Overview
A worm gear drive consists 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 component.
From its appearance, the worm resembles a bolt, while the worm wheel looks like a helical cylindrical gear.
During operation, the worm wheel teeth slide and roll along the helical surface of the worm.
A worm is a gear with one or more helical teeth that meshes with the worm wheel to form an intersecting shaft gear pair. Its pitch surface can be cylindrical, conical, or toroidal.
There are four types: Archimedean worm, involute worm, normal straight-profile worm, and conical-enclosed cylindrical worm.
Like threads, worms can be right-handed or left-handed, referred to as right-hand worms and left-hand worms, respectively.
To improve tooth contact, the worm wheel is made into an arc shape along the tooth width direction, enclosing part of the worm. This means that the worm gear meshes via line contact, not point contact.
Disadvantages of worm gear drives:
✦ Because the two shafts are perpendicular, and the pitch line velocities of the two gears are perpendicular, the relative sliding speed is very high, leading to heat generation and wear.
✦ Low efficiency, typically between 0.7 and 0.8; worm gears with self-locking mechanisms have even lower efficiency, 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 Pitch 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 Lead = π × Module × Number of Threads
7. Helix Angle (Lead Angle) tanB = (Module × Number of Threads) ÷ Worm Pitch Diameter
8. Worm Lead = π × Module × Number of Threads
9. Module = Pitch Circle Diameter / Number of Teeth
Number of Threads in a Worm: Single-threaded worm (only one helix on the worm, i.e., one revolution of the worm corresponds to one tooth rotation of the worm gear); Double-threaded worm (two helices on the worm, i.e., one revolution of the worm corresponds to two tooth rotations of the worm gear). The module refers to the size of the helix on the screw; the larger the module, the larger the helix.
The diameter coefficient refers to the thickness of the screw.
Module: The pitch circle of a gear is the reference for designing and calculating the dimensions of its various parts. The circumference of the pitch circle = 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. To facilitate calculation, manufacturing, and inspection, the ratio p/π is artificially defined as a simple numerical value, and this ratio is called the module, denoted by m.
05 Types of Worm Gear Drives
According to the shape of the worm, worms can be divided into cylindrical worm gear drives, toroidal worm gear drives, and conical worm gear drives. Among them, cylindrical worm gear drives are the most widely used.
Ordinary cylindrical worm gears are typically machined on a lathe using a cutting tool with a straight generatrix cutting edge. Depending on the tool's mounting position and the type of tool used, four types of worm gears with different tooth profiles in the cross-section perpendicular to the axis can be obtained: involute worm gear (ZI type), Archimedean worm gear (ZA type), normal straight-profile worm gear (ZN type), and conical-enveloping cylindrical worm gear (ZK type).
Involute worm gear (ZI type) – The cutting edge plane is tangent to the worm's base cylinder, and the end face teeth are involute. Suitable for higher speeds and higher power.
Archimedean worm gear (ZA type) – The tooth profile perpendicular to the axis plane is an Archimedean spiral, while the tooth profile in the plane passing through the axis is a straight line. Simple to machine, but with lower precision. (Axial straight-profile worm gear).
Normal straight-profile worm gear (ZN type) – Can be ground with a modified grinding wheel, relatively simple to machine, often used for multi-start worm gears, with a transmission efficiency of up to 0.9.
Conical Enveloping Cylindrical Worm (ZK) – This is a non-linear helical worm. It cannot be machined on a lathe; it can only 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. Determining the Material of the Blank
⑴ Excellent machinability, achieving good surface finish and low residual internal stress, minimizing tool wear.
⑵ Tensile strength is generally not less than 588 MPa.
⑶ Good heat treatment processability, good hardenability, not easily cracked during quenching, uniform microstructure, small heat treatment deformation, and high hardness, thus ensuring the wear resistance and dimensional stability of the worm.
⑷ Uniform material hardness and metallographic structure conforming to standards. Commonly used materials include: T10A, T12A, 45, 9Mn2V, CrMn, etc. 9Mn2V has good processability and stability, but poor hardenability. Its advantage is small deformation after heat treatment, making it suitable for manufacturing high-precision parts, but it is prone to cracking and has poor grinding processability. Higher worm hardness increases wear resistance, but it is difficult to grind during manufacturing.
2. Selection of Machining Positioning Datum
Worm positioning datum: Structurally, worms come in two forms: fitted worms and integral worms. Fitted worms use the inner hole as the machining datum, therefore, the inner hole should be precision machined first, and then the outer diameter and supporting journal should be machined using the inner hole as the datum. Thread machining also uses the inner hole as the datum, thus requiring a mandrel. Generally, the inner hole accuracy requirements for precision indexing worms are very high, and some require grinding to ensure accuracy.
Generally, the inner hole accuracy of a precision indexing worm should be no lower than Grade 1, the surface roughness no lower than 0.12, and the end face runout of the inner hole no less than 0.005mm. When machining a worm gear mounted on a mandrel, 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 after each subsequent operation. Similarly, during worm gear assembly, the radial runout of the shoulders at both ends must be checked. The mandrel's accuracy must be equal to or higher than the accuracy of the shaft mating with the worm gear.
The integral worm gear uses the center hole as the machining datum. 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 operation. The support journal should ensure coaxiality with the center hole and its own geometric accuracy. Before semi-finishing and finishing operations, the radial runout, radial runout, and axial runout of the end face of the support journal should be checked to ensure they are within tolerance.
When selecting a rough datum, the focus should be on ensuring sufficient allowance for each machined surface so that the dimensions and positions between the unmachined datum and the machined surface conform to the drawing requirements.
The selection of a rough datum should meet the following requirements:
(1) The rough datum should be based on the machined surface. This is to ensure the accuracy of the positional relationship between machined and unmachined surfaces. If the workpiece has several surfaces that do not require machining, the surface with the highest positional accuracy requirement relative to the machined surface should be selected as the rough datum. This aims to achieve uniform wall thickness, symmetrical shape, and fewer clamping operations.
⑵ Select an important surface with uniform machining allowance as the rough datum.
⑶ Select the surface with the smallest machining allowance as the rough datum. This ensures that the surface has sufficient machining allowance.
⑷ Choose a flat, smooth surface with a sufficiently large area as the rough datum to ensure accurate positioning and reliable clamping. Surfaces with gates, risers, burrs, or rough edges should not be selected as rough datums and should be pre-machined if necessary.
⑸ Avoid reusing the rough datum, as most rough datum surfaces are irregular and repeated use makes it difficult to guarantee the positional accuracy between outer surfaces.
Following the selection principles of the rough datum, clamping the outer circle and machining most of the surface in one clamping operation ensures the coaxiality of the outer circle and the inner hole, as well as the perpendicularity of the end face to the axis.
Metal Worm Gear Machining Process Route
⑴ Unhardened Integral Worm Gear
Material preparation – Normalizing – Rough turning – (Tempering) – Semi-finish turning of outer diameter, rough turning of helical surface – Artificial aging – Finish turning (fine grinding) of inner end face – Keyway insertion – Semi-finish turning of helical surface – Clamping (repairing incomplete teeth) – Semi-finish grinding of outer diameter – Fine grinding of helical surface – Low-temperature aging – Grinding of center hole – Fine grinding of outer diameter – Fine grinding of helical surface
⑵ Carburized and Quenched Integral Worm Gear
Forging – Annealing – Rough turning – Normalizing – Semi-finish turning of outer diameter and helical surface – Clamping (repairing incomplete teeth) – Carburizing – Finish turning of outer diameter (removing parts not requiring carburizing) – Quenching and tempering – Grinding of center hole – Turning of fastening thread – Milling groove – Semi-finish grinding of outer diameter – Semi-finish grinding of helical surface – Low-temperature aging – Grinding of center hole – Fine grinding of outer ring and end face – Fine grinding of helical surface
Material blanking: According to standard requirements, the blank must undergo forging treatment to obtain good metal fibrous structure.
Rough turning: Ensure coaxiality and allow for appropriate finishing allowance.
Heat treatment (HRC28-32), semi-finish turning: allow 0.5mm finishing allowance for each part during semi-finish turning. Turn the worm section and the relief grooves at both ends to the required specifications. Rough turning of the worm, using either layering or bottom cutting methods, is acceptable.
Measure the allowance at the mid-diameter. The semi-finish turning allowance provides a good foundation for a good finish.
Low-speed finish turning on three sides to the required specifications: The tool must be sharp, and the cutting edge roughness must be good, ensuring a smooth finish on each side. Finish turning all parts to the required specifications to ensure coaxiality.
If a common cylindrical worm is machined on a lathe using a straight cutting edge, depending on the tool installation position, the resulting worm can be classified as an Archimedean worm (ZA), an involute worm (ZI), or a normal straight profile worm (ZN), etc. ZA Archimedean worm: The cutting edge plane of the lathe tool passes through the worm axis, and the worm is cut with a cutting edge angle of 2α = 40°. The resulting worm has a straight tooth profile in the axial plane, and the normal section of the tooth profile is an outwardly convex curve. The tooth profile curve on the end face is an Archimedean spiral, hence the name Archimedean worm. This type of worm is relatively easy to machine and measure, and therefore widely used.
However, machining becomes difficult when the lead angle γ is too large. It is difficult to grind precise tooth profiles with a grinding wheel, resulting in lower transmission accuracy and efficiency.
ZI Involute worm: The cutting edge plane of the lathe tool is tangent to the base cylinder of the worm. The resulting worm has a convex profile curve in the axial plane, and the tooth profile on the end face perpendicular to the axis is an involute, hence the name involute worm. This type of worm can be ground, resulting in higher transmission accuracy and efficiency, suitable for mass production and high-power, high-speed precision transmission.
ZN Normal Straight Profile Worm: When the worm lead angle γ is large, to obtain reasonable rake and clearance angles 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 worm cut in this way 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 beneficial 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, further increases in cutting speed are needed, creating a bottleneck in turning methods, leading to the development of whirling 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.
Whirling milling methods for worms are divided into two types: internal whirling and external milling.
Internal cyclone: The workpiece circumference is internally tangent to the cutter tooth circumference (worm gear inside the cutter head). Accuracy up to DIN7 Ra0.8. External cyclone: The workpiece circumference is externally tangent to the cutter tooth circumference (worm gear outside the cutter head). Accuracy up to DIN6 Ra0.4.
