style="width:3.30667in;height:3.4067in" /> 本文是学习GB-T 10089-2018 圆柱蜗杆、蜗轮精度. 而整理的学习笔记,分享出来希望更多人受益,如果存在侵权请及时联系我们
本标准规定了圆柱蜗杆蜗轮传动机构的精度。
本标准适用于轴交角 ∑=90°,最大模数m=40 mm及最大分度圆直径 d=2500 mm
的圆柱蜗杆
蜗轮传动机构。最大分度圆直径 d>2500 mm
的圆柱蜗杆蜗轮传动机构可参照本标准使用。
下列文件对于本文件的应用是必不可少的。凡是注日期的引用文件，仅注日期的版本适用于本文
件。凡是不注日期的引用文件，其最新版本(包括所有的修改单)适用于本文件。
GB/T 3374.2 齿轮术语和定义 第2部分：蜗轮几何学定义
GB/T 3374.2界定的以及下列术语和定义适用于本文件。
3.1.1
齿廓总偏差 total profile deviation
。
在轴向截面的计值范围L。
(齿廓的工作范围)内，包容实际齿廓迹线的两条设计齿廓迹线间的轴
向距离。示例见图1。
style="width:3.30667in;height:3.4067in" />
图 1 ZC 蜗杆轴向截面内的齿廓总偏差 Fal
在齿廓检验图中(见图2),齿廓总偏差 F。
为两个设计齿廓迹线之间的距离(垂直于设计齿廓迹线
测量)。
注：在图2中，设计齿廓和蜗杆的齿面形状 A、N、I、K及C
无关并用直线标出，实际齿廓包含在画出的范围内。
GB/T 10089—2018
style="width:5.66007in;height:3.8335in" />
齿廓总偏差 齿廓倾斜偏差 齿廓形状偏差
图 2 计值范围La 内的齿廓检验图
3.1.2
齿廓形状偏差 profile form deviation
fial
在轴向截面的计值范围La
内，包容实际齿廓迹线的，与平均齿廓迹线平行的两条辅助线间的距离
(垂直于设计齿廓迹线测量，见图2)。
注：本标准没有给出齿廓形状偏差fa 的允许值。
3.1.3
齿廓倾斜偏差 profile slope deviation
fHal
在轴向截面的计值范围La
内，与平均齿廓迹线相交的两条平行于设计齿廓迹线的辅助线间的距
离(见图2)。
注：本标准没有给出齿廓倾斜偏差fHoi的允许值。
3.1.4
轴向齿距偏差 axial pitch deviation
fpx
在蜗杆轴向截面内实际齿距和公称齿距之差。
3.1.5
相邻轴向齿距偏差 adjacent axial pitch deviation
fux
在蜗杆轴向截面内两相邻齿距之差。
3.1.6
径向跳动偏差 radial run-out deviation
Fn
在蜗杆任意一转范围内，测头在齿槽内与齿高中部的齿面双面接触，其测头相对于蜗杆主导轴线的
径向最大变动量。
注：径向跳动偏差是由蜗杆轮齿中点圆柱面的轴线和蜗杆轴承位置决定的蜗杆主导轴线之间的距离和交叉角度造
成的。
3.1.7
导程偏差 lead deviation
Fz
蜗杆导程的实际尺寸和公称尺寸之差。
GB/T 10089—2018
3.2.1
单个齿距偏差 single pitch deviation
fp₂
在蜗轮分度圆上，实际齿距与公称齿距之差。
用相对法测量时，公称齿距是指所有实际齿距的平均值。
注：当实际齿距大于平均值时为正偏差；当实际齿距小于平均值时为负偏差。
3.2.2
齿距累积总偏差 total cumulative pitch deviation
Fp₂
在蜗轮分度圆上，任意两个同侧齿面间的实际弧长与公称弧长之差的最大绝对值。
3.2.3
相邻齿距偏差 adjacent pitch deviation
fu₂
蜗轮右齿面或左齿面两个相邻齿距的实际尺寸之差。
3.2.4
齿廓总偏差 total profile deviation
。
在轮齿给定截面的计值范围内，包容实际齿廓迹线的两条设计齿廓迹线间的距离。
3.2.5
径向跳动偏差 radial run-out deviation
F₂
在蜗轮一转范围内，测头在靠近中间平面的齿槽内与齿高中部的齿面双面接触，其测头相对于蜗轮
轴线径向距离的最大变动量。
注： 径向跳动偏差是由轮齿偏心以及由于右齿面和左齿面的齿距偏差而产生的齿槽宽的不均匀性和轮齿轴线相对
于主导轴线的偏移量(偏心量)造成的。
3.3.1
单面啮合偏差 single-flank enagement deviation
F'
蜗轮实际旋转位置和理论旋转位置的波动。理论旋转位置是由蜗杆的旋转确定的。当旋转方向确
定时(左侧齿面啮合或右侧齿面啮合),单面啮合偏差等于蜗轮旋转一周范围内相对于起始位置的最大
偏差之和(见图3)。
style="width:6.61996in;height:2.58676in" />
注 ：单面啮合偏差F¹ 和 F2
是用标准蜗轮或者标准蜗杆测量得到的。如果没有标准蜗轮和标准蜗杆，则使用配对
的蜗杆蜗轮副，其单面啮合偏差为Fiz。
图 3 蜗轮旋转时单面啮合偏差 F/和单面一齿啮合偏差
fl
GB/T 10089—2018
3.3.2
单面一齿啮合偏差 tooth-to-tooth single-flank
engagement deviation
fì
一个齿啮合过程中旋转位置的偏差(见图3)。
注：单面一齿啮合偏差¹和fu
是用标准蜗轮或者标准蜗杆测量得到的。如果没有标准蜗轮和标准蜗杆，则使用
配对的蜗杆蜗轮副，其单面一齿啮合偏差为fiz。
3.3.3
蜗杆副的接触斑点 worm gearing engagement pattern
安装好的蜗杆副中，在轻微力的制动下，蜗杆与蜗轮啮合运转后，在蜗轮齿面上分布的接触痕迹。
注：接触斑点以接触面积大小、形状和分布位置表示(见图4)。
接触面积大小按接触痕迹的百分比计算确定：
沿齿长方向——接触痕迹的长度b"与工作长度b'之比的百分数，即(b"/b')×100%(在确定接触痕迹长度
b"时，应扣
除超过模数值的断开部分);
沿齿高方向——接触痕迹的平均高度h"与工作高度 h
'之比的百分数，即(h”/h')x100%。
接触形状以齿面接触痕迹总的几何形状的状态确定。
接触位置以接触痕迹离齿面啮入、啮出端或齿顶、齿根的位置确定。
style="width:4.69341in;height:5.0666in" />
蜗杆的旋转方向
style="width:4.30008in;height:5.22016in" />
图 4 蜗杆副的接触斑点
GB/T 10089—2018
下列符号适用于本文件。
4.1 蜗杆、蜗轮的参数(长度单位：毫米)
a 中心距
b′ 蜗杆副接触面的工作长度
b" 蜗杆副接触痕迹的长度
d₁ 蜗杆分度圆直径
d。 蜗轮分度圆直径
h′ 蜗杆副接触面的工作高度
h" 蜗杆副接触痕迹的平均高度
l 蜗杆测量长度
mx 蜗杆轴向模数
m. 蜗轮端面模数
x 蜗杆头数
x₂ 蜗轮齿数
L. 齿廓计值范围
φ 精度等级级间公比
4.2 蜗杆、蜗轮的偏差(单位：微米)
f 单项偏差
fr 齿廓形状偏差
fa 蜗杆齿廓形状偏差
fio₂ 蜗轮齿廓形状偏差
fHe 齿廓倾斜偏差
fHa 蜗杆齿廓倾斜偏差
fHe₂ 蜗轮齿廓倾斜偏差
f' 单面一齿啮合偏差
f¹ 用标准蜗轮测量得到的单面一齿啮合偏差
fi 用标准蜗杆测量得到的单面一齿啮合偏差
flz 用配对的蜗杆副测量得到的单面一齿啮合偏差
f。 单个齿距偏差
fn 蜗杆轴向齿距偏差
f 蜗轮单个齿距偏差
f. 相邻齿距偏差
fu 蜗杆相邻轴向齿距偏差
fu 蜗轮相邻齿距偏差
F 总偏差
F' 单面啮合偏差
Fl 用标准蜗轮测量得到的单面啮合偏差
GB/T 10089—2018
F₂ 用标准蜗杆测量得到的单面啮合偏差
Fliz 用配对的蜗杆副测量得到的单面啮合偏差
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为了满足蜗杆蜗轮传动机构的所有性能要求，如传动的平稳性、载荷分布均匀性、传递运动的准确
性以及长使用寿命，应保证蜗杆蜗轮的轮齿尺寸参数偏差以及中心距偏差和轴交角偏差在规定的允许
值范围内。
注：中心距偏差和轴交角偏差的允许值在本标准中未作规定。
单项偏差f
是指蜗杆蜗轮传动机构轮齿单项尺寸参数的偏差，例如齿距偏差等。总偏差 F
包括多
个单项偏差的综合影响。蜗杆蜗轮传动机构轮齿尺寸参数偏差的定义在第3章中给出。
本标准对蜗杆蜗轮传动机构规定了12个精度等级；第1级的精度最高，第12级的精度最低。
根据使用要求不同，允许选用不同精度等级的偏差组合。
蜗杆和配对蜗轮的精度等级一般取成相同，也允许取成不相同。在硬度高的钢制蜗杆和材质较软
的蜗轮组成的传动机构中，可选择比蜗轮精度等级高的蜗杆，在磨合期可使蜗轮的精度提高。例如蜗杆
可以选择8级精度，蜗轮选择9级精度。
把测量出的偏差与表1～表12规定的数值进行比较，以评定蜗杆蜗轮的精度等级。表中的数值是
用第6章中对5级精度规定的公式乘以级间公比φ计算出来的。
两相邻精度等级的级间公比φ为：φ=1.4(1～9级精度);φ=1.6(9级精度以下);径向跳动偏差
F, 的级间公比为φ=1.4(1～12级精度)。
例如，计算7级精度的偏差允许值时，5级精度的未修约的计算值乘以1.4²,然后再按照5.5规定的
规则修约。
表1～表12列出的数值是用第6章的公式计算并修约后的数值。如果计算值小于10
μm, 修约到
最接近的相差小于0.5 μm 的小数或整数，如果大于10μm,
修约到最接近的整数。
style="width:0.46665in" />GB/T 10089—2018
6 5级精度的蜗杆蜗轮偏差允许值的计算公式
6.1 单个齿距偏差fp 的计算公式：
f。=4+0.315 · (m,+0.25 · √d)
6.2 相邻齿距偏差f. 的计算公式：
f.=5+0.4 · (m,+0.25 · √d)
6.3 导程偏差 F 的计算公式：
Fm=4+0.5 · ×1+5 · √x₁ · (lgm,)²
6.4 齿距累积总偏差 F 的计算公式：
1
F2=7.25 ·d2 ·mx
F.=√(fma)²+(fa)²
6.6 齿廓倾斜偏差 fma的计算公式：
fHa=2.5+0.25 · (m,+3 · √m₁)
6.7 齿廓形状偏差f 的计算公式：
fa=1.5+0.25 · (m,+9 · √m 6.8 径向跳动偏差 F, 的计算公式：
F,=1.68+2. 18 · √m₄+(2.3+1.2lgm,) ·d÷ 6.9 单面啮合偏差 F{ 的计算公式：
1
7
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)
style="width:3.62669in;height:0.37334in" />
6.10 单面一齿啮合偏差f/ 的计算公式：
fl=0.7 · (fp+F.)
6.11 公式中的参数mx 、d 和 z
的取值为各参数分段界限值的几何平均值；公式中m 、和 d 的单位均 为 mm,
偏差允许值的单位为 μm ; 公式中的蜗杆头数 x₁ >6 时取平均数x₁=8.5
计算；公式中蜗杆蜗轮 的模数mx=m,; 计算 F. 、F 和f! 偏差允许值时应取fHa
、fh 、F。和f, 计算修约后的数值。
蜗轮：应测量蜗轮分度圆的齿宽中间位置。
蜗杆： 一般通过间接测量齿距变动得到径向跳动偏差值。
蜗轮：应测量蜗轮分度圆的齿宽中间位置。
蜗杆：在分度圆柱面测量轴向齿距偏差。多头蜗杆还要测量其他轴向截面，直到获得蜗杆所有齿的偏差。
蜗轮：应测量蜗轮分度圆的齿宽中间位置。
7.4 单面啮合偏差和单面 一齿啮合偏差
单面啮合检验反映了蜗杆蜗轮啮合过程中的轮齿单项参数偏差对啮合过程的综合影响。蜗杆和蜗
GB/T 10089—2018
轮在给定的中心距内啮合，蜗杆右齿面或者左齿面始终与蜗轮配对齿面处于啮合状态，如果没有固定的
工作齿面，则必须检测右齿面和左齿面。
使用标准蜗杆蜗轮副检验单面啮合偏差F/ 和单面一齿啮合偏差f' 。
一般来说没有标准的蜗杆蜗
轮副，在企业中一般使用单面啮合检测仪检验配对蜗杆蜗轮副。如果企业中没有用于单面啮合检验的
单面啮合检测仪，也可检验配对蜗杆蜗轮副的接触斑点，其要求见附录 A。
应在齿根圆和齿顶圆范围内测量齿廓总偏差。在蜗杆轴向截面内测量齿廓总偏差，在蜗轮中间平
面内测量齿廓总偏差。
在蜗杆啮合范围内的测量长度 l
内测量导程偏差。测量长度可参照表1～表12的规定。如果蜗
杆实际啮合长度小于规定的测量长度l,蜗杆导程偏差F。要直接按照实际啮合长度测量。
蜗杆蜗轮轮齿尺寸参数偏差各精度等级的允许值见表1～表12。表中的数值和蜗杆轴向模数mx、
蜗轮端面模数m 、分度圆直径d 以及蜗杆头数
有关。测量蜗杆偏差时要用到蜗杆分度圆直径d₁, 测
量蜗轮偏差时要用到蜗轮分度圆直径d₂
对于蜗杆副的单面啮合偏差F/ 和单面一齿啮合偏差f
'的偏差允许值，其计算公式为：
F{=√(F¹)²+(F₂)
f'=√(fh)²+(f)²
表 1 1级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表1(续)
单位为微米
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GB/T 10089—2018
表 2 2级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 3 3级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 4 4级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 5 5级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 6 6级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 7 7级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 8 8级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表 9 9级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表10 10级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表11 11 级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
表12 12级精度轮齿偏差的允许值 单位为微米
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GB/T 10089—2018
(规范性附录)
蜗杆副的接触斑点要求
蜗杆副的接触斑点主要按其形状、分布位置与面积大小来评定。接触斑点的要求应符合表
A.1 的
规定。
表 A.1 蜗杆副接触斑点的要求
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更多内容 可以 GB-T 10089-2018 圆柱蜗杆、蜗轮精度. 进一步学习