, 黎柏春2, 张景强3 1. 东北大学秦皇岛分校 控制工程学院, 河北 秦皇岛 066004;
2. 东北大学 机械工程与自动化学院, 辽宁 沈阳 110819;
3. 沈阳航空航天大学 机电工程学院, 辽宁 沈阳 110136
收稿日期：2018-06-29
基金项目：国家自然科学基金青年基金资助项目(51505303);中央高校基本科研业务费专项资金资助项目(N160303001，N182303034);东北大学秦皇岛分校科研基金资助项目(XNB201714)。
作者简介：张荣闯(1984-), 男, 辽宁辽阳人, 东北大学秦皇岛分校讲师，博士。
摘要：切削力是滚齿工艺参数优化、刀具磨损预测和机床设计的重要依据.针对圆柱齿轮滚齿加工, 提出了一种基于实体建模技术的切削过程几何仿真方法, 实现了未变形切屑的准确提取, 进而计算出未变形切屑厚度.基于微分离散思想, 将滚刀刀齿切削刃离散成一系列微元切削刃, 采用Kienzle-Victor力模型, 建立微元切削力模型, 进而构建整体滚刀切削力模型.结合Kistler 9123C旋转测力仪和DMU50五轴立式加工中心进行滚齿切削力测量试验, 试验结果表明, 预测的滚削力在幅值和变化趋势上与试验测量结果吻合良好, 验证了该滚削力预测方法的有效性.
关键词：滚齿切削力实体建模未变形切屑厚度几何仿真
Prediction of Cutting Forces in Gear Hobbing of Cylindrical Gears
ZHANG Rong-chuang1
, LI Bai-chun2, ZHANG Jing-qiang3 1. School of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China;
2. School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China;
3. School of Mechatronics Engineering, Shenyang Aerospace University, Shenyang 110136, China
Corresponding author: ZHANG Rong-chuang, E-mail:zhangrongchuang@neuq.edu.cn
Abstract: The cutting forces involved during gear hobbing play an important role in process parameter optimization, hob wear prediction and hobbing machine design. The geometrical simulation of the gear hobbing process based on solid modelling was realized. Solid chips were extracted accurately and undeformed chip thickness was calculated. To model the hobbing process, the tool cutting edge was divided into small differential cutting edge segments. The cutting forces exerted on each cutting edge element were calculated based on Kienzle-Victor′s equations and the total force components acting on the hob were obtained by integrating the elementary force components. To validate the predictive model of gear cutting forces, the experiments were carried out in DMU50 five-axis CNC machining center equipped with a Kistler 9123C rotary dynamometer. The simulation results are compared with the experiments. The cutting process is well captured by the predictive model, and good correlations in cutting forces are observed between the predictions and experiments.
Key words: gear hobbingcutting forcesolid modellingundeformed chip thicknessgeometrical simulation
高精度圆柱齿轮是高性能齿轮传动系统的重要组成部分.在圆柱齿轮加工方法中, 滚齿加工是一种被广泛应用的粗加工方法, 滚齿切削力是表征加工过程的一个重要物理参数.实现滚削力的准确预测是研究滚刀磨损与切削振动特性以及切削参数优化的关键理论基础和依据[1].
Umezaki等利用解析法分析滚齿切削过程, 综合考虑切屑流动方向、连续/断续切削对切削力系数的影响, 计算出整体滚刀的切削力[2]. Abood建立一个功能运动模型来模拟滚齿切削过程, 利用数值计算方法求出未变形切屑厚度, 进而构建出瞬时滚削力学模型, 并通过试验进行验证[3]. Klocke等基于空间离散方法开发出滚齿切削仿真软件SPARTApro, 实现切削力精确计算[4]. Tapoglou等利用CAD软件模拟滚齿切削过程, 计算出切削过程几何参量, 结合Kienzle-Victor力学模型, 预测出单齿和整体滚刀切削力[5]. Sabkhi等借助CAD软件计算出滚齿切削未变形切屑厚度, 基于ALE法确定切削力系数, 进而计算出滚削力[6]. Bouzakis等通过集成仿真环境对滚齿加工中切屑形成机制进行仿真, 同时对切削过程中的切削温度和应力进行了预测[7]. Friderikos等为研究高速钢滚刀的崩刃现象, 利用三维刚黏塑性有限元方法对切屑形成过程进行仿真, 明确了切屑挤压现象产生的机理, 获取了切屑形成过程中的应力、应变等物理量[8]. Stark等为确定导致齿轮加工过程热变形的热流密度, 通过有限元仿真软件对飞刀切齿过程切削力和切削温度进行仿真和试验验证[9]. Liu等利用有限元软件Third Wave AdvantEdge对滚齿加工过程中的切削力进行仿真, 并通过单齿铣削力试验进行验证[10]. Habibi等基于空间离散法构建端面滚齿切削过程, 实现未变形切屑有效提取, 结合斜角切削理论计算切削力[11].
本文在已有的基于实体建模的滚齿切削过程仿真研究基础上, 将滚刀切削刃离散为微元切削刃, 构建微元切削力, 进而通过积分、求和运算获得整体滚刀的滚齿切削力预测模型; 便于滚齿切削力测量, 结合Kistler 9123C旋转测力仪和DMU50五轴数控加工中心进行滚齿切削力测量试验, 试验结果验证了该滚削力建模方法的有效性.
1 滚齿切削过程建模1.1 切削过程几何仿真图 1所示, 与常规的铣削和车削等加工方式不同, 滚齿切削中滚刀轴向进给的同时与工件也必须保持严格的展成运动关系, 具有多刃断续切削和变切屑厚度的特点, 属于典型的非自由切削; 针对滚齿切削, 作者前期研究中[12-13]构建了基于实体建模技术的滚齿切削几何仿真模型, 该模型准确描述滚刀上任意一刀齿的材料去除过程和精确计算出未变形切屑厚度.
图 1(Fig. 1)
 | 图 1 滚齿切削运动示意图Fig.1 Basic kinematics of gear hobbing |
1.2 切削力建模本文采用Kienzle-Victor力学模型计算切削力, 则滚刀刀齿切削刃上每一微元切削力表示为
 | (1) |
由图 2所示, 微元切削力的方向与参与微元切削刃的位置有关, 通过投影可以得到第k个刀齿坐标系Ohkxhkyhkzhk下切削刃上第i个微元切削力:
图 2(Fig. 2)
 | 图 2 切削刃离散与坐标系Fig.2 Cutting edge discretisation and coordinate |
 | (2) |
 |
沿切削刃累加求和, 可得k号刀齿产生的滚削力, 即
 | (3) |
图 3(Fig. 3)
 | 图 3 刀齿坐标系Fig.3 Hob tooth coordinate system |
 | (4) |
 | (5) |
表 1(Table 1)
 表 1 仿真案例几何、切削参数Table 1 Process parameters for gear hobbing
| 表 1 仿真案例几何、切削参数 Table 1 Process parameters for gear hobbing |
2.2 未变形切屑几何仿真表 2所示为通过仿真计算后各刀齿在其展成位置形成的未变形切屑几何实体. 图 4所示为典型的未变形切屑厚度分布.
表 2(Table 2)
表 2 未变形切屑几何实体Table 2 Undeformed chips for gear hobbing
| 表 2 未变形切屑几何实体 Table 2 Undeformed chips for gear hobbing |
图 4(Fig. 4)
 | 图 4 典型的未变形切屑厚度分布Fig.4 Undeformed chip thickness in the typical hob tooth (a)—0号刀齿; (b)—6号刀齿; (c)—11号刀齿. |
2.3 滚削力试验设计滚齿切削力试验所用机床为DMU50五轴立式加工中心, 旋转测力仪型号为Kistler9123C. 图 5所示为滚削力在线采集过程示意图, 图 6所示为滚削力测量现场图.
图 5(Fig. 5)
 | 图 5 滚削力在线采集过程示意图Fig.5 On-line data acquisition for hobbing forces |
图 6(Fig. 6)
 | 图 6 滚削力测量现场图Fig.6 Scene diagram of hobbing force measurement |
2.4 滚削力仿真采用切削力系数如表 3所示.由于滚刀刀齿瞬时切削状态的复杂性, 当存在切屑流动干涉时, 切削力急剧增加, 采用单一切削力系数将会降低切削力预测精度.因此, 本文中以未变形切屑厚度在刀齿切削刃上的几何分布为依据, 将顶刃、圆弧刃和侧刃同时产生切屑视为存在切屑流动干涉, 采用1组切削力系数计算滚削力; 否则视为单刃直角切削, 采用2组切削力系数计算滚削力.
表 3(Table 3)
表 3 切削力系数Table 3 Cutting force coefficients
| 表 3 切削力系数 Table 3 Cutting force coefficients |
如图 7所示, 为便于与实际测量值进行对比分析, 还应将式(5)滚削力预测值从滚刀坐标系O6x6y6z6转换到测力仪坐标系Odxdydzd下, 即
图 7(Fig. 7)
 | 图 7 测力仪坐标系Fig.7 Coordinate system of dynamic dynamometer |
 | (6) |
图 8(Fig. 8)
 | 图 8 滚削力的预测值和实测值对比Fig.8 Comparison between calculated and measured cutting forces in gear hobbing (a)—实测值; (b)—预测值. |
3 结论1) 基于实体建模技术建立了滚齿切削过程几何仿真方法, 有效地提取出未变形切屑厚度.
2) 基于Kienzle-Victor力学模型, 结合微分离散的思想, 建立了滚齿切削力预测模型.
3) 采用Kistler9123C测力仪, 结合DMU50五轴立式加工中心, 构建了滚齿切削力测量方法.
4) 试验结果表明, 本文提出的方法能够很好地预测滚齿加工中的切削力幅值及其变化规律.
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