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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 59, 2017 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Zhuo Yang, Junjie Ba, Jing Pan 
Copyright © 2017, AIDIC Servizi S.r.l. 
ISBN 978-88-95608- 49-5; ISSN 2283-9216 

Research on the Optimization Design of Spindle Load of CNC 
Machine Tools 

Xionghui Long*, Dan Su 
Guangzhou Institute of Railway Technology, Guangzhou 510000, China 
XionghuiLong@126.com 

This paper established the finite element machine tool spindle and accessories model, accurate simulation of 
the boundary conditions, constraints and external loads, and the analysis of static and dynamic characteristics 
of spindle, the spindle optimization design based on ANSYS software, the performance comparison before 
and after optimization of the spindle; according to the results of optimization design and design experience of 
spindle. Analysis and interval of each size most likely made spindle, combined with orthogonal design method, 
the change of the size of the spindle under the condition of static and dynamic performance analysis of the 
spindle, and then obtain the optimal combination of the size of the spindle, spindle performance comparison 
optimal size composition and original spindle; based on the analysis results of different combinations of 
spindle size the static and dynamic performance of the orthogonal experiment, the response surface method 
were obtained and the performance function related to deflection and strength and modal The performance 
function, and considering the influence of spindle performance uncertainties, the reliability optimization design 
of spindle, spindle performance analysis of the optimized and the original spindle; integrated optimization 
design results of the comparison of the three methods shows: considering the uncertainty of the optimization 
design can according to the actual situation on the basis of improving the performance of the spindle. 

1. Introduction 
In recent years, our country and the developed countries in the world increasingly close ties between the 
increasingly fierce competitions, the equipment manufacturing industry has become related to China's 
international status and industrial revitalization and national prosperity of the important symbol (Liu et al., 
2016). Compared with foreign CNC machine tools, CNC machine tools in our country are reasonable in price, 
relatively mature in technical specifications, and have certain market competitiveness (Zhu et al., 2015). 
Universal milling head diagram as shown in Figure 1, Longmen CNC boring machine universal milling head is 
one of the core components, divided into spindle type and mechanical spindle two categories. Electric spindle 
is mainly used in high speed finishing, such as high speed rail train industry, such as aluminum alloy, titanium 
alloy, high temperature resistant alloy and composite material, such as high-strength lightweight parts. 
Mechanical spindle type is mainly used in high torque strong cutting, such as the energy industry of the turbine 
blade, the ship industry, such as screw propeller parts (Zhou and He, 2015). Longmen boring machine spindle 
type universal milling head has two mutually perpendicular planes of rotation, not only can complete the 
milling work in machining surface, can be obtained through various spindle position universal milling head 
horizontal and oblique axes of rotation, in order to adapt to the different requirements of the edges, grooves 
and other processing various parts in particular, it has important practical value in the two maintenances. 
Longmen GMC2000 boring machine universal milling head with double swing head is the appropriate speed, 
dynamic angle, An axis swing angle of plus or minus 110 degrees, C axis swing angle + 360 degrees. The tool 
center is always maintained in the normal direction of the work piece, and avoids zero cutting speed. Electric 
spindle rotary tool, high speed (up to 24000rpm), especially suitable for processing mound and non-ferrous 
metal materials, can also be different spindle power and torque configured according to user requirements, 
CNC machine tool structure schematic diagram shown in Figure 1. 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1759012

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Xionghui Long, Dan Su, 2017, Research on the optimization design of spindle load of cnc machine tools, Chemical 
Engineering Transactions, 59, 67-72  DOI:10.3303/CET1759012   

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Figure 1: Schematic diagram of universal milling head and Schematic diagram of the structure of NC chine 
tools 

The spindle is the core component of the universal milling head, whose function is to drive the cutting tool 
(grinding wheel) to rotate. The spindle has a great influence on the machining accuracy, surface quality and 
productivity. With the development of modern industry to the requirement of machine machining precision and 
efficiency increasing requirements on the performance of machine tools spindle is higher: wide speed range, 
high precision, high rigidity, small vibration, low noise, small deformation, and has good resistance ability of 
forced vibration and self-excited vibration. (Wan, 2014). 

2. Literature review and theoretical exposition 
2.1 Introduction to finite element method 

Finite element method (FEM) is a kind of highly effective and commonly used numerical method. The field of 
scientific computing, often need to solve all kinds of differential equations, and many analytical solutions of 
differential equations is generally difficult to obtain, using the finite element method of differential equation is 
discretized, can be programmed using computer aided solution. The solution domain discrete continuous 
combined body of a unit, the approximate function hypothesis in each unit to slice representation of the 
unknown field function solution domain to solve, approximate function is usually expressed by the unknown 
function and its derivative numerical interpolation function at each node unit (Zhang et al., 2014). Thus, a 
continuous infinite degree of freedom problem is transformed into a discrete finite degree of freedom problem. 
Feng Kang summed up this, made systematic theoretical results (Liu et al., 2015). The finite element method 
solving domain is discretized into finite element (grid), unit node connection between nodes, transfer 
interaction between units, node field as a function of the unknown quantity, and piecewise difference field 
distribution simulation function, and solving. Therefore, the complicated engineering problem is reduced to a 
simple problem with high accuracy, and the stress and strain distribution of the element is shown in Figure 2.  

 

Figure 2: Schematic diagram of element stress and strain distribution 

2.2 Basic theory of orthogonal test design 

In order to determine the optimal combination of factors, the authors put forward a kind of fast and efficient 
experimental design method, orthogonal test design (Duan and Ding, 2015). The orthogonal test design is a 
design method of optimal level for multi factor experiment, which is based on the orthogonality of the selected 
part of the comprehensive test representative, the test of representative and comprehensive test compared 
with the equilibrium dispersion characteristics of neat comparable". The orthogonal test design is a scientific 

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method for the design and analysis of a proper orthogonal table. The orthogonal design is a design method of 
multi factors and multi levels, it is based on the orthogonality selected from comprehensive test of some 
representative points test, and these representative points have "evenly dispersed, neat features than the 
orthogonal test design is the main method of fractional factorial design. Suppose that a comprehensive test of 
the three factors, each of which has three level tests, then we need 33 =27 test, comprehensive experiments 
of three factors and three levels of the diagram as shown in Figure 3, in the orthogonal test, each level of each 
factor and each factor collocation are uniform, only three times the test. So the orthogonal test can get almost 
the same effect as the full-scale experiment. In the three combinations, the level of factor B and factor C is 
only one of the three levels of factor A, which is the same as the. That is to say, if we compare three influence 
factors of A level of the test results, the experimental groups containing A1, A2, A3 were added, B and C for 
the factors of A, equivalent to a fixed.  

 

Figure 3: Schematic diagram of comprehensive experiments of three factors and three levels 

2.3 Orthogonal experiment design 

The orthogonal test design includes: designing orthogonal test scheme, orthogonal test, calculation and 
analysis of the experimental results and the four parts of the test. The first step is to clarify the purpose of the 
design. In the orthogonal design, the first step is to clarify what is the purpose of the test, or what is the reason, 
which is the basis of orthogonal test. After determining the purpose of the experiment, then determine the 
corresponding test indicators. The test index is a measure of the value of the experimental results. Secondly, 
choose the appropriate factors and factors (Wang et al., 2016). The first step and the second step are very 
dependent on the experimental design experience and expertise of the experimenter. A good experimenter 
can successfully complete the orthogonal test, and get good results. Secondly, choose the orthogonal table 
and table design. The reliability optimization design considering random variables and interval variables can 
obtain the optimal combination of design variables under the condition of ensuring the reliability of the results. 
In this section, we mainly introduce the reliability optimization design of double loop, which is the reliability 
optimization design under the condition of random variables and interval variables (Yang, 2016). The results of 
the orthogonal test results are shown in Figure 4, and the core codes are listed as follows (Li and Zhang, 
2016). 

 

Figure 4: Schematic diagram of digital building technology 

1. settings = cordexch(3,13,'q'); % settings; 2. mr = p(2,:); % mr: middle row, i.e., middle level 3. mr = 
mr(ones(13,1),:); 4. hr = (p(1,:) - p(3,:))/2; 5. hr = hr(ones(13,1),:); 6. expCond = settings.*hr + mr; 7. p1 = 
expCond(:,1); 8. p2 = expCond(:,2); 9. p3 = expCond(:,3); 10. y = zeros(13,1); 11. for k = 1:13; 12. y(k) = 

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1.25*(p2(k) - p3(k)/1.5183)./(1 + 0.064*p1(k) ... ; 13. + 0.0378*p2(k) + 0.1326*p3(k))*normrnd(1,0.02); 14. end; 
15. data = [expCond y]; 16. settings = cordexch(3,13,'q'); % settings; 17. mr = p(2,:); % mr: middle row, i.e., 
middle level; 18. mr = mr(ones(13,1),:); 19. hr = (p(1,:) - p(3,:))/2; 20. hr = hr(ones(13,1),:); 21. expCond = 
settings.*hr + mr; 22. p1 = expCond(:,1); 23. p2 = expCond(:,2); 24. p3 = expCond(:,3); 25. y = zeros(13,1);  
26. for k = 1:13; 27. y(k) = 1.25*(p2(k) - p3(k)/1.5183)./(1 + 0.064*p1(k) ...; 28. + 0.0378*p2(k) + 
0.1326*p3(k))*normrnd(1,0.02); 29. end; 30. data = [expCond y] 

3. Finite element analysis and optimization design of spindle 
3.1 Analysis and calculation of spindle and bearing 

The main content of this chapter is the quantitative analysis of the external forces of the spindle components, 
simplifying the combination of bearing parts and bearings and spindle, the establishment of accurate digital 
simulation model, in order to analyze the static and dynamic characteristics of the spindle. Finally, the optimal 
design based on ANSYS software. In order to establish the finite element model of the spindle is simple and 
effective, we must thoroughly understand the Longmen boring machine universal milling head structure and its 
operation mode. The cutting force decomposition is shown in Figure 5, the static and dynamic problems of the 
shaft, according to the combination between the bearing and the shaft and the bearing surface modeling 
problem, and the nonlinear contact problem of the bearing itself is not the focus, simplify the combination 
between the bearing and the shaft and the bearing surface does not affect the purpose of the study, but also 
improve the modeling speed and precision, and improve computing efficiency. Therefore, the bearing is 
simplified as a simple radial spring and damper characteristics by using the finite difference analysis model of 
Longmen boring machine spindle. The main intention of deformation icon as shown in Figure 5, in combination 
with the actual simulation of bearing and the bearing and the shaft surface, the node consolidation of the end 
of the spring on the main shaft, and the other end (P1, P2, P3, P4 four nodes) for complete consolidation, 
each radial stiffness (K/2 single row radial thrust ball bearing stiffness). The 3 column ball bearing front spindle 
with radial 3 columns of the same radial spring distribution to simulate the bearing stiffness, axial column using 
3 axial spring simulation bearing stiffness; simulation above 2 column ball bearing spindle end. In the analysis 
and design of the spindle system, the bearing stiffness is one of the important factors, but due to the nonlinear 
bearing stiffness and bearing type, material, shape and other factors, so to accurately determine the bearing 
stiffness is not realistic. Zhu et al., the use of inductance measurement of a set of bearing stiffness test device, 
more accurate measurement of the stiffness of the bearing (Ma et al., 2014). 

  

Figure 5: Schematic diagram of cutting force decomposition and Schematic diagram of spindle deformation 

3.2 Spindle finite element analysis 

Finite element analysis is the foundation of the whole research. It includes the selection of unit type, the 
establishment of numerical analysis model and finite element analysis. Determine the type of units required for 
the network before the model is established. The selection of unit type is based on the analysis of the 
complexity of the object, the characteristics of the stress and strain, the accuracy of the calculation 
requirements and the computing power of the computer. According to the characteristics of the solid modeling 
of the machine tool spindle system and the structural mechanical characteristics reflected in the motion, the 
SOLID45 unit is used to divide the machine tool spindle components. The SOLID45 element is used for 3D 
solid structure model for 3-D solid structure unit. The unit consists of eight nodes. Each node has three 
degrees of freedom in X, y, and Z, as shown in Figure 6 represents a deformed SOLID45 unit. SOLID45 unit 
can be simple control, more accurate simulation of the actual situation. The SOLID45 element can be used to 
simulate plasticity, creep and expansion, but also to meet the stress hardening, large deformation and large 
strain characteristics. In order to simplify the meshing of the bearing with COMBIN14 element, the element 

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has the axial or torsional elastic damping properties of one-dimensional, two-dimensional or three-dimensional. 
The model is the basis of network, has a direct impact on the process of network model is reasonable. If the 
model is large and regular, ANSYS software provides a method for static analysis and dynamic analysis. In 
addition, the distributed computing method, the bandwidth optimization and the wave front processing method. 
Longmen GMC2000 boring machine spindle finite element model as shown in Figure 6, the internal model as 
shown in figure 6. In the model of the Z coordinates of the 126.5 small ladders, the analysis can be ignored. In 
order to more accurately simulate the axis in the work force, the axial force of the work directly loaded in the 
handle, so the handle part modeling as a part of the spindle. When the boundary condition is loaded, the rear 
end of the spindle does not change when the motion is carried out, so the rear end of the model spindle is 
completely fixed. Because the front-end milling cutter, so draw a solid. Finite element analysis is based on the 
solid grid. If the calculation precision of the result is high, the precision of meshing should be improved. 
Otherwise, the result of finite element analysis does not accord with the actual requirement, which will 
seriously affect the effect of the whole research project. If the structure of the research object is complex, the 
structure of the key part of the refinement of the grid, for example, the temperature gradient, stress gradient, 
large deformation of the structure, in the non-critical part of the coarse mesh.  The purpose of model checking 
is to check whether the mesh is reasonable.  However, because the model is not the geometry of the ideal 
rules, the actual grid cannot be a rule. So it is necessary to check the model in order to limit the deformation of 
the mesh to a certain extent. 

   

Figure 6: Schematic diagram of SOLID45 unit structure and Schematic diagram of the spindle structure after 
loading of spindle 1/4 boundary conditions and Schematic diagram 

4. Orthogonal test design and analysis of spindle load 
In this paper, we choose the comprehensive balance method to analyze the results of orthogonal test. The 
effects of different factors on the test results were different. The larger the range, indicating that the change of 
the factors in the test range will lead to the change of the test index, so the line is the biggest influence on the 
test results, which is the most important factor. To determine the optimal scheme, such as the index of the 
bigger the better, intuitive sake, draw the factors and indicators of the trend, the trend diagram as shown in 
figure 7, select the optimal scheme of comprehensive balance: 1 factors, 5 indexes are 3 level, the choice of 3 
levels. 

 

Figure 7: Schematic diagram of the trend factor 

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With the development of modern computer technology, and in-depth study of response surface method and 
improvement of the theory, the scientific computing model is becoming more and more complicated, the 
response surface method is obtained including chemistry, and biology and engineering favor (Hui et al., 2014). 
It has been proved that the response surface method has a high status in the field of engineering, such as 
reliability analysis, optimization design, dynamics research and engineering process control. In order to apply 
the two-order response surface approximation model, the first step is to find the optimal region by using the 
low order method, and then the polynomial approximation is used in the optimal region. 

5. Conclusions 
The importance of machine tool spindle is self-evident, many scholars devoted their lives to improve the 
performance of the machine tool spindle, and pay it to practice. Based on the optimization design of the 
spindle of the spindle, reduce weight, reduce material consumption and production cost, improve the working 
performance of the machine, can greatly shorten the design cycle of the spindle, and obtained the most 
consistent with the actual situation of the optimization method. An accurate finite element of machine tool 
spindle parts and accessories of the model, analysis of spindle of the static and dynamic performance, 
optimized design based on ANSYS software, and compared the performance of the spindle before and after 
optimization; response surface method were obtained and the performance function related to deflection, 
strength and modal based on the performance of the resulting function, comprehensive considering the 
influence of spindle performance uncertainties, the reliability optimization design of spindle and spindle after 
optimization and performance analysis of the spindle, and comprehensive optimization design results of the 
comparison of the three methods, the most practical method can greatly improve the spindle safety 
performance and processing performance. 

Acknowledgments  

This work is supported by the research and practice of Guangdong Province vocational education numerical 
control skill competition information platform construction (Guangdong education and scientific research "11th 
Five-Year" planning 2011 Annual project) (2011TJK252). 

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