负半径滚子直动推杆盘形凸轮机构运动保真及其解域研究

doi:10.3969/j.issn.1004-132X.2026.03.010

摘要/Abstract

摘要：

负半径滚子机构运动失真问题极易发生、非常突出。通过揭示凸轮理论轮廓、工作轮廓为异向等距曲线，获得了基于凸轮理论轮廓的运动保真新判据。以基圆半径和偏距构造二维坐标系，采取离散-遍历方法，发现必失真/或失真取值域，提出非滚子型/滚子型失真的新概念。讨论了行程、往程/返程运动角以及运动规律对必失真区域的影响。以滚子半径建立垂直数轴，分析了两类滚子半径取值分布特征。基于上述坐标系和数轴构建三维坐标系，获得了运动保真的解域和非解域，深入剖析了两类非解域内的“燕尾交叉Ⅰ型/Ⅱ型”两类凸轮轮廓形貌特征。运动保真解域直观阐释满足运动保真条件的凸轮基本参数取值域、机构最小尺寸解等。通过设计案例验证了所提出理论与方法的正确性和有效性。

关键词: 负半径滚子机构, 异向等距曲线, 必失真/或失真取值域, 运动保真解域

Abstract:

The issue of “undercutting” in mechanisms with negative radius follower was highly prone to occur and was very prominent. By discovering the offset curve with opposite direction relationship between the cam pitch curve and cam profile， a new criterion was proposed for no-undercutting based on cam pitch curve. Based on this new criterion， the issue of undercutting was conducted in-depth research. Firstly， a coordinate system was established based on the base circle radius and eccentric offset， and the discrete-traversal method was employed. The inevitable /possible undercutting regions were discovered. The new concepts of non-roller-type/roller-type undercutting were proposed. And the impact of stroke， rise/return phase motion angle， and motion law on inevitable undercutting regions were discussed. Secondly， a vertical numerical axis was established based on roller radius to analyze the distribution characteristics of two types of roller radius values. Then， based on the three-dimensional coordinate system established with the base circle radius， eccentric offset， and roller radius， the solution space and two types of non-solution spaces were obtained for ensuring no-undercutting. Two types of cam profile morphological characteristics， specifically the “swallowtail-shaped- type Ⅰ/type Ⅱ” corresponding to the two types of non-solution spaces were analyzed. This solution space expresses the range of values for the base circle radius， eccentric offset， and roller radius that satisfied the no-undercutting conditions， as well as the minimum size of the cam profile， etc. Finally， the correctness and effectiveness of the proposed theory and method were verified through design cases.

Key words: mechanism with negative radius roller, offset curve with opposite direction, inevitable /possible undercutting region, solution space of no-undercutting

中图分类号:

TH112

胡志超, 常勇, 杨富富, 温圣兴. 负半径滚子直动推杆盘形凸轮机构运动保真及其解域研究[J]. 中国机械工程, 2026, 37(3): 604-611.

HU Zhichao, CHANG Yong, YANG Fufu, WEN Shengxing. Study on No-undercutting and Its Solution Spaces of Cam Mechanisms with Negative Radius Roller Follower[J]. China Mechanical Engineering, 2026, 37(3): 604-611.

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链接本文: https://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2026.03.010

https://www.cmemo.org.cn/CN/Y2026/V37/I3/604

图/表 13

图1 负半径滚子直动推杆盘形凸轮机构

Fig.1 The cam mechanism with negative radius follower

表1 预知机构运动信息

Tab.1 Main motion information of the mechanism

h

/mm

Φ g

Φ r

Φ n

Φ f

s g (φ)

s r (φ)

ω 1

3-4-5

多项式

3-4-5

多项式

顺时针

表1 预知机构运动信息

Tab.1 Main motion information of the mechanism

h

/mm

Φ g

Φ r

Φ n

Φ f

s g (φ)

s r (φ)

ω 1

150°

160°

20°

30°

3-4-5

多项式

3-4-5

多项式

顺时针

图2 理论轮廓与工作轮廓的内在关系

Fig.2 The intrinsic relationship between the cam pitch curve and cam profile

图3 (r0,e)的两类取值域

Fig.3 Two types of regions of (r0,e)

图4 不同运动信息的必失真取值域DⅠg对比

Fig.4 Comparison of the inevitable undercutting regions DⅠg for different motion information

图5 DⅡ区域内R取值分布特征

Fig.5 Distribution characteristics of R values under DⅡ area

图6 (r0,e,R)空间模型

Fig.6 Three-dimensional spatial model of (r0,e,R)

图7 运动保真非解域ΩⅠu、ΩⅡu和解域Ω*

Fig.7 The solution space Ω* and two types of non-solution space ΩⅠu、ΩⅡu for ensuring no-undercutting

图8 非解域ΩⅠu内凸轮轮廓及曲率半径曲线

Fig.8 The cam profile and curvature radius curves under the non⁃solution space of ΩⅠu

图9 非解域ΩⅡu的凸轮轮廓及其曲率半径曲线

Fig.9 The cam profile and curvature radius curves under the non⁃solution of ΩⅡu

图10 e=15 mm运动失真和保真区域

Fig.10 The region of undercutting and no-undercutting of e=15 mm

表2 e不同取值的结果

Tab.2 The results for different e value

e

$r 0$ /

$R m i n$ /

表2 e不同取值的结果

Tab.2 The results for different e value

e

/mm

-15

-10

-5

$r 0$ /

144.78

139.36

139.09

144.72

150.08

154.32

156.85

$R m i n$ /

176.18

177.88

179.40

185.89

191.28

195.87

199.84

图11 实物样机

Fig.11 The physical prototype

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