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Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Formula

GoMinimum Number of Teeth on Pinion to Avoid Interference Formula

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Minimum number of teeth on pinion is the count of teeth on pinion. Check FAQs

Z min = \frac{2 \cdot A w}{\frac{T}{Z p} \cdot (\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)}

Z_min - Minimum Number of Teeth on Pinion?A_w - Addendum of Wheel?T - Number of Teeth on Wheel?Z_p - Number of Teeth on Pinion?Φ_gear - Pressure Angle of Gear?

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Example

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Here is how the Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels equation looks like with Values.

Here is how the Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels equation looks like with Units.

Here is how the Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels equation looks like.

0.1448 = \frac{2 \cdot 24.5}{\frac{0.13}{0.09} \cdot (\sqrt{1 + \frac{0.09}{0.13} \cdot (\frac{0.09}{0.13} + 2) \cdot {(\sin (32))}^{2}} - 1)}

0.1448 = \frac{2 \cdot 24.5mm}{\frac{0.13}{0.09} \cdot (\sqrt{1 + \frac{0.09}{0.13} \cdot (\frac{0.09}{0.13} + 2) \cdot {(\sin (32°))}^{2}} - 1)}

0.1448 = \frac{2 \cdot 24.5}{\frac{0.13}{0.09} \cdot (\sqrt{1 + \frac{0.09}{0.13} \cdot (\frac{0.09}{0.13} + 2) \cdot {(\sin (32))}^{2}} - 1)}

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Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Solution

Follow our step by step solution on how to calculate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels?

FIRST Step Consider the formula

Z min = \frac{2 \cdot A w}{\frac{T}{Z p} \cdot (\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1)}

Next Step Substitute values of Variables

∴

Z min = \frac{2 \cdot 24.5mm}{\frac{0.13}{0.09} \cdot (\sqrt{1 + \frac{0.09}{0.13} \cdot (\frac{0.09}{0.13} + 2) \cdot {(\sin (32°))}^{2}} - 1)}

Next Step Convert Units

∴

Z min = \frac{2 \cdot 0.0245m}{\frac{0.13}{0.09} \cdot (\sqrt{1 + \frac{0.09}{0.13} \cdot (\frac{0.09}{0.13} + 2) \cdot {(\sin (0.5585rad))}^{2}} - 1)}

Next Step Prepare to Evaluate

∴

Z min = \frac{2 \cdot 0.0245}{\frac{0.13}{0.09} \cdot (\sqrt{1 + \frac{0.09}{0.13} \cdot (\frac{0.09}{0.13} + 2) \cdot {(\sin (0.5585))}^{2}} - 1)}

Next Step Evaluate

∴

Z min = 0.144806069702272

LAST Step Rounding Answer

∴

Z min = 0.1448

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Formula Elements

Variables

Functions

Minimum Number of Teeth on Pinion

Minimum number of teeth on pinion is the count of teeth on pinion.

Symbol: Z_min

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Minimum Number of Teeth on Pinion

Addendum of Wheel

Addendum of wheel is the height by which a tooth of a gear projects beyond (outside for external, or inside for internal) the standard pitch circle or pitch line.

Symbol: A_w

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Addendum of Wheel

Number of Teeth on Wheel

Number of teeth on wheel is the count of teeths on the wheel.

Symbol: T

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Number of Teeth on Wheel

Number of Teeth on Pinion

Number of teeth on pinion is the count of teeth on pinion.

Symbol: Z_p

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Pinion

Pressure Angle of Gear

The pressure angle of gear also known as the angle of obliquity is the angle between the tooth face and the gear wheel tangent.

Symbol: Φ_gear

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Pressure Angle of Gear

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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 to find Minimum Number of Teeth on Pinion

Go Minimum Number of Teeth on Pinion to Avoid Interference

Z min = \frac{2 \cdot A w}{\sqrt{1 + \frac{Z p}{T} \cdot (\frac{Z p}{T} + 2) \cdot {(\sin (Φ gear))}^{2}} - 1}

Other formulas in Minimum Number of Teeth category

Go Minimum Number of Teeth on Pinion for Involute Rack to Avoid Interference

Z p = \frac{2 \cdot A R}{{(\sin (Φ gear))}^{2}}

Go Minimum Number of Teeth on Pinion to Avoid Interference given Pinion and Wheel have Equal Teeth

Z p = \frac{2 \cdot A p}{\sqrt{1 + 3 \cdot {(\sin (Φ gear))}^{2}} - 1}

Go Minimum Number of Teeth on Pinion to Avoid Interference given Addendum of Pinion

Z p = \frac{2 \cdot A p}{\sqrt{1 + G \cdot (G + 2) \cdot {(\sin (Φ gear))}^{2}} - 1}

Go Minimum Teeth on Wheel to Avoid Interference if Pinion and Wheel have Equal Teeth

T = \frac{2 \cdot A w}{\sqrt{1 + 3 \cdot {(\sin (Φ gear))}^{2}} - 1}

How to Evaluate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels?

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels evaluator uses Minimum Number of Teeth on Pinion = (2*Addendum of Wheel)/(Number of Teeth on Wheel/Number of Teeth on Pinion*(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)) to evaluate the Minimum Number of Teeth on Pinion, Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels formula is defined as the smallest number of teeth required on the pinion gear to prevent interference with the addendum of the mating wheels in a gear train, ensuring smooth and efficient power transmission. Minimum Number of Teeth on Pinion is denoted by Z_min symbol.

How to evaluate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels using this online evaluator? To use this online evaluator for Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels, enter Addendum of Wheel (A_w), Number of Teeth on Wheel (T), Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear) and hit the calculate button.

FAQs on Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels

What is the formula to find Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels?

The formula of Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels is expressed as Minimum Number of Teeth on Pinion = (2*Addendum of Wheel)/(Number of Teeth on Wheel/Number of Teeth on Pinion*(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)). Here is an example- 0.144806 = (2*0.0245)/(0.13/0.09*(sqrt(1+0.09/0.13*(0.09/0.13+2)*(sin(0.55850536063808))^2)-1)).

How to calculate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels?

With Addendum of Wheel (A_w), Number of Teeth on Wheel (T), Number of Teeth on Pinion (Z_p) & Pressure Angle of Gear (Φ_gear) we can find Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels using the formula - Minimum Number of Teeth on Pinion = (2*Addendum of Wheel)/(Number of Teeth on Wheel/Number of Teeth on Pinion*(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)). This formula also uses Sine (sin), Square Root (sqrt) function(s).

What are the other ways to Calculate Minimum Number of Teeth on Pinion?

Here are the different ways to Calculate Minimum Number of Teeth on Pinion-

Minimum Number of Teeth on Pinion=(2*Addendum of Wheel)/(sqrt(1+Number of Teeth on Pinion/Number of Teeth on Wheel*(Number of Teeth on Pinion/Number of Teeth on Wheel+2)*(sin(Pressure Angle of Gear))^2)-1)

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Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Formula

​GoMinimum Number of Teeth on Pinion to Avoid Interference Formula

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Example

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Solution

Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels Formula Elements

Other Formulas to find Minimum Number of Teeth on Pinion

Other formulas in Minimum Number of Teeth category

How to Evaluate Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels?

FAQs on Minimum Teeth on Pinion to Avoid Interference given Addendum of Wheels

Variable Name

GoMinimum Number of Teeth on Pinion to Avoid Interference Formula