Name: sizing a transmission shaft by torque
Uploaded: 2024-05-23T12:59:41.000Z
Duration: 1 min 16 s
Channel: JoVE

トランスミッションシャフトに求められる設計仕様は、シャフトが伝達する動力とその回転数です。
これらの仕様に基づいて、シャフトの材料と断面寸法は、材料によって許容される最大せん断応力が弾性限界内に留まり、指定された速度で必要な動力を伝達することを保証することによって選択されます。
現在、システムに関連付けられている電力は、印加されるトルクによって異なります。用語を並べ替えると、シャフトに加えられるトルクを計算できます。この式は、シャフトの電力要件と回転周波数の両方を考慮します。
次に、計算されたトルクと最大許容応力が弾性ねじり式に適用され、シャフト半径の最小許容値が決定されます。
中実の円形シャフトの場合、シャフトの半径に対する極慣性モーメントのこの比率は、シャフトの半径の3乗として変化します。これを置き換えると、シャフト半径に必要な最小値が得られます。
中空円筒の場合、シャフトの外径の最小許容値が計算されます。

トランスミッションシャフトの設計

トランスミッション シャフトの設計は、伝達する動力と回転速度という 2 つの主な仕様によって決まります。 これらのパラメータはシャフトの材質と断面寸法の選択の指針となり、所定の速度で必要なパワーを伝達しながら、素材の最大せん断応力が弾性限界内に確実に保たれるようにします。 システムの出力は、本質的に加えられるトルクに関連しています。 項を再構成することでシャフトにかかるトルクを計算できます。


<img alt="Equation 1" src="/files/ftp_upload/15617/15617_Equation_1.svg" style="text-align: center; height: 38px;">

この計算では、動力要件とシャフトの回転速度の両方が考慮されます。 トルクと最大許容応力が計算されると、それらは弾性ねじり公式に組み込まれます。 このプロセスにより、シャフト半径の最小許容値が得られます。 中実シャフトの場合、極慣性モーメントとシャフト半径の比は、シャフト半径の 3 乗で変化します。 この値を代入することで、シャフト半径の最小必要値が計算されます。


<img alt="Equation 2" src="/files/ftp_upload/15617/15617_Equation_2.svg" style="text-align: center; height: 62px;">

中空シャフトの場合、計算によりシャフトの外径の最小許容値が表示されます。 その結果、トランスミッションシャフトの設計プロセスでは、出力、速度、限界応力、物理的寸法のバランスを注意深く考慮する必要があります。

<img alt="Equation 3" src="/files/ftp_upload/15617/15617_Equation_3.svg" style="text-align: center; height: 62px;">

トランスミッションシャフトに求められる設計仕様は、シャフトが伝達する動力とその回転数です。
これらの仕様に基づいて、...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Torsion

ねじれ

KEY TERMS AND CONCEPTS

主要用語と概念

Design of Transmission Shafts

sizing a transmission shaft by torque

A transmission shaft is sized from the power it must carry and the speed it rotates at. These two design limits guide the choice of shaft material and cross-sectional size. The goal is to keep the maximum shearing stress within the elastic limit while still transmitting the needed power.

Power is directly linked to torque, which is the twisting force applied to the shaft. By rearranging the power relation, the torque can be found from the required power and the shaft speed. That torque value is then used with the maximum allowable stress in the elastic torsion formula.

The torsion calculation gives the minimum allowed shaft radius. For a solid circular shaft, the polar moment of inertia divided by the radius changes with the cube of the radius, so this value is used to find the minimum radius. For a hollow cylindrical shaft, the same process gives the minimum outer radius. In this way, shaft design balances power, speed, stress limits, and physical size.

Sizing a Transmission Shaft by Torque

stresses in a shaft

Torque and Shear in a Twisted Shaft

A shaft under torque develops internal shear forces as it twists. In this setup, equal and opposite torques act on the shaft PQ. To study the effect, a section is cut perpendicular to the shaft axis at an arbitrary point R. The free-body diagram of the QR segment shows the shearing forces applied by the PR portion. These forces act as the shaft resists twisting. Using equilibrium on the QR segment links the internal shear forces in the cut section to the internal torque. Here, r is the...

deformation in a circular shaft

Shear Strain in a Circular Shaft

Shear strain in a circular shaft describes how the shaft’s surface changes shape under torsion. A circular shaft keeps each cross-section flat and undistorted as it twists. Each section behaves like a rigid slab that rotates in place. To study the strain inside the shaft, consider a cylindrical section with length L and radius R. One end of this section is fixed. The radius at a point inside the section is labeled r. Before the load is applied, a small square element lies on the surface of...

circular shaft - stresses in linear range

Torsion Formula for Circular Shafts

Torsion in a circular shaft is analyzed when the applied torque stays within Hooke's law. In this linear range, the shaft does not undergo permanent deformation. The discussion uses shearing strain, shearing stress, and the modulus of rigidity to build the stress equation. The derivation also requires the moments of the small forces on a cross-section to equal the applied torque. When the shearing stress expression is rewritten, an integral term appears. This term represents the polar moment...

angle of twist - elastic range

Elastic Twist in a Circular Shaft

Elastic twist in a circular shaft describes how a cylindrical shaft rotates when torque is applied. The shaft has a length L and a uniform radius r. A torque at the free end creates shearing strain, which is greatest at points farther from the shaft axis. When the shaft stays within the elastic range, the shearing strain can be written in terms of the applied torque, radial distance, polar moment of inertia, and modulus of rigidity. The polar moment of inertia is a geometric measure of how the...

angle of twist: problem solving

Shaft Torsion Between Pulleys B and C

Shaft torsion between pulleys B and C is found by analyzing how torque twists an aluminum shaft. An electric motor applies 700 N·m of torque and produces stable rotation. The shaft carries pulleys B and C, which experience torques of 300 N·m and 400 N·m. The calculation starts with a section cut between pulleys B and C. A free-body diagram is used to study the cut cross-section. Because pulley B has an anticlockwise torque, the torque at the cut must balance it in the opposite direction. The...

design of transmission shafts

A transmission shaft is sized from the power it must carry and the speed it rotates at. These two design limits guide the choice of shaft material and cross-sectional size. The goal is to keep the maximum shearing stress within the elastic limit while still transmitting the needed power. Power is directly linked to torque, which is the twisting force applied to the shaft. By rearranging the power relation, the torque can be found from the required power and the shaft speed. That torque value...

stress concentrations in circular shafts

Why Shafts Develop Local Stress Peaks

Circular shafts can develop local stress peaks when torque is applied through real machine parts. The elastic torsion formula works best for a circular shaft with a uniform cross-section and rigid plates fixed to its ends. In practice, torque is often passed through flange couplings or gears, and these parts use keys in keyways to connect to the shaft. That loading method changes the stress pattern near the point where torque enters the shaft. The stress distribution no longer matches the...

plastic deformation in circular shafts

Torsional Failure and Plastic Strain in Shafts

Plastic deformation in circular shafts happens when torsional force pushes the material past its yield strength. At that point, the shaft does not return to its original shape. Instead, it keeps a permanent strain. To measure this change, the stress pattern inside the shaft must be understood. The maximum shearing stress is calculated first. Then a shearing-stress-strain diagram can be drawn to find the maximum shearing strain. Shearing strain changes linearly with the distance from the shaft...

circular shafts - elastoplastic materials

Torsion Limits in Circular Shafts

Circular shafts under torsion show a clear change from elastic behavior to plastic deformation as torque increases. In the elastic limit, stress rises in direct proportion to the distance from the shaft’s center. The outer material carries the highest stress first, and the shaft can still return to its original shape. At a critical stress level, the shaft begins to yield. This marks the maximum torque the shaft can carry without permanent deformation. Beyond this point, a plastic region forms...

residual stresses in circular shafts

Residual Stress After Shaft Torsion

Residual stress can remain in a circular shaft after torque causes plastic deformation. This happens in elastoplastic materials, which show both elastic and plastic behavior. The plastic change can come from high shearing stress or large strain. Residual stress is the internal stress that stays in the material after the external force is removed. In a shaft under torque, the angle of twist does not return fully to its original value. That lasting change shows that residual stress is still...

torsion of noncircular members

Torsion in Square and Rectangular Bars

Torsion in square and rectangular bars shows how shape changes the way a material twists. Circular shafts keep their cross-sections nearly unchanged because they are axis-symmetric. That symmetry helps the stress spread evenly, so the shaft can resist torsion without distorting. Square bars behave differently because they do not have the same axial symmetry. When twisted, their cross-sections distort, although the diagonals and the lines connecting the midpoints stay as exceptions. This means...

thin-walled hollow shafts

Shear Flow in Thin-Walled Shafts

Shear flow in a thin-walled hollow shaft describes how torsional force is carried through the wall. When a small segment of width dx is isolated, it is still in equilibrium, but it experiences torsional shearing forces at its ends. These forces come from the longitudinal shearing stress on the segment's minor surface multiplied by that surface area. The result is a uniform shear flow through the structure. To study the wall more closely, a small section with length ds is considered. The force...

key terms and concepts

Learn how transmission shaft size is set by power, speed, torque, and allowable shear stress. See how solid and hollow shafts are designed.

Sizing a Transmission Shaft by Torque | JoVE K12

JoVE Core 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Sizing a Transmission Shaft by Torque

Description

Transcript