Chapter 3 Design Of Machine Tool Structure And Analysis

Introduction

Nowadays, a variety of machine tools have been broadly applied in different industries for fabricating various components or products, including metal parts for machinery, biomedical engineering, and green industries. It is estimated that 15% of mechanical products in the world are produced by machine tools. To fabricate the different mechanical parts, the majority of machine tools are designed and developed based on the functional considerations for industrial applications. In the meantime, the demand for low price and high capability are urgently desired by customers facing the global market competition. This also prompts the manufacturer to seek innovative design of the machine tools which can be operated at higher cutting speeds with high precisions and efficiency; however, reducing production costs and enhancing the structure performance of machine tools are another key issue needed to be concerned at this moment.

Basically, the machining performance is related to the material remove rate with high surface precision, which can further be defined in terms of the chatter-free machining conditions of a specific cutter.^1,2 The optimum machining conditions without chatter can be determined from stability diagram, which is evaluated from the frequency response function measured at the tool point according to the stability analysis criteria.^3,4 Following the machining mechanics, the machining performance can thus be determined by the dynamically interaction between the structural characteristics of machine spindle tool system and the dynamics of the cutting process.^5,6 Based on this concept, different approaches were developed for machine manufacturer to follow to improve machine productivity and energy efficiency, including the new materials^7,8 and design methodologies.^9–11 Optimization criteria of the machine tool design have been carried out by incorporating the dynamics of machine tool with the consideration of machining stability in process.^11,12 The main components or key modulus as well as their properties affecting the static and dynamic characteristics of the milling tool system have been clarified, including the machine frame structure, linear components, feeding mechanism configuration, and spindle tool holder/tool modulus.^13–15

Regarding the application of the variety of available materials, machine tool structure made with candidate materials are mainly expected to satisfy the low-cost demands and increasing processing efficiency.¹⁶ Basically, the deformation of machine tool structures under cutting forces and structural loads are responsible for the poor quality of products and vibration produced in operation. To improve both the static and dynamic characteristics, the machine tool structures should have high static stiffness and damping ability. Generally, the static stiffness of a machine tool may be increased using higher modulus material or more material in the structure through the geometry design. But it may be difficult to increase the dynamic stiffness of a machine tool because of the poor damping properties of the material. For most production of machine tool structures, gray cast iron remain the primary choice because of low cost, good damping with relatively high strength, good machinability, and consistently achievable manufacturing and processing requirements. However, with increasing demand on high-speed machining, and consistent machining accuracies, the structural rigidity, thermal stability, and vibration damping are becoming major design considerations for construction of machine tools structure.

Consequently, some nonconventional materials such as epoxy concrete, ceramic resin concrete, and artificial granite have been widely adopted in machine tools.^7,16 The artificial granite material, also known as polymer concrete, is a compound material composed of different ingredients such as synthetic resin as the binder and natural stone as the major composition. Artificial granite possess the mechanical properties as the pouring forming at normal temperature, better production environment, precise size, and smooth surfaces in fabrication. It has 50% larger heat capacity than cast iron. Also, the good damping property enables the granite to vibrate at the fast logarithmic decreased rate, about 5–10 times of cast iron.^17–20 Obviously, because of the anti-vibration property, the machine tools constructed with composite materials are expected to produce better surface roughness and the shape accuracy of the machined parts. For example, Chang and colleagues^21,22 and Lee et al.²³ used composite materials in the design of machine tool structures in an attempt to improve structural damping of machine tool structures. The composite materials was constituted by adhesively bonding glass fiber reinforced epoxy composite plates to a cast iron structure such as the machine column or head stock, which were experimentally verified to show an increase in the damping ability with the range of 1.5–5.7 times for different structure modulus and simultaneously reduced the structure weight with the range of 26%–34%.

To maximize the effectiveness and advantage of the use of composite material, the modification of the structure configuration, in addition to the material selection, is important for enhancing the structural performance. Nowadays, the finite element (FE) approach has been recognized as an effective tool in modeling the machine tool, which can accurately predict the dynamic behavior of the prototype designs without physically building any parts. This approach of designing prototype machines in software has been termed virtual prototyping.^24,25 Bustillo et al.¹⁰ proposed a strategy to redesign and manufacture the milling head made of aluminum alloys, in which the metal tubular conduits were implemented by overcoming metal contraction during manufacturing process. As demonstrated in the experimental validation, the new prototype provides sufficient mechanical performance and reliability. In the study of Cho et al.²⁶ they applied carbon/epoxy composites and resin concrete to fabricate table-top machine tool structure. The types of composites and stacking sequences for fibrous composites were determined by finite element analyses (FEAs) with respect to structural stiffness and damping capacity. The redesigned structure provided 36.8% weight reduction, 16% increased stiffness, and up to 3.64% higher loss factor. In a study of 3-axis micro computer numerical control (CNC) machining center, Kim and Chang²⁷ fabricated two hybrid columns made of carbon epoxy composite/aluminum hybrid structures with friction layers. In order to clarify the effect of stacking angle and thickness of the composites, the FE method is further employed to analyze the static deflection due to deadweight and the first natural frequency.

Summarizing the above researches, the advancement of computer aided analysis technologies integrated with FE method enable various virtualization designs to be more mature and help validate the machine models with desired overall stiffness or minimum mass with topology designs. The practical validation and investigation on the structure performances and the dynamic characteristics of the machine tool made of artificial granite material are still worthy for investigated. Therefore, the aim of this study was to evaluate the effectiveness of the structure design of machine tool made with artificial granite material. In order to gain insight into the proper and optimized configuration of the milling machine, the FEAs were performed to assess static and dynamic characteristics of the milling machines with cast iron and granite composites, respectively, for comparison. With this, evaluations of the machine with different geometry design in spindle head were made to examine the experimental measurements on the prototype machine. This can help the designer to understand the possible conditions and problems before producing machine tools and hence provide the improvements for further fabrications.

Design analysis of milling machine

Model descriptions

Figure 1(a) illustrates main components of a vertical milling machine, including the machine base, saddle, working table, vertical column, and spindle head stock. Basically, the structural modules are made of cast iron. The machine base servers as the foundation to support other structure components and the vertical column is bolted on the machine base. The moving modulus, such as the spindle head stock, saddle, and table, can be driven to move along the guide ways in longitudinal direction, respectively. The linear feeding mechanism is constructed by linear rolling guides and ball screw and supporting bearings.

Figure 1. (a) Vertical milling machine, (b) milling machine made of all cast iron, and (c) milling machine designed with artificial granite materials.

In this study, the milling machine to be reformed is shown in Figure 1(b) . The weights of the main modulus are 1600 kg (machine base), 970 kg (vertical column), 272 kg (spindle head stock), 320 kg (saddle), and 320 kg (working table). But considering thermal effect from the spindle during long-term operation, the use of artificial granite material in constructing the machine tool structure has been regarded as a good substitute, instead of the cast iron. Table 1 compares the basic properties of artificial granite and cast iron materials.³ As show in Figure 1(c) , the machine base, vertical column, and spindle head stock were designed with similar exterior structure geometries and were made of artificial granite materials, having the weights of 1478 kg (machine base), 1595 kg (vertical column), and 274 kg (spindle head).

Table 1. Material properties of artificial granite and casting iron.

FE models

To evaluate the structure performance of the milling machine with different materials, the FE method was employed to modeling the static and dynamic behaviors of the two machine models under different loading conditions. The commercial FEA software code ANSYS 12.0 was used for the modeling of the milling machine. The FE model of machine structure is shown in Figure 2 . Each structural component of the system was meshed using 8-node hexahedron and 10-node tetrahedral element, with a total of 130,850 elements and 451,533 nodes. Regarding the linear components in the feeding mechanism of the spindle head stock, the ball screw was neglected, while the linear guide modulus were included in the FE model since they were demonstrated to affect the mechanical behaviors of the spindle heads.²⁸ The rolling interfaces between rolling balls and raceways were simulated as surface-surface contact elements with adequate contact stiffness. The rigidity of the linear guides is 1000 and 3000 N/µm in horizontal and vertical directions, respectively.²⁹ Mechanical properties for the structural deformable materials used in the FEA are summarized in Table 1. The loading conditions associated with analysis modes, as shown in Figure 2 , were given as follows:

1. Static analysis under gravity forces, without any external force;

2. Static analysis under gravity forces and external force of 6000 N in Z direction;

3. Static analysis under external force of 6000 N applied at the spindle head nose in X, Y, and Z directions, respectively;

4. Harmonic analysis for the dynamic response to the force applied at the spindle head nose in X and Y axial directions, respectively.

Figure 2. (A) Finite element model of milling machine and (B) loading and boundary conditions applied on the machine base (1) three-point supports and (2) six-point supports.

Two different boundary conditions were, respectively, imposed on the machine base, including (1) three-point supports and (2) six-point supports, as shown in Figure 2 . These supports are the positions with anchoring bolts, which support and prohibit the machine base to move in any directions.

The harmonic analysis was performed to measure the frequency response at the spindle head stock. In the FE governing equation for harmonic analysis, the damping matrix was assumed to be proportional to the structural stiffness matrix [K] according to the relationship [C] = β[K]. The value β represents the structural damping constant, depending on the damping properties of the material. Here, the damping constant was assumed as 0.002 and 0.025 for cast iron and granite material, respectively.³⁰

Analysis results

For a clear comparison of the structure performance of the milling machine formed with different materials, the static stiffness and dynamic stiffness at the head stock in each loading direction are measured according to the static and harmonic analysis results under different loading conditions.

Case I

Figure 3 illustrates the deformations of the milling machines under the self-weight. It can be found from the figure that the head stock associated with the vertical column was deflected greatly by the bending moment due to the overhang weight of these components. The maximum deformations in the three axial directions of the two different machine models under different constraints are listed in Table 2, which reveals that the deflections of the spindle head stock with granite material are close to those of cast iron model, irrespective of constraints imposed on the machine bases. For machine with six-point supports, the rotational bending stiffness of the spindle head stock against the rotation about X axis is predicted as 9.85 × 10⁶ and 8.96 × 10⁶ N m/rad for original and reformed machine model, respectively. The static stiffness for original and reformed machines under three-point supports is reduced by 23% due to less constraints on the machine bases.

Figure 3. Deformation shape of milling machine under self-weight loading conditions.

Table 2. Comparisons of the predicted deformation at the spindle head nose of milling machine with different materials (loading mode I and II) predicted deformation at the spindle head nose of milling machine under three axial force and six-point supports.

Case II

The deformations of the spindle nose of milling machine under self-gravity force and external force applied in Z axis are listed in Table 2. In this case, the applied force is opposite to the gravity force. Therefore, the milling machine shows a smaller deformation than that under the first loading case. As indicated in Table 2, the Z-axial static stiffness of the original cast iron model and granite model with six-point supports are estimated approximately 330 and 286 N/µm, respectively. The static stiffness for original and reformed machines under three-point supports is 115 and 109 N/μm, respectively.

Case III

Figure 4 illustrates the deformations of the different milling machines under the specific loading conditions. As observed, the head stock is greatly deformed due to twisting effects of the force that is applied at the bottom of spindle head stock. When a vertical force is applied at the bottom of spindle head stock, the head stock is bent upward and partly constrained by the linear guides on vertical column. The predicted deformations at the spindle nose of the milling machine under three-point and six-point supporters are listed in Table 3. For machine bases constrained at six points, the static stiffness of original model in X, Y, and Z directions is calculated as 44.7, 102, and 111 N/µm, respectively and the static stiffness of model reformed with granite material is 40.8, 89.5, and 113.2 N/µm in X, Y, and Z directions, respectively. For machine bases under three-point supports, the static stiffness of original model in X, Y, and Z directions is 39.7, 111, and 125 N/µm, respectively, and the static stiffness of granite model is 36.5, 98.4, and 130 N/µm in X, Y, and Z directions, respectively. Concluding this analysis, it can be found that the static stiffness of the machine model with granite material is comparable to that of the machine with cast iron material.

Figure 4. Deformation shape of milling machine under external forces: (a) deformation of milling machine under lateral force along X axis and (b) deformation of milling machine under vertical force along Z axis.

Table 3. Comparisons of the predicted deformation at the spindle head nose of milling machine with different materials (loading mode III).

Frequency response functions

The dynamic performances reflect structure's resistance to vibration. Therefore, modal analysis was performed to determine the first four fundamental vibration modes, as shown in Figure 5 , which is predicted for the model with granite material. The first vibration modes at 53 Hz is forward bending motion of the spindle head stock associated with vertical column along Y-Z plane; the second mode at 75 Hz is the lateral bending of column along X-Z plane, accompanied with the twisting of the spindle head about Y axis; the third mode occurs at 115 Hz, which is the twisting motion of the spindle head stock associated with vertical column about Z axis; the fourth mode occurs at 172 Hz, being the backward bending motion of the spindle head stock associated with vertical column along Y-Z plane. Machine model with cast gray iron also shows similar vibration behaviors at higher frequencies because of its high material stiffness. The corresponding four natural frequencies are 85, 108, 168, and 195 Hz, respectively.

Figure 5. Fundamental vibration mode shapes of a milling machine.

Figure 6 illustrates the predicted frequency response at the end of spindle head of the milling machine in X and Y directions, respectively, which are expressed in terms of dynamic compliance in magnitude as a function of the frequency. As observed in the figure, for milling machine designed with granite material, the maximum compliance in X and Y direction is 0.185 µm/N (115 Hz) and 0.085 µm/N (55 Hz), respectively. For milling machine designed with cast iron, the maximum compliance in X and Y direction is 0.275 µm/N (110 Hz) and 0.198 µm/N (195 Hz), respectively. The minimum dynamic stiffness in X and Y axis is 5.45 and 11.8 N/µm for granite model. The corresponding values for casting model are 3.63 and 5.05 N/µm. Overall, the milling machine with granite material shows a superior dynamic structure performance than the conventional casting machine.

Figure 6. Comparisons of the frequency response functions at head sock of milling machines with different materials.

As shown in Figure 3 , the significant deformation of the spindle head stock is partly contributed by the deformation of the structure components including vertical column and head stock and partly by the deformation or displacement at the sliding guides which are used to mount the head stock on the guide rails on vertical column. In this analysis, the two different machine models are equipped with the same linear guide components and hence the structure material plays an important role in determining the structure rigidity. From these analysis and comparisons, we can find that the milling machine made of the traditional cast iron shows higher structure rigidity than the machine made of the artificial granite. However, considering the desired requirement for high-precision machining, the dynamic characteristics with higher damping ability is more important. From the dynamic analysis of the whole machine, we can find that the machine designed with granite shows superior dynamic stiffness at the dominant vibration modes, which indeed is more appropriate for milling machine with better structural performance.

Design analysis of spindle head

Model description of spindle head stock

Following the analysis results of the whole milling machine, we can find that the use of the artificial granite material in construction of the machine frame enables the milling machine behaving better dynamic characteristics. Besides, because of the better thermal characteristics and damping ability, in this study, the artificial granite material was used for the main modulus of the machine frame. Moreover, considering the requirement of the low-motion inertia and the structure rigidity, the spindle head stock was still made of the cast iron. However, the structure geometry of the spindle head was concerned to enhance the stiffness with reduction of the weight. Therefore, in this section, this study proposed a series of different redesigned head stocks, and their structure characteristics were examined in terms of the static analysis.

Figure 7 shows the original and redesigned casting spindle head stock. Based on the original one, the other four spindle head stocks were designed by adding stiffened ribs of different thickness on the outer housing with attempt to enhance the structure rigidity. The FE model of the spindle head stock is shown in Figure 7 , which is meshed using 8-node hexahedron and 10-node tetrahedral element, with a total of 15,042 elements and 46,060 nodes. Also, in this analysis, in order to clarify the influence of the added ribs, the static analysis was performed on the individual spindle stock model, which was isolated from the vertical column. Therefore, the stock models were constrained at the locations where the linear guide modulus and ball nut were mounted. A force was applied at the head nose in X direction (Figure 7 ). Again, the deformed amounts of the spindle heads were assessed for comparisons.

Figure 7. (a) Spindle head stocks with different stiffened ribs and (b) finite element model and boundary condition.

Analysis results

Table 4 compares the deformation at the head nose of the different spindle head stock models under the force applied in X direction. It is found that the second and fifth stock models show least deformation of the spindle head in X direction, which is equivalent to the axial stiffness of 286 N/µm, approximately. Compared with the original model, the stiffness is increased by about 36% due to the stiffened rib added on the head stock, but the weight only increased by 13%. Therefore, the second and fifth stock modes were the candidates for further analysis in application on the whole machine model.

Table 4. Comparisons of the maximum deformations of the different spindle head stock.

Machine model with different spindle head stocks

In this section, the candidates of the stiffened stock models were installed on the vertical milling machine model through the linear guide modulus, in which the linear guide modulus were simulated in the same way as stated in section "FE models." With these machine models, the structural characteristics were examined again to clarify the influence of the geometry design of the head stock on their structure performances. The different machine models are shown in Figure 8 . In FEA, the structure modulus such as machine base and vertical column are made of artificial granite, in addition to the spindle head stock which is made of cast iron. Again, the machine base of the models was constrained at the six-point supports, as described in section "FE models." A cutting force of 6000 N was applied at the spindle head nose in X direction.

Figure 8. (a) Whole milling machine with different stiffened head stock ribs and (b) finite element model.

Analysis results

Table 5 compares the deformation at the head nose of the different machine with different spindle head stock under the force applied in X direction. For the three models, the static stiffness in X direction was examined because the machine is weaker in X direction than in Y and Z directions. The stiffness is estimated as 44.7, 47.6, and 67.4 N/µm, respectively. It is obvious that the third machine modeled with more stiffened ribs on head stock shows highest structure rigidity. Compared with the original one, the structure stiffness of the fifth redesigned head is increased by 50%, only 6% increment in the weight of the machine. Therefore, the fifth stock mode was the final selection for fabrication of the whole machine model.

Table 5. Comparisons of the maximum deformations of the whole milling machine with different spindle head stock.

Verification of machine prototype

In order to meet quality requirements, the examinations of the geometry precision and alignment of machine tools are essential. The geometric accuracy of assembled structural modulus is the basis for milling machine being able to produce parts with required precision. Therefore, for verifying the feasibility of the use of artificial granite in construction of milling machine, we fabricated the prototype according to the design model proposed in section "Design analysis of spindle head," as shown in Figure 9 . Using this machine prototype, the assemblage precisions were first examined for following tests.

Figure 9. (a) Solid model of milling machine and (b) prototype made of artificial granite.

Geometry accuracy measurement

Following the accuracy examination standards, we conducted the essential examination to ensure the assemblage precision and structure rigidity can satisfy the requirement of the machine product.

X-Y table flatness

The geometry precision was first examined by measuring the dynamic level of working table on X-Y plane using two engineer spirit levels. Figure 10 shows the measuring positions of spirit levels on working table. There are nine points to be measured in X and Y directions with two spirit levels (precision = 0.02 mm/M). The measured precisions were listed in Table 6, which shows the dynamic levels are within the standard of 0.06 mm/M.

Figure 10. Schematic diagram of measuring positions of working table.

Table 6. Measured dynamic levels of working table (0.02 mm/m).

Parallelism and perpendicularity of spindle axis

The geometric accuracy test was carried out using dial gauge indicator and square gage following the ISO standard 10791. The examinations include (1) the parallelism between the spindle axis, (2) the vertical displacement in vertical XZ and YZ plane, and (3) perpendicularity between spindle axis and X axis in XZ and YZ plane. The results were listed in Table 7.

Table 7. Parallelism and perpendicularity of the spindle tool with respect to the working table.

Measurement of thermal displacement

The non-contact displacement meter was used to measure the variation of displacement in X, Y, and Z axis with time under environment conditions. The spindle head is served as the measuring point to examine the displacement variations in the three axial directions. Through this examination, it can be understood about the variations of displacement caused by temperature variations. Figure 11 shows the measurement configurations, in which three displacement sensors were, respectively, mounted on the working table to measure the variation of displacements of spindle head in X, Y, and Z axes. The displacement sensor is a type of eddy current displacement meter with a resolution of 0.1 µm and measuring range of 2 mm. Besides, two temperature sensors (accuracy ±0.15 °C, range: 30°C–350°C) were, respectively, mounted on vertical column and machine base to measure temperature variation of the column and environment. Figure 12 shows the thermal deformation history varying with the time. A shown in the figure, the variation in X axis ranges from +4 to +7 µm, variation in Y axis ranges from −1.5 to 3 µm, and 2.5 to 12.5 µm for Z axis. The temperature variations of the vertical column and environment are 0.7°C and 2.83°C, respectively. It is noted that the displacement variation in Z axis is more significant than those in other axis. However, the stability is within acceptable range.

Figure 11. Configuration for measuring thermal deformations in three axes.

Figure 12. Time history of the axial variation of thermal deformation.

Dynamic characteristics

The dynamic response and natural frequency of the machine base were measured by vibration tests, which are recorded with an impact hammer and an accelerometer. Three machine bases made of different structural materials are measured for comparing their dynamic characteristics. The three machine bases were made of all cast iron, all artificial granite and steel filled with granite materials. The frequency responses measured in vibration test are illustrated in Figure 13 , which are expressed in terms of compliance as a function of the frequency. From the frequency response, the natural frequencies and the dynamic stiffness associated with the dominant vibration modes were evaluated.

Figure 13. Comparisons of the frequency responses of the machine bases with different structure materials.

According to Figure 13 , it can be found that the all casting iron machine base behaves four fundamental vibration modes at natural frequencies of 196, 316, 395, and 450 Hz, respectively. The machine base composed of granite and steel shows two fundamental modes with natural frequencies of 315 and 420 Hz. The machine base made of all granite shows two vibration modes with natural frequencies of 338 and 475 Hz. The maximum compliances of the three machine base are 4.2 µm/kN (at 196 Hz), 0.84 µm/kN (at 338 Hz), and 2.0 µm/kN (at 316 Hz) for structural material of cast iron, granite, and composition of granite and steel, respectively. From this comparison, it is apparent that the machine base made of all granite material shows highest dynamic stiffness than those of the machines made of other materials. This can be ascribed that the granite material has a better damping characteristics to resist the vibration, as stated previously, which also can be a major contribution to the high dynamic stiffness or lower compliance of the machine base. Current results also show that the use of artificial granite material can benefit more in the dynamic characteristics of the milling machine.

Conclusion

This study presented the investigations on the structure design of the machine tools made of artificial granite material through the FE approach. A prototype machine was further fabricated for experiment to realize the feasibility of granite material in construction of the machine tool.

Results of static analysis show that the static stiffness of the machine model with granite material is comparable to that of the machine with cast iron material. Furthermore, according to the harmonic analysis, the minimum dynamic stiffness of the granite model is higher than that of casting machine, about 0.5–1.3 times. Overall, the milling machine with granite material shows a superior dynamic structure performance than the conventional casting machine. Regarding the moving component, the structure stiffness of the casting head stock redesigned with stiffened ribs is increased by 50%, only 6% increment of the weight. Experimental investigation on the prototype made of artificial granite also shows the great thermal stability in the three axis feeding mechanism. The vibration tests of the machine bases indicate that the maximum compliances of the machines are 4.2 µm/kN (at 196 Hz), 0.84 µm/kN (at 338 Hz), and 1.65 µm/kN (at 316 Hz) for structural material of cast iron, granite, and composition of granite and steel, respectively. This also verifies the superiority of the anti-vibration ability of the granite material.

As a conclusion of the investigation, an appropriate redesign of the machine frame structure is a prerequisite when attempting to take benefit from the use of artificial granite material, instead of the conventional casting iron. In future work toward an innovative design of machine tool with alternative materials, the redesign work can be fulfilled in an effective way through FE techniques, in which the interactive effects of the dynamic behaviors of the physical spindle tool module and machine frame structure should be taken into considerations in the evaluation machining performance.

Acknowledgements

The authors thank the assistance of Quaser Machine Tools Inc. and Precision Machinery Research & Development Center (PMC) in the completion of this study.

Academic Editor: Stephen D Prior

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Chapter 3 Design Of Machine Tool Structure And Analysis

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