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# Gear Design and Rack Radius

02/17/2009 6:32 PM

how to calculate module for rack ?

As we know tht module = pitch circle diameter/ number of teeth,

considering rack its radius is infinite so how to calculate module for rack ?

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Guru

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#1

### Re: how to calculate module for rack ?

02/17/2009 6:50 PM

Have you had a look in one of the books for gear design? If not have it and you shall see the rack and gear drawings and all will be explained.

Any way to help you the module is ALWAYS the same for both gears, if not they cannot mesh! Got it?

Sincerely I seldom read such a ..... question.

Anonymous Poster
#10

### Re: how to calculate module for rack ?

02/19/2009 1:51 AM
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#23

### Re: how to calculate module for rack ?

02/27/2009 6:00 AM

There are several aspects to be discussed:

- the teeth of one gear have to be such that on the contact circles they have same thickness as the between teeth space of the other gear, this is in fact the only condition for meshing, the second is that the profiles are such that no wedging can occur (interferences), this is in internal gears a problem even for standard angles since it depends on the number of teeth.

- when a profile is "shifted" the common tangent to the 2 circles does NOT present same angle as for zero correction, the possibility to mesh 2 different (but not so different) modules comes combined with an angle change in order to respect the first condition.

- increasing the angle leads to a higher bending portance but reduces the length of the common tangent on which two pairs are in contact and should be used thus better with helical gears which have a greater contact due to the helix.

- asymmetrical gears are used since a long time in transmissions which do not have to be used under load in reverse, the positive aspect reflects only in the flank capability to transmit loads and not always in the root bending level. It allows the use lower grade steels.

- such solutions are only to be considered in big and very big series where the tooling does not have an impact on the product cost, in small series only the standards are economical since tooling is VERY expensive.

It was interesting to see the paper I shall try to get more informations from the authors.

Anonymous Poster
#25

### Re: how to calculate module for rack ?

10/21/2010 1:09 AM

how to calculate the module having base tangent length and tip diameter???? Please reply soon.

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#13

### Re: how to calculate module for rack ?

02/19/2009 4:53 AM

Modules Number of meshing gear teeth is always same.And,Either in circular or in Straight gear[rack],the pressure angle is 20deg for smooth motions.Generally,we should have in hand few more deffinitions/formulae for easy designing gear elements.For example:-

Pressure angle,ω=20 deg.This is the angle between "Line of action {common tangent of base circle of gear wheel & rack/mating gear} AND common tangents of pitch circle & pitch line of rack.

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#24

### Re: how to calculate module for rack ?

02/25/2010 8:31 AM

i want model calculation for rack and pinion.........

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#2

### Re: how to calculate module for rack ?

02/18/2009 8:39 AM

Pitch diameter X Pi = pinion circumference = linear distance moved on/of gear rack.

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#3

### Re: how to calculate module for rack ?

02/18/2009 8:43 AM

I am sorry Bill, but you do not answer the question.

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#4

### Re: how to calculate module for rack ?

02/18/2009 8:48 AM

Well, I certainly did answer the question. Whether or not my answer is correct, and whether or not this is the information the original poster requested is another matter.

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#5

### Re: how to calculate module for rack ?

02/18/2009 8:52 AM

The question was "how to calculate module of rack ?".

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#6

### Re: how to calculate module for rack ?

02/18/2009 9:16 AM

My mistake -- I misread what he wanted. I use the term, "pitch," whereas he uses the term, "module."

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#7

### Re: how to calculate module for rack ?

02/18/2009 7:07 PM

thanq

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#8

### Re: how to calculate module for rack ?

02/18/2009 11:53 PM

In rack & pinion drive always pinion subjected more load compare to rack , so you first decide the module for pinion as per your torque and axial force acting on the pinion

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#9

### Re: how to calculate module for rack ?

02/19/2009 1:29 AM

Load is the same only stress levels are different due to the teeth profiles. This is valid only for bending since the contact stress is the same (according to Mr. Hertz!).

Engineering is a precise business, words have a meaning and physics have to be respected!!!!!!!

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#11

### Re: Gear Design and Rack Radius

02/19/2009 3:33 AM

Pitch dia is Imperial and module is metric. If you have a gear of 4" pitch dia with 40 teeth it is 40/4 = 10DP = .1 X 3.1417 circular pitch =.31417 pitch on rack. If you have 100mm pitch dia with 40 teeth it is 100/40 = 2.5 Module =2.5 X 3.1417= 7.85 pitch on rack.

I hope this makes sense.

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#12

### Re: Gear Design and Rack Radius

02/19/2009 4:13 AM
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#14

### Gear Design and Rack Radius

02/19/2009 4:59 AM

measure the pitch in mm & divide it by pi (3.1416). you will get the module

i have given below an extract fro machinery's handbook (i could not copy the figure & paste it)

Gear Design Based upon Module System.The module of a gear is equal to the pitch

diameter divided by the number of teeth, whereas diametral pitch is equal to the number of

teeth divided by the pitch diameter. The module system (see accompanying table and diagram)

is in general use in countries that have adopted the metric system; hence, the term

module is usually understood to mean the pitch diameter in millimeters divided by the

number of teeth. The module system, however, may also be based on inch measurements

and then it is known as the English module to avoid confusion with the metric module.

Module is an actual dimension, whereas diametral pitch is only a ratio. Thus, if the pitch

diameter of a gear is 50 millimeters and the number of teeth 25, the module is 2, which

means that there are 2 millimeters of pitch diameter for each tooth. The table Tooth Dimensions

Based Upon Module System shows the relation among module, diametral pitch, and

circular pitch.

German Standard Tooth Form for Spur and Bevel Gears

DIN 867

Formulas for dedendum and total depth, marked (*) are used when clearance equals 0.157 × module.

Formulas marked (**) are used when clearance equals one-sixth module. It is common practice

among American cutter manufacturers to make the clearance of metric or module cutters equal to

0.157 × module.

The flanks or sides are straight (involute system) and the pressure angle is 20 degrees. The shape of

the root clearance space and the amount of clearance depend upon the method of cutting and special

requirements. The amount of clearance may vary from 0.1 × module to 0.3 × module.

To Find Module Known Circular Pitch Known

Addendum Equals module 0.31823 × Circular pitch

Dedendum 1.157 × module*

1.167 × module**

0.3683 × Circular pitch*

0.3714 × Circular pitch**

Working Depth 2 × module 0.6366 × Circular pitch

Total Depth 2.157 × module*

2.167 × module**

0.6866 × Circular pitch*

0.6898 × Circulate pitch**

Tooth Thickness on

Pitch Line 1.5708 × module 0.5 × Circular pitch

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#15

### Re: Gear Design and Rack Radius

02/19/2009 9:29 AM

Hello venkat,

You have done well and a GA to you sir!

Though for the life of me I do not understand why this already formulated and well figured subject was even asked about?

Take care...................

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#17

### Re: Gear Design and Rack Radius

02/19/2009 12:55 PM

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#22

### Re: Gear Design and Rack Radius

02/19/2009 7:09 PM

thankq

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#26

### Re: Gear Design and Rack Radius

02/17/2013 2:27 AM

Dear Mr.venkat,

You have mentioned that "Tooth Thickness on Pitch Line 1.5708 × module 0.5 × Circular pitch" There is another Formula to calculate tooth thickness.

The tooth thickness (called as WIDTH also) at Pitch Circle is given by t or w = M x Pi/2 i.e Module x 3.14/2 = M x 1.57

In fact there is formula to calculate the thickness above PCD and below PCD for the entire tooth height.

You have mentioned as follows " I have given below an extract from machinery's handbook (i could not copy the figure & paste it)"

Pl. furnish in this link or through CR4 private messaging facility the name of the Author of the Hand Book and Publisher's Name and if possible Library Catalogue No. - so that it can be down loaded either freely or on payment basis from the links provided in the www.zone4info.com

DHAYANANDHAN.S

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#16

### Re: Gear Design and Rack Radius

02/19/2009 11:03 AM

A metric gear of pitch diameter of say 100 mm and 20 teeth, you have a module of 5, simply dividing 100 PD by 20 teeth.

Now, if you would cut the gear open and lay it flat, (imaginary) then you have a straight tooth rack, correct? Well, then you figure out the straight length of the rack which will be 100 mm * pi = 314.16 mm.

So to answer your question, simply divide the length of the rack by pi and calculate just as if it would do before having a circular gear.

That holds true for the imperial system as well where the pitch diameter is the number of teeth divided by the diametrical pitch. Example:

36 teeth, DP = 12, hence: PD = 36 / 12 = 3 inch diameter. The equivalent straight rack of 36 teeth would be 3" * pi = 9.4248 inch long.

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#18

### Re: Gear Design and Rack Radius

02/19/2009 2:04 PM

Once you are done figuring this out, how about a good elliptical gear. I have not had anyone that could definitely give me equations on elliptical gears that would actually work. I worked for a couple of months trying to work on an equation for such said animal, but only had a pair of calipers and a magnifying glass. I figure a good shadow comparator would have helped to reverse engineer the gear I had at the time, but we only can work with what we have.

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#20

### Re: Gear Design and Rack Radius

02/19/2009 3:53 PM

Hello foofire,

Is there anything here that will help? Let me know whatever please, OK?

A mathematical digression " Successful Software ... using equations to calculation elliptical gears with the correct parameters would do the trick. ... Elliptical gears use the ratio between the ...successfulsoftware.net/2008/07/18/a-mathematical-digression - 109k - Cached

[PDF] Surface Involutions with Applications to Gear Mechanics 904k - Adobe PDF - View as html This equation can be clearly understood by noticing that the integrand represents the arc ... By applying similar methods an elliptical gear is developed (Fig. 8) ...

www.cims.nyu.edu/vigrenew/ug_research/DavidValdman.pdf

Cunningham Industries Home Page Equations for N-Lobed. Elliptical Gears. Non-Circular Gears. Typical Applications ... been manufacturing elliptical and other non circular gears for companies large ...

cunningham-ind.com - Cached

Gears - Numericana (2005-12-10) Elliptical Spur Gears: From Ellipse Pinion to Sine Rack ... from its focus obey the differential equation (r-a) dq = r dj which may be ...

[PDF] The approximation of Kepler�s laws through mechanical gearing mechanisms 989k - Adobe PDF - View as html The equation of center is necessarily zero at both perihelion (t = 0) ... cometaria either having offset circular, or elliptical gear/pulley wheel drive trains. ...

uregina.ca/~astro/comet/equal_area.pdf

Equations For N-Lobed Elliptical Gears Equations for N-Lobed Elliptical Gears. The angular displacement relation is: The velocity ratio is given by: ... 203-324-2942. Cunningham Industries, Inc. 102 ...

www.cunningham-ind.com/equate.htm - Cached

Take care and good mathing!

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#21

### Re: Gear Design and Rack Radius

02/19/2009 5:00 PM

Hello foofire,

have a look at this. http://mysite.du.edu/~jcalvert/math/ellarc.htm

Not sure if it will help, but it seems to explain it gradually.

Take care.....................

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#19

### Re: Gear Design and Rack Radius

02/19/2009 3:38 PM

Hello Floram:

Well explained! .........GA to you sir!

Take care..........................

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