CVD matching analysis of worm grinding and dressing roller based on sector concentric-ring model
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摘要: 齿轮作为重大装备的核心基础部件，其齿面精度最终靠磨齿工序保证。电镀蜗杆磨修整滚轮作为磨齿工序用蜗杆砂轮修整不可或缺的精密加工工具，间接决定了齿轮的加工质量以及制造成本。但电镀蜗杆磨修整滚轮的齿形呈三角形结构，其齿顶磨粒附着难度大、修整状况恶劣，且齿顶相比齿侧提前失效，造成滚轮提前报废。CVD齿顶增强技术作为当前修整滚轮制造的关键技术，可有效解决上述问题。借助扇形同心环模型，搭建电镀蜗杆磨修整滚轮的磨粒分布理论模型，采用赋值法对模型进行理论分析。结果表明：当CVD材料一定时，CVD的匹配数量主要决定于滚轮模数，并与滚轮模数呈一定的线型负相关关系；且与滚轮尖角圆弧有关，与滚轮压力角关系不大。通过白刚玉砂轮修整实验，发现理论模型与实际测试结果仅存在5%细微差距，可为滚轮返修保留修整余量，进而延长工具使用寿命，降低齿轮制造成本。Abstract: Objectives: As the core component of major equipment, the tooth surface accuracy of gears is ultimately guaranteed by the gear grinding process. The electroplated worm grinding roller is an indispensable precision machining tool for dressing worm grinding wheels, which indirectly plays a decisive role in the machining quality and manufacturing cost of gears. However, the tooth shape of the electroplated worm grinding roller is triangular, which leads to several issues: the adhesion difficulty of abrasive particles at the top of the tooth increases significantly, the distribution of abrasive particles becomes sparse, and the dressing condition deteriorates. The isolated abrasive particles at the top of the tooth resemble a cantilever beam structure and are easily dislodged during the dressing process. As a result, the abrasive particles at the top of the roller tooth fail earlier than those on the sides of the tooth, leading to premature roller wear and scrapping, which seriously affects the manufacturing cost of the gear. To address these issues effectively, this study uses CVD (chemical vapor deposition) reinforced material embedded composite electroplating technology to manufacture worm grinding rollers, guided by the CVD matching theory to improve the grinding stability of the rollers. Methods: First, the equivalent wear model of CVD and diamond abrasive particles is established. Then, the abrasive particle distribution theory model of electroplating worm grinding and dressing rollers is developed using the sector concentric ring model. Next, the CVD matching model is derived through rigorous mathematical formulation. However, since the theoretical model of abrasive particle distribution is complex and difficult to solve, the assignment method is used for more detailed theoretical analysis. Finally, the accuracy of the model is verified through practical applications. Results: (1) The CVD matching quality is closely related to several parameters, such as the relative material properties, electroplating process level, diamond abrasive crystal type characteristics, and roller structure. Among these, material properties, electroplating process level, and abrasive crystal type are relatively fixed. Therefore, in practical engineering applications, emphasis should be placed on the relationship between the number of CVD inserts and the geometric parameters of the worm gear grinding roller structure. (2) When the CVD material is determined, the matching number is primarily influenced by the roller module, with a certain linear negative correlation to the roller module. Additionally, there is a weak negative correlation with the radius R of the CVD arc of the roller, while the relationship with the pressure angle of the machined gear is not significant. (3) When the modulus mn and the arc radius R are both 0.80 mm, the matching number K of CVD in the roller is most suitable between 40 and 50 grains. When the pressure angle or tooth tip arc is too small, the number of CVD inlays should be appropriately increased. Generally, the change in the number of CVD inserts due to the pressure angle is no more than 10%. At the same pressure angle, when R is 0.50, 0.20, and 0.10 mm, the K value is 1.3, 2.2, and 3.3 times that when R is 0.80 mm. (4) The application verification of the trimming roller shows that when the CVD embedding quantity K reaches ROUNDUP (Kmin) or more, the service life of the trimming roller remains largely unchanged with the increase of K. Conversely, when K is reduced, the service life of the trimming roller decreases significantly. When the CVD quantity K decreases by 15%, the service life of the trimming roller is reduced by 17.6%. (5) When dressing the grinding wheel under the same dressing process parameters, the service life of the dressing roller is judged based on the number of dressing cycles after which either grinding burn or tooth profile accuracy deviation occurs. A slight difference of 5% is observed between the actual verification results and the theoretical model results. Based on this, the CVD matching quantity of the roller can be designed according to theoretical calculation results in engineering practice. This ensures proper matching of the tooth tip and side loss of the roller while allowing for a repair margin for failed rollers, effectively reducing tool manufacturing costs. Conclusions: The fan-shaped concentric ring CVD matching model simulates the actual distribution of abrasive particles and CVD inserts in worm grinding rollers and introduces the relative wear performance index between diamond abrasive particles and CVD materials. The established model effectively predicts the top and side wear of CVD grinding rollers, enabling the calculation of the appropriate number of CVD inserts. This helps guide the design of worm gear grinding rollers. The model's accuracy is verified through practical applications, and its results can be applied to optimize the grinding process, reduce tool manufacturing costs, and improve the stability and efficiency of worm gear production.
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图 13 不同颗粒CVD时的齿轮齿廓检测结果
Figure 13. Detection results of gear tooth profile under different particle CVD conditions
表 1 国内不同厂家CVD品级及性能
Table 1. CVD grades and performances from different domestic manufacturers
厂家 品级 维氏硬度
Hv / (kg·mm−2)热导率
λ / [W·(m·K)−1]断裂强度
KIC / MPa磨耗比
RAA 标准料 8000 > 1000 450 10 × 104～20 × 104 中质料 9000 1000 ～2000 550 20 × 104～35 × 104 高质料 10000 > 2000 600 35 × 104～55 × 104 B 标准料 8000 550～850 450～600 >15 × 104 C 标准料 8000 >800 500～ 1000 10 × 104～20 × 104 高质料 > 8000 800～ 2000 500～ 1000 30 × 104～35 × 104 D 标准料 8000 > 1000 350 20 × 104 高品料 10000 > 1500 550 40 × 104 E 标准料 8000 ～10000 1800 ～2200 350～550 20 × 104～35 × 104 
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模数 mn / mm 修正系数 ηm 0.80 1.50 1.00 1.42 1.25 1.35 1.50 1.15 2.00 1.00
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表 3 齿轮参数
Table 3. Gear parameters
项目 数值 模数mn / mm 1.50 齿数 Z / 个 34 压力角 αn / (°) 20 螺旋角 β / (°) 33 法向变位系数 xn 0.306 齿顶高系数 han* 1.0 顶系系数 Cn* 0.25
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表 4 滚轮参数
Table 4. Roller parameters
项目 规格或取值 直径 D / mm 120 齿形半角 α / (°) 20.0 分割圆直径 d1 / mm 107.03 CVD高度 × 厚度 × 尖角圆弧 1.5 mm × 1.0 mm × 0.8 mm ηm 1.15 磨料 天然金刚石 粒度代号 40/45
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表 5 C统计值
Table 5. C Statistical average values
单位：μm 统计值 均值 329 350 310 350 340 333 331 332 325 295 285 329 342 350 329 350 309 305 310 299 333 349 322 345 295 325 332 302 319 325 326 339 340 303 303 324 325 323 333 332 356 308 295 340 327 327 340 295 345 319 309 310 329 319 343 310 333 320 335 309 305 322 333 328 319 319 330 343 309 329 329 324 329 318 326 329 342 336 335 333 345
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表 6 EM相对测量数据
Table 6. EM相对 measurement data
磨耗比 测量值 平均值 EM相对 ED 29.2 28.2 28.3 29.700 0.962 29.2 30.1 30.1 28.3 29.5 29.2 29.2 30.3 30.2 32.2 31.2 31.1 26.5 30.6 32.2 30.3 29.5 30.3 29.2 30.2 29.2 29.6 29.6 28.2 29.8 29.2 30.3 ECVD 30.2 31.3 31.1 30.877 31.2 32.2 30.2 31.3 30.3 32.5 30.2 29.6 30.3 30.3 31.4 29.5 29.2 30.3 31.4 29.3 29.2 33.6 31.2 32.3 30.5 30.3 33.6 31.3 31.5 30.5 30.5
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表 7 λ计算值
Table 7. λ calculated value
参数 计算值 λ1 22.7562 λ2 0.0059 λ3 0.4078 λ4 0.5762 λ5 1.5390 λ6 0.5264 λ7 13689.0000
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表 8 蜗杆砂轮修整参数
Table 8. Dressing parameters of worm wheel
粗修 滚轮转速
n1 / (r·min−1)−3 200 总余量 Δ1 / mm 0.45 砂轮转速
n2 / (r·min-1)80 单次吃刀量 Δ2 / mm 0.03 精修 滚轮转速
n3 / (r·min−1)−3 200 总余量 Δ3 / mm 0.02 砂轮转速
n4 / (r·min−1)50 单次吃刀量 Δ4 / mm 0.01
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表 9 不同CVD数量滚轮的使用寿命
Table 9. Roller life with different CVD numbers
CVD数量 K / 粒 修整次数 N′ 修整滚轮失效形式 36 73 901 齿轮齿顶烧伤 40 89 092 齿轮齿廓精度超差 42 89 658 齿轮齿廓精度超差 48 90 102 齿轮齿廓精度超差
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表 10 不同失效滚轮对应的末件齿轮齿廓检测数据
Table 10. Tooth profile detection data of final gears corresponding to different failure rollers
CVD数量 K / 粒 检测项目 最大允许误差 误差均值 误差实测值 36 齿廓倾斜误差 fHα / μm 6.5 2.1 2.6 1.8 2.0 1.8 1.5 1.9 2.6 2.2 齿廓总偏差 Fα / μm 7.5 3.2 3.3 2.9 2.2 2.8 6.0 3.5 2.5 2.2 齿廓形状偏差 ffα / μm 8.0 2.6 1.8 2.1 1.9 1.8 3.2 3.2 3.2 3.2 40 齿廓倾斜误差 fHα / μm 6.5 3.1 2.6 1.0 1.3 2.5 5.2 4.8 3.9 3.2 齿廓总偏差 Fα / μm 7.5 11.4 12.3 11.3 12.2 10.1 8.0 9.5 15.2 12.2 齿廓形状偏差 ffα / μm 8.0 7.7 8.2 7.5 6.8 7.2 5.2 6.9 9.2 10.3 42 齿廓倾斜误差 fHα / μm 6.5 3.2 2.2 1.9 2.0 2.5 4.2 4.9 3.9 3.8 齿廓总偏差 Fα / μm 7.5 11.1 10.3 11.5 11.3 10.1 9.0 9.2 14.2 13.2 齿廓形状偏差 ffα / μm 8.0 8.0 9.2 7.8 6.9 7.2 6.2 6.9 8.5 11.3 48 齿廓倾斜误差 fHα / μm 6.5 3.1 3.2 2.2 2.0 2.6 3.2 3.9 3.9 3.8 齿廓总偏差 Fα / μm 7.5 11.8 11.3 11.5 12.3 10.8 10.2 9.9 15.2 12.8 齿廓形状偏差 ffα / μm 8.0 9.2 8.8 7.9 7.5 8.4 8.8 7.8 11.5 12.8
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