滚齿、插齿、顶切、根切、内外啮合传动————动画

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We further subdivide the geometry of worm and wheel gearing by classifying the tooth form. We use a two-letter designator to define tooth form geometry. In addition to the various designations of contact, there are five active profile designations typically used worldwide. They are classified as ZA, ZK, ZC, ZN, and ZI. The various profiles are a function of both design application and manufacturing. The tooth form in part defines the interaction between the teeth. It is generally accepted that one would not mix any of the ‘Z’ designates with any other.

ZA: Worm gear with straight-line (trapezoidal) tooth profile in axial section. The tooth sides are slightly convex in the normal section; the cross-section results in the spiral of Archimedes. The elements in the axial section are usually standardized (i.e. mx=m, ax=a). The gearing is produced using lathes or thread-cutting machines (the worm resembles a motion screw with trapezoidal threads). A tool shaped as the basic profile is applied onto the workpiece in the axial plane. With larger γ angles, different cutting angles occur in the forming tool on the lateral edges, which results in unequal cutting-edge loading and blunting. The lateral worm areas can only be sharpened using a special form grinding wheel. Therefore, spiral gearing is used in worms with a low pitch angle (γ<10°) in those cases when tooth sides are not treated thermally and do not require regrinding.

ZN: Worm with a straight-line tooth profile in normal tooth section, namely;

a) On the mean helix of space.

b) On the mean helix of tooth.

In the axial section, tooth sides are slightly convex and the cross-section results in a general evolvent curve (in an extended or shortened evolvent). The elements in the normal plane are standardized, (i.e. mn=m, an=a). The gearing is worked in case with one and in case and with two forming in the normal plane. The cutting angles are identical with great angles γ. Thermally treated sides can be ground using a grinding wheel with straight-line bevel areas on thread grinding machines. This grinding process results in non-straight-line lateral areas which, however, rather approximate the theoretical ones. If also the screw milling cutter used to produce worm gear toothing is subject to this grinding process, the worm and the worm gear create a theoretically proper pair. The common gearing is also suitable for worms with greater angles γ and for worms with thermally treated tooth sides that require regrinding.

ZI: Worm with an evolvent profile (a straight-line tooth profile in a plane tangential to the main cylinder). The tooth sides are convex in both the centerline and normal sections and the cross-section results in an evolvent. The elements in the normal plane are standardized (i.e. mn=m, an=a). The gearing is worked using two tools applied onto the workpiece. The tool cutting edge lies in the tangent direction toward the helix on the main cylinder. The evolvent gearing is used in worms with a higher number of teeth (e.g. z1 > 4); the worm resembles a cylindrical gear with helical teeth. Tooth sides can be ground with the flat side of the grinding wheel. Special grinding machines must be used given the relatively small angle γ.

ZK: Profile formed by a cone ground using a wheel and / or shank tool.

ZH: Concave tooth profile (highest accuracy / precision and most expensive).

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Worm gearing is most commonly used for high ratio reduction and increased precision positioning. Precision in position is gained by high ratio reduction. As the ratio increases, the output slows relative to the input, the reduction in backlash is similar to the ratio changes. Using worm and wheel designs, as an example, a simple drive with less than precise rotational position control will experience a significant increase in positional accuracy.

In terms of the working contact patch and service life, worm gearing does not share the contact parameters that parallel axis involute-based gearing does. Parallel axis gearing based on the involute tooth profile runs through a point during the engagement mesh where the two teeth exhibit no sliding, only rolling action. We define this contact point or rotational relationship as the pitch point. Worm gears have no point of pure rolling during their mesh engagement. Thus, all contact action is sliding. Interestingly enough, the predicted service life of a worm gear set is based largely on the wear rate as a function of the amount of material that can be sacrificed, the thickness of the tooth. Since predicted service life is based on wear rate and lubrication, and since the output wheel typically rotates slowly, traditional elastohydrodynamic lubricant development is difficult to develop or maintain. Thus, we usually rely on grease or a more adhesive lubricant and lubrication system to keep the gear teeth from touching. We also employ subtle geometric features of the tooth face, generally called a lubrication entry gap. The concept is to promote development of a wedge of lubricant to be drawn into the mesh. The geometric details of the entry gap are a function of the gear materials, lubrication, and interfacial speed.

Geometry also plays a role in the mesh efficiency. With the worm driving the wheel, the mesh efficiency is on the order of 60 percent to 80 percent. However, if the wheel drives the worm, the efficiency is generally less than 10 percent. From this, we tend to call worm and wheel gearing as non-backdrivable. It is not, but with these low efficiencies it is unlikely under typical circumstances that the wheel will effectively drive the worm. If, on the other hand, the gear mesh is exposed to an external vibration source, the wheel driving worm efficiency may climb as high as 40 percent, which invalidates the concept of non-back-drivability.

zengxiaodong

zengxiaodong 发表于 2023-1-23 11:25
蜗轮蜗杆也可以制作接触动画，普通的蜗杆传动其接触线与滑动速度近乎平行，所以形成油碶的效果很不好！

...

弗兰德Flender的蜗杆（商标CAVEX）是ZC蜗杆的一种，这种CAVEX蜗杆就是ZH蜗杆


Cylindrical Wormgearings with Progressively Curved Shape of Teeth Flanks.pdf (894.49 KB, 下载次数: 3)

2023-2-1 11:42 上传

点击文件名下载附件

zengxiaodong

zengxiaodong 发表于 2023-1-28 14:44
顺便再补充一个斜齿轮内啮合传动的接触迹线动画

这个内齿轮啮合接触迹线动画有可能丢帧了，所以重新提供如下：





关于内啮合还有话题可以讨论，那就是内啮合是没有交错轴传动的，Why？

原因很简单，那就是会出现干涉问题！这个问题也是内齿圈无法进行滚齿加工、无法用蜗杆砂轮磨齿的根本原因。
为了解决干涉问题，有人提出了球形滚刀实现滚内齿；而日本三菱重工（被尼得科收购）内齿展成磨齿机ZI20A，其砂轮必须是桶形的，目的也是避免干涉。

woodykissme

zengxiaodong 发表于 2023-2-2 09:45
这个内齿轮啮合接触迹线动画有可能丢帧了，所以重新提供如下：

向您学习

zengxiaodong

费尽九牛二虎之力，搞出了蜗杆齿条交错啮合的动画。

特点：
用3头渐开线蜗杆与直齿条啮合，属于交错轴传动，这样做的好处是齿条上接触线的位置不是固定不变的，也就是齿条齿面的工作范围显著加大了，因此可以极大增加齿条的磨损寿命。

根据齿轮理论，这个啮合属于线接触，而且接触线与齿面相对滑动速度近乎垂直，有利于润滑油卷吸进入接触区域形成流体动力润滑，另外，同时接触的齿数达到惊人的8齿，因此承载能力也将是很好的。

zengxiaodong

zengxiaodong 发表于 2023-1-28 07:43
空间交错齿轮齿条传动，有很多的特殊性，其计算理论似乎也有待完善。这种传动在汽车转向系中用得很多，普通 ...

前面我们介绍过，空间交错斜齿轮传动属于点啮合，存在一个临界齿轮宽度，也就是大于这个宽度的齿面不参与接触，因此从接触强度的观点看来，多余的齿轮宽度属于无效宽度！


因此，这种齿轮计算重合度时，也是大于临界齿轮宽度以后，重合度数值始终保持不变！

但是，这个计算理论在空间交错齿轮齿条传动中却不成立，因为这种特殊情况下，点接触演变成了线接触。因此，随着齿轮宽度的增加，齿面接触线最大长度虽然不是一直延长的（增长到最大值，然后保持不变，这点与平行轴斜齿轮啮合相同），但是同时参与接触的齿数却是逐步增加的。

zengxiaodong

上贴2个图是完全一样的齿轮参数，仅齿轮齿条宽度增加，根据Kisssoft的计算，其端面重合度、纵向重合度以及总重合度这3个计算值均保持不变，很显然，这个计算结果是不符合逻辑的！

zengxiaodong

交错轴齿轮齿条传动，如果逐步减小轴线角的话，意味着越来越接近平行轴传动。


但当轴线角设为0°时，出现错误不能计算；假设输入一个很小的轴线角例如0.0001°，虽不出错可以计算，可是结果却令人诧异，安全系数会达到不可思议的程度！

zengxiaodong

交错轴齿轮齿条传动，如果轴线角等于小齿轮的螺旋角，也就是齿条变成直齿条，则计算也出现奇怪的结果。