又一个大模型AI 被连问三次 才能输出正确结果

寂静回声

提问
圆柱内齿轮，齿数23，模数1.058，分度圆24.34，变位系数-0.022。
列出齿轮的各个几何尺寸，并分析这个齿轮是否合理存在？

计算结果就是齿顶圆直径小于基圆直径，但因为是内齿轮，这意味着内齿轮齿顶部分的齿廓不是渐开线，渐开线仅能在基圆外生成，而是过渡曲线。当与外齿轮啮合时，会发生齿廓干涉，无法平稳传递运动，甚至卡死。
特别容易发生在小齿轮的齿数较少时，所以避免渐开线曲线干涉的条件就是内齿轮齿数不能小于34。
另外，从齿轮加工的角度看，对于内齿轮，加工时通常使用插齿刀。内齿轮是否根切，取决于插齿刀的齿数与变位，但有一个简化判断：内齿轮不产生根切的最小齿数约为 34。
齿数为 23，且变位系数为 -0.022，负变位会使基圆附近未参与啮合的渐开线齿廓部分更靠近齿根圆，这加剧了根切的风险。
23齿远小于34齿，即使采用正变位也难以完全避免根切，何况这里是负变位。这意味着在加工过程中，插齿刀的齿顶很容易切掉该内齿轮齿廓的渐开线根部，导致齿根变窄、强度下降，且啮合时产生干涉。

知道豆包大模型是怎么回答这个提问的吗？
它是一而再，再而三的说齿轮没问题，齿顶圆直径小于基圆直径，那就没有渐开线，是过渡曲线。然后呢，就没了，能正常啮合吗。
删除提问第三次提问，这回豆包大模型才承认这个齿轮参数有问题。
再把上面的分析扔给豆包大模型，它老老实实承认：

咦，我的分析这么专业，为什么去问大模型呢。
豆包大模型你刚刚升级到2.0，不是号称更……，更……，更……吗。

这种不止在豆包大模型上发生，这个提问也问过Gemini3，它也回答这个齿轮正常，没大毛病啊。
直到把上面的分析同样扔给Gemini3，它也老实了。

You've got a sharp eye—you caught the geometric "illegal move" that standard textbook formulas sometimes gloss over. You are absolutely right: on paper, this gear is a recipe for a mechanical jam.
The fact that the **addendum circle diameter ( mm)** is smaller than the **base circle diameter ( mm)** is the mathematical "smoking gun." In an internal gear, the teeth point inward, so if the tip circle is smaller than the base circle, those tips are protruding into a zone where the involute curve literally does not exist.
Here is a deeper breakdown of why this specific configuration is technically "unreasonable" for standard applications:
### 1. The "Involute Void" Problem
Since the involute profile only begins at the base circle and radiates outward, the portion of the tooth between mm and mm will be a non-involute transition curve (usually a fillet or a straight line depending on the tool).
* **The Result:** When a mating pinion tries to mesh, its tips will lose contact with an involute surface and instead "dig" into the non-involute tips of your internal gear. This causes **heavy vibration, noise, and rapid wear.**
### 2. The Interference Triple Threat
With only 23 teeth and a negative modification, this gear faces three distinct types of interference:
* **Involute Interference:** As you noted, the pinion tip will sweep through the non-involute root/tip area of the internal gear.
* **Trimming (Radial) Interference:** This is the "hidden" killer of internal gears. Because the tooth counts are so close (assuming a pinion with, say, 17–19 teeth), the teeth will physically overlap when you try to slide the gears together radially. You’d have to assemble them axially, and even then, they would likely lock up during rotation.
* **Undercutting:** During manufacturing with a standard shaper cutter (usually 20+ teeth), the cutter's own addendum will "sweep out" too much material at the root of your 23-tooth gear, weakening the teeth significantly.
### 3. The Impact of Negative Modification ()
Usually, we use **positive modification** () on small internal gears to pull the tip diameter away from the base circle and avoid interference.
By choosing a **negative modification**, you have effectively:
1. Pushed the tip circle even further away from the safety of the base circle.
2. Thinned the tooth at the root.
3. Increased the likelihood of the shaper cutter "gouging" the profile during production.

而这也不是孤证，谷歌研究人员发现，把同一条提示词重复提问几次，能让大语言模型的准确率提升21%到97%。

所以这TMD能办正经事吗，口口声声说大模型AI能提高效率，结果这么折腾还TMD有效率吗，我老老实实计算查设计手册也不会这么低效的。

这个事的诡异之处在于，除了豆包大模型之外，其他国产大模型都认为这个齿轮参数不合理，认为合理的就只有豆包大模型和GEmini3。所以难不成是你豆包大模型蒸馏了Gemini3，这才导致同步出错吗？