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Dynamic load on Gear Formula

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The Dynamic Load on Spur Gear is the load on a spur gear due to dynamic conditions between two meshing teeth. Check FAQs

P d = \frac{(21 \cdot v) \cdot ((C \cdot Σe \cdot b) + (P t))}{(21 \cdot v) + \sqrt{(C \cdot Σe \cdot b) + (P t)}}

P_d - Dynamic Load on Spur Gear?v - Pitch Line Velocity of Spur Gear?C - Deformation Factor for Spur Gear?Σe - Sum of Error for Meshing Gear Teeth?b - Face Width of Spur Gear Tooth?P_t - Tangential Force on Spur Gear?

Dynamic load on Gear Example

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Here is how the Dynamic load on Gear equation looks like with Values.

Here is how the Dynamic load on Gear equation looks like with Units.

Here is how the Dynamic load on Gear equation looks like.

1676.0832 = \frac{(21 \cdot 3.7) \cdot ((1100 \cdot 0.05 \cdot 34) + (952))}{(21 \cdot 3.7) + \sqrt{(1100 \cdot 0.05 \cdot 34) + (952)}}

1676.0832N = \frac{(21 \cdot 3.7m/s) \cdot ((1100N/mm² \cdot 0.05mm \cdot 34mm) + (952N))}{(21 \cdot 3.7m/s) + \sqrt{(1100N/mm² \cdot 0.05mm \cdot 34mm) + (952N)}}

1676.0832 = \frac{(21 \cdot 3.7) \cdot ((1100 \cdot 0.05 \cdot 34) + (952))}{(21 \cdot 3.7) + \sqrt{(1100 \cdot 0.05 \cdot 34) + (952)}}

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Dynamic load on Gear Solution

Follow our step by step solution on how to calculate Dynamic load on Gear?

FIRST Step Consider the formula

P d = \frac{(21 \cdot v) \cdot ((C \cdot Σe \cdot b) + (P t))}{(21 \cdot v) + \sqrt{(C \cdot Σe \cdot b) + (P t)}}

Next Step Substitute values of Variables

∴

P d = \frac{(21 \cdot 3.7m/s) \cdot ((1100N/mm² \cdot 0.05mm \cdot 34mm) + (952N))}{(21 \cdot 3.7m/s) + \sqrt{(1100N/mm² \cdot 0.05mm \cdot 34mm) + (952N)}}

Next Step Convert Units

∴

P d = \frac{(21 \cdot 3.7m/s) \cdot ((1.1E+9Pa \cdot 5E-5m \cdot 0.034m) + (952N))}{(21 \cdot 3.7m/s) + \sqrt{(1.1E+9Pa \cdot 5E-5m \cdot 0.034m) + (952N)}}

Next Step Prepare to Evaluate

∴

P d = \frac{(21 \cdot 3.7) \cdot ((1.1E+9 \cdot 5E-5 \cdot 0.034) + (952))}{(21 \cdot 3.7) + \sqrt{(1.1E+9 \cdot 5E-5 \cdot 0.034) + (952)}}

Next Step Evaluate

∴

P d = 1676.08324331516N

LAST Step Rounding Answer

∴

P d = 1676.0832N

Dynamic load on Gear Formula Elements

Variables

Functions

Dynamic Load on Spur Gear

The Dynamic Load on Spur Gear is the load on a spur gear due to dynamic conditions between two meshing teeth.

Symbol: P_d

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Dynamic Load on Spur Gear

Pitch Line Velocity of Spur Gear

The Pitch Line Velocity of Spur Gear is defined as the velocity of a point on the pitch circle of gear.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Pitch Line Velocity of Spur Gear

Deformation Factor for Spur Gear

The Deformation Factor for Spur Gear is a factor accounting for the deformation of the gear tooth.

Symbol: C

Measurement: PressureUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Deformation Factor for Spur Gear

Sum of Error for Meshing Gear Teeth

Sum of Error for Meshing Gear Teeth can be defined as the total error in dimensions of the two meshing gear teeth.

Symbol: Σe

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Sum of Error for Meshing Gear Teeth

Face Width of Spur Gear Tooth

Face Width of Spur Gear Tooth is the length of the gear tooth parallel to the gear axis.

Symbol: b

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Face Width of Spur Gear Tooth

Tangential Force on Spur Gear

Tangential Force on Spur Gear is the force that acts on a spur gear in the direction of a tangent to the curved path of the gear circumference..

Symbol: P_t

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Tangential Force on Spur Gear

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Dynamics of Spur Gear category

Go Torque Transmitted by Gear given Tangential Force and Pitch Circle Diameter

M t = P t \cdot \frac{d}{2}

Go Tangential Force on Gear given Torque and Pitch Circle Diameter

P t = 2 \cdot \frac{M t}{d}

Go Radial Force of Gear given Tangential Force and Pressure Angle

P r = P t \cdot \tan (Φ)

Go Tangential Force on Gear given Radial Force and Pressure Angle

P t = P r \cdot \cot (Φ)

How to Evaluate Dynamic load on Gear?

Dynamic load on Gear evaluator uses Dynamic Load on Spur Gear = ((21*Pitch Line Velocity of Spur Gear)*((Deformation Factor for Spur Gear*Sum of Error for Meshing Gear Teeth*Face Width of Spur Gear Tooth)+(Tangential Force on Spur Gear)))/((21*Pitch Line Velocity of Spur Gear)+sqrt((Deformation Factor for Spur Gear*Sum of Error for Meshing Gear Teeth*Face Width of Spur Gear Tooth)+(Tangential Force on Spur Gear))) to evaluate the Dynamic Load on Spur Gear, Dynamic load on Gear is the additional load due to the dynamic conditions associated with the two meshing gear teeth. It depends upon the pitch line velocity, deformation factor, face width, and the error in the gear teeth. Dynamic Load on Spur Gear is denoted by P_d symbol.

How to evaluate Dynamic load on Gear using this online evaluator? To use this online evaluator for Dynamic load on Gear, enter Pitch Line Velocity of Spur Gear (v), Deformation Factor for Spur Gear (C), Sum of Error for Meshing Gear Teeth (Σe), Face Width of Spur Gear Tooth (b) & Tangential Force on Spur Gear (P_t) and hit the calculate button.

FAQs on Dynamic load on Gear

What is the formula to find Dynamic load on Gear?

The formula of Dynamic load on Gear is expressed as Dynamic Load on Spur Gear = ((21*Pitch Line Velocity of Spur Gear)*((Deformation Factor for Spur Gear*Sum of Error for Meshing Gear Teeth*Face Width of Spur Gear Tooth)+(Tangential Force on Spur Gear)))/((21*Pitch Line Velocity of Spur Gear)+sqrt((Deformation Factor for Spur Gear*Sum of Error for Meshing Gear Teeth*Face Width of Spur Gear Tooth)+(Tangential Force on Spur Gear))). Here is an example- 1676.083 = ((21*3.7)*((1100000000*5E-05*0.034)+(952)))/((21*3.7)+sqrt((1100000000*5E-05*0.034)+(952))).

How to calculate Dynamic load on Gear?

With Pitch Line Velocity of Spur Gear (v), Deformation Factor for Spur Gear (C), Sum of Error for Meshing Gear Teeth (Σe), Face Width of Spur Gear Tooth (b) & Tangential Force on Spur Gear (P_t) we can find Dynamic load on Gear using the formula - Dynamic Load on Spur Gear = ((21*Pitch Line Velocity of Spur Gear)*((Deformation Factor for Spur Gear*Sum of Error for Meshing Gear Teeth*Face Width of Spur Gear Tooth)+(Tangential Force on Spur Gear)))/((21*Pitch Line Velocity of Spur Gear)+sqrt((Deformation Factor for Spur Gear*Sum of Error for Meshing Gear Teeth*Face Width of Spur Gear Tooth)+(Tangential Force on Spur Gear))). This formula also uses Square Root (sqrt) function(s).

Can the Dynamic load on Gear be negative?

No, the Dynamic load on Gear, measured in Force cannot be negative.

Which unit is used to measure Dynamic load on Gear?

Dynamic load on Gear is usually measured using the Newton[N] for Force. Exanewton[N], Meganewton[N], Kilonewton[N] are the few other units in which Dynamic load on Gear can be measured.

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Dynamic load on Gear Formula

Dynamic load on Gear Example

Dynamic load on Gear Solution

Dynamic load on Gear Formula Elements

Other formulas in Dynamics of Spur Gear category

How to Evaluate Dynamic load on Gear?

FAQs on Dynamic load on Gear

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