Optimization of gear modification for transmission systems of rolling mills

doi:10.3785/j.issn.1006-754X.2026.05.169

Chinese Journal of Engineering Design

2026, Vol. 33

Issue (2): 254-264 DOI: 10.3785/j.issn.1006-754X.2026.05.169

Optimization Design

Optimization of gear modification for transmission systems of rolling mills

Xinwei YANG^1,²(

),Junnan GUAN¹(

),Hui LIU^1,²,Jiadong ZHOU¹

^1.School of Mechanical Engineering, Liaoning Technical University, Fuxin 123000, China
^2.Erdos Research Institute, Liaoning Technical University, Erdos 017010, China

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Abstract

To meet the high-reliability demands of the gear transmission systems in aero-engine blade rolling mills, multi-dimensional simulation and optimization methods were employed to improve the comprehensive performance. A virtual gear transmission system model was built using Romax software, and the high-load gears Z₃ and Z₆ were identified by combining static and dynamic analyses. Internal excitation analysis revealed the gear meshing impact characteristics, and a tooth surface flash temperature model was built based on Blok theory to obtain the temperature distribution along the tooth surface distance and the rolling angle. The second-generation genetic algorithm was used to optimize the composite modification of high-load gears. The results showed that after modification, the contact stress distribution on the tooth surface was improved from a step-like pattern to a uniform arch-shaped pattern, with the maximum stress reduced by 20.47%-44.94%. The fluctuation range of transmission error was reduced from 11.97-14.56 μm to 2.26-4.53 μm, and the amplitude was reduced by 68.89%-84.15%. The maximum tooth surface temperature decreased by 5.3%-13.18%, and the thermal concentration phenomenon was significantly alleviated. This study demonstrates that composite modification can synergistically optimize the mechanical, kinematic, and thermodynamic performance of gear transmission systems, providing a theoretical basis for the reliability design of high-precision gears in aviation rolling mills.

Key words： Romax gear modification gear dynamics design optimization

Received: 14 August 2025 Published: 28 April 2026

CLC:

TH 122

Corresponding Authors: Junnan GUAN E-mail: ybestxinwei@163.com;15840663421@163.com

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Cite this article:

Xinwei YANG,Junnan GUAN,Hui LIU,Jiadong ZHOU. Optimization of gear modification for transmission systems of rolling mills. Chinese Journal of Engineering Design, 2026, 33(2): 254-264.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.169 OR https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/254

辊轧机传动系统齿轮修形优化

面向航空发动机叶片辊轧机齿轮传动系统的高可靠性需求，采用多维度仿真与优化方法提升其综合性能。利用Romax软件构建齿轮传动系统的虚拟模型，结合静力学与动力学分析，识别出高载齿轮Z₃、Z₆；通过内部激励分析揭示齿轮啮合冲击特性，并基于Blok理论建立齿面闪温模型，获得温度沿齿面距离及滚动角的分布规律。采用第2代遗传算法对高载齿轮进行复合修形优化，结果表明：修形后齿面接触应力分布由阶梯状改善为均匀拱形，最大应力降低了20.47%~44.94%；传动误差波动范围从11.97~14.56 μm缩小至2.26~4.53 μm，幅值降低了68.89%~84.15%；齿面最高温度下降了5.3%~13.18%，热集中现象显著缓解。研究证实，复合修形可以协同优化齿轮传动系统的力学、运动学及热力学性能，为航空辊轧机高精度齿轮的可靠性设计提供了理论依据。

关键词： Romax, 齿轮修形, 齿轮动力学, 优化设计

Fig.1 Model of rolling mill transmission system

Table 1 Main parameters of gear pairs

Fig.2 Schematic diagram of rolling mill torque and speed

Table 2 Working conditions of roller mill

Fig.3 Lateral offset of intermediate idler under external excitation

Table 3 Contact stress during gear meshing

Table 4 Gear mesh transmission error

Fig.4 Meshing forces of gear pairs Z₁-Z₂ and Z₅-Z₆

Fig.5 Meshing forces of gear pairs Z₂-Z₃ and Z₆-Z₇

Fig.6 Meshing forces of gear pairs Z₃-Z₄ and Z₇-Z₈

Table 5 Key parameters and results of tooth surface flash temperature analysis

Fig.7 Typical types of gear modification

Fig.8 Schematic diagram of working tooth surfaces of pinions Z₃ and Z₆

Fig.9 Scores of pinion Z₃ modification schemes

Fig.10 Scores of pinion Z₆ modification schemes

Table 6 Optimal modification scheme after genetic algorithm optimization

Fig.11 Contact stress distribution at meshing position of Z₃ and lower idler

Fig.12 Contact stress distribution at meshing positions of Z₃/Z₆ and intermediate idler

Fig.13 Contact stress distribution at meshing position of Z₆ and upper idler

Table 7 Reduction of maximum contact stress at different meshing positions

Fig.14 Transmission error at meshing position of Z₃ and lower idler

Fig.15 Transmission error at meshing positions of Z₃/Z₆ and intermediate idler

Fig.16 Transmission error at meshing position of Z₆ and upper idler

Table 8 Transmission error reduction at different meshing positions

Fig.17 Tooth surface temperature at meshing position of Z₃ and lower idler

Fig.18 Tooth surface temperature at meshing positions of Z₃/Z₆ and intermediate idler

Fig.19 Tooth surface temperature at meshing position of Z₆ and upper idler

Table 9 Reduction of maximum tooth surface temperature at different meshing positions


[[1]]	房雪洋，马自勇，田英虎，等. 矿用点线啮合齿轮齿廓修形及接触特性研究［J］. 太原科技大学学报， 2025， 46（1）： 34-40. FANG X Y， MA Z Y， TIAN Y H， et al. Study on profile modification and contact of point-line meshing gear used in mining machine ［J］. Journal of Taiyuan University of Science and Technology， 2025， 46（1）： 34-40.

[[2]]	李大庆，毛亚洲，张宇轩，等. 齿面修形量对面齿轮副啮合性能的影响［J］. 现代制造工程， 2025（1）： 80-86. LI D Q， MAO Y Z， ZHANG Y X， et al. The influence of pinion modification amount on the meshing performance of face gears ［J］. Modern Manufacturing Engineering， 2025（1）： 80-86.

[[3]]	薛建华，李威. 齿廓修形机理及其对温度场的影响［J］. 东北大学学报（自然科学版）， 2013， 34（12）： 1763-1767. doi：10.3969/j.issn.1005-3026.2013.12.022 XUE J H， LI W. Tooth profile modification mechanism and its influence on temperature fields ［J］. Journal of Northeastern University （Natural Science）， 2013， 34（12）： 1763-1767. doi: 10.3969/j.issn.1005-3026.2013.12.022

[[4]]	杨微，许刚. 某同轴型电驱减速器齿轮修形优化分析［J］. 科技与创新， 2025（ 1）： 159-161. YANG W， XU G. Optimization analysis of gear modification of a coaxial electric drive reducer ［J］. Science and Technology & Innovation， 2025 （1）： 159-161.

[[5]]	汤海乐，赵秀栩，张景，等. 新能源汽车变速箱齿轮修形分析与优化［J］. 重庆理工大学学报（自然科学）， 2025， 39（1）： 177-184. doi：10.3969/j.issn.1674-8425(z).2025.01.023 TANG H L， ZHAO X X， ZHANG J， et al. Analysis and optimization of gearing modification of gearbox of new energy vehicles ［J］. Journal of Chongqing University of Technology （Natural Science）， 2025， 39（1）： 177-184. doi: 10.3969/j.issn.1674-8425(z).2025.01.023

[[6]]	侯晓燕，王曦，周越. 考虑圆弧修形和交错角的人字齿轮啮合行为分析［J］. 西安交通大学学报， 2025， 59（4）：180-192. HOU X Y， WANG X， ZHOU Y. Analysis on the meshing behavior of double helical gear considering arc modification and stagger angle ［J］.Journal of Xi’an Jiaotong University， 2025， 59（4）： 180-192.

[[7]]	苏进展，冯要克，刘镔，等. 双圆弧刀具加工直齿锥齿轮的啮合性能分析及优化［J］. 中国机械工程， 2025， 36（8）： 1683-1690. doi：10.3969/j.issn.1004-132X.2025.08.004 SU J Z， FENG Y K， LIU B， et al. Analysis and optimization of meshing performance of straight bevel gears machined by dual interlocking circular cutters ［J］. China Mechanical Engineering， 2025， 36（8）： 1683-1690. doi: 10.3969/j.issn.1004-132X.2025.08.004

[[8]]	王振博，郑鹏，刘逸飞. 基于神经网络优化的正交试验内齿轮齿面偏载矫正研究［J］. 机械传动， 2023， 47（8）： 16-23. WANG Z B， ZHENG P， LIU Y F. Research on correcting eccentric load of the internal gear tooth surface by orthogonal tests based on neural network optimization ［J］. Journal of Mechanical Transmission， 2023， 47（8）：16-23.

[[9]]	RAUT A S， KHOT S M， SALUNKHE V G. Optimization of geometrical features of spur gear pair teeth for minimization of vibration generation ［J］. Journal of Vibration Engineering & Technologies， 2024， 12（1）： 533-545.

[[10]]	GHOSH S S， CHAKRABORTY G. On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs ［J］. Mechanism and Machine Theory， 2016， 105： 145-163.

[[11]]	CARBONELLI A， RIGAUD E， PERRET-LIAUDET J. Vibro-acoustic analysis of geared systems：predicting and controlling the whining noise ［M］ //Automotive NVH Technology. Cham：Springer， 2016： 63-79.

[[12]]	BRUYÈRE J， Velex P. Towards general performance diagrams to define optimum profile and lead modifications with regard to transmission error in spur and helical gears ［J］. Mechanism and Machine Theory， 2022， 176： 105021.

[[13]]	刘震.高精度叶片辊轧机传动系统动态特性的研究［D］.阜新：辽宁工程技术大学， 2014. LIU Z. Study on the dynamic characteristics of the high precision leaf-roller rolling mill drive system ［D］. Fuxin：Liaoning Technical University， 2014.

[[14]]	CHAARI F， FAKHFAKH T， HADDAR M. Analytical modelling of spur gear tooth crack and influence on gear mesh stiffness ［J］. European Journal of Mechanics A/Solids， 2008， 28（3）： 461-468.

[[15]]	陈洪月，李玉珠，张钊，等. 采煤机摇臂齿轮传动系统固-热-力耦合特性分析［J］. 煤炭学报， 2018， 43（3）： 878-887. CHEN H Y， LI Y Z， ZHANG Z， et al. Analysis of solid-thermal-mechanical coupling characteristics of rocker-arm gear drive system of shearer ［J］. Journal of China Coal Society， 2018， 43（3）： 878-887.

[[16]]	薛建华，李威. 斜齿圆柱齿轮副热机耦合三维有限元分析［J］. 华中科技大学学报（自然科学版）， 2013， 41（10）： 54-58. XUE J H， LI W. Analyzing thermo-mechanical coupling of helical gear pair by three-dimensional finite element model ［J］. Journal of Huazhong University of Science and Technology （Natural Science Edition）， 2013，41（10）： 54-58.

[[17]]	靳立红. 采煤机截割部齿轮传动系统温度场分析与承载接触性能研究［D］. 哈尔滨：哈尔滨理工大学， 2023. JIN L H. Analysis of temperature field and load-bearing contact performance of gear transmission system of shearer cutting section ［D］. Harbin： Harbin University of Science and Technology， 2023.

[[18]]	石莹. 基于摩擦学的机车牵引齿轮力学性能研究［D］. 大连：大连交通大学， 2013. SHI Y. Study on mechanical properties of locomotive traction gear based on tribology ［D］. Dalian： Dalian Jiaotong University， 2013.

[[19]]	BLOK H. Theoretical study of temperature rise at surface of actual contact under oiliness lubricating conditions ［C］//General Discussion on Lubrication & Lubricants. London： Institution of Mechanical Engineers， 1937： 222-235.

[[20]]	杨萍，杨沛然. 斜齿圆柱齿轮的热弹流润滑理论［J］. 机械工程学报， 2006（10）： 43-48. doi：10.3321/j.issn:0577-6686.2006.10.007 YANG P， YANG P R. Theory of thermal elastohydrodynamic lubrication for helical gears ［J］. Journal of Mechanical Engineering， 2006（10）： 43-48. doi: 10.3321/j.issn:0577-6686.2006.10.007

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