砂带磨损对螺杆转子磨削去除深度影响分析

陈斯睿; 孙兴伟; 杨赫然; 刘寅

doi:10.13394/j.cnki.jgszz.2023.0094

砂带磨损对螺杆转子磨削去除深度影响分析

doi: 10.13394/j.cnki.jgszz.2023.0094

陈斯睿^{1, 2,},
孙兴伟^{1, 2, ,},
杨赫然^{1, 2},
刘寅^{1, 2}

1.
沈阳工业大学机械工程学院, 沈阳 110870
2.
辽宁省复杂曲面数控制造技术重点实验室, 沈阳 110870

基金项目: 辽宁省应用基础研究计划项目（2022JH2/101300214）;2022年度辽宁省教育厅高等学校基本科研项目面上项目(LJKMZ20220459)。

详细信息

作者简介:
陈斯睿，男，1998年生，硕士研究生。主要研究方向：复杂曲面精密加工。Email: a13897990910@163.com

通讯作者:
孙兴伟，女，1970年生，教授，博士研究生导师。主要研究方向：数控装备及理论。Email：ww7247@126.com

中图分类号: TG70；TG580
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- 被引次数: 0
出版历程
- 收稿日期: 2023-04-23
- 修回日期: 2023-06-30
- 录用日期: 2023-07-26
- 刊出日期: 2024-04-01

Analysis of the influence of abrasive belt wear on the removal depth of grinding screw rotor

CHEN Sirui^{1, 2
,},
SUN Xingwei^{1, 2
, ,},
YANG Heran^{1, 2},
LIU Yin^{1, 2}

1.
School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China
2.
Key Laboratory of Numerical Control Manufacturing Technology for Complex Surfaces of Liaoning Province, Shenyang 110870, China

摘要

摘要: 为保证螺杆转子表面磨削加工材料去除的均匀性，考虑砂带磨料磨损对磨削去除深度的影响，建立螺杆转子材料去除深度数学模型。根据弹塑性变形理论，结合磨削过程中磨粒的磨损规律，建立单颗磨粒材料去除率理论模型。将磨粒的磨损分为快速磨损阶段和稳定磨损阶段2个阶段。基于单位接触面积上磨粒的数目和磨粒的出刃规律，运用数值积分和接触压力计算出磨粒的最大切削深度，利用积分建立基于砂带磨损的宏观材料去除率数学模型。该数学模型考虑了砂带的磨损，其预测值和试验值相比，最大误差为9.6%，最小误差为4.1%。该试验数据充分验证了模型的有效性，可以为保障螺杆转子廓形精度提供理论基础。
- 砂带磨损 /
- 数学模型 /
- 去除深度 /
- 螺杆转子 /
- 模型验证
Abstract: To ensure the uniformity of material removal during surface grinding of screw rotors, a mathematical model for the material removal depth of screw rotors is established, considering the impact of abrasive wear on grinding removal depth. Based on the theory of elastic-plastic deformation and the wear pattern of abrasive particles during grinding, a theoretical model for the removal rate of single abrasive material is established. The wear of abrasive particles is divided into two stages: the rapid wear stage and the stable wear stage. Based on the number of abrasive particles per unit contact area and the rule of abrasive cutting edge, the maximum cutting depth of abrasive particles is calculated by numerical integration and contact pressure, and the mathematical model of macroscopic material removal rate based on abrasive belt wear is established. The model consideres the wear of the sand belt. The maximum error of the predicted value is 9.6%, and the minimum error is 4.1% compared with the experimental value. The experimental data fully verify the effectiveness of the model, and can provide a theoretical basis for ensuring the profile accuracy of the screw rotor.
- belt wear /
- mathematical model /
- removal depth /
- screw rotor /
- model verification

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图 1 单磨粒材料去除机理图

Figure 1. Removal mechanism of single abrasive material

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图 2 砂带磨粒简图

Figure 2. Schematic diagram of abrasive belt particles

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图 3 磨粒磨损高度示意图

Figure 3. Schematic diagram of abrasive wear of sand belt

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图 4 超景深显微镜测量界面

Figure 4. Measurement interface of ultra-depth of field microscope

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图 5 未磨损砂带表面图像

Figure 5. Digital image of unworn sand belt

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图 6 磨损后砂带表面图像

Figure 6. Digital image of the worn sand belt

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图 7 砂带平均高度随时间变化关系

Figure 7. Relationship between the average height of the sand belt and time

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图 8 磨削时螺杆转子表面粗糙度

Figure 8. Surface roughness of screw rotor during grinding

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图 9 接触轮与螺杆转子间的接触压力分布

Figure 9. Contact pressure distribution between contact wheel and screw rotor

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图 10 顶端半径10 μm的单颗磨粒磨削仿真结果

Figure 10. Simulation results of single abrasive grinding with a top radius of 10 μm

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图 11 顶端半径30 μm的单颗磨粒磨削仿真结果

Figure 11. Simulation results of single abrasive grinding with a top radius of 30 μm

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图 12 顶端半径55 μm的单颗磨粒磨削仿真结果

Figure 12. Simulation results of single abrasive grinding with a top radius of 55 μm

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图 13 不同圆顶半径磨粒的磨削力曲线

Figure 13. Grinding force curves of abrasive particles with different top radius

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图 14 单颗磨粒与工件作用示意图

Figure 14. Action diagram of single abrasive particle and workpiece

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图 15 磨粒出刃高度及与工件表面作用图

Figure 15. The height of abrasive edge and its action with workpiece surface

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图 16 磨粒的出刃高度

Figure 16. Edge height of abrasive particles

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图 17 磨粒的微观材料去除

Figure 17. Microscopic material removal of abrasive particles

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图 18 砂带磨削螺杆转子材料去除量求解流程

Figure 18. Flow chart of solving material removal amount of screw rotor in abrasive belt grinding

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图 19 测量试验现场

Figure 19. Measurement experiment site

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表 1 砂带类型及属性

Table 1. Types and properties of sand belts

	锆刚玉砂带	棕刚玉砂带	碳化硅砂带	陶瓷砂带
耐磨性	最好	较好	较好	一般
磨削效率	较高	一般	最高	较高
耐热性	一般	较好	最好	较好
适合加工材料	合金钢、不锈钢	合金钢、高碳钢	非金属、有色金属	难加工材料

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表 2 材料属性表

Table 2. Material attribute table

组成部分	密度 ρ / (kg·m⁻³)	弹性模量 E / GPa	泊松比 μ	比热容 c / (J·kg⁻¹·K⁻¹)	热膨胀系数 a /(10⁻⁶·K⁻¹)
螺杆转子	7 850	210 000	0.28	556	13
接触轮	1 150	1 000	0.49	670	670

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表 3 螺杆截面数据点

Table 3. screw cross section data points

序列	X轴坐标	Y轴坐标
1	98.067 0	87.502 1
2	99.009 0	86.136 7
3	99.951 2	84.576 2
4	100.736 2	82.820 7
…	…	…
…	…	…
…	…	…
48	127.899 4	63.900 0
49	129.155 6	62.729 7
50	130.725 8	60.779 1

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表 4 材料去除深度试验值与理论值对比

Table 4. Comparison between experimental and theoretical values of material removal depth

编号	线速度V_s / （m·s⁻¹）	接触压力p/MPa	磨削时间t / min	进给速度V_f / （mm·min⁻¹）	测量值h₁ /μm	计算值h₂ /μm	误差s/%
1	10.0	0.45	5	40	60.4	57.9	4.1
2	5.0	0.60	10	40	33.8	30.8	8.9
3	12.5	0.40	15	40	26.1	28.5	9.2
4	10.0	0.50	20	40	29.1	26.3	9.6
5	7.5	0.35	5	40	48.1	44.3	7.9
6	12.5	0.45	15	40	47.4	44.5	6.1
7	7.5	0.50	5	40	66.2	61.3	7.4
8	10.0	0.35	10	40	55.4	50.1	9.6

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