Precision cutting mechanics and mechanical performance testing on the spindle of machine tool

The manufacturing industry is the foundation of national development. With science and technology developing, precision turning technology has gradually become one of the cutting-edge technologies of advanced manufacturing technology. In the paper, the turning mechanics model is established based on the principle of metal cutting, and the corresponding cutting force is calculated. Considering the cutting force, material weight, flange weight, and other loads, the analysis model of the CK61125 machine tool spindle is constructed based on the finite element method, and the corresponding maximum strain and modal solution are calculated. The results are that when the 30, 000 N load is applied, the largest strain of the spindle is 0.0013 mm/mm, and the largest stress is 265 MPa. When the 100, 000 N load is applied, the strain of the spindle largest is 0.0015 mm/mm, and the stress is 290 MPa. The four orders of vibration modes of the spindle are obtained, which are 215.3 Hz, 256.2 Hz, 436.33 Hz, and 974.5 Hz. By comparison with the experiment, the spindle vibration frequencies are 87.8 Hz and 625 Hz, while the spindle rotating testing speeds are 100 rpm, 500 rpm, and 800 rpm.


Introduction
The machinery manufacturing industry is an important symbol of the overall level of industrial development of a country, in which turning processing occupies a pivotal position and has been widely used in aviation, aerospace, shipbuilding, and medical industries [1].Turning performance is a very important point that affects the surface workpiece quality and limits the productivity of the turning process.Cutting force is one of the important indicators of the workpiece elastic deformation, which is the workpiece distortion caused by the residual stress of the cutting surface.The processing vibration affects the machining accuracy and quality.It is of great significance to establish the cutting force model of the tool for studying the mechanism of precision turning [2].Traditional turning force prediction models are mainly divided into the following three categories: The first is a complete prediction model based on a cutting experiment [3]; The second is a semi-empirical prediction model based on mechanical analysis [4]; The third is an analytical prediction model based on cutting theory and material properties.Ding et al. [3] established a new analytical prediction model of precision turning force based on a metal cutting mechanism and material constitutive relationship.Qin et al. [5] obtained the strain rate from the experiment of right-angle cutting based on the material constitutive relationship, and then extended it to the oblique cutting and established the milling force prediction model.Shamoto extended to bevel cutting and proposed a calculated bevel geometric angle method.Wang [6] proposed a parallel plane shear zone model for right-angle cutting.Hao [7] established the bevel-cutting model and obtained the relationship between shear flow angle and chip flow angle.
Based on the principle of cutting mechanics, cutting mechanics modeling is carried out.Considering the influence of cutting force and other factors on the machine tool spindle, the mechanical characteristics of the machine tool spindle are carried out.Combined with the field engineering test results, the working characteristics of the machine tool are analyzed.

Analytical modeling of turning force
In the process of metal cutting, the metal material undergoes a transition deformation under the action of the cutting tool.It is from elastic deformation to plastic deformation.Chips continuously flow out along the front tool face under the action of the main cutting force.The tool is mainly subjected to pressure and friction between the cut metal and the front tool face.
The force-cutting process analysis is shown in Figure 1.It is assumed that the machining process is a steady-state cutting process, and the force acting on the front tool face and the combined force acting on the shear surface is a pair of balanced forces.Generally, the cutting resultant force F can be decomposed into the shear force F s along the cutting surface and the pressure of normal F n perpendicular to the cutting surface, as well as the friction force F u along the tool rake surface and the normal pressure F v perpendicular to the tool surface.The cutting force F can be decomposed into the two forces.There are the tangential force F c along the cutting speed direction and the feed force F f along the cutting thickness direction.sin sin Where A is the cutting layer area, h is the cutting width, b is the cutting depth, and A s is the shear plane area.
Where s  is the stress of the shear flow on the plane for shear, and  is the angle for shear during the cutting process.
Based on the geometric relationship between the forces in Figure 1, we can derive the equation for s F and F .

cos( ) cos( )sin
Where  is the nominal tool angle.It is assumed that  is the angle between the force F and the plane for shear, that is,        , and  angles vary freely at 45° with different values of the material.
cos( )sin According to the theory and experiment of material mechanics, the relationship between the true shear force  , strain  , and yield strength s  during the metal cutting process is: The practice has shown that in metal cutting, changes in the angle affect the deformation coefficient and relative slip.Figure 2 is a schematic diagram of shear deformation during metal cutting.During the cutting process, the cutting layer OHNM on the workpiece undergoes slip deformation to form OGPM. The concept of relative slip includes: ) sin cos( ) The tool front angle α can be measured by three-dimensional confocal microscopy, the shear flow stress s  can be calculated by the Johnson-Cook shear flow stress model, and the friction angle β can be calibrated by cutting experiments.The shear angle  in the cutting process is solved based on the minimum energy theory proposed by the merchant.

The dynamic characteristics and analysis principle of the spindle
The modal spindle system frequencies and vibration modes are obtained by using ANSYS.These parameters are very important for dynamic characteristics analysis.
The spindle structure is divided into finite units.The K is the spindle system stiffness, M is spindle system mass,   is the amplitude and  is the frequency, we can obtain: The homogeneous equation is: When the spindle is vibration-free, each node amplitude is not zero, and the coefficient determinant is zero.

Stress characteristic modeling of spindle
Taking the situation of processing machine tools, the spindle mechanical performances are analyzed.Its machining load is 3 tons and 10 tons, respectively.From Figure 4, we can see that the spindle strain is the workpiece 30, 000 N of 0.0013 mm/mm.From Figure 5, the spindle maximum stress is 265 MPa.However, 45 steel allowable stress has a value of 355 MPa. Figure 7.The stress for 100, 000 N. From Figure 6, we can see that the spindle strain is the workpiece 100, 000 N of 0.0015 mm/mm.From Figure 7, the spindle maximum stress is 290 MPa.However, 45 steel allowable stress has a value of 355 MPa.The values are all less than the allowable stress of spindle materials.

Modal analysis of spindle
The spindle model and calculation use ANSYS.The natural frequency and vibration mode for the spindle system are obtained, as shown in Table 1.

Conclusion
For the CK61125 machine tool spindle parts, we analyze the spindle cutting force and strain under certain loads by using the finite element analysis method and analyze the spindle modal frequency, pointing out the weak spot of the spindle structure.Through the machine tool spindle under the condition of different speeds of analysis and testing of cutting work, the spindle vibration frequency is obtained.By comparison with the experiment and theoretical analysis, it validates the correctness of theoretical analysis.

Figure 1 .
Figure 1.Schematic of cutting force.It is assumed that the shear force is uniformly distributed.The force F s on the plane can be obtained by multiplying the shear flow stress.

Figure 2 .
Figure 2. Schematic of cut deform.From the relationship between the forces in Figure2, it can be obtained that the force of Tangential

4 .
The characteristics analysis of spindle4.1The spindle system parametersWe use the CK61125 horizontal CNC lathe spindle as an object.The spindle material is 45 steel that is quenched and tempered.

Figure 3 .
Figure 3. Schematic of simplified loading of spindle.The spindle torque is transited by a motor through the synchronous belt wheel, and the torque value is z 12 M  Nꞏm.The assembly speed range of the spindle is from 100 rpm to 800 rpm.While the spindle is working, the workpiece's mass and the cutting force are simplified to the end plane center O, as shown in Figure 3.The parameter values are z 25 F  kN, x 15 F  kN, and y 10 M  kNꞏm.

Figure 6 .
Figure 6.The stain for 100, 000 N.Figure7.The stress for 100, 000 N. From Figure6, we can see that the spindle strain is the workpiece 100, 000 N of 0.0015 mm/mm.From Figure7, the spindle maximum stress is 290 MPa.However, 45 steel allowable stress has a value of 355 MPa.The values are all less than the allowable stress of spindle materials.

5 .
The dynamic performance testing of the spindle systemTo evaluate the spindle static and dynamic performance in the engineering application, we installed it on the CK61125 numerical control lathe.The spindle rotating speeds are 100 rpm, 500 rpm, and 800 rpm.The spindle vibration response signals are obtained through the sensor's axial and radial direction.The testing points are shown in Figure8and Figure9.

Figure 8 .
Figure 8. Radial vibration testing of spindle.Figure 9. Axial and radial vibration testing of spindle.

Figure 9 .
Figure 8. Radial vibration testing of spindle.Figure 9. Axial and radial vibration testing of spindle.

Table 2 .
The testing vibration frequency parameters of the spindle.

Table 2 ,
we can see that the frequency of the spindle box mainly is 87.8 Hz and 625 Hz.