The geometric errors of rotary axes are crucial error sources of a five-axis machine tool. They directly affect the machining accuracy, and therefore become one of the most important items for ...accuracy design. In this paper, a prediction and identification method for the geometric errors of rotary axes on a five-axis machine tool is proposed. The prediction is realized by calculating the mapping relationship between tolerances and geometric errors of rotary axes, which is based on exploring rotary axes’ motion regulation and Fourier series fitting. Then in order to figure out the practical geometric errors of rotary axes, the identifying model is established based on homogeneous transform matrix (HTM). Double ball-bar (DBB) is adopted to test error motions of rotary axes. Finally, a demonstration experiment has been conducted for verifying the effectiveness and precision of the proposed prediction model. The experimental results show that the predicting model is able to reflect the motion principle of rotary axes’ kinematic errors. The SSE, which expresses residual sum of squares between estimated value and identified point, of
ε
z
(
c
),
δ
x
(
c
),
ε
y
(
c
),
δ
z
(
c
),
ε
x
(
c
), and
δ
y
(
c
), are 7.7716 × 10
−11
, 1.2064 × 10
−4
, 2.7838 × 10
−10
, 2.9639 × 10
−7
, 1.8966 × 10
−10
, and 2.7838 × 10
−10
, respectively. And
R
2
, who represent fitting equation’s coefficient of determination, of abovementioned geometric errors, are 0.8978, 0.9876, 0.9978, 0.9453, 0.9985, and 0.9978, respectively. The computing results show that two kinds of curves are basically coincide, and the proposed method is proven to be feasibility.
The machining precision of grinding machine determines the precision of parts. To improve the machining accuracy, an effective geometric error modeling and compensation method was proposed. Firstly, ...the comprehensive error model of grinding machine was established based on differential theory. In contrast to the multi-body system theory, the proposed modeling method can simplify the calculation process and reflect the influence of each component on the tool. Secondly, MATLAB curve fitting tool was used to fit the known error function, and a link between 24 basic geometric error terms (BGETs) and milling instructions was discovered using the sum of sine function. Finally, the compensation dosage (dx dz db dc) for the grinding machine comprehensive error was determined by combining 24 fitting functions, the known error, the differential matrix of each part, and the Jacobian matrix. To test the feasibility of the above method, the grinding machine geometric error compensation experiment was conducted. The average machining accuracy is increased by 15.948%. It is showed that the proposed method can realize the error compensation of CNC grinding machine well.
This paper proposes a new iterative compensation methodology of geometric errors to improve the machining accuracy of a non-orthogonal five-axis machine tool (NOFAMT). Firstly, based on homogeneous ...transform matrix (HTM) and multi-body system (MBS) theory, the relative motion constraint equations (TRMCEs) of the tool tip position and tool orientation vector related to a NOFAMT with a nutating rotary B axis are established. Then, by utilizing TRMCEs, the mapping relationships between tool path and the numerical control (NC) command without and with considering the geometric errors are constructed respectively. In order to truly reproduce tool motion trajectory of the machine tool driven by the given NC command, the mapping relationship between the NC command and tool cutting trajectory is also established. Meanwhile, procedures of iterative compensation are described by using the aforementioned mapping relationships without the traditional inverse calculation, and the actual NC code is generated in self-developed compensation software. It is not difficult to find that the new approach takes the difference between tool path and tool cutting trajectory as the control objective and can directly obtain the actual NC code controlling the machine tool to achieve the desired machining accuracy. Finally, a cutting test is carried out on the DMU60P NOFAMT. Experimental results show the developed iterative compensation methodology is precise and effective for NOFAMTs. Therefore, compared with the existing methods, the new method is more direct and accurate. And its basic idea can be applied to other type of machine tools.
•First, the relative motion constraint equations of a non-orthogonal five-axis machine tool are established.•Second, the mutual mapping relationships between tool path, NC command and tool cutting trajectory are established respectively.•Third, a new iterative compensation methodology is presented.•Fourth, a cutting experiment is proposed to verify the machining accuracy improvement of the researched machine tool.
•The influence mechanism of geometric errors on the form errors of S-shaped test piece is investigated.•The quantitative interval sensitivity analysis method for identifying key geometric errors at ...different intervals is proposed.•The compensation for the identified key geometric errors is conducted and verified by the simulation and experiment.
Error compensation is a common method to improve the machining accuracy of five-axis machine tools (FAMTs). Before that, in order to identify the key geometric errors that affect the machining accuracy, sensitivity analysis (SA) in entire machining region or a specified point is usually used. However, since the influence of geometric errors on form errors is different in each interval, the result of SA would be affected, which decreases the compensating accuracy. For this reason, a new approach for accuracy enhancement of FAMTs based on quantitative interval sensitivity analysis (QISA) is presented in this paper. First, based on multi-body system theory and homogeneous transform matrix, the volumetric error model of the FAMT is established. Then, the geometric error model of the FAMT is formulated. Second, development of form error model is involved in this paper to clarify the effect law of geometric error on form error. Moreover, the machining region of S-shaped test piece is divided into five intervals. Then, the QISA method is presented to calculate the sensitivity index of each geometric error and identify key geometric errors at different intervals. Finally, simulations and experiments are conducted to validate the feasibility and effectiveness of the presented method.
This paper proposes an integrated geometric error prediction and compensation method to eliminate the positioning inaccuracy of tool ball for a double ball bar (DBB) caused by the translational axes’ ...geometric errors in a multi-axis machine tool (MAMT). Firstly, based on homogeneous transform matrix (HTM) and multi-body system (MBS) theory, the positioning error model only considering the translational axes of a MAMT is established. Then, an integrated error parameter identification method (IEPIM) by using a laser interferometer is proposed. Meanwhile, the identification discrete results of geometric error parameters for the translational axes are obtained by identification experiments. According to the discrete values, the optimal polynomials of 18 position-dependent geometric errors (PDGEs) are founded. As a basis, an iterative compensation method is constructed to modify the NC codes generated with the ordinary compensation method in self-developed compensation software. Finally, simulation verification is conducted with these two compensation methods. Simulation results show the positioning errors for test path of tool ball calculated with the iterative compensation method that are limited within 0.001 mm, and its average accuracy and accuracy stability are improved by 79.5 and 52.2%, respectively. In order to further verify the feasibility of the presented method, a measuring experiment is carried out in
XY
plane of a five-axis machine tool by using DBB. The experiment results show that the maximum circularity error with the iterative compensation method is reduced about 40.4% than that with the ordinary compensation method. It is therefore reasonable to conclude that the proposed method in this paper can avoid the influence of the translational axes’ geometric errors on rotary ones during a DBB test.
Geometric error is one of the important errors that affect the machining of five-axis machine tools and how to identify th8e vital geometric error is effective for compensation. For this reason, the ...global sensitivity analysis of geometric errors for five-axis machine tools is an effective means to find the vital geometric error items that affect the machining accuracy of machine tools. However, it is difficult to deal with the higher order items of error parameter coupling in the global sensitivity analysis. In this paper, a novel global sensitivity analysis method for vital geometric error based on multi-body theory and truncated Fourier expansion is proposed. First, multi-body system (MBS) and homogeneous transformation matric (HTM) methods are used to establish the position error of the machine tool. Then, the output value of the error parameter is represented as the amplitude of the truncated Fourier series and the global sensitivity index is represented by the ratio of its amplitude variance to the total function variance through normalization processing. Moreover, the global sensitivity analysis method is presented to calculate the sensitivity index of each geometric error parameter and the vital geometric error parameters have been identified. Finally, an experiment on compensating for vital geometric error parameters is performed and the experimental results show that the proposed method is feasible and accurate.
Due to the effect of gravity on machine tools, the small deformations inevitably exist. The existing tolerance allocation methods are based on the rigid body assumption, which ignore the small ...deformations. It will make optimization results inaccurate and increase manufacturing cost. Therefore, a new optimal tolerance allocation method, which integrates the small deformations, is presented in this paper. The establishment of a geometric error model based on tolerance is involved at first. Based on this model and multi-body system theory, the mapping relationship between tolerance and volumetric error of the five-axis machine tool (FAMT) is formulated. Secondly, the small deformations of the FAMT are obtained based on finite element analysis. Then, the optimal tolerance allocation model is established by integrating the small deformations into the constraint conditions. Thirdly, simulation analysis is carried out with this model by using a genetic algorithm. Then, the optimal tolerance allocation scheme is obtained, and the total manufacturing cost after optimization is reduced by approximately 11.5%. Finally, the volumetric errors of the FAMT are calculated based on the two tolerance allocation schemes. The results show that the volumetric errors are within the permitted ranges. Therefore, the proposed method in consideration of the small deformation is feasible and effective.
Thermal deformation is the main factor of the machining accuracy for grinding machines, which seriously restricts the precision improvement of grinding machines. However, at present, there are little ...researches on thermal error prediction, and the accuracy of the prediction model is comparatively low. Thus, a novel approach for thermal deformation prediction of grinding machine spindle based on heat energy conduction principle and neural network is proposed in this paper. Firstly, the temperature sensors’ pairs are applied to measure the temperature deviation between the spindle surface and its adjacent ambient which are directly related to the heat energy exchange. Secondly, the temperature deviations of each segment of the spindle are taken as inputs, which will exist and accumulate in the form of heat energy subsequently in the convolutional neural network. Meanwhile, the accumulated heat energy is mixed and transferred to the different segments of the spindle in the convolutional neural network. Thirdly, the thermal deformation caused by the increment of heat energy is considered as the output of thermal error prediction result based on the principle of heat energy conduction. Finally, the simulations and experiments are implemented to validate the feasibility and effectiveness of the proposed method.
The existing aerostatic spindle dynamic model only analyses the effects of mass imbalance and external load, ignoring the influence of cutting system on the spindle dynamic characteristics under ...cutting conditions. In this paper, a 5-DOFs aerostatic spindle dynamic model is established considering the influence of the micro-scale non-linear dynamic performance of the aerostatic spindle and cutting process damping. First, an analytical identification model of process damping with blunt circular cutter is established. Then, the micro-scale dynamic characteristics of the aerostatic spindle are analyzed and a 5-DOFs aerostatic spindle dynamic model is established considering the influence of process damping. Finally, the model is simulated and the influence of process damping on the dynamic characteristics of aerostatic spindle is analyzed. The simulation results show that the process damping of the cutting system has a significant influence on the dynamic characteristics of the aerostatic spindle. This study can provide theoretical guidance for coupling research of cutting system and spindle system.
In this paper, a 3D surface topography model for ultra-precision turning is proposed, in which the coupling effect of turning dynamics and dynamics of the aerostatic spindle in microscale is ...considered. Firstly, the identification model of the tool-workpiece interference area is established by the analytical method, and then the accurate process damping coefficient is obtained. Meanwhile, considering the influence of the dynamic characteristics of the aerostatic spindle on the formation of the workpiece surface morphology, a 5-DOF aerostatic spindle dynamic model is established under the influence of the process damping effect in the cutting process and the microscale effect of the gas film. Then, based on the dynamic model of turning and aerostatic spindle, the surface topography model of ultra-precision turning is established. The effects of spindle speed, cutting width, and feed rate on the surface topography of ultra-precision turning are also analyzed. Finally, the cutting experiment is carried out, the surface morphology obtained from the simulation and experiment is characterized by three-dimensional surface roughness parameters, and the error between the simulation and experimental results is analyzed. The results show that the 3D surface morphology model built in this paper matches the experimental results better, which proves the effectiveness of the model.
