Self Aligning Moment or Torque on Wheels Calculator

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Front Axle and Steering

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Moments, Loads, Angles acting on Steering system and Axles

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Angles Acting on Steering System and Axles

Moments Acting on Steering System and Axles

✖Aligning Moment Acting on Left Tires is defined as the moment acting on the left side of the tires.ⓘ Aligning Moment Acting on Left Tires [M_zl]			+10% -10%
✖Aligning Moment on Right Tires is defined as the moment acting on the right side of the tires.ⓘ Aligning Moment on Right Tires [M_zr]			+10% -10%
✖Lateral Inclination Angle is the inclination of the kingpin with respect to the vertical axis laterally.ⓘ Lateral Inclination Angle [λ_l]			+10% -10%
✖Caster Angle is the angle that identifies the forward or backward slope of a line that is drawn through the upper and lower steering pivot points.ⓘ Caster Angle [ν]			+10% -10%

✖Self Aligning Moment is the moment that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis.ⓘ Self Aligning Moment or Torque on Wheels [M_at]

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Formula

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Self Aligning Moment or Torque on Wheels

Formula

`"M"_{"at"} = ("M"_{"zl"}+"M"_{"zr"})*cos("λ"_{"l"})*cos("ν")`

Example

`"100.1407N*m"=("27N*m"+"75N*m")*cos("10°")*cos("4.5°")`

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Download Moments, Loads, Angles acting on Steering system and Axles Formulas PDF

Self Aligning Moment or Torque on Wheels Solution

STEP 0: Pre-Calculation Summary

Formula Used

Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle)
M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν)
This formula uses 1 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Self Aligning Moment - (Measured in Newton Meter) - Self Aligning Moment is the moment that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis.
Aligning Moment Acting on Left Tires - (Measured in Newton Meter) - Aligning Moment Acting on Left Tires is defined as the moment acting on the left side of the tires.
Aligning Moment on Right Tires - (Measured in Newton Meter) - Aligning Moment on Right Tires is defined as the moment acting on the right side of the tires.
Lateral Inclination Angle - (Measured in Radian) - Lateral Inclination Angle is the inclination of the kingpin with respect to the vertical axis laterally.
Caster Angle - (Measured in Radian) - Caster Angle is the angle that identifies the forward or backward slope of a line that is drawn through the upper and lower steering pivot points.

STEP 1: Convert Input(s) to Base Unit

Aligning Moment Acting on Left Tires: 27 Newton Meter --> 27 Newton Meter No Conversion Required
Aligning Moment on Right Tires: 75 Newton Meter --> 75 Newton Meter No Conversion Required
Lateral Inclination Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Caster Angle: 4.5 Degree --> 0.0785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν) --> (27+75)*cos(0.1745329251994)*cos(0.0785398163397301)

Evaluating ... ...

M_at = 100.14073577601

STEP 3: Convert Result to Output's Unit

100.14073577601 Newton Meter --> No Conversion Required

FINAL ANSWER

100.14073577601 ≈ 100.1407 Newton Meter <-- Self Aligning Moment

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Front Axle and Steering » Moments, Loads, Angles acting on Steering system and Axles » Self Aligning Moment or Torque on Wheels

Credits

Created by Syed Adnan

Ramaiah University of Applied Sciences (RUAS), bangalore

Syed Adnan has created this Calculator and 200+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

Kartikay Pandit has verified this Calculator and 400+ more calculators!

< 11 Moments, Loads, Angles acting on Steering system and Axles Calculators

Self Aligning Moment or Torque on Wheels

Go Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle)

Front Slip Angle at High Cornering Speed

Go Slip Angle of Front Wheel = Vehicle Body Slip Angle+(((Distance of c.g from Front Axle*Yaw Velocity)/Total Velocity)-Steer Angle)

Critical Speed for Oversteer Vehicle

Go Critical Speed for Oversteer Vehicles = -sqrt((57.3*Wheelbase of Vehicle*Acceleration due to Gravity)/(Understeer Gradient))

Track Width of Vehicle using Ackermann Condition

Go Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle

Characteristic Speed for Understeer Vehicles

Go Characteristic Speed for Understeer Vehicles = sqrt((57.3*Wheelbase of Vehicle*Acceleration due to Gravity)/Understeer Gradient)

Rear Slip Angle due to High Speed Cornering

Go Slip Angle of Rear Wheel = Vehicle Body Slip Angle-((Distance of c.g from Rear Axle*Yaw Velocity)/Total Velocity)

Load on Front Axle at High Speed Cornering

Go Load on Front Axle at High Speed Cornering = (Total Load of Vehicle*Distance of c.g from Rear Axle)/Wheelbase of Vehicle

Load on Rear Axle at High Speed Cornering

Go Load on Rear Axle at High Speed Cornering = (Total Load of Vehicle*Distance of c.g from Front Axle)/Wheelbase of Vehicle

Centripetal Acceleration during Cornering

Go Centripetal Acceleration during Cornering = (Total Velocity*Total Velocity)/Radius of Turn

Lateral Acceleration during Cornering of Car

Go Horizontal Lateral Acceleration = Centripetal Acceleration during Cornering/Acceleration due to Gravity

Driveline Torque

Go Driveline Torque = Tractive Force*Radius of Tire

Self Aligning Moment or Torque on Wheels Formula

Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle)
M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν)

What is self aligning moment on wheels?

The self aligning moment of a tire acts vertically and can result in a component parallel to the pivot axis. The alignment moment is therefore transmitted to the steering system. In normal conditions, self aligning torques always tend to reduce the steer angle so that they have an understeer condition.

How to Calculate Self Aligning Moment or Torque on Wheels?

Self Aligning Moment or Torque on Wheels calculator uses Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle) to calculate the Self Aligning Moment, Self aligning moment or torque on wheels formula is defined as the torque that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis. In the presence of a non-zero slip angle, this torque tends to steer the tire toward the direction in which it is traveling. Self Aligning Moment is denoted by M_at symbol.

How to calculate Self Aligning Moment or Torque on Wheels using this online calculator? To use this online calculator for Self Aligning Moment or Torque on Wheels, enter Aligning Moment Acting on Left Tires (M_zl), Aligning Moment on Right Tires (M_zr), Lateral Inclination Angle (λ_l) & Caster Angle (ν) and hit the calculate button. Here is how the Self Aligning Moment or Torque on Wheels calculation can be explained with given input values -> 100.4503 = (27+75)*cos(0.1745329251994)*cos(0.0785398163397301).

FAQ

What is Self Aligning Moment or Torque on Wheels?

Self aligning moment or torque on wheels formula is defined as the torque that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis. In the presence of a non-zero slip angle, this torque tends to steer the tire toward the direction in which it is traveling and is represented as M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν) or Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle). Aligning Moment Acting on Left Tires is defined as the moment acting on the left side of the tires, Aligning Moment on Right Tires is defined as the moment acting on the right side of the tires, Lateral Inclination Angle is the inclination of the kingpin with respect to the vertical axis laterally & Caster Angle is the angle that identifies the forward or backward slope of a line that is drawn through the upper and lower steering pivot points.

How to calculate Self Aligning Moment or Torque on Wheels?

Self aligning moment or torque on wheels formula is defined as the torque that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis. In the presence of a non-zero slip angle, this torque tends to steer the tire toward the direction in which it is traveling is calculated using Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle). To calculate Self Aligning Moment or Torque on Wheels, you need Aligning Moment Acting on Left Tires (M_zl), Aligning Moment on Right Tires (M_zr), Lateral Inclination Angle (λ_l) & Caster Angle (ν). With our tool, you need to enter the respective value for Aligning Moment Acting on Left Tires, Aligning Moment on Right Tires, Lateral Inclination Angle & Caster Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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