Optimization of the mechanical properties of machine tool with steel reinforced mineral concrete

High damping and high static stiffness are essential to improve the static and dynamic characteristics of machine tools. Traditionally, the structural parts of machine tools are usually made of cast iron and steel, which may lead to poor surface finish and inaccurate dimensions of finished products. Therefore, many scholars have investigated other alternatives of structural material for machine tools, such as concrete, polymer concrete and epoxy granite. Although epoxy granite has better damping properties, its structural stiffness (as measured by Young’s modulus) is only 1/3 of the gray cast iron. Thus, this study would introduce several steel bar designs into epoxy granite to improve the static stiffness and quantitatively review the performance by finite element analysis. The results showed that the equivalent static stiffness and natural frequency were about 12 to 20% higher than the structural material of cast iron. Therefore, the proposed finite element model of vertical machining center (VMC) column in epoxy granite could serve as a feasible alternative to achieve higher damping or static stiffness, as it was also more environmentally friendly to the manufacturing process.


Introduction
Structural components are important parts that affect the static and dynamic characteristics of vertical machining center (VMC).At present, most machine tool beds are made of cast iron, that although it has larger damping coefficient than that of carbon steel and is easier to shape, its dynamic rigidity or vibration resistance is not as ideal, and given the scarcity of raw materials like cast iron, the huge consumption of power and the pollution to the environment during the process, it does not meet the requirements of green manufacturing and developing of low carbon economy in the long run [1][2].With the scarcity of mineral resources and the increasing awareness of environmental protection, new and more environmentally friendly materials are urgently needed to replace the traditional tool bed materials [3].Reinforced concrete has the advantages of easy shaping, high damping, good thermal properties, and low price.As early as 1917, Schlesinger in Germany first proposed the application of reinforced concrete in the basic structure of machine tools, and then Boehringer of Germany was the first to produce reinforced concrete lathe bed in the 1940s, where it was quickly adopted by the former Soviet Union and the United States in the manufacturing of large lathe beds and gantry milling machines in the 1960s.They soon found that reinforced concrete tends to fracture and not resistant to corrosion, especially not able to withstand the erosion of cutting fluid and workpiece collision, which greatly limited its popularity [4][5].Resin concrete, on the other hand, not only has the advantages of high damping, high specific rigidity, low thermal conductivity and small thermal deformation, but also has the characteristics of resisting corrosion and fracturing, while yet remaining malleable.In the early 1970s, STUDER, a Swiss precision grinder manufacturer, was already in the business of manufacturing resin concrete beds of S40 and S50 series for CNC cylindrical grinders.After 1990, East Star Granite Precision Measure Company in Shandong has also manufactured resin concrete beds and introduced a series of the products.Although the resin concrete bed has excellent technical performance, it is costly to manufacture; thus, limiting its use in expensive high-end precision machining centers and not for general use [6][7][8][9].Vertical machining center (VMC) is consisted of structural components like base, column, cross beam, spindle box and guide rail [10], for they are playing a key role in the operation and performance of the apparatus.In fact, the performance of these structural components will directly determine the accuracy and stability of the tool [11][12].The base, column and cross beam of most vertical machining centers are made of original or modified gray cast iron [13].Because gray cast iron is brittle and susceptible to fracture to yield poor strength and mechanical properties, it easily leads to problems like inaccuracy and jitter when processing workpiece [14][15].For this reason, we proposed high-strength Portland reinforced concrete as the core body to be coated externally with resin mineral composite concrete to serve as the bed for vertical machining center, which shall combine the strengths of both types of concrete.It not only has the characteristics of high damping, high specific rigidity, corrosion resistance, anti-cracking, low thermal conductivity and low thermal deformation required for the tool bed, but most importantly, the manufacturing cost is relatively low, which is calculated to be about 2/3 of that of the corresponding cast iron bed and 1/3 of that of the resin concrete bed ̴ ], providing that it has a very high cost-performance ratio and favorable to wide range of application in ultra-precision vertical machining centers.

Combination of mineral composite
In this study, the new mineral composite material had two parts.The outer layer of epoxy resin concrete covered the clad inner layer of silicate reinforced concrete to integrate the unique properties of both materials into a new form of mineral composite (Figure 1).

Composite elements and properties of resin concrete
The resin concrete was made of E51 epoxy resin as the base material, dibutyl phthalate (DBP) as the toughening agent, AGE as the active diluent, ethylenediamine as the curing agent, and fly ash as the filler.Jinan granites of diameter of 2.3～5mm were chosen as the coarse aggregate, the fine aggregate was river sand, and the mud content was less than 1%, as the moisture was limited to less than 0.5%.The ratios of the three main elements (E51, ethylenediamine and DBP) were adjusted and evaluated by the strength, hardness, damping, thermal conductivity and linear expansion coefficient as the criteria.Then, we conducted the orthogonal test to find the best mixture ratio of E51: AGE: DBP: ethylenediamine: fly ash: fine aggregate: coarse aggregate shown in Figure 1a, for the resin concrete materials as follows: 120:5:5:7.2:80:100:300:9033.8 in which the reasonable proportion of aggregate gradation proved to be beneficial to improve the mechanical properties of resin mineral composites [18].By referring to the sample model data in the literatures [19] , we set the minimum aggregate diameter to 0.1～0.3mmand the maximum size to 2.36～5mm.The aggregates were then separated into five grades of size, with the amount of each grade shown in Table 1.In the preparation process, the fly ash was mixed evenly with fine aggregates and epoxy resin, before the coarse aggregates were added by sedimentation method to ensure uniform and dense distribution as shown in Figure 1(b).

Composite elements and properties of portland cement concrete
Portland concrete uses high-strength silicate cement of 52.5R as the base material, in mix with Jinan granites of diameter of 2.5-10mm as the main aggregate and river sand of 0.15-2.5mmas the fine aggregate.
Pure water and additive such as superplasticizer are mixed in designed formula of specific proportion to yield such high strength in cement [20].The specific ratio of the materials is calculated as follows: Cement: River Sand: Water: Coarse Aggregate: Medium Aggregate: Fine Aggregate: Steel bar=0.4:0.4:0.12:0.2:0.65:0.23.
In this study, low-cost Portland cement with steel fibers was used as the core of concrete, while it was then coated with high-performance epoxy resin concrete on the surface, which would greatly reduce the overall cost of the machine tool bed and improve the cost-performance (as shown in Figure 2).The bonding surface between the inner layer of Portland cement steel fiber concrete (Figure 2: a) and the surface layer of epoxy resin concrete (Figure 2: b) is shown in the illustration as a trapezoidal toothed surface (Figure 3).

Manufacturing process of the bed structure test piece (as a 100mm³ cube)
A. Follow the instruction manual and design blueprint for both the core and the surface of a machine tool bed, B. First, dry mix the steel fibers, cement and aggregates, before adding water and diluent in accordance with the preparation manual to produce Portland cement steel fiber concrete, C. Pour the concrete into the core mold, D. Let it cure for 12 hours under the condition of ambient temperature at 20-30 ℃ and humidity of 70%-95% before draft patterns, place the core (Figure 3:a) at an ambient temperature of 20-30℃ and the humidity of 70%～95% without exposure to light for 21 to 28 days of timed curing, E. Fix the embedded parts (such as steel bars) in the surface mold, F. Prepare the epoxy resin concrete according to the operation manual, G. Put the core (Figure 3:a) into the surface mold and pour epoxy resin H. Let it cure for 3-5 hours under the condition of ambient temperature at 20～ 30 ℃ and humidity of 70%～95%.After draft, the bed structure is placed at an ambient temperature of 20~30℃ and the humidity of 70%～95% without exposure to strong light for 48～72 hours of timed curing.The surface mold is made of steel and the core mold can be either wooden .The mass ratio of epoxy resin concrete is as follows: (epoxy resin 8%-9%; diluent 1.6%～2%; curing agent 0.4%～0.5%;filler 16%～18%; fine sand 17%～20%; coarse sand 12%～15%; gravel 40%～50%).The curing agent is ethylenediamine, the filler is made of quartz and calcium carbonate powder, the diameter of  fine sand is less than 1.2mm, and the diameter of coarse sand is 1.2mm-3.0mm,and the diameter of crushed stone is 3-6mm.The result is the production of a (100mm³) cube of concrete test piece, which will be subjected to physical performance tests.

Performance test of mineral concrete
The Universal Testing Machine (UTM), for its versatility, can be used to perform various testing, including tensile/compression test, bending test, peeling test, tear test and other mechanical tests.The tests are all standards-compliant and applicable to a wide range of materials.The testing machine consists of a force sensor, a cross beam, an extensometer, a sample holder, an electronic control system and a drive motor system.It is controlled via software, which will adopt specific test parameters set by North American and international testing standards (such as ASTM and ISO), to measure compressive or tensile strength of a material and help the designer or manufacturer predict the use of the material.

Performance and price comparison of mineral concrete
Cast iron resources are increasingly scarce and due to its huge power consumption to produce and pollute the environment during the manufacturing process, it is not the ideal choice in the face of the requirements for green manufacturing and the development of a low-carbon economy.The use of low-cost Portland cement with steel fibers as the core of concrete and high-performance epoxy resin concrete on the surface would significantly reduce the manufacturing cost of machine tool bed and improve the performance.As seen in Table 2, the Portland cement concrete coated with epoxy resin in this study was the most competitive in terms of low manufacturing cost (Table 3), not to mention its high resistance to impact to provide the widest application in the future market.

Materials
Mass unit price (USD/ton)

Testing and comparison of damping coefficient of mineral composite
Rigidity, quality and damping are the three main parameters that affect the structural mechanics of a machine tool, especially the damping properties, since it is for controlling the vibration and has a significant impact on the dynamic performance of the bed.The damping coefficient is the main highlight of the synthetic mineral concrete, as illustrated in the vibration test (Figure 5), where it was measured by the response of load cell at the end of impact rod (Figure 5), showing as decreasing amplitude over time.From (Figure 6), it was found that the damping ratio of Portland cement concrete with the mix of steel fibers was 6.5 times higher than that of cast iron.

Application of steel reinforced Portland cement concrete in vertical machining center 2.2.1. Establishment of the geometric model for the machine tool bed
Based on the structural dimensions of the V850 vertical machining center shown in Table 4, the SolidWorks 3D software was used to construct its structural diagram (Figure 7), to be used to compare and analyze the seismic performance of this reinforced mineral composite by comparing similar tool beds (Figure 8) of two different materials and embedded steels in key parts.Once geometrically optimized, the model was imported into ANSYS WORKBENCH R17 for finite element analysis.Since small features such as chamfers, round holes, and small holes have a minimal effect on the whole but generate a large number of irregular finite cells when delineating finite circular meshes, reduce the quality of the mesh and prolong the computation time, small features and small components are ignored [21].

Material properties and boundary condition
For the traditional cast iron machining center, the material grade is HT300.After importing the 3D model into Ansys workbench R17, it is necessary to redefine the material properties.On the other hand, the import of a Portland cement epoxy resin concrete with embedded steel material (HT300) in key parts would require setting up a new material library in Ansys workbench R17 and the relevant parameter values were set according to the properties shown in Table 5.To constrain the structure and simulate the actual condition, the bed was completely bolted and fixed to the ground.

Mesh division of the body
Considering the complexity of both the internal and external of the vertical machining center, a tetrahedron mesh division was adopted in the Ansys workbenchR17, along with the Patch Conforming algorithm to mesh divide the resin polymer bed into 92837 nodes and 53203 units (Figure 9), while the cast iron bed was divided into 84173 nodes and 45243 units (Figure 10).

Static analysis of the bed structure
Structural supports generally have great influence on the performance of the whole mechanism of the vertical machining center.The supports mainly refer to the bed, column, beam, etc., with the role to support other functional components of the machining center, such as the spindle box, tool holder, etc., for these parts to withstand a variety of forces.By using the ANSYS simulation software for static analysis of the bed, which was completed fixed and loaded with 2000 N pressure at the guided rail like in the real environment, the maximum deformation of cast iron occurred at 5.43×10 8 µm, as shown in Figure 11.The maximum deformation of the mineral composite concrete was 2.036×10 8 µm, as shown in Figure 12.The comparison revealed a reduction of 17% in the resin concrete bed.Considering that the density of resin polymer is only 1/3 of that of cast iron, it is possible to increase the wall thickness of the bed of resin mix or add reinforcement to improve the bed stiffness, all of which still showed that the static performance of the resin concrete bed was better than that of cast iron.

Modal analysis of the bed structure
The spindle of the vertical machining center (VMC) showed a sinusoidal pattern of displacement over time due to the vibration of the bed during the cutting process.The natural frequency (a.k.a.period of vibration) is specifically related to the inherent characteristics of the bed (e.g.stiffness, mass, shape and size), in which the harder the bed and the smaller the mass, the higher the natural frequency will be and the more difficult it is to produce resonance.Since the increase of the natural frequencies of the two beds was less after reaching the 6th order of vibration, we would ignore and list only the natural frequencies prior the 6th order [22], showing in Table 6.The first-order vibration diagram for the two beds is shown in Figure 13.Modal analysis is to analyze the natural frequency and vibration pattern of the bed with the main purpose of directing the design to avoid resonance when the bed is loaded.It plays an important role in eliminating noise and vibration [23][24].In general, the modal analysis usually will involve no loading and both the resin and the cast iron beds would be fixed in our study.The natural frequency and vibration pattern were analyzed by the ANSYS WORKBENCH software.As shown in Table 6, the initial frequency of the resin composite material was 136.38 Hz, maximum deformation is 0.046953 μm shown in Figure 14, which was higher when compared with the initial frequency of 89.81 Hz and the maximum deformation is 0.063966 μm shown in Figure 13 for the cast iron bed.So it concluded that the maximum strain of mineral material is 26.59% less than of cast iron bed.The vibration patterns of the 2～6th order of the resin composite material was also much higher than that of cast iron bed.When analyzing the distribution pattern of the vibration frequency, it showed the resin composite material having relatively dispersed range, which could probable to be beneficial in the selection of other components to avoid resonance and the improvement of the machine's accuracy.Thus, the results were the indication of superior performance in vibration resistance for the resin concrete bed to that of the cast iron bed.

Analysis of the results
(1) In term of static performance, the maximum deformation of the cast iron bed was 2.44 μm and the maximum deformation of the Portland cement concrete bed was 2.033 μm.Compared with the two values, the maximum deformation of resin concrete was reduced by 17%, significantly improving static performance.It was possibly due to the high specific rigidity of Portland cement concrete and the large cross sectional area of the bed to help evenly distribute the force among the body and the feet.
(2) In term of dynamic performance, due to the use of better support and structure, the natural frequency of Portland cement composite concrete bed was significantly improved, for this would avoid the interference of most external vibration of low-frequency, as well as some high-frequency vibration sources, during high-speed processing of vertical machining center; thus, improving the overall stability of the machine tool.Damping is the primary determinant of controlling the vibration and has a significant impact on the dynamic performance of the bed.In this study, the Portland cement concrete bed with steel bars showed 6.5 times higher in damping ratio than cast iron.The vibration problem of vertical machining center during high-speed cutting would limit the range and the direction of its application.

Conclusion
Silicate steel reinforced composite concrete can serve as a manufacturing material for machine tool bodies, and can meet the requirements of high precision, high speed, and high efficiency in terms of performance.Especially, it greatly improves the anti-vibration ability with its larger damping characteristics.In addition, it has the advantages of low manufacturing cost, corrosion resistance, and easy molding, which is of great significance for improving the machining accuracy of precision machine tools, reducing errors, and lowering production costs.Furthermore, its raw materials are widely available, making it an excellent manufacturing material for machine tool bodies, and can provide reference for application by machine tool manufacturers.

Figure 1 .
Figure 1.Illustration of gradation of granite composites.

Figure 3 .
Figure 3. Joint surface between the inner layer and the outer layer of the concretes in trapezoidal jigsaw pattern.

Figure 2 .
Figure 2. Machine tool bed of mixed concrete.

Table 4 .
Specific parameters of vertical machining center.

Figure 9 .
Figure 9. Mesh division of cast iron bed.

Figure 10 .
Figure 10.Mesh division of mineral composite bed.

Figure 12 .
Figure 12.Deformation diagram of the mineral composite concrete.

Figure 13 .
Figure 13.The first-order natural frequency of resin composite material.Figure 14.The first-order natural frequency of cast iron.

Figure 14 .
Figure 13.The first-order natural frequency of resin composite material.Figure 14.The first-order natural frequency of cast iron.

Table 1 .
Aggregate grading formula of resin mineral composite.

Table 2 .
Price comparison of three types of machine tool.
Figure 4. Structural diagram of universal testing.

Table 3 .
Physical performance comparison of three types of machine tool.

Table 5 .
Cast iron and Portland cement steel reinforced concrete.

Table 6 .
Modal analysis results of the beds.