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Abstract

The ball screw and linear guide are important transmission components of a feed system, and their structure directly influences the static and dynamic characteristics of a machine tool. This study used finite element analysis to analyze the static and dynamic characteristics of the spinning machine with different structural designs. Results showed that the feed system is the key functional component that influences the static and dynamic characteristics of the entire machine. A design method is proposed for the structural optimization of the spinning machine based on the structure of the ball screw and the linear guide. Four three-roller models and five counter-roller models are established. A single-factor analysis method is adopted for the contrastive analysis of the static and dynamic characteristics. Finally, the structure of computer numerical control spinning machine with the optimal feed system structure is optimized. The analysis indicates that the reasonable optimization of the structure of the ball screw and the linear guide can effectively improve the optimization efficiency and substantially improve the static and dynamic characteristics of the computer numerical control spinning machine.

Keywords

Ball screw linear guide structure computer numerical control spinning machine static and dynamic characteristics

Introduction

Spinning is a near-net-shape-forming process that is mainly applied to manufacturing parts with axial symmetry, thin walls, and hollow circular sections.¹ The spinning technique is an important element of manufacturing technologies in aeronautics, astronautics, shipbuilding, automobile, and engineering machinery, among other fields.^2,3 The spinning equipment is the concrete implementation of the spinning technology. Computer numerical control (CNC) spinning machines in the machinery manufacturing industry have been given increasing attention owing to their advantages of high processing accuracy, high efficiency, and high material utilization rate. The static and dynamic characteristics (SDC) have considerable influences on the machining efficiency and processing quality of the machine tool. They are important indicators for measuring the vibration resistance of the machine tool. With the continuous development of modern technologies, the machine tool industry is facing new challenges and demands, such as high speed, high precision, and high reliability. Therefore, more stringent requirements are imposed on machining performance of CNC spinning machine.

The feed system with a ball screw and a linear guide as its main transmission components is the primary functional component of a machine tool.^4,5 The structure of the ball screw and the linear guide directly influences the SDC of the machine tool and consequently influences positioning precision, stability, and processing quality of the entire machine tool.

Traditional feed system mainly adopts a single ball screw to drive the linear guide. Many scholars have carried out a great deal of research on a single ball screw and linear guide^6–9 and on the SDC of the traditional feed system.^10–13 With the uninterrupted development of machine tools, the feed system with a dual-screw driven linear guide has been gradually extensively applied due to its excellent vibration resistance, high system stiffness, quick system response, and other advantages. Huang et al.¹⁴ analyzed the differences of finite element calculation results of the spindle and headstock connection and modal test values in double-screw-driven feed system. Ding et al.¹⁵ researched on equivalent vibration models of the single-ball-screw-driven and double-ball-screw-driven feed systems and calculated vibration modes and natural frequencies of both systems. Wang et al.¹⁶ established a 3D mechanical model for a double-ball-screw transmission workbench and developed an analysis formula for a comprehensive method and used numerical simulation method to study the frequency variation of different heights of gravitational center, nut positions, and platform masses. Xu et al.¹⁷ conducted the modal analysis of a workbench with a linear guide feed unit driven by double screws. The modal parameters of the linear guide feed units driven by a single ball screw and twin ball screws were analyzed, and the results were compared when nuts were located at the left, middle, and right positions of the twin ball screws. However, the influence of the structure of the ball screw and the linear guide on the machine tool has not been considered in the design of dual-drive systems. Furthermore, research on the factors influencing the SDC of a dual-drive feed system remains limited. CNC spinning machines with different forms exhibit different characteristics, structure, and stresses; thus, conclusions presented in studies on general feed systems cannot be applied to the spinning machines.¹⁸ At present, the existing studies not only lacks the analysis of the SDC of CNC spinning machines but also lacks the optimization of the structure of a feed system.

This study used finite element analysis to analyze the SDC of the spinning machine with different structural designs. Results showed that the feed system is the key functional component that influences the SDC of the entire machine. A design method is proposed for the structural optimization of the spinning machine based on the structure of the ball screw and the linear guide. Four three-roller models and five counter-roller models are established. A single-factor analysis method is adopted for the contrastive analysis of the SDC. Finally, the structure of CNC spinning machine with the optimal feed system structure is optimized. The analysis indicates that the reasonable optimization of the structure of the ball screw and the linear guide can greatly improve the SDC of the CNC spinning machine.

Forming principle and model simplification

Forming principle

Figure 1 shows the forming principle of the three-roller spinning machine. Three rollers are uniformly installed on the carriage, and the workpiece is tightened on the mandrel by the tailstock. The downward and axial movements of the rollers cause plastic deformation of the workpiece into a thin-walled long tubular part.¹⁹

Figure 1.

The forming principle of the three-roller spinning machine.

Counter-roller spinning uses internal rollers instead of mandrels and applies certain spinning forming forces on the workpiece by internal and external rollers to induce the plastic deformation simultaneously on the inner and outer surfaces of the workpiece.²⁰ The principle of counter-roller spinning is shown in Figure 2. The internal rollers and the external rollers are fixed and installed on the inner and outer columns, and the workpiece is installed on the headstock. The axial movement of the headstock causes plastic deformation of the workpiece into a thin-walled long tubular part.

Figure 2.

The forming principle of the counter-roller spinning machine.

Simplification of the model of the entire machine

The overall structure of the three-roller spinning machine with the structure of one screw and two guides needs to be optimized is shown in Figure 3.The machine tool used heavy-load ball screw and heavy-load roller guide. The ball screw is 5520 mm in length and 125 mm in diameter. Model 65 is adopted for the roller guide, whose total length is 6005 mm. The axial stroke is 3000 mm.

Figure 3.

The overall structure of three-roller spinning machine with the structure of one screw and two guides (before optimization).

The overall structure of the counter-roller spinning machine with the structure of two guides in two directions needs to be optimized is shown in Figure 4. The machine tool used large heavy-load ball screw and heavy-load roller guide. The ball screw is 5360 mm in length and 160 mm in diameter. Model 100 is adopted for the roller guide, whose total length is 3777 mm. The axial stroke is 1800 mm.

Figure 4.

The overall structure of counter-roller spinning machine with the structure of two guides in two directions (before optimization).

The CNC spinning machine is simplified as a single-degree-of-freedom spring–damper–mass system. The simplified model is shown in Figure 5.

Figure 5.

Simplification model of single degree of freedom.

The system will generate a microdisplacement x when an external stimulation F is applied. The vibration equation is defined as

$mx ″ + cx' + kx = F$ (1)

where m is the mass, k is the spring, and c is damping.

The modal parameters of the structure are unrelated to the external stimulus, and the undamped natural frequency of the system can be obtained by ignoring the influence of structural damping

$ω_{n} = \sqrt{\frac{k}{m}}$ (2)

where $ω_{n}$ is the natural frequency of the system.

When an external force $F = F_{0} \sin ω_{0} t$ is applied to the system, the structure’s vibration amplitude caused at the resonance point is

$X = \frac{F_{0}}{c \cdot ω_{n}}$ (3)

where $F$ is the external stimulation, $F_{0}$ is the amplitude of external stimulation, and $ω_{0}$ is the frequency of external stimulation.

Formulas (2) and (3) show that the increase in the system stiffness or natural frequency can increase the resonance frequency of the system and reduce the vibration amplitude at the resonance point in the case of the system damping and the mass are unchanged.

The SDC analysis and the optimization target determination

ANSYS Workbench software is adopted for the analysis of the SDC of the model. The finite element model of the structure of the three-roller spinning machine and counter-roller spinning machine is established. To reduce computation and improve the analysis efficiency, the model is simplified.

The multiple microstructures in the CNC spinning machine, including the chamfer, filleted corner, small hole, and boss, are ignored in the model simplification. The rolling surface mainly includes the joint surface of the bearing, the ball screw and nut, and the rolling guide and the slider. They are simplified as spring–damper elements. The simplified model of the ball screw pair and the linear guide pair is shown in Figures 6 and 7, respectively.

Figure 6.

The simplified model of the ball screw pair.

Figure 7.

The simplified model of the linear guide pair.

Static performance analysis

Static performance analysis mainly investigates the deformation and stress in the machine tool under effects of unchanged static load. The spinning machines set the bottom of the bed to “Fixed Support” and the applied load type to “Remote Force.” A radial spinning force (Fr) of 100 kN and an axial spinning force (Fa) of 100 kN are applied at the rollers in the limit condition. The static structure of the spinning machines with different structures is analyzed (see Figure 8).

Figure 8.

The static structure of the spinning machines with different structures: (a) three-roller spinning machine with the structure of one screw and two guides and (b) counter-roller spinning machine with the structure of two guides in two directions.

Figure 8(a) shows that the maximum deformation (0.19574 mm) occurs at the upper part of the carriage, and the maximum equivalent stress is 36.065 MPa. Figure 8(b) shows that the maximum deformation (0.032268 mm) occurs at the upper part of the column without the installation of the linear guide, and the maximum equivalent stress is 113.06 MPa.

Modal analysis

Through modal analysis, the natural frequency and modal vibration modes at various orders of the machine tool can be obtained. The dynamic stiffness and anti-vibration capacity of the spinning machine can be improved by increasing the natural frequency. The natural frequencies of the spinning machines with different structures are given in Table 1. The vibration modes are shown in Figure 9.

Table 1.

The natural frequencies of the spinning machines with different structures.

Order	Three-roller spinning machine (Hz)	Counter-roller spinning machine (Hz)
First	71.512	68.383
Second	95.542	79.378
Third	169.62	80.289
Fourth	171.48	81.879
Fifth	172.54	81.925
Sixth	174.7	82.676

Figure 9.

The modal vibration modes of the spinning machines with different structures. (a) Three-roller spinning machine with the structure of one screw and two guides: (i) first order, (ii) second order, and (iii) third order. (b) Counter-roller spinning machine with the structure of two guides in two directions: (i) first order, (ii) second order, (iii) third order, and (iv) fourth order.

Table 1 and Figure 9 show that the modal vibration modes of the entire machine are in the form of vibration based on the feed system. Thus, the feed system is the key functional component that influences the SDC of the entire machine.

Harmonic response analysis

Harmonic response analysis focuses on analyzing the structural response under excitation within a frequency range, within which the resonance vibration, fatigue, and other adverse effects brought by forced vibration can be overcome. Set the applied load type to “Remote Force.” The radial resonant force (Fr) of 100 kN and an axial resonant force (Fa) of 100 kN with frequencies of 200 or 300 Hz are applied at the rollers. The displacement–frequency response curves in the three directions of the spinning machine with different structures are analyzed, and the analysis results are shown in Figure 10. The frequencies at the maximum resonance peak are shown in Table 2.

Figure 10.

The displacement–frequency response curves in three directions of the spinning machines with different structures. (a) Three-roller spinning machine with the structure of one screw and two guides. (b) Counter-roller spinning machine with the structure of two guides in two directions.

Table 2.

Maximum resonance peak (resonance vibration frequency) of the spinning machines.

Maximum resonance peak direction	X direction (mm)	Y direction (mm)	Z direction (mm)
Three-roller spinning machine with the structure of one screw and two guides	2.26 (60 Hz)	1.06 (60 Hz)	0.05674 (162 Hz)
Counter-roller spinning machine with the structure of two guides in two directions	0.218 (51 Hz)	0.336 (60 Hz)	0.318 (46 Hz)

Figure 10(a) shows that the maximum amplitudes in the X and Y directions correspond to the first-order natural frequency of the three-roller spinning machine. Figure 10(b) shows that the maximum amplitudes in the X, the first resonance peak in Y, and Z directions also correspond to the first-order natural frequency of the counter-roller spinning machine.

The optimization target determination

The given analysis indicates that the feed system has the strongest influence on the low-order vibration mode of the spinning machine. The natural frequency at each order in the structure corresponds to the vibration mode. Furthermore, the low-order natural frequency of the entire machine has the strongest influence on the dynamic performance of the machine tool. Therefore, the feed system is the key structural component that influences the dynamic performance of the spinning machine. By the optimization design of the feed system with different structures of the ball screw and the linear guide, blindness to the optimization of the dynamic performance can be reduced, and the optimization efficiency can be improved.

Structural optimization of the spinning machine with different structures of the ball screw and the linear guide

Structural optimization of the three-roller feed system with different structures of the ball screw and the linear guide

As shown in Figure 11, four structural models are established for the three-roller feed system with different structures of the ball screw and the linear guide. Owing to the different weight of the structural models of the entire machine, the results cannot be compared. Therefore, the feed system is adopted separately for the contrastive analysis of the SDC. A single-factor analysis is adopted for the contrastive analysis of the SDC of the feed system with one screw and two guides, small-span two screws and two guides, large-span two screws and two guides, and two screws and three guides.

Figure 11.

Four structural models of the three-roller feed system: (a) one screw and two guides, (b) small-span two screws and two guides, (c) large-span two screws and two guides, and (d) two screws and three guides.

The four structural models set the installation surface of the linear guide and the ball screw seat to “Fixed Support,” and the applied load type to “Remote Force.” The same radial spinning force (Fr = 100 kN) and axial spinning force (Fa = 100 kN) are applied at the three rollers in the four structural models. The static characteristics of the four structural models are analyzed (see Table 3).

Table 3.

The static performances of the four structural models.

	One screw and two guides	Small-span two screws and two guides	Large-span two screws and two guides	Two screws and three guides
Total deformation (mm)	0.15993	0.15121	0.055245	0.029753
Maximum equivalent stress (MPa)	30.034	28.21	16.728	12.985
Weight (kg)	11,703	12,012	12,357	12,545
Number of parts	39	42	45	48

The total deformations of the four three-roller feed systems with different structures of the ball screw and the linear guide are gradually reduced. The maximum equivalent stresses have the same law of diminishing value. The weight and number of parts of three-roller feed system with different structures are compared. The total weight of the two screws and three guides is only 842 kg heavier than that of the one screw and two guides, while the number of parts is only 9 more.

The natural frequencies of the four structural models are also analyzed under the same conditions (see Table 4).

Table 4.

The natural frequencies of the four structural models.

Order	One screw and two guides (Hz)	Small-span two screws and two guides (Hz)	Large-span two screws and two guides (Hz)	Two screws and three guides (Hz)
First	69.002	70.404	98.901	111.06
Second	92.426	93.424	110.44	111.96
Third	110.87	111.65	111.99	112.04
Fourth	113.72	111.84	112.91	113.81
Fifth	210.02	113.46	114.43	173.21
Sixth	234.73	113.56	117.5	196.58

The natural frequencies of the two screws and two guides are remarkably higher than those of the one screw and two guides. The natural frequencies of the large-span two screws and two guides are remarkably higher than those of the small-span two screws and two guides. Among the four structural models, the structure of two screws and three guides exhibits the highest natural frequencies.

Set the applied load type to “Remote Force.” A radial resonant force (Fr) of 100 kN and an axial resonant force (Fa) of 100 kN with frequency of 300 Hz are applied at each of the three rollers. The displacement–frequency response curves in the three directions of the four structural models are analyzed and shown in Figure 12. The frequencies at the maximum resonance peak are shown in Table 5.

Figure 12.

The displacement–frequency response curves in three directions of the four structural models: (a) X direction, (b) Y direction, and (c) Z direction.

Table 5.

Maximum resonance peak (resonance vibration frequency) of the four structural models.

Maximum resonance peak direction	One screw and two guides	Small-span two screws and two guides	Large-span two screws and two guides	Two screws and three guides
X direction (mm)	7.6835 (66 Hz)	4.5413 (75 Hz)	1.2022 (84 Hz)	0.864 (165 Hz)
Y direction (mm)	3.7682 (66 Hz)	2.2192 (75 Hz)	0.58561 (84 Hz)	0.40859 (165 Hz)
Z direction (mm)	2.8039 (90 Hz)	0.53007 (126 Hz)	0.33007 (144 Hz)	0.1134 (156 Hz)

The displacement–frequency response curves show that for the four structural models, the maximum resonance peaks in the three directions are gradually reduced, and the corresponding resonance vibration frequencies are gradually improved.

In summary, the total deformations of the structure of two screws and three guides are reduced by 81.40%, 80.32%, and 46.14% compared with the one screw and two guides, small-span two screws and two guides, and large-span two screws and two guides, respectively, and the maximum equivalent stresses are reduced by 56.77%, 53.97%, and 22.38%, respectively. The first six orders of natural frequency show that the natural frequency at each order in the structure of two screws and three guides is improved in different degrees. The weight of the two screws and three guides is only 7.19% higher than that of the one screw and two guides, and the number of parts is only 9 more. This result indicates that the quantity of the screw guides and the distance of the screw span are important factors influencing the SDC of the feed system. In contrast, the structure of two screws and three guides exhibits the best SDC.

Structural optimization of the counter-roller spinning machine with different structures of the linear guide

As shown in Figure 13, five structural models are established for the counter-roller spinning machine with different structures of the linear guide. Figure 13 actually wants to show the entire machine model of the counter-roller spinning machine. Because of the occlusion of columns, the structural forms of different feed systems cannot be seen, so different feed systems are adopted to replace the entire machine model. The influences on the SDC of the counter-roller spinning machine of the two guides in two directions, four guides in two directions, four guides in four directions, six guides in four directions, and eight guides in four directions are investigated.

Figure 13.

Five structural models of the counter-roller spinning machine: (a) two guides in two directions, (b) four guides in two directions, (c) four guides in four directions, (d) six guides in four directions, and (e) eight guides in four directions.

The five structural models set the installation surface of the linear guide and the ball screw seat to “Fixed Support” and the applied load type to “Remote Force.” The same radial spinning force (Fr = 100 kN) and axial spinning force (Fa = 100 kN) are applied at each roller in the five structural models. The static performances of the five structural models are analyzed (see Table 6).

Table 6.

The static performances of the five structural models.

	Two guides in two directions	Four guides in two directions	Four guides in four directions	Six guides in four directions	Eight guides in four directions
Total deformation (mm)	0.032268	0.032141	0.031529	0.031404	0.031129
Maximum equivalent stress (MPa)	113.06	101.96	101.58	101.42	101.34

The total deformations of the five counter-roller spinning machines with different structures of the linear guide gradually decrease, but it does not change very much. The maximum equivalent stresses have the same law. The natural frequencies of the five structural models are analyzed under the same conditions (see Table 7).

Table 7.

The natural frequencies of the five structural models.

Order	Two guides in two directions	Four guides in two directions	Four guides in four directions	Six guides in four directions	Eight guides in four directions
First	68.383	74.311	83.115	83.122	83.13
Second	79.378	77.392	83.133	83.137	83.145
Third	80.289	83.006	84.031	84.041	84.046
Fourth	81.879	83.126	84.041	84.049	84.054
Fifth	81.925	83.191	85.792	87.784	89.124
Sixth	82.676	84.036	86.461	88.329	89.282

The natural frequencies of the structures of two guides in two directions, four guides in two directions, and four guides in four directions gradually increase. However, the natural frequencies of the structures of four guides in four directions, six guides in four directions, and eight guides in four directions are basically consistent and the increase is minimal.

Set the applied load type to “Remote Force.” A radial resonant force (Fr) of 100 kN and an axial resonant force (Fa) of 100 kN with a frequency of 300 Hz are applied at each of the eight rollers. The displacement–frequency response curves in the three directions of the five structural models are analyzed and shown in Figure 14. The frequencies at the maximum resonance peak are shown in Table 8.

Figure 14.

The displacement–frequency response curves in three directions of the five structural models: (a) X direction, (b) Y direction, and (c) Z direction.

Table 8.

Maximum resonance peak (resonance vibration frequency) of the five structural models.

Maximum resonance peak in direction	Two guides in two directions	Four guides in two directions	Four guides in four directions	Six guides in four directions	Eight guides in four directions
X direction (mm)	0.21836 (51 Hz)	0.098719 (75 Hz)	0.049054 (174 Hz)	0.035754 (189 Hz)	0.02452 (198 Hz)
Y direction (mm)	2.1261 (138 Hz)	0.73221 (168 Hz)	0.69374 (186 Hz)	0.58412 (195 Hz)	0.58737 (204 Hz)
Z direction (mm)	0.31817 (48 Hz)	0.10725 (57 Hz)	0.069214 (180 Hz)	0.056805 (195 Hz)	0.029973 (198 Hz)

The displacement–frequency response curves of the five structural models show that the maximum resonance peaks in the three directions are gradually reduced, and the corresponding resonance vibration frequencies are gradually improved.

Optimization result validation of the entire machine

Validation of the three-roller spinning machine

The overall structure of the optimized three-roller spinning machine with the structure of two screws and three guides is shown in Figure 15.

Figure 15.

The overall structure of three-roller spinning machine with the structure of two screws and three guides (after optimization).

Under the same force conditions, the SDC of the entire machine about one screw and two guides and the two screws and three guides are analyzed (see Table 9).

Table 9.

Comparison of the SDC of the entire machine.

	Total deformation (mm)	Equivalent stress (MPa)	First order (Hz)	Second order (Hz)	Third order (Hz)
One screw and two guides	0.19574	36.065	71.512	95.542	169.62
Two screws and three guides	0.029378	11.381	51.972	103.8	130.1

SDC: static and dynamic characteristics.

In Table 9, in order to install the third linear guide and the upper ball screw seat, the three-roller spinning machine with the structure of two screws and three guides has added the beam, the front, and back brackets. According to formula (2), as the total weight of the spinning machine increases, the natural frequency decreases relatively.

As shown in Figure 16, the maximum amplitudes of the three-roller spinning machine with the structure of two screws and three guides in the X, Y, and Z directions are near the 90 Hz frequency.

Figure 16.

The displacement–frequency response curves in three directions of the three-roller spinning machine with the structure of two screws and three guides.

These results indicate that the structure of two screws and three guides exhibits reduced total deformation (84.99%), reduced maximum equivalent stress (68.44%), and increased maximum resonance vibration frequency (50%). Therefore, QX63 Series three-roller CNC spinning machine with the structure of two screws and three guides is adopted.

2. Validation of the counter-roller spinning machine

The overall structure of the optimized counter-roller spinning machine with the structure of four guides in four directions is shown in Figure 17.

Figure 17.

The overall structure of counter-roller spinning machine with the structure of four guides in four directions (after optimization).

According to analysis results of the entire machine of the counter-roller spinning machine in section “Structural optimization of the counter–roller spinning machine with different structures of the linear guide,” the changes in the SDC of the entire machine are minimal for the structures of four guides in four directions, six guides in four directions, and eight guides in four directions. This result indicates that the increase in system stiffness is minimal if the linear guides are increased and are arranged in four directions. In consideration of the economic benefits and processing assembly, the structure of four guides in four directions is optimal.

Compared with the structure of two guides in two directions, the structure of four guides in four directions exhibits reduced total deformation (2.29%) and reduced maximum equivalent stress (10.15%). The first six orders of the natural frequency of the structure of four guides in four directions are also improved accordingly. In the harmonic response analysis, the maximum resonance peaks of the same structure decrease by 77.54%, 67.37%, and 78.25% in the X, Y, and Z directions; and its resonance vibration frequencies increase by 241.2%, 34.78%, and 275% in the X, Y, and Z. Therefore, QX54 Series counter-roller CNC spinning machine with the structure of four guides in four directions is adopted.

Conclusion

Through the optimization of the different structures of the ball screw and the linear guide, four structural models are established for the three-roller spinning machine. The optimization results indicate that the quantity of screw guides and the distance of the screw span are the important factors influencing the SDC of the feed system. After optimization, there are 84.99% decrease in total deformation, 68.44% decrease in maximum equivalent stress, and 50% increase in maximum resonance vibration frequency.

According to optimization of the different structures of the linear guide, five structural models are established for the counter-roller spinning machine. The optimization results indicate that arranging the linear guides in each direction is better in a symmetrical double-screw structure. The increase in system stiffness is minimal if the linear guides are increased and arranged in four directions. In consideration of the economic benefits and processing assembly, the structure of four guides in four directions is optimal. After optimization, there are 2.29% decrease in total deformation and 10.15% decrease in maximum equivalent stress. In the harmonic response analysis, the maximum resonance peak decreases by 74.39% and the resonance vibration frequency increases by 183.66% on average in the three directions.

Footnotes

The authors would like to acknowledge Prof. Zhaojun Yang and Prof. Fei Chen of Jilin University for guidance and assistance in this paper.

Handling Editor: Zengtao Chen

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) disclosed receipt of following financial support for the research,authorship,and/or publication of this article: This article was funded by National Science and Technology Major Project (No. 2016ZX04004-004) and Project of Jilin Natural Science Foundation (No. 20160101278JC).

ORCID iD

Wei Luo

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A research of spinning machine: Effect of different structures of feed system on the static and dynamic characteristics

Abstract

Keywords

Introduction

Forming principle and model simplification

Forming principle

Simplification of the model of the entire machine

The SDC analysis and the optimization target determination

Static performance analysis

Modal analysis

Harmonic response analysis

The optimization target determination

Structural optimization of the spinning machine with different structures of the ball screw and the linear guide

Structural optimization of the three-roller feed system with different structures of the ball screw and the linear guide

Structural optimization of the counter-roller spinning machine with different structures of the linear guide

Optimization result validation of the entire machine

Conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References