01 Overview
Worm gear drives consist of a worm and a worm wheel, used to transmit motion and power between intersecting shafts, typically with a 90° intersection angle. In general worm gear drives, the worm is the driving element.
In terms of appearance, the worm resembles a bolt, while the worm wheel looks very much like a helical cylindrical gear.
During operation, the worm gear teeth slide and roll along the helical surface of the worm.
A worm gear is a gear with one or more helical teeth that meshes with a worm wheel to form an interlocking gear pair. Its pitch surface can be a cylindrical surface, a conical surface, or a toroidal surface.
There are four types: Archimedes' worm, involute worm, normal straight profile worm, and conical envelope cylindrical worm.
Like threads, worms can be either right-handed or left-handed, and are called right-handed worms and left-handed worms, respectively.
To improve the contact between the gear teeth, the worm gear is made into an arc shape along the tooth width, so that it covers the worm. This results in line contact rather than point contact when the worm and worm gear mesh.
02 Advantages of worm gear drives
✦The single-stage transmission ratio is large, typically i=10~100. In indexing mechanisms for power transmission, the maximum ratio can reach over 1500.
✦The meshing is a line contact, which can withstand greater power.
✦Compact structure, smooth transmission, and low noise.
✦When the worm's helix angle is less than the equivalent friction angle between the gears, it has a reverse stroke self-locking property, meaning that the worm can only drive the worm wheel, and the worm wheel cannot drive the worm.
03 Disadvantages of worm gear drives
✦When the two axes are perpendicular and the nodal linear velocities of the two wheels are perpendicular, the relative sliding speed is very high, which easily leads to heat generation and wear. ✦The efficiency is low, generally between 0.7 and 0.8; the efficiency of self-locking worm gears is even lower, generally less than 0.5.
04 Calculation formulas for worm gears and worms
1. Transmission ratio = Number of worm gear teeth ÷ Number of worm threads
2. Center distance = (worm gear pitch diameter + worm pitch diameter) ÷ 2
3. Worm gear diameter = (number of teeth + 2) × module
4. Worm gear pitch diameter = module × number of teeth
5. Worm pitch diameter = worm outer diameter - 2 × module
6. Worm gear lead = π × module × number of threads
7. Helix angle (lead angle) tgB = (module × number of threads) ÷ worm pitch diameter
8. Worm gear lead = π × module × number of threads
9. Module = Pitch circle diameter / Number of teeth
Number of threads in a worm: Single-threaded worm (the worm has only one helix, meaning that when the worm rotates one revolution, the worm wheel rotates one tooth); Double-threaded worm (the worm has two helices, meaning that when the worm rotates one revolution, the worm wheel rotates two teeth).
The module refers to the size of the helix on the screw. In other words, the larger the module, the larger the helix on the screw. The diameter factor refers to the thickness of the screw.
Module: The pitch circle of a gear is the reference for designing and calculating the dimensions of each part of the gear. The circumference of the pitch circle is πd = zp, therefore the diameter of the pitch circle is d = zp/π.
Since π is an irrational number in the above formula, it is not convenient for positioning the pitch circle as a reference. In order to facilitate calculation, manufacturing and inspection, the ratio p/π is artificially defined as some simple numerical value, and this ratio is called the module, denoted by m.
05 Types of worm gear drives
Based on their shape, worms can be classified into cylindrical worm drives, toroidal worm drives, and conical worm drives. Among them, cylindrical worm drives are the most widely used.
Ordinary cylindrical worm gears are mostly cut on a lathe using a cutting tool with a straight generatrix. Depending on the installation position of the cutting tool and the type of cutting tool used, four types of worm gears with different tooth profiles on the cross section of the vertical axis can be obtained: involute worm gear (ZI type), Archimedes worm gear (ZA type), normal straight profile worm gear (ZN), and conical envelope cylindrical worm gear (ZK).
Involute worm (ZI type) – The cutting edge plane is tangent to the base cylinder of the worm, and the end face teeth are involute, suitable for higher speeds and greater power.
Archimedes' worm gear (ZA type) – The tooth profile perpendicular to the axis plane is an Archimedes' helix, while the tooth profile in the plane passing through the axis is a straight line. It is simple to manufacture but has lower precision. (Axial straight profile worm gear).
Normal straight profile worm (ZN) – can be ground with a modified grinding wheel, making it relatively simple to machine. It is often used to make multi-start worms, with a transmission efficiency of up to 0.9.
The conical envelope cylindrical worm (ZK) is a type of non-linear helical worm. It cannot be machined on a lathe and must be milled on a milling machine and ground on a grinding machine. This type of worm is easy to grind, has high precision, and is increasingly widely used.
06 Machining Process of Metal Worms
1. Determine the material of the blank.
(1) It has excellent processing performance, can obtain good surface finish and small residual internal stress, and has little effect on tool wear.
(2) The tensile strength is generally not less than 588 MPa.
(3) It has good heat treatment processability, good hardenability, is not easy to crack during quenching, has a uniform structure, small heat treatment deformation, and can obtain high hardness, thereby ensuring the wear resistance and dimensional stability of the worm.
(4) The material has uniform hardness and its metallographic structure meets the standards. Commonly used materials include: T10A, T12A, 45, 9Mn2V, CrMn, etc. Among them, 9Mn2V has good processability and stability, but poor hardenability; its advantage is that it has small deformation after heat treatment and is suitable for making high-precision parts, but it is prone to cracking and has poor grinding processability. The higher the hardness of the worm gear, the more wear-resistant it is, but it is not easy to grind during manufacturing.
2. Selection of machining positioning datum surface
Worm Gear Positioning Datum: Structurally, worm gears come in two forms: fitted worm gears and integral worm gears. Fitted worm gears use the inner bore as the machining datum, therefore the inner bore should be precision machined first, and then the outer diameter and supporting journal should be machined using the inner bore as the datum. Thread machining also uses the inner bore as the datum, thus requiring a mandrel. Generally, precision indexing worm gears have very high requirements for inner bore accuracy, and some require grinding to ensure precision.
For general precision indexing worm gears, the inner bore should have a precision grade of no less than 1, a surface roughness of no less than 0.12, and an end face runout of no less than 0.005 mm. When the worm gear is mounted on a mandrel for machining, the radial runout of the shoulders at both ends should be checked first to ensure it is within the specified tolerance. This check should be performed at each subsequent process. Similarly, during worm gear assembly, the radial runout of the shoulders at both ends must be checked. The mandrel precision must be equal to or higher than the precision of the shaft mating with the worm gear.
The integral worm gear uses the center hole as the machining datum surface, and the requirements for the center hole are very high. It should have a tapered end to ensure surface finish and contact area. The center hole should be checked and corrected before each process. The support journal should be guaranteed to be coaxial with the center hole and have its own geometric accuracy. Before the semi-finishing and finishing processes, the radial runout, diameter runout and axial runout of the end face of the support journal should be checked to see if they are within the tolerance.
When selecting a rough datum, the key consideration is to ensure that each machined surface has sufficient allowance so that the dimensions and positions between the unmachined datum surface and the machined surface meet the requirements of the drawing.
The selection of a coarse datum should meet the following requirements:
(1) The rough datum should be selected based on the machined surface. This is to ensure the accuracy of the relative positional relationship between the machined and unmachined surfaces. If there are several surfaces on the upper surface of the workpiece that do not need to be machined, the surface with the highest relative positional accuracy requirement to the machined surface should be selected as the rough datum. This aims to achieve uniform wall thickness, symmetrical shape, and fewer clamping operations.
(2) Select an important surface with uniform machining allowance as the rough reference.
(3) The surface with the smallest machining allowance should be selected as the rough reference. This ensures that the surface has sufficient machining allowance.
(4) A flat, smooth surface with a sufficiently large area should be selected as the rough reference to ensure accurate positioning and reliable clamping. Surfaces with gates, risers, flash, or burrs should not be used as the rough reference and should be pre-machined if necessary.
(5) Coarse references should be avoided from being reused, because the surface of a coarse reference is mostly rough and irregular, and it is difficult to guarantee the positional accuracy between the outer surfaces if it is used repeatedly.
According to the selection principle of rough datum, clamping the outer circle and machining most of the surface in one clamping can ensure the coaxiality of the outer circle and the inner hole and the perpendicularity of the end face to the axis.
Metal worm gear machining process route
1. Unhardened worm gear set
Material preparation – Normalizing – Rough turning – (Adjustment) – Semi-finish turning of outer diameter, rough turning of helical surface – Artificial aging – Finish turning (fine grinding) of inner end face – Keyway cutting – Semi-finish turning of helical surface – Fitting (restoring incomplete teeth) – Semi-finish grinding of outer diameter – Finish grinding of helical surface – Low-temperature aging – Grinding of center hole – Finish grinding of outer diameter – Finish grinding of helical surface
2. Carburized and quenched integral worm gear
Forging – Annealing – Rough Turning – Normalizing – Semi-finish Turning of Outer Diameter and Helical Surface – Fitting (Repairing Incomplete Teeth) – Carburizing – Finish Turning of Outer Diameter (Removing Unnecessary Carburized Parts) – Quenching and Tempering – Grinding the Center Hole – Turning Fastening Threads – Milling Grooves – Semi-finish Grinding of Outer Diameter – Semi-finish Grinding of Helical Surface – Low Temperature Aging – Grinding the Center Hole – Finish Grinding of Outer Ring and End Face – Finish Grinding of Helical Surface
Material preparation: According to regulations, the billet must be forged to obtain good metal fibrous structure.
Rough turning: Ensure coaxiality and allow for appropriate finishing allowance.
Heat treatment and tempering to HRC28-32, semi-finish turning, leave 0.5mm finishing allowance for each part during semi-finish turning, turn the worm gear and the relief grooves at both ends to the required size, pick the worm gear, rough pick the worm gear, regardless of whether the layered cutting method or the entry method is used.
The amount of material retained at the middle section is measured, and the semi-fine retention is a good basis for fine finishing.
For low-speed precision finishing of three sides, the cutting tool must be sharp, with excellent edge roughness, and each side must be smooth. For precision machining of all parts, coaxiality must be guaranteed.
When a common cylindrical worm gear is machined on a lathe using a straight cutting edge, the resulting worm gear can be classified into Archimedean worms (ZA), involute worms (ZI), and normal straight profile worms (ZN), depending on the tool mounting position. A ZA Archimedean worm gear, where the cutting edge plane passes through the worm's axis and the cutting edge angle is 2α = 40°, produces a worm gear with a straight tooth profile in the axial plane and a convex curve in the normal section. The tooth profile curve on the end face is an Archimedean spiral, hence the name Archimedean worm. This type of worm gear is relatively easy to machine and measure, and therefore widely used.
However, machining becomes difficult when the lead angle γ is too large. It's hard to achieve a precise tooth profile using a grinding wheel, resulting in lower transmission accuracy and efficiency. The cutting edge plane of a ZI involute worm cutting tool is tangent to the base cylinder of the worm. The cut worm has a convex profile curve on the axial plane, while the tooth profile on the end face perpendicular to the axis is involute, hence the name involute worm. This type of worm can be ground, thus offering higher transmission accuracy and efficiency, making it suitable for mass production and high-power, high-speed precision transmission.
When the worm lead angle γ is large, to obtain a reasonable rake and clearance angle for the cutting tool, the cutting edge plane of the cutting tool is placed on the normal plane of the worm helix during turning. The resulting worm has a straight tooth profile on the normal section, hence the name "normal straight profile worm." The tooth profile curve on the end face perpendicular to the axis is an extended involute, thus it is also called an extended involute worm. This type of worm has good cutting performance, is advantageous for machining multi-start worms, and can be ground with grinding wheels, commonly used in multi-start precision worm drives on machine tools. With advancements in technology and product requirements, there is a need for further increases in cutting speed. Turning methods have become a bottleneck, leading to the development of cyclone milling. This involves using a rotating cutting tool to increase the cutting speed (up to 400 meters per minute), while the workpiece does not need to rotate at high speed.
There are two types of whirling machining methods for worm gears: internal whirling and external whirling.
Internal cyclone: The workpiece circumference is internally tangent to the cutter tooth circumference (the worm gear is inside the cutter head), achieving an accuracy of DIN7 Ra0.8.
External cyclone: The workpiece circumference is externally tangent to the cutter tooth circumference (the worm gear is outside the cutter head), achieving an accuracy of DIN6 Ra0.4.
