阴阳理论下的经济学架构

  1. 引言

此文章是《阴阳理论下的XX学架构》系列的第四篇;也就是以阴阳理论为基础,来给经济学树立架构。什么是经济活动?那是人类社会里的个体进行劳动生产力的交换来提高生活质量。劳动生产力的交换产生了需求方与供给方的观念。物物交换是最原始的经济活动形式并且延伸出价值的概念。我们可以用阴阳理论的太极图来概括 (图 1.) 。

1. 太极图

2. 经济活动形式的更高层次

分工使劳动生产力多元,催生更高层次的经济活动形式也就是以“钱”作为价值衡量、交易的媒介。钱可视为为劳动生产力的另一种形态。 由钱和交易会延生出货币、资产、买卖、劳资的概念。以上所说可用图2.来概括。

图2. 两个层次的经济活动概括图

3. 经济活动的基本领域

      经济活动的基本领域对应着人类社会所需的基本生活质量,而每一个人应当有机会参与经济活动及享有最基本的生活质量。现代社会的经济活动的基本领域是医药、食品、住宿、交通。如图3.。

图 3. 经济活动的基本领域概括图

4.    “看不见的手”与“无为而治”

      “看不见的手”出自于亚当·斯密所著的《国富论》,可被诠释为经济活动是有规律的。“无为而治”来自老子的《道德经》,何为“无为而治”?可以简单的诠释为政府应以遵从经济活动的规律为依据,设计一套机制适度并恰当的干预经济活动。目的为让社会里的每一个人应当有机会参与经济活动及享有最基本的生活质量。(如同工程师遵从物理定律来建造桥梁)

5. 资本主义、社会主义与共产主义

      我们应当如何看待资本主义、社会主义与共产主义?我就以费曼在丹茲講座系列演講《價值的不確定性》的一段话与大家共勉:

“我不认为在社会主义和资本主义之间存在着什么问题,问题存在于钳制思想和解放思想之间。如果能够解放思想, 而且社会主义又比共产主义好,自然就会朝着这个方向前进, 对每个人也会比较好。如果资本主义比社会主义好,情况也是一样的。”

(或许大家会更喜欢邓小平的那一句话:不管黑猫还是白猫,能抓老鼠的就是好猫。)

6.结论

由阴阳理论作推导而得到物理学、数学、中医学的架构,再由本文用阴阳理论作推广而得到经济学的架构; 印证了老子的一句话:道生一,一生二,三生万物。

牛顿第三定律的疑惑与修正

牛顿第三定律:相互作用的两个物体之间的作用力和反作用力总是大小相等,方向相反,作用在同一条直线上。

Feynman 说:

“Newton told us only two things about the nature of forces. In the case of gravitation, he gave us the complete law of the force. In the case of the very complicated forces between atoms, he was not aware of the right laws for the forces; however, he discovered one rule, one general property of forces, which is expressed in his Third Law, and that is the total knowledge that Newton had about the nature of forces—the law of gravitation and this principle, but no other details.

This principle is that action equals reaction.

What is meant is something of this kind: Suppose we have two small bodies, say particles, and suppose that the first one exerts a force on the second one, pushing it with a certain force. Then, simultaneously, according to Newton’s Third Law, the second particle wnill push on the first with an equal force, in the opposite direction; furthermore, these forces effectively act in the same line. This is the hypothesis, or law, that Newton proposed, and it seems to be quite accurate, though not exact (we shall discuss the errors later). ”
你也可看https://www.wired.com/ 的A Closer Look at Newton’s Third Law

“————–Let me make something clear. Isaac Newton had it tough. Here he is trying to make a model that describes what forces do to objects. However, he just doesn’t have all the words we have – like momentum, acceleration, velocity.Fortunately, there is an online translation of the original works of Newton. Here is an older translation into English of Newton’s The Mathematical Principles of Natural Philosophy (volume 1).The part about the Third Law says:To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.He also writes:
If you press a stone with your finger, the finger is also pressed by the stone.This above example could indicate that he did not mean the stone and the finger have to move. I would suggest that perhaps Newton meant the word “action” to really mean “force”. However, he later uses the word force so I’m not exactly sure of his intentions. Perhaps by “action” he means a force that actually does something. I don’t know.Oh, and it seems Newton does use the words momentum and velocity (if you read more of the passage). Maybe he was just trying to be poetic with his use of the words “action” and “reaction”.”

此”第三定律“更确切是一个力传送原理———应用于接触并相对静止的物体。在大一的statics(静力学)里的刚体的平衡系统里,”第三定理“就用来创建模型。但是在相对运动的物体呢?

以上图的物体与地上是相对静止的,你的手指对物体施加的力的大小=于你的手指的反作用力(指力)的。基于对此”力传送原理”的认识,促成我完成《行星齿轮的动力学》并发表在《知识创新与应用》2020 年 第12 期。*

以上图的物体与地上是相对运动的,你的手指对物体施加的力的大小若是等于于你的手指的反作用力(指力),那你的手指对物体施加的力只是用来抵抗摩檫力,物体会以等速运动。
你的手指对物体施加的力的大小若是大于动摩擦力,那物体会有一个加速度,而于你的手指的反作用力(指力)等同于动摩擦力。

以上两个图在Y轴方向,物体与地上是相对静止的,所以作用于物体的重力的大小等于于物体的反作用力(重力)的大小。

再来看两个相对接触的转动圆柱的力传送模型,也就是齿轮的力传送机制。以上图取自我的《行星齿轮的动力学》

圆柱 A 与圆柱 B在接触点是相对静止的。圆柱 A 在接触点施加力, Ftr 在圆柱B 身上 ,而同时会有一个同样大小的反作用力在圆柱 A身上。

切线力,Ft 促成圆柱B 旋转,我们可以把Ftr =Ft 因为Ѳ 很小。而圆柱 A半径是rA,圆柱 B半径是rB

扭矩比= Ftr . rB / Ftr . rA = rB /rA

而角速度比是扭矩比的倒数

以上的推导是以我对第三定律修正后推导出来的——”第三定律更确切是一个力传送原理———应用于接触并相对静止的物体,相互作用的两个物体之间的作用力和反作用力总是大小相等,方向相反,作用在同一条直线上。”

*为何写《行星齿轮的动力学》?
就如newgnay在网站:知乎    《行星齿轮原理的详细图文介绍(含超详细的公式推导)》的开场白:  

这几天我对行星齿轮的原理很感兴趣,但看了知乎上(以及百度到的)很多关于行星轮原理的介绍后,发现它们不是太过简略就是太过专业(不加推导地使用了太多专业公式),以至于连我这个凝聚态理论专业的研究人员也看不懂。无奈,我只得根据网上找到的行星齿轮结构,自已推导了行星齿轮的工作原理,在此给大家分享一下。

而若要看我的论文《行星齿轮的动力学》全文按以下link
https://limsaukong.com/%e8%a1%8c%e6%98%9f%e9%bd%bf%e8%bd%ae%e7%bb%84%e7%9a%84%e5%8a%a8%e5%8a%9b%e5%ad%a6-dynamics-of-planetary-gear-set/

Dynamics of Planetary Gear-set

Chinese version published in 《Technology Innovation and Application/科技创新与应用》ISSN 2095-2945, 12th edition, page 69-70 , April 28 2020

Abstract

The objectives to study planetary gear set often are to find torque ratio and velocity ratio between input and output shaft. This paper aims to achieve these objectives by develop a new method which is kinetics method in compare to traditional kinematics or tabular method[1]. This new method is direct and easy method, developed to study single stage planetary gear set in steady and unsteady state by first establishes the principle of force transfer at contact point between a pair of rotating cylinders. In others words the established principle described the power flow from one rotating cylinder to another by elaborates the force transfer mechanism at contact point between the rotating cylinders. By relying on the established principle, the model of force transfer in single stage planetary gear set for various arrangements could be derived. From the force transfer model of selected planetary gear set arrangement, the force transferred to output shaft of planetary gear set is shown in the free body diagram, hence the output torque could be directly obtained. The power at input and output shaft is a constant, which is equivalent to product of torque and angular velocity. By knowing the torque at output shaft, the angular velocity of output shaft then could be found.

Keywords: Planetary gear set, Torque ratio, Velocity ratio, Friction, Power Transmission

1. Introduction

Conventional approach in study planetary gear set is using tabular method[1]. The objective of this paper is to develop a direct method to obtain torque ratio & velocity ratio of input & output shaft of single stage planetary gear set in steady and unsteady state. First the underlying principle of force transfer at contact point in between a pair of rotating cylinders is established, follow by building the model of force transfer for two different arrangements of the planetary gear set[2]. Then the method in finding the torque ratio for the respective arrangement of planetary gear set is described and explained in logically and easy to understand manner.

2. Nomenclature

wout Output angular velocity

win   Input angular velocity

Ft     Tangential force

Ftr    Transfer force

Ff     Friction force   

Fre   Reaction force

N     Normal force

µ     Coefficient of friction

Fpt   Planet gear tangential force

Fret   Tangential component of reaction force

Tin   Input torque

To    Output torque

rp     Radius of planet gear

rs     Radius of sun gear

rc     Radius of carrier shaft  

Fc   Carrier shaft tangential force

Ѳ     Angle

3. Underlying Principle

The dynamics at contact point of a pair of rotating cylinders used to transfer force from a rotating cylinder to another is studied and a model is developed. It is the underlying principle to study planetary gear set in both steady and unsteady state.

Fig. 1: Model of transfer force from a rotating cylinder to another

Tangential force, Ft responsible to rotate the cylinder B. If the tangential force, Ft is larger than friction force, Ff , the slip condition occurred. Gear set is used in such condition to avoid slippage.

3.1 Single Stage Planetary Gear Set Arrangement 1  

Ring gear      : Fixed

Carrier          : Output

Sun gear        : Input

The established model to show the force interaction of the above arrangement as in Fig. 2 below.

Fig, 2: Model of force transfer of single stage planetary gear set arrangement 1

The Ftr could be decomposed into X-Y direction components as illustrate in Fig. 3 below.

Fig. 3: X-Y directions components of transfer force, Ftr  

The Fpt acted on fixed ring resulted a reaction force, Fre on planet gear. The reaction force, Fre could decompose into XY direction components as illustrate in Fig. 4 below.

Fig. 4: X-Y directions components of reaction force, Fre   

Input torque calculated as Fig. 5 below.

Fig. 5: Illustration of input torque    

Input torque, 𝑇in=𝐹tr . 𝑟                                                      (1)                                           

Output torque at carrier is calculated as Fig. 6 below.

Fig. 6: Illustration of output torque   

Output torque, To=Fret . ( 2rp+rs)                                                          (2) 

(2rp+rs) is radius of ring gear, therefore torque ratio is simply the ring gear size divide by sun gear size. This finding is matching with the illustration of a gear manufacturer “wittenstein” in the video “Made simple:Design and operating principle of a low-backlash planetary gearbox(1: 21 ~1:26)[3].

Angular velocity ratio simply is the reciprocal of torque ratio.

For the example in which the planet gear size is equal to sun gear,

3.2 Single Stage Planetary Gear Set Arrangement 2

Ring gear      : Output

Carrier          : Input

Sun gear        : Fixed

The model established to show the force interaction of the above arrangement as in Fig. 7 below.

Fig. 7: Model of force transfer of single stage planetary gear set arrangement 2

When the carrier rotated, Ftr is distributed to sun and ring gear as shown in Fig. 7. Ftr acted on fixed sun gear resulted a reaction force, Fre , this reaction force shall acts on ring gear. This means transfer force, Ftr generated by carrier finally caused the ring gear to rotate. By neglecting the friction force

4. Conclusion

The torque ratio of planetary gear set could easily be found by establish a model of force transfer for the selected arrangement of the planetary gear set based on the underlying principle described in this paper.

References

[1]          Norton, Design of Machinery (2004), pp.495-499, McGraw-Hill.

[2]    https://www.kggear.co.jp/en/wp-content/themes/bizvektor-global-edition/pdf/9.9_Calculation-for-Planetary-gear-mechanism_TechnicalData_KGSTOCKGEARS.pdf

[3]    https://www.youtube.com/watch?v=GiVHimmrxjE

阴阳理论下的中医学架构

摘要: 本文是以我所著的《阴阳理论下的物理学架构》【1】同样的思维方式,来构建中医学的架构。首先描述生命的首要现象就是物理现象,也就是元气在人体经络有规律的活动。然后以阴阳理论作推广而得到第二层次的生命现象;那就是“五行” (人体五个能量传送系统)有规律的活动,而“精”是维持五行的基本物质。在这些基础上再作推广就会得到第三层次的生命现象那就是元气与五行的活动会受到周遭环境(风)的影响而产生变化(水)。

关键词:阴阳,中医学架构,五行,生命现象

1. 引言 物理学家告诉我们世界的一切现象唯一不变的是变化,而且变化是有规律的[1]。这也代表生命的现象是有规律。什么是生命的现象?生命的首要现象是元气在个体也就是封闭系统的运动。元气在人体的运动产生了生死观念及经络与穴位的概念。我们可以用阴阳理论的太极图来概括 (图 1.) 。

1. 太极图

中医学已经有了人体经络与穴位图,但是还没有创建元气运动的原理。

2. 第二层次的生命现象

人体元气的运动会延生出五个不同的能量传送系统,每个能量传送系统具有不同的功能。简称为“五行”。五行的活动是比元气运动低一层次的生命现象。“精”是维持五行活动的基本物质。五行的能量形式及基本物质在运行时会产生变化。有系统的活动就是有规律的活动,所以由五行及精作会得到生理与病理的观念。以上所说可用(图2.)来概括。

图2. 两个层次的生命现象概括图

3. 第三层次的生命现象

      元气与五行的运行会受周遭环境(风)影响而产生变化(水)是属于第三层次的生命现象。我们用“春” 、“夏” 、“秋“、“冬”的概念来概括这个层次的生命现象(图3.)。

图 3. 三个层次的生命现象概括图

4.    结论

由阴阳理论作推导而得到物理学的架构【1】来描述世界的一切现象的变化规律,再由本文用阴阳理论作进一步推广而得到中医学的架构来描述生命现象; 印证了费曼所说的一句话:物理学是最基本且无所不包的一门科学[2]。但也能用老子的一句话来概括:道生一,一生二,三生万物。

参考文献

【1】 Lim Sau Kong 著. 阴阳理论下的物理学架构. 《知识窗 教师版》录用,拟2020五月见刊

【2】Richard P. Feynman, Robert B. Leighton, Matthew Sands 著. 师明睿译. 费曼物理学讲义【I】,  力学、辐射与热1. 台北市:远见天下文化出版. 2013第二版, 第三章,94.