Dynamic and static characteristics of the ultra precision cycloid wheel forming grinding machine tool bed of hybrid fiber artificial granite

Xue-tao QIAO, Peng WANG, Hua-wei XU, Cun-fu YAN, Long WU, Yan-long CAO,2

(1School of Electrical and Mechanical Engineering, Zhongyuan University of Technology, Zhengzhou 451191, China)(2School of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China)

Abstract: By means of orthogonal test, the hybrid fiber artificial granite specimens with different mixing ratios were designed and fabricated. The finite element analysis of artificial granite with similar structure hybrid fiber, artificial granite without fiber and cast iron (HT250) cycloid wheel forming grinder bed was carried out on the ANSYS Workbench platform.The results show that: (1) adding hybrid fiber can improve the strength of artificial granite material; (2) the equivalent deformation of hybrid fiber artificial granite bed is the smallest, the equivalent stress is low, and the natural frequency of the first 5 orders is the highest.

Key words: Artificial granite, Orthogonal test,Hybrid fiber, Ultra precision cycloid wheel forming grinder bed, Finite element analysis

1 Introduction

RV reducer as the robot joint reducer, its keytechnology has been mastered by Japan. Cycloidal gear is one of the key components of RV reducer, and the requirement of machining accuracy and surface roughness are very high. It needs to be processed by a special form grinding machine which has high requirements on machining accuracy, dynamic stabilities,thermal stability and any other aspects[1-2].As one of the key basic parts of the ultra-precision cycloid wheel forming grinding machine，the lathe bed plays a role in supporting workpiece and connecting worktable or any other key components. Its strength, stiffness, damping, creep and other properties directly affect the machining accuracy of ultra-precision machine and the surface quality of components which is related to the accuracy reliability and service life of ultra-precision machine [3].

The traditional material of the lathe bed is cast iron，it is mainly because the cast iron material has the high strength and easy to processed, high precision can be obtained by scraping, its technology is mature,but the damping properties is low which can't effectively reduce the vibration generated during the processing. Moreover, the cast iron materials have high energy consumption, serious pollution, complex manufacturing process, long manufacturing cycle, high cost, residual thermal stress can't be completely eliminated, poor thermal stability. Although ordinary concrete has low manufacturing cost, but its strength is low, its surface is easy to corrode and its dimensional stability is poor. The machine bed made by welded steel has low cost and good formability, but it has large thermal deformation, low precision and poor corrosion resistance. The surface of natural granite lathe bed can be grinded precisely to obtain high precision, but it is highly demanded by the environment, the surface is easy deformed by damp, the precision is lost after deformation, and there are certain requirements for stone [4]. Therefore, looking for high-performance composite materials to replace traditional materials to make ultra-precision machine tool bed has become a research hotspot at home and abroad.

Artificial granite (also known as polymer concrete, resin concrete, mineral casting composite material) is made of natural granite particles as an aggregate, using an organic resin such as epoxy resin as a binder, and adding filler, thinner and toughening in an appropriate ratio, it's a new composite material which is polymerized by curing under normal temperature and pressure conditions. It has good damping properties, dynamic and static properties, thermal stability, high integration, acid and alkali resistance, green without pollution and other advantages. It is an ideal material for making high-end equipment basic parts such as ultra-precision machine tools and precision measuring instruments, but the strength of this material is lower than that of cast iron materials.

In this paper, on the basis of preliminary experiments of the research group, the hybrid fiber artificial granite specimens were made by orthogonal test method, and the effect of hybrid fiber on the compressive strength of the materials was studied. The finite element analysis method was used to analyze and verify the ultra-precision cycloid wheel grinding machine bed of hybrid fiber artificial granite.

2 Orthogonal test of hybrid fiber artificial granite

2.1 Test raw material

The resin is bisphenol A type epoxy resin, bisphenol A type epoxy resin E44, curing agent is 650 polyamide resin, diluent is AGE active diluent, toughening agent is DBP, release agent is silicone oil type release agent.

Aggregate: Jinan green aggregate crushed by hammer crusher, the aggregate is divided into five sizes by linear vibrating screen. The sizes and specifications are: fine aggregate 0～0.18 mm; 0.18～2.36 mm; coarse aggregate 2.36～5 mm; 5～10 mm; 10～15 mm.

Fiber: Steel fiber is produced from Zhengzhou Yujian Steel Fiber Co., Ltd. The surface is copper-plated, slender, bending at both ends, diameter 0.5 mm, length-diameter ratio is 70. Polypropylene fiber is produced from Nanjing paill Technology Industrial Co., Ltd., with a length of 12mm, 19mm. Carbon fiber is produced from Shanghai gjit Chemical Technology Co., Ltd. its carbon fiber diameter is 7 μm and its length is 1～5 mm. Glass fiber is produced from Nanjing paill Technology Industrial Co., Ltd., with a diameter of 5～13 m and a length of 12 mm.

Filler: Magnesium Sulfate particle size 60 mesh, content of more than 99%, produced in Zhengzhou Jiahong chemical products Co., Ltd. Mica powder has a size of 1250 mesh and moisture content of <0.1%, which is produced by Gongyi Chun Jing refractories company.

2.2 Orthogonal test design table

On the basis of the previous research, this paper selects aggregate gradation, binder, filler and hybrid fiber as the influencing factors, makesL9(3×4) orthogonal table, and carries out orthogonal experiment of three levels and four factors. Table 1 is the orthogonal test table of hybrid fiber artificial granite.

Table 1 Orthogonal test table for 5 kg ratio of hybrid fiber artificial granite

The aggregate in Tab. 1 consists of various specifications, among which: the particle size is 0～0.18 mm, accounting for 10% of the total aggregate, the particle size is 0.18～2.36 mm, accounting for 15% of the total aggregate, and the particle size is 2.36～5 mm, accounting for 40% of the total aggregate, particle size of 5～10 mm, accounting for 35% of the total aggregate, particle size of 10～15 mm, accounting for 15% of the total aggregate. The ratio of raw materials in the bonding is E44∶650∶AGE∶DBP mass ratio: 15∶10∶3∶1, Magnesium sulfate: the mass ratio of mica powder is 1:2, steel fiber: glass fiber: carbon fiber mass ratio is 1∶0.6∶1.

2.3 Test piece preparation process

As shown in Fig. 1, the preparation process flow chart of hybrid fiber artificial granite specimen is presented. The specific steps are as follows: ① Rock cleaning； ② Rock breakage； ③ Aggregate sieving； ④ Aggregate drying；⑤ Weight of aggregate，the fiber is weighed and pretreated and mixed with aggregate； ⑥ Weight of the packing, weight of the binder, mixing and mixing； ⑦ Pour the mixture of step ⑤ and ⑥ into the forced mixer and stir 5 min； ⑧ The mixture material is poured into the steel mold which is pre coated with the release agent； ⑨ Vibrate, while vibrating, add the mixture to the mold until the mixture is no longer settling； ⑩ Curing at room temperature 24 h, curing 48 h, demolding. In the binder system, epoxy resin, curing agent and diluent are mixed in proportion, then a certain amount of toughening agent is added, and then the weighed filler is added to form mixture 1, aggregate and a certain amount of fibers are added to form mixture 2, and mixture 1 and mixture 2 are mixed in proportion to form specimens in the steel mould coated with release agent through vibration, demoulding and curing. Fig.2 is a three joint concrete test and forming specimen.

Fig.1 Fabrication process of hybrid fiber artificial granite composite material

Fig.2 Triaxial concrete test and forming specimen

2.4 Compressive strength test

According to the metal room temperature compression test standard，with the aid of universal servo testing machine the strength of the cube specimen was tested.

The following points should be noted before conducting the test of specimens:

(1)The surface of adjusting pads and bearing block on the working table should be cleaned up;

(2)The placement of the cube specimen should coincide with the center of the adjusting pad on the worktable;

(3)Raise the work table to the scale value between 0 and 10 mm to offset the weight of the beam before the compression test;

(4) Uniformly loading, with loading speed of 0.8～1.0 MPa, until the specimen is severely, stop loading and reset.

The compressive strength of the cube specimen can be obtained from the following formula:

In this formula：Fis maximum load(N)；fccis compressive strength of the cube specimen(MPa);Ais the load area of the specimen (mm2).

Fig.3 Cubic compressive strength device

Fig.4 Cubic compressive strength curve

When the strain reaches 6%, the maximum stress appears in the specimen. With the increase of strain, stress failure occurs at the interface of aggregate resin and fiber resin, and the internal cohesive force of the specimen decreases sharply. The external performance is the failure of the specimen.

Fig.5 Cubic compressive strength of cube specimen in orthogonal test table

3 Finite element analysis of grinding machine body of ultra-precision cycloidal wheel

3.1 3D modeling of the ultra-precision cycloid grinding machine

SolidWorks 3D design software was used to create a solid model of ultra-precision cycloid forming grinding machine, and the model effect is shown in Fig.6. It mainly includes the mixed fiber artificial granite bed body, column, grinding wheel structure, dressing mechanism, dividing numerical control turntable, counterweight mechanism, slip plate, foot, servo motor, ball screw, linear guide and other purchased parts.

1.counterweight bracket; 2.pillar; 3.dresser Z-axis servo motor; 4.counterweight; 5.dresser X-axis servo motor; 6.hybrid fiber artificial granite bed; 7.footing; 8.servo motor of lather bed; 9.indexing numerical control turntable; 10.dressing parts; 11.grinding wheel parts; 12.dressing wheel; 13.servo motor

The method of machining the tooth shape on the gear blank by the forming grinding wheel which is used for machining the tooth slot shape of the gear. To process the cycloid wheel by using the ultra precision cycloid wheel forming grinder, the first thing is to design the structure of the forming grinding wheel, that is, the grinding wheel must be completely consistent with the profile curve of the gear to be processed to finish the dressing of the wheel profile. The forming grinding wheel grinds the cycloid gear, and the grinding schematic diagram is shown in Fig.7.

1.Shaping and dressing roller; 2.Shaping grinding wheel; 3. Cycloid gear

3.2 Finite element analysis of lathe bed

In order to consider the influence of external environment on the experiment, the experimental environment of different material beds is set at room temperature.

Static stress analysis of cast iron bed and hybrid fibre artificial granite bed is carried out respectively. According to the actual processing needs, the data needed for simulation analysis are imported into ANSYS Workbench to simulate the stress and strain of the bed under specific loads. The static characteristics of the two beds were compared.

The 3D model of the lathe bed is saved as step format and imported into ANSYS Workbench for finite element analysis. Fig.8 is the solid model of the lathe bed. The wall thickness of the hybrid fiber artificial granite bed designed in this paper is 60 mm.

Fig.8 Solid model of lathe bed

3.2.1Materialpropertiesofmachinetoolbed

The compressive strength test results of hybrid fiber artificial granite specimens prepared by different proportions in Table 1 were compared, and the material properties of group 7 were taken as the reference value of ultra-precision cycloid grinding machine body of hybrid fiber artificial granite. Table 2 is the material properties of hybrid fiber artificial granite materials, non-added hybrid fiber artificial granite materials and gray cast iron materials.

Table 2 Properties of 3 kinds of bed materials

3.2.2 Mesh generation

The finite element method calculates each small area and then analyses the stress of the whole bed. Each mesh is a small area. The system will adopt automatic meshing according to the structure of the machine bed. When meshing the bed body model, the relationship between the density and the calculation accuracy of the grid is fully taken into account. The simplified model of the bed body of hybrid fiber artificial granite adopts the method of integral automatic partitioning and local refinement of the guide surface. The results of meshing are shown in Fig.9.

Fig.9 Mesh generation

3.2.3 Load and boundary conditions

In order to simulate the load borne by the actual work of the bed body, the weight of the remaining unit parts on the bed body is converted to the support surface corresponding to the bed body. The support surface of the bed shaft is under pressure of 8 000 N, and the direction is vertical downward. Because the weight of the bed body is heavier, the weight of the bed body cannot be ignored, imposing fixed constraints on the foot of the bed body.

3.2.4 Analysis results

The elastic modulus of cast iron material is about 4 times that of the other two materials, so the lateral wall thickness of cast iron bed is 1/4 of that of the other two. As shown in figure 10, under the same load and constraint conditions, the equivalent deformation of the bed body and the equivalent stress of the bed body of the three kinds of materials. Table 3 is the finite element analysis results of the three kinds of material bed bodies.

Table 3 Results of bed analysis of three materials

Hybrid fibers used in artificial granite can effectively exert the advantages of different kinds of fibers. Steel fibers and carbon fibers have large elastic modulus and high tensile strength, which can effectively inhibit the micro-deformation of artificial granite matrix. The combination of glass fibers, polypropylene fibers and epoxy resin binder increases the toughness of artificial granite matrix. Hybrid fibers and epoxy resin binders form a resin-fiber interface, which can consume energy generated by vibration loads and improve the damping properties of materials.

Fig.10 Equivalent deformation and equivalent stress of lathe bed for 3 kinds of material

Compared with hybrid fiber artificial granite, the mechanical properties of artificial granite are lower, the strain is larger under smaller stress, and the anti-vibration performance is lower, which has a greater impact on the processing accuracy of machine tools.

4 Conclusion

Based on the above research, the following conclusions are drawn:

(1) The compressive strength of artificial granite can be improved by adding hybrid fiber.

(2) On the basis of determining the percentage of each component of artificial granite, three kinds of fibers (steel fiber, carbon fiber and glass fiber) were added in proportion. When the mass percentages of aggregate, binder, filler and hybrid fiber were 82%, 12%, 4% and 4%, respectively, the compressive strength of the material reached the maximum value of 138.4mpa.

(3) According to the finite element analysis of the bed body of three materials with similar structure, the equivalent deformation of the bed body of the super-precision cycloid grinding machine made of hybrid fiber artificial granite is small, the equivalent stress is low, and the first 5 natural frequencies of the bed body are the highest, indicating that the dynamic and static characteristics of the bed made of this material are better than the other two materials.