concrete and main reinforcement. Deplanations from a special geometric figure of deformations in a complex function have been found. There are vectors of several triangles and gradients where the proportions of a hypotenuse, cathetuses and vectors have been derived. Conclusions. It is also important that similar relative values can be obtained for any vectors. A field of small squares have been plotted and jumps from lateral, normal and other cracks appear have been determined. Fillings of the deformation (stress) diagrams have been obtained for the analysis of the moments in bending with torsion using simple expressions or in a full form. The research on the complex function of linear and angular deformations and the approximation of a function from Timoshenko-Goodyear have been carried out. The error of the deformations value of using the complex function at the points under study is 2% and is 7% at any points of the cross section.

This paper presents an integrated machining error compensation method based on captured images of tool deflection shapes in flat end-milling processes. This approach allows us to avoid modeling machining characteristics (cutting forces, tool deflections and machining errors etc.) and accumulating calculation errors induced by several simulations. For this, a high-speed camera captured images of real deformed tool shapes which were cutting under given machining conditions. Using image processes and a machining error model, it is possible to estimate tool deflection in cutting conditions modeled and to compensate for machining errors using an iterative algorithm correcting tool paths. This corrected tool path can effectively reduce machining errors in the flat end-milling process. Experiments are carried out to validate the approaches proposed in this paper. The proposed error compensation method can be effectively implemented in a real machining situation, producing much smaller errors.

The high-performance machining of curved surfaces is a highly critical process that is crucial in modern engineering applications. Different methodologies and CAM tools have been developed by manufacturers to improve the efficiency of the sculptured surface milling. The determination of appropriate tool path strategies and milling conditions is crucial in ensuring a high productivity rate, meeting the bettersurface texture values, and lower cutting forces, tool deflection, and surface errors. The objective of this research is to analyse the effect oftool path strategies on dynamic tool deflection, cutting forces, machining time, effective cutter diameter (ECD), cutter/workpiece engagement (CWE) area, instantaneous material removal rate (IMRR), and machining errors in rough machining of a sculptured surface. The B-rep solid modeling-based simulation and the optimization system were developed and integrated with the commercial CAD/CAM software for 3-axis ball-end milling. The experimental results clearly show the influence of the cutter path strategies on machining times and their importance for reducing time needed and, consequently, costs. It was observed that the profiles of deflection, IMRR values, cutting forces, machining errors and ECD values match very well for cutting strategies. Machining strategies employed include various degrees of zig-zag, profiling, and spiral. The conclusion is that the 90° zig-zag strategy provokes the lowest cutting forces, tool deflection, and surface error values. The in-house NC simulation system performed well in determining values and the location of milling form errors on the surface.

Study of Deformations Field in the Working Zone of Vertical Milling Machine

In the 1st part of this investigation, the analysis of tool deflection and locus of tool axis during ball end milling along a contour line was presented. In the paper, cutting force data predicted by using the cutting model proposed in a previous paper and the Finite Element Method were used for analyzing the deformation of a tool. In this paper, tool deflection in the milling of an inclined surface is measured under various slopes of the surface and compared with the predicted results. The predicted results agree with the measured results well enough. Geometrical configurations of the machined surface and the machining errors obtained from the analysis are shown for various slopes of the inclined surface. It is found that machining errors disagree with the magnitudes of deflection of the tool axis in a plane normal to the feed direction, so the errors can't be evaluated by neglecting the condition of cutting edge engaged with the workpiece such as rotational angle and tool geometry. The machining error caused by tool deflection becomes small for milling of an inclined surface where the left side of the feed direction is higher.

Virtual manufacturing systems can provide useful means for products to be manufactured without the need of physical testing on the shop floor. As a result, the time and cost of part production can be decreased. There are different error sources in machine tools such as tool deflection, geometrical deviations of moving axis and thermal distortions of machine tool structures. Some of these errors can be decreased by controlling the machining process and environmental parameters. However other errors like tool deflection and geometrical errors which have a big portion of the total error, need more attention. This paper presents a virtual machining system in order to enforce dimensional, geometrical and tool deflection errors in three-axis milling operations. The system receives 21 dimensional and geometrical errors of a machine tool and machining codes of a specific part as input. The output of the system is the modified codes which will produce actual machined part in the virtual environment.

Depending on cutting conditions, unacceptable machining errors are caused by tool deflection in end milling operations. Many studies have proposed methods for predicting the machining error owing to the tool deflection to achieve the theoretical optimization of the cutting conditions. However, the conventional machining error simulation is not practically utilized to determine the optimal cutting conditions. Tool system stiffness parameters and cutting coefficients must be identified in advance to simulate machining errors. However, dynamometers and displacement sensors are required for parameter identification. Therefore, it is impossible to identify the required parameters in typical factories, which do not possess such special equipment. In this study, a practical method was developed to identify the stiffness parameters that can be determined in factories. The proposed method employs on-machine measurement and sensor-less cutting force monitoring to achieve practical parameter identification. In the proposed method, the profile milling is first conducted. During the milling operation, the cutting force and cutting torque are monitored through a controller based on the sensor-less monitoring technique. After the operation, the machining error distribution on the machined surface is measured on machine using a touch probe. The required parameters are identified by minimizing the differences between the measured and theoretical forces, torques, and machining error distributions.

It is well known that the total machining errors of the engine cylinder liner are mainly dominated by the elastic deformation caused by the cutting force and the thermal expansion caused by the temperature rise during the boring process. Clarification of the amount of machining errors resulting from the cutting force and thermal expansion is useful for determining whether thermal expansion or the cutting force has a larger influence on machining errors during the boring process. This would provide a clear approach to the optimization of cutting conditions or to product improvement, leading to a higher degree of machining accuracy. In this paper, in order to clarify the amount of machining errors, the machining error caused by the thermal expansion apart from the elastic deformation of a cylinder liner caused by the cutting force was first determined. For this purpose, an experimental method is suggested in this paper. The temperature rise that causes the thermal expansion of the cylinder liner was simulated by a YAG laser heating process instead of by an actual boring process. During this heating process, the machining errors caused by the thermal expansion could be solely investigated. First, an actual cylinder boring process was performed (cutting speed: 900 m/min, feed rate: 0.2 mm/rev, depth of cut: 0.3 mm, dry cutting). The total machining errors caused by the cutting force and thermal expansion were measured. Then, the YAG laser heating experiment was also carried out. Comparing the results between the two experiments, it was clarified that the thermal expansion of the cylinder liner caused by the cutting energy is dominant and the deflection caused by the cutting force is small.

Introduction. The paper proposes a method of accounting for energy dissipation for the Timoshenko beam by constructing a damping matrix based on a modified Rayleigh function in the numerical solution of the problem. In this modification, the velocity of displacements is replaced by the velocities of linear and angular deformations. This approach allows us to take into account energy dissipation due to internal friction in the material when both its volume and shape change. The presented technique is promising in practical calculations of structures when shear stiffness has a significant impact on their stress-strain state. Materials and methods. Several proven methods of energy dissipation accounting are considered, including those that make it possible to take into account the energy loss of a moving structure during friction with the external environment (external damping) and dissipation due to friction in the material of the structure deformed in motion (internal damping). Methods for determining the damping coefficients for each of them are presented. The finite element method is used to calculate rod systems. Damping matrices are derived from the condition of stationarity of the total energy of deformation of a mechanical system in motion, including linear and angular deformation rates. Results. Damping matrices proportional to strain rates obtained on the basis of the modified dissipative Rayleigh function are given. A method for determining the damping coefficient taking into account the rates of angular deformation is proposed. Conclusions. The damping matrices presented in the paper describe the energy dissipation during vibrations of mechanical systems due to internal friction in the material. The internal damping matrix was obtained taking into account the influence of linear and angular deformation rates to simulate the dynamic behaviour of short bending structural elements, the deformation of which is described using the Timoshenko model. The performed dimensional check additionally confirms the correctness of the damping matrix construction. Moreover, the dimension of the proposed shear damping coefficient is the same as that of the widely used viscosity coefficient.

In this research, a novel and generalized analytical expression of cutting force and tool deflection in end milling is presented as a function of tool rotational angle and other cutting parameters. The discontinuous cutting force function caused by periodic tool entry and exit is changed to an integrable continuous function using Fourier series expansion. Tool deflection is also formulated explicitly by the direct integration of the distributed loads along the helical cutting edges. Cutting conditions, tool geometry, runout components, and the stiffness of tool clamping part are considered in estimating the cutting force and tool deflection. Cumbersome computational procedures needed to check whether segmented cutting edges are engaged in cutting or not are eliminated by this proposed method. The presented analytical approach has advantages in flexibility, prediction time, and accuracy as compared with other numerical techniques. In addition, the effects of cutting conditions and run-outs, such as eccentricity and tilting on the cutting force and tool deflection, can be analyzed quantitatively in the time domain or frequency domain. The validity and effectiveness of the suggested method are verified through a series of cutting tests. The model presented in this research can be used in real-time machining error estimation and cutting condition selection for error minimization since the form accuracy is easily estimated from the acquired tool deflection curve.

The influence of the parameters of the elastic system of the finishing and boring machine on static deformations, oscillations and accuracy of fine boring is studied. Based on experimental studies of the effect of spindle imbalance with a boring rod on machining accuracy, a method was developed for calculating deviations from roundness caused by the action of cutting forces and centrifugal forces on elastic systems with anisotropic rigidity. Static errors and deformation features in the closed dynamic system of the machine were also studied. The total deviation from roundness caused by elastic deformations is calculated as the sum of static and dynamic components. The mean values of the imbalance me, the mean square deviations of χ and the deviation of the maximum values of the imbalance memax to the permissible [me] are given. The effect of imbalance on the roughness of the treated surface has been established. Since the increase in deviations from roundness is caused by the ovalization of the hole, the reason for the violation of the accuracy of the cross-sectional shape with an increase in the transverse force is the anisotropy of the radial rigidity of the elastic system of the machine. Testing units of the same standard size under the same conditions, the ovalization of the holes does not remain constant, therefore, the anisotropy of elastic properties is associated with the individual quality of the spindle assembly, namely, with the accuracy of individual parts of the unit and their assembly.

This paper presents a real-time tool deflection compensation technique to improve micromilling machining accuracy. Lateral and axial errors of the cutter location (CL) caused by tool deflection were estimated using the cutting force and compensated by applying an additional feed to the workpiece that is equivalent to the estimated CL errors. To evaluate the proposed method, a workpiece holder comprising a three-axis stage and a tool dynamometer was installed on the work table of a machine tool. A proportional derivative (PD) position controller with a model-based tool deflection estimator was designed and implemented on a real-time computer to control the workpiece holder. Lateral and axial machining errors in side milling and radii errors in circular slot milling are discussed to demonstrate the effect of tool deflection compensation.

Virtual manufacturing systems carry out the simulation of manufacturing processes in digital environment in order to increase accuracy as well as productivity in part production. There are different error sources in machine tools, such as tool deflection, geometrical deviations of moving axis, and thermal distortions of machine tool structures. The errors due to tool deflection are caused by cutting forces and have direct effects on dimensional accuracy, surface roughness of the parts, and efficient life of the cutting tool, holder, and spindle. This paper presents an application of virtual machining systems in order to improve the accuracy and productivity of part manufacturing by monitoring and minimizing the tool deflection error. The tool deflection error along machining paths is monitored to present a useful methodology in controlling the produced parts with regard to desired tolerances. Suitable tool and spindle can also be selected due to the ability of error monitoring. In order to minimize the error, optimization technique based on genetic algorithms is used to determine optimized machining parameters. Free-form profile of virtual and real machined parts with tool deflection error is compared in order to validate reliability as well as accuracy of the software.

A typical aircraft panel is the assembly consisting of a multitude of thin and lightweight compliant parts. In panel assembly process, part-to-part locating scheme has been widely adopted in order to reduce fixtures. By this locating scheme, a part is located onto the pre-fixed part/subassembly by determinant assembly (DA) holes, and temporary fasteners (e.g., spring pin) are used for joining these DA hole-hole pairs. The temporary fasteners can fasten DA hole-hole pairs in the axial and radial directions of DA holes. The fastening in the radial directions is realized by the expansion of temporary fasteners. Although the usage of temporary fasteners helps reduce the positional differences between hole-hole pairs, their clamping forces thereby may lead to elastic deformation of compliant parts/subassemblies. Limited research has been conducted on such elastic deformation produced by temporary fastener and its influence on assembly dimensional quality. This paper proposes a novel rigid-compliant variation analysis method for aircraft panel assembly, incorporating the deformation in part-to-part locating process. Based on the kinematic theory and linear elasticity deformation assumption, the variation propagation through the locating process, as well as the entire assembly process of an aircraft panel, is formulated. Then, the statistical variation analysis is performed with Monte Carlo (MC) simulation. Finally, the proposed method is validated by a case study. The result shows the deformation in the part-to-part locating process significantly impacts the assembly variations, and our method can provide a more accurate and reliable prediction.