# How to Calculate and Solve for Helix Angle

On the cylindrical surface, the acute angle between the tangent of the cylindrical helix and the straight generatrix of the cylindrical surface passing through the tangent point is called the helix angle.

## What Is Helix Angle

- On the cylindrical surface, the acute angle between the tangent of the cylindrical helix and the straight generatrix of the cylindrical surface passing through the tangent point is called the helix angle.
- On the conical surface, the acute angle between the tangent of the conical spiral and the straight generatrix of the conical surface passing through the tangent point is also called the spiral angle.
- The angle formed by the spiral edge and the central axis of the tool. Increasing the helix angle β can increase the axial coincidence εβ=Bsinβ/πmn. Generally, εβ>1~1.15 is required to improve the stability of the transmission and reduce the noise, making the transmission stable, but the axial force will increase accordingly (referring to the oblique gear). The helix angle direction of the two gears on the same axis should be the same so that the axial forces cancel each other out. Making the helix angle of the high-speed stage larger and the helix angle of the low-speed stage smaller to reduce the axial force of the low-speed stage is also a desirable solution for some designs. Appropriate selection of β can round up the center distance a, so that a has a rounded value. If the helix angle is determined by offsetting the machine tool exchange gear error, the helix angle error of the hobbing gear can be effectively reduced.

## Gear Helix Angle Type

For parts such as helical gears and worm gears, the**helix angle**is generally used to indicate the degree of inclination of the gear teeth. The helix angle of the worm is very large and is customarily expressed by the lead angle. Gear helix angle types are as follows:

- Pitch circle helix angle β: the angle between the gear tooth length curve and the axis on the pitch cylinder. The helix angle of a helical rack is the intersection angle between the axial plane and the tangential plane on the pitch plane. Unless otherwise specified, the helix angle refers to the helix angle on the pitch cylinder.
- Base circle helix angle βb: The base circle helix angle refers to the helix angle on the base cylinder.
- Axial base circle helix angle βxb: Axial base circle helix angle refers to the angle between the tangent plane and the axial plane on the axial action plane.

## Helix Angle Selection

To process gears with different helix angles on a gear shaping machine, it is necessary to replace the spiral guide rails with different helix angles and to manufacture gear shaping cutters with different helix angles. Here, it is very troublesome to replace a set of spiral guide rails, and it is not easy to manufacture a rake helical gear shaper. If we specify a spiral guide rail, according to the standard module, the number of teeth of the gear shaping cutter is changed to adapt to a certain range of different helix angles. In other words, when we design the parameters of the internal and external gears, if we can select the helix angle specified by the lead of this spiral guide rail according to the module size, then using the same spiral guide rail, we can process a certain amount of work by simply changing the gear shaping cutter. A range of internal gears with different helix angles are available. In this way, the auxiliary time for replacing the spiral guide rail is greatly shortened, and the precision machining economy is very outstanding.## Helix Angle Measurement

There are many ways to measure the helix angle. It is best if there is a ready-made helix angle measuring instrument. Otherwise, the following methods can be used:- Roll printing method: Apply a thin layer of red oil to the addendum circle of the gear, place its end face against the ruler, and roll it on white paper. At this time, there will be tooth marks on the paper, and the helix angle β of the tooth marks can be calculated using a protractor. The helix angle measured by this method is the helix angle β of the tooth tip circle and the helix angle βf on the graduation circle, which can be solved according to the corresponding formula. The helix angle obtained by this method is an approximate value, and there is an error due to β. This method basically meets the requirements when mapping helical gears that are replaced in pairs. But when only one gear is changed, this measurement method cannot meet the requirements. Especially for displacement helical cylindrical gears, this method is not suitable for measuring the helix angle. Because the helix angle and displacement coefficient of helical gears compensate for each other, that is to say, the measurement error of the helix angle will affect the value of the displacement coefficient.
- In order to make the modifications appropriate without affecting the original design performance, a measurement method with higher numerical accuracy must be used. Commonly used methods include "universal milling machine method", "ball method", "measuring tooth pitch method" and so on.

## How to Calculate and Solve for Helix Angle

### #How to calculate the helix angle of helical gear?

Install the indexing head on the workbench of the milling machine, install the helical gear to be measured on a plunger that has been inspected to comply with relevant regulations and requirements, and install the indexing head on it. Select a good quality tooth on the helical gear as the measurement object. Take a dial indicator. The meter base is installed on the milling machine bed and does not move with the workbench. The meter head is pressed on point A at one end of the tooth to be measured, and the dial indicator pointer is set to "0". Move the workbench to the right and rotate the indexing head at the same time to make the helical gear rotate clockwise until the helical gear rotates to point B and stops when the dial indicator pointer points to the "0" position again. At this time, the moving distance h of the workbench is the lead from point A to point B on the helical gear spiral (h should be chosen as long as possible). Assume that the angle of view of the indexing head turned at this time is α, then the lead of the entire spiral is A=360°h/a. According to the corresponding relationship between helix angle β and lead A, tgβ=πd/A (d is the diameter of the graduated circle), substituting d=mz/cosβ, tgβ=sinβ/cosβ into the above formula, we can get: Asinβcosβ=πmzcosβsinβ=πmz/ A From this, the helix angle of the helical gear can be calculated as:### #How to determine the helix angle when designing helical gears?

When designing helical cylindrical gear transmission, the helix angle β is selected within the range of 8° to 25° in most cases. The helix angle of the helical gear is determined according to the design requirements. In most cases, high-speed and lightly loaded gears adopt a large helix angle; low-speed and heavily loaded gears adopt a smaller helix angle. According to the design requirements, in most cases it is between 8 degrees and 25 degrees (no strict limit). The helix is too small and the smoothness of the gear meshing movement is also reduced. If the helix angle is too large, there will be a large force component on the bearing and spindle. Apart from this factor, it is difficult to process helix angle gears with large viewing angles. The helix angle of helical gears is determined according to the design needs. In most cases, high-speed and light-load gears adopt a large helix angle; low-speed and heavy-load gears adopt a smaller helix angle. According to the design requirements, it is usually between 5 degrees and 35 degrees in most cases. Because the helix is too small, the smoothness of the gear meshing movement is also reduced. If the helix angle is too large, there will be a large force component on the bearing and spindle. It is also very troublesome to process helix angle gears with a large angle of view and will be restricted by the machine tool itself.### #Complete helical gear calculation formulas?

The formula for the outer diameter of the helical gear: D=mZ/cosβ+2m) m-normal module β-helix angle Z-number of teeth D-tooth tip circle diameter (outer diameter). For example, the number of teeth is 75, the helix angle is 27.3 degrees, and the calculated normal module value is 1.425. Calculate the outer diameter of the helical gear. D=mZ/cosβ+2m)=1.425*75/27.3+2*1.425)=123.2MM Helical cylindrical gear transmission is higher than spur gear, and can have a compact center distance for high speed and heavy load. Helical gear reducers are novel and relatively popular reduction transmission devices. How is the helix angle of helical cylindrical gears determined? Generally within what range? Why? The recommended value range for the helix angle β of helical cylindrical gears is 10° to 25° (there is no fixed statement for this). If the helix angle is too large (for example, greater than 30°), the axial force will be greater, which is detrimental to the force on the gears and shafts; if the helix angle is too small (for example, less than 8°), the axial coincidence will be very small, and the characteristics of the helical gear will be lost. It makes sense.### #Helical gear normal module calculation formula?

Calculation formula: module m = pitch circle diameter d / number of teeth z = tooth pitch p / pi. Gear module is defined as a basic parameter of modular gear teeth, which is a number artificially abstracted to measure the size of gear teeth. In gear design, the module is the decisive element in determining gear tooth size. Different countries have certain differences in how they define modulus. The typical ones are international standards (except for the United Kingdom, the standards of other countries including China are in line with international standards) and imperial standards. The principle of the international standard definition of module is to define the length of the arc (gear) / straight line (rack) occupied by a single gear tooth in the graduation circle (gear) / or line (rack), and its length is π * m , m is the modulus. It can be seen from here that the module has a unit, and its standard unit is millimeters (mm). Many people are accustomed to the abbreviation of module. For example, for a gear with a module of 1mm, the abbreviation m=1; candidates have gradually accepted this way of writing, because it is okay for this reason. However, a small number of colleagues who do not have a thorough understanding of gear modules think that modules have no units, and this concept is wrong. The normal module of the helical gear is the standard module and is selected according to the standard module value. The end face module of the helical gear has a corresponding relationship with the normal face module and helix angle. Mt = Mn/cosβ. Mn, normal module; Mt, end module; β, helix angle.- 1. Calculation method of gear diameter: Tip circle diameter = (number of teeth +) * Module indexing circle diameter = Number of teeth * Module root circle diameter = Tooth tip circle diameter -. Module: M tooth tip circle diameter = (+)*=mm graduation circle diameter.
- 2. The center distance is equal to the number of teeth of the two gears and the multiplied module divided by twice the COS helix angle.
- 3. Helical gear end face module mt=mn/cosβ, where: mn is the normal surface module of the helical gear, which is the standard module of the helical gear, and β is the helix angle (grading circle) of the helical gear. , end face section Pt=πmt=πmn/cosβ, end face base section Pbt.
- 4. Calculation principle and method: Differential hanging wheel formula: Differential fixed number *sinB/Mn*K=a/b*c/d Description: Differential fixed number - the fixed number of each model of roller bed is different and needs to be checked What is the fixed number of your own machine tool? sinB-helix angle Mn of the workpiece

### #How to calculate the module of helical gear?

The normal module of the helical gear is the standard module and is selected according to the standard module value. The end face module of the helical gear has a corresponding relationship with the normal face module and helix angle. The end face module of the helical gear mt=mn/cosβ, where: mn is the normal module of the helical gear, which is the standard module of the helical gear, and β is the helix angle (gradation circle) of the helical gear. , end face section Pt=πmt=πmn/cosβ, end face base section Pbt. Modulus m=d/Z (the unit of d is mm). It can be seen: m=（1/P）*25.4=25.4/PP=（1/m）*25.4=25.4/ mFor this reason, the relationship between module m and diameter pitch P is reciprocal to each other, but the unit system is different. Corresponding to the conversion of units, there is a relationship between diameter pitch and module. Please see the specific content below: P=π/ρ=25.4/m. In the formula, P is the diameter pitch (1/inch); ρ is the tooth pitch (inch). ; m is the module (mm).- (1) Industrial definition: The graduation circle of the gear is the basis for designing and calculating the size of each part of the gear, and the circumference of the gear graduation circle = πd = z p, so the diameter of the graduation circle is d = z p / π.
- (2) Chemical definition: the ratio of moles. (For example: the chemical formula is R2O·n SiO2, n is the ratio of the moles of SiO2 and R2O, which is called the modulus of R2O·n SiO2.) For the standardized value of extended information modulus, please refer to GB1357-87. The first series is: 0.1, 0.12, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.8, 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16 , 20, 25, 32, 40, 50. (The first series is preferred).

### #Helical tooth pitch calculation formula?

To calculate helical gear parameters, you need to know the basic parameters: Normal module m_n, number of teeth Z, normal pressure angle α_n, helix angle β The tooth top height coefficient h* is taken to be 1 in most cases, and the tooth root height coefficient c* is taken to be 0.25 in most cases. If there is a displacement, you also need to calculate the displacement: x The basic parameters are calculated below End face module:m_t=m_n/cosβ End face pressure angle calculation formula: tan (α_t)=tan (α_t)/cos(β) Diameter of graduation circle: D=m_n×z/cos(β) Tip circle diameter: No displacement: Da=D+2×m_n×h* With displacement: Da=D+2×m_n × (h*+x) Root circle diameter: without displacement: Df=D-2×m_n×(h*+c*) with displacement: Df=D-2×m_n×(h*+c*-x) Base circle diameter: Db=D×cos (α_t) In addition, there are very important dimensions such as: normal tooth pitch, end face pitch, etc., which can be obtained by checking the relevant manuals.- Module m=tooth pitch p/pi ratio π
- Tooth pitch p = module m * pi π
- Occlusion center line Ho = rack height Hk - module m
- Modulus m = tooth pitch p/(pi π*trigonometric function cosB)
- Tooth pitch p=module m*(pi*trigonometric function cosB)