基于烏鴉搜索算法的行星滾柱絲杠參數優化

蔡威; 劉更; 馬尚君; 周勇; 付曉軍; 張建新

doi:10.13374/j.issn2095-9389.2022.04.12.009

基于烏鴉搜索算法的行星滾柱絲杠參數優化

doi: 10.13374/j.issn2095-9389.2022.04.12.009

蔡威¹,
劉更^1, ,,
馬尚君^1, ,,
周勇²,
付曉軍¹,
張建新^{1, 3}

1.
西北工業大學機電學院陜西省機電傳動與控制工程實驗室，西安 710072
2.
西北工業大學航空學院，西安 710072
3.
湖北江山重工有限責任公司，襄陽 441057

基金項目: 國家自然科學基金資助項目（51875458,51905428）；陜西省重點研發計劃資助項目（2021ZDLGY10-08）；陜西省一般項目—青年項目（2020JQ-178）

詳細信息

通訊作者:
劉更，E-mail: npuliug@nwpu.edu.cn

馬尚君，E-mail: mashangjun@nwpu.edu.cn

中圖分類號: TH132.1
計量
- 文章訪問數: 452
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- PDF下載量: 87
- 被引次數: 0
出版歷程
- 收稿日期: 2022-04-12
- 網絡出版日期: 2022-07-19
- 刊出日期: 2023-05-31

Optimization research of planetary roller screw mechanism parameters based on crow search algorithm

CAI Wei¹,
LIU Geng^{1
, ,},
MA Shang-jun^{1
, ,},
ZHOU Yong²,
FU Xiao-jun¹,
ZHANG Jian-xin^{1, 3}

1.
Shaanxi Engineering Laboratory for Transmissions and Controls, School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, China
2.
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China
3.
Hubei Jiangshan Heavy Industries Co., Ltd., Xiangyang 441057, China

More Information

Corresponding author: LIU Geng, E-mail: npuliug@nwpu.edu.cn; MA Shang-jun, E-mail: mashangjun@nwpu.edu.cn

摘要

摘要: 針對行星滾柱絲杠結構參數匹配問題，提出一種基于烏鴉搜索算法的參數優化模型。考慮行星滾柱絲杠螺紋嚙合點位置的影響，建立絲杠、滾柱以及螺母空間螺旋曲面方程，得到螺紋嚙合點處位置與螺紋牙厚之間的關系。根據螺紋副和齒輪副嚙合關系，確定內齒圈和滾柱端部輪齒設計參數。利用空間螺旋曲面方程，獲得螺紋嚙合點處的法向量，并推導行星滾柱絲杠各零件間的受力關系。以行星滾柱絲杠結構參數作為設計變量，以螺母外徑、絲杠中徑、滾柱長度等參數最小為優化目標，考慮行星滾柱絲杠結構約束和主要承力部件強度約束，利用烏鴉搜索算法作為優化算法，建立行星滾柱絲杠參數優化模型，從而實現優化變量最佳匹配。最后，針對三種負載，利用該優化模型得到三組行星滾柱絲杠結構參數，并將其優化結果與國外產品手冊進行對比，從而驗證了本文優化模型有效性。
- 行星滾柱絲杠 /
- 結構參數 /
- 優化設計 /
- 烏鴉搜索算法 /
- 多目標優化
Abstract: Because structural parameter matching has a strong influence on the service behavior of planetary roller screw mechanisms (PRSM), understanding how to effectively design the structural parameters of PRSM is highly important in practical industrial applications. This study proposes a parameter optimization model based on a crow search algorithm (CSA) to solve the structural parameter matching problem of PRSM. The relationship between the main structural parameters of PRSM can be deduced according to the working principle and geometric conditions. The screw, roller, and nut space spiral surface equation are established by considering the influence of the meshing point position of PRSM on thread meshing clearance. The relationship between the meshing point position and PRSM tooth thickness is obtained using the tangent contact condition of the spiral surface. To achieve no backlash meshing and improve PRSM transmission accuracy, the thread tooth thickness of the screw, roller, and nut can be adjusted. According to the meshing relationship between the thread pair and the gear pair of PRSM, the structural parameters of the annular gear and the gear at the end of the roller are determined. The normal vectors at the meshing point of the screw, roller, and nut are calculated using space spiral surface equations. To test the strength of the PRSM, static analysis of the roller is used to deduce the force relations between the main parts of the PRSM. PRSM structural parameters serve as design variables. An optimization goal is to reduce the outer diameter of the nut, the nominal diameter of the screw, and the length of the roller. The spatial structure constraints and component strength constraints of PRSM are considered. The CSA was introduced to be the optimization algorithm. The parameter optimization model of PRSM is established for achieving optimum matching of the optimization variables. Finally, using the proposed optimization model, three groups of PRSM structural parameters are obtained for three different types of load. In this study, the optimization results are compared with a foreign PRSM product manual to validate the effectiveness of the optimization model. The results show that the PRSM structural parameters obtained from the proposed model are essentially consistent with those from the foreign PRSM product manual. Furthermore, the proposed model provides the structural parameters of thread teeth, which are not included in the foreign product manual. The proposed PRSM optimization model is promising for its application in actual production.
- planetary roller screw mechanism /
- structural parameters /
- optimization design /
- crow search algorithm /
- multi-objective optimization

HTML全文

圖 1 PRSM結構圖

Figure 1. Structure graphing of PRSM

下載: 全尺寸圖片幻燈片

圖 2 空間螺旋曲面

Figure 2. Space helix surface

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圖 3 絲杠(a)、滾柱(b)以及螺母(c)螺紋牙輪廓

Figure 3. Thread profile of the screw (a), roller (b), and nut (c)

下載: 全尺寸圖片幻燈片

圖 4 絲杠與滾柱嚙合點位置

Figure 4. Meshing position of the screw and roller

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圖 5 螺母與滾柱嚙合點位置

Figure 5. Meshing position of the nut and roller

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圖 6 PRSM運動簡圖

Figure 6. Kinematic sketch of PRSM

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圖 7 滾柱安裝示意圖

Figure 7. Schematic of the roller installation

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圖 8 滾柱受力圖

Figure 8. Force diagram of the roller

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圖 9 PRSM結構參數優化過程

Figure 9. Structural parameter optimization process of PRSM

下載: 全尺寸圖片幻燈片

表 1 PRSM材料屬性^[23–24]

Table 1. Material properties of PRSM^[23–24]

Material properties	Corresponding value/MPa
Ultimate tensile strength	2073
Ultimate shear strength	1036.5
Ultimate bending strength	3200
Bending fatigue limit	735
Contact fatigue limit	1400

下載: 導出CSV

表 2 PRSM結構參數對比

Table 2. Comparison of PRSM structure parameters

Structure parameter	F = 51000 N		F = 102100 N		F = 221600 N
Structure parameter	Proposed model	Rollvis	Proposed model	Rollvis	Proposed model	Rollvis
Nominal diameter of screw/mm	15	15	20	19.5	29	30
Nominal diameter of roller/mm	5	5	6.67	6.5	9.67	10
Pitch diameter of nut/mm	25	25	33.33	32.5	48.33	50
Pitch of thread/mm	0.4	0.4	0.6	0.4	1	0.8
Starts of screw thread	5	5	5	5	5	5
External diameter of nut/mm	31.4180	26	39.20	42	56.41	62
Thread tooth thickness of roller/mm	0.216	—	0.304	—	0.484	—
Thread tooth thickness of screw/mm	0.1754	—	0.2814	—	0.488	—
Thread tooth thickness of nut/mm	0.184	—	0.296	—	0.516	—
Teeth number of annular gear	20	—	26	—	38	—
Teeth number of gear at the end of the roller	100	—	130	—	190	—
Modulus/mm	0.25	—	0.25	—	0.25	—
Modification coefficient of annular gear	–0.3680	—	0.1413	—	0.5013	—
Modification coefficient of gear at the end of the roller	0.3680	—	–0.1413	—	–0.5013	—

下載: 導出CSV

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