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Gear Ratio BJ-worm gears are available with the following nominal gear ratios: Dimensioning Gear Size and Gear Ratio By using the graphs on subsequent pages, you can dimension gear size, gear ratio and number of revolutions as well as motor according to your requirement. Alternatively, you can use the tables on pages 27 to 29. Gear Design National Broach and Machine Division,of Lear Siegler, Inc. A gear can be defined as a toothed wheel which, when meshed with another toothed wheel with similar configura-tion, will transmit rotation from one shaft to another. Depending upon the type and accuracy of motion desired, the gears and the profiles of the gear teeth can be.

The gear hob design must be altered in accordance with the changing of helix angle β, even when the module m t and the pressure angle α t are the same. Obviously, the manufacturing of helical gears is easier with the normal system than with the radial system in the plane perpendicular to the axis. » Helical Gear Calculations - Continued on.

What is a gear calculator ?

The gear calculator is a comprehensive software which, after inputting various parameters related to gear calculations, computes on-line automatically gear sizes, strengths, working forces, tooth forms, backlash conversions, etc. Because gear calculations require many complex formulas related to strengths and sizes, traditional gear design situations require highly specialized knowledge and suitable design time. By utilizing the gear calculator introduced here, it is possible to reduce these burdens substantially. Among the parameters requiring user input are the unit to specify gear tooth such as module or diametral pitch (DP) and its value, pressure angle, helix angle, number of teeth, coefficient of profile shift, center distance, material, rpm (rotational speed), face width, safety ratio, circumferential backlash, etc. This gear calculator software also handles gear calculations of various types of gears such as spur gears, worm gears, gear racks, bevel gears, internal gears, screw gears, etc.

What is a gear drawing software ?

The gear drawing software means an on-line automatic program to produce gear drawings when users input various parameters needed to define gear sizes. It also allows downloading the produced original (custom) gear drawings in the dxf format and expands them by using CAD software. Without this kind of dedicated gear drawing software, it would be necessary, after gear sizes have been determined, to use conventional CAD software and draw the gears from scratch. Therefore, the use of this kind of gear drawing software allows large scale improvement in gear designs. Among the parameters requiring user input are the unit to specify gear tooth such as module or diametral pitch (DP) and its value, standard cross section of the tooth, coefficient of profile shift, precision grade such as JIS, hub diameter, bore diameter and its tolerance, size of the chamfer, various sizes related to keyway, number and positions of tapped and counterbore holes, etc. As with the gear calculator, this gear drawing software also handles making drawing of various types of gears such as spur gears, worm gears, gear racks, bevel gears, internal gears, screw gears, etc.

GCSW - Free Gear Calculator

Spur Gears
Worm Gears
Bevel Gears
Rack and Pinion
Screw Gears
Internal Gears
To register to use this calculator, click here
To check your registration status, click here

GDSW - Free Gear Drawing Software

Spur Gears

Worm Gear Design Calculator

Worm Gears
Bevel Gears
Gear Rack
Screw Gears
Internal Gears
To register to use this calculator, click here
To check your registration status, click here

Example of the Parameter Input Screen of this Gear Calculator :

As an example, we will introduce the parameter setup screen for the bending strength calculation of spur (or helical) gears.

1.
In this section, we input the tooth size.
For the unit of the tooth size, you can choose the international standard of module, inch based diametral pitch (DP) or circular pitch.
For the tooth's standard cross section, it is possible to select the normal to the tooth or perpendicular to its shaft.

2.
In this section, we can input pressure angle normal to the tooth, tooth's twisting angle, addendum and dedendum coefficients.

3.
Here, you input the number of teeth of the pinion and the gear.
Also, you can input each coefficient of normal profile shift of the gears.

Besides the strength calculation, this gear calculator can also compute sizes, forces acting on the teeth, tooth forms, etc.
However, for this example, we will focus on the required parameters for strength calculation (bending strength).
For strength calculation, you can compute the bending strengths and gear surface durability.
For MC Nylon gears, only the bending strength calculation is available.

In this section, we input the parameters associated with the gears' actual usage environment.
4.
Input the center distance between the pinion and the gear.
5.
If needed, also input the gear cutting tool's tip rounding radius coefficient.
6.
Input the number of teeth of the pinion and the gear.
7.
Enter the precision grades of the two gears as well as absence or existence of tooth form correction(s).
8.
Here you can select the materials of the two gears such as S45C, SCM415, SCM440, etc. In addition, selection of surface hardness such as induction hardening, carburizing, nitriding, normalizing, hardening and tempering, etc. can be made. Also, detailed settings of hardness of center (HB)(HV), tooth surface durability (HB)(HV), allowable bending stress (σFlim), allowable Hertz stress (σHlim), etc. are possible.
9.
Input the rotational speed (rpm) of the pinion here.
10.
Here you enter the number of repetitions.
11.
It is possible to enter the safety factor here.
12.
Enter the overload coefficient.
13.
It is possible to select the unit of force in kgf or Nm.
14.
As soon as the parameter entries have been completed, press this button to display the results of the calculations.

Example of Results of the Strength Calculations (Tooth Bending Strength Calculations) for Spur and Helical Gears

15.
3utools carrier unlock. Allowable torques (Nm) for the pinion and the gear respectively are displayed based on the strength calculations.

Other Functions

Calculation of force acting on gears

Backlash conversion

DISCLAIMER

This software is provided as an exclusive service to our registered users.
The contents of the software may be revised for improvements without notice.
Any damages directly or indirectly suffered by the users of this software are the responsibility of the users and we do not offer any compensation.
We are not responsible for your loss of data from system malfunctions.
Calculation results such as values of strength are not guaranteed values. Please use them as reference values.
This software is protected by copyright law. You are prohibited from changing or copying the contents without writtten consent from us.

For customers without SSL :

In order to avoid interception of our customer's important information, our software has high security settings.
Please contact your system administrator if you have problems opening GCSW, GDSW or the comment form.
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Resources:

Spur Gear design formula for geometry, pitch, tooth clearance and critical functional data.
(Inch Units Applicable for Constants)

Where:
φ = Pressure Angle
a = Addendum
a_G = Addendum of Gear
a_P = Addendum of Pinion
b = Dedendum
c = Clearance
C = Center Distance
D = Pitch Diameter
D_G = Pitch Diameter of Gear
D_P = Pitch Diameter of Pinion
D_B = Base Circle Diameter
D_O = Outside Diameter
DR = Root Diameter
F = Face Width
h_k = Working Depth of Tooth
h_t = Whole Depth of Tooth
m_G = Gear Ratio
N = Number of Teeth
N_G = Number of Teeth in Gear
N_P = Number of Teeth in Pinion
p = Circular Pitch
P=Diametral Pitch

Equations for Standards Spur Gears

To Find	Equation
Base Circle Pitch	DB = D cosφ
Circular Pitch	p = ( π D )/ N p = π / P
Center Distance	C = Np (mG + 1) / 2P C = ( Dp + DG ) / 2 C = ( NG + Np ) / 2P C = (NG + Np) p / 2P C = (NG + Np) p / 6.2832
Diametral Pitch	P = π / p P = N / D P = [ Np ( mG + 1) ] / 2C
Gear Ratio	mG = NG / Np
Number of Teeth	N = P D N = ( π D ) / p
Outside Diameter (Full Depth Teeth)	DO = ( N + 2 ) / P DO = [ ( N + 2 ) p ] / π
Outside Diameter (American Standard Stub Teeth)	DO = ( N + 1.6 ) / P DO = [ ( N + 1.6 ) p ] / π
Outside Diameter	DO = D + 2a
Pitch Diameter	D = N / P D = (N p ) / π
Root Diameter	DR = D - 2b
Whole Depth	a + b
Working Depth	aG + ap

Formulas for Tooth Parts, 20-and 25-degree Involute Full-depth Teeth
ANSI Coarse Pitch Spur Gear Tooth Forms ANSI B6.1

To Calculate	Circular Pitch, p, Known
Addendum	a = 0.3183 × p
Dedendum (Preferred)	b = 0.3979 × p
(Shaved or Ground Teeth)a	b = 0.4297 × p
Working Depth	hk = 0.6366 × p
Whole Depth (Preferred)	ht = 0.7162 × p
(Shaved or Ground Teeth)	ht = 0.7480 × p
Clearance (Preferred)b	c = 0.0796 × p
(Shaved or Ground Teeth)	c = 0.1114 × p
Fillet Radius (Rack)c	rf = 0.0955 × p
Pitch Diameter	D = 0.3183 × Np
Outside Diameter	DO = 0.3183 × (N + 2) p
Root Diameter (Preferred)	DR = 0.3183 × (N − 2.5) p
Root Diameter (Shaved or Ground Teeth)	DR = 0.3183 × (N − 2.7) p
Circular Thickness Basic	t = p / 2

Equations Tooth Parts, 20-and 25-degree Involute Full-depth Teeth ANSI Coarse Pitch Spur Gear Tooth Forms ANSI B6.1

^a When gears are preshave cut on a gear shaper the dedendum will usually need to be increased to 1.40/P to allow for the higher fillet trochoid produced by the shaper cutter. This is of particular importance on gears of few teeth or if the gear blank configuration requires the use of a small diameter shaper cutter, in which case the dedendum may need to be increased to as much as 1.45/P. This should be avoided on highly loaded gears where the consequently reduced J factor will increase gear tooth stress excessively.
^b A minimum clearance of 0.157/P may be used for the basic 20-degree and 25-degree pressure angle rack in the case of shallow root sections and use of existing hobs or cutters.
^c The fillet radius of the basic rack should not exceed 0.235/P for a 20-degree pressure angle rack or 0.270/P for a 25-degree pressure angle rack for a clearance of 0.157/P. The basic rack fillet radius must be reduced for teeth with a 25-degree pressure angle having a clearance in excess of 0.250/P.

Worm Gear Calculation Formula

Helical Gear

When Defined
Normal D.P. (Pn)	Pn= P / cos A
Number of teeth (N) and the Helix Angle (A)
Pitch Diameter (D)	Number of teeth (N), the Normal Diametral Pitch and the Helix Angle (A)
Outside Diameter (OD)	OD = D + (2 X a)
Normal Diametral Pitch (P) and the Pitch Diameter (D)
Helix Angle (A) for Parallel Shaft Drive	Number of Teeth (N), Pitch Diameter (D) and the Diametral Pitch (P)
Addendum (a)	a = 1 / Pn
Pitch Diameter (D) and Pitch Helix Angle

Circular Pitches and Equivalent Diametral Pitches Table

Circular Pitch	Module	Addendum	Dedendum or Depth of Space Below Pitch Line
4	0.7854	32.3402	2.0000	1.2732	2.5464	1.4732	2.7464
3 - 1/2	0.8976	28.2581	1.7500	1.1140	2.2281	1.2890	2.4031
3	1.0472	24.2552	1.5000	0.9549	1.9098	1.1049	2.0598
2 - 3/4	1.1424	22.2339	1.3750	0.8753	1.7506	1.0128	1.8881
2 - 1/2	1.2566	20.2117	1.2500	0.7957	1.5915	0.9207	1.7165
2 - 1/4	1.3963	18.1913	1.1250	0.7162	1.4323	0.8287	1.5448
2	1.5708	16.1701	1.0000	0.6366	1.2732	0.7366	1.3732
1 - 7/8	1.6755	15.1595	0.9375	0.5968	1.1937	0.6906	1.2874
1 - 3/4	1.7952	14.1488	0.8750	0.5570	1.1141	0.6445	1.2016
1 - 5/8	1.9333	13.1382	0.8125	0.5173	1.0345	0.5985	1.1158
1 - 1/2	2.0944	12.1276	0.7500	0.4775	0.9549	0.5525	1.0299
1 - 7/16	2.1855	11.6223	0.7187	0.4576	0.9151	0.5294	0.9870
1 - 3/8	2.2848	11.1169	0.6875	0.4377	0.8754	0.5064	0.9441
1 - 5/16	2.3936	10.6116	0.6562	0.4178	0.8356	0.4834	0.9012
1 - 1/4	2.5133	10.1062	0.6250	0.3979	0.7958	0.4604	0.8583
1 - 3/16	2.6456	9.6010	0.5937	0.3780	0.7560	0.4374	0.8154
1 - 1/8	2.7925	9.0958	0.5625	0.3581	0.7162	0.4143	0.7724
1 - 1/16	2.9568	8.5904	0.5312	0.3382	0.6764	0.3913	0.7295
1	3.1416	8.0851	0.5000	0.3183	0.6366	0.3683	0.6866
15/16	3.3510	7.5798	0.4687	0.2984	0.5968	0.3453	0.6437
7/8	3.5904	7.0744	0.4375	0.2785	0.5570	0.3223	0.6007
13/16	3.8666	6.5692	0.4062	0.2586	0.5173	0.2993	0.5579
3/4	4.1888	6.0639	0.3750	0.2387	0.4775	0.2762	0.5150
11/16	4.5696	5.5586	0.3437	0.2189	0.4377	0.2532	0.4720
2/3	4.7124	5.3903	0.3333	0.2122	0.4244	0.2455	0.4577
5/8	5.0265	5.0532	0.3125	0.1989	0.3979	0.2301	0.4291
9/16	5.5851	4.5479	0.2812	0.1790	0.3581	0.2071	0.3862
1/2	6.2832	4.0426	0.2500	0.1592	0.3183	0.1842	0.3433
7/16	7.1808	3.5373	0.2187	0.1393	0.2785	0.1611	0.3003
2/5	7.8540	3.2340	0.2000	0.1273	0.2546	0.1473	0.2746
3/8	8.3776	3.0319	0.1875	0.1194	0.2387	0.1381	0.2575
1/3	9.4248	2.6947	0.1666	0.1061	0.2122	0.1228	0.2289
5/16	10.0531	2.5266	0.1562	0.0995	0.1989	0.1151	0.2146
2/7	10.9956	2.3100	0.1429	0.0909	0.1819	0.1052	0.1962
1/4	12.5664	2.0213	0.1250	0.0796	0.1591	0.0921	0.1716
2/9	14.1372	1.7967	0.1111	0.0707	0.1415	0.0818	0.1526
1/5	15.7080	1.6170	0.1000	0.0637	0.1273	0.0737	0.1373
3/16	16.7552	1.5160	0.0937	0.0597	0.1194	0.0690	0.1287
1/6	18.8496	.5053	0.0833	0.0531	0.1061	0.0614	0.1144

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