01Overview
A worm gear drive consists of a
worm and a worm wheel, used to transmit motion and power between intersecting shafts, usually with an intersection angle of 90°. In general worm gear drives, the worm is the driving component.
In appearance, the worm resembles a bolt, while the worm wheel is very similar to a helical cylindrical gear.
During operation, the teeth of the worm wheel slide and roll along the helical surface of the worm.
A worm is a gear with one or more helical teeth that meshes with a worm wheel to form a crossed-axis 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 enveloping cylindrical worm.
Like threads, worms are divided into right-hand and left-hand types, called right-hand worms and left-hand worms, respectively.
To improve the contact between the teeth, the worm wheel is made into an arc shape along the tooth width direction, so that it partially encloses the worm. This results in line contact between the worm and worm wheel during meshing, rather than point contact.
02Advantages of Worm Gear Drives
✦ Large single-stage transmission ratio, generally i = 10~100. In indexing mechanisms for power transmission, it can reach over 1500.
✦ The meshing is line contact, allowing it to withstand greater power.
✦ Compact structure, smooth transmission, and low noise.
✦ When the worm lead angle is less than the equivalent friction angle between the gears, it has self-locking properties in the reverse direction, meaning that the worm can drive the worm wheel, but the worm wheel cannot drive the worm.
03Disadvantages of Worm Gear Drives
✦ Since the two shafts are perpendicular and the nodal line velocities of the two gears are perpendicular, the relative sliding speed is very high, leading to heat generation and wear.
✦ Low efficiency, generally 0.7~0.8; worm gears with self-locking properties have even lower efficiency, generally less than 0.5.
04Calculation 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 Outside Diameter = (Number of Teeth + 2) × Module
4. Worm Gear Pitch Diameter = Module × Number of Teeth
5. Worm Pitch Diameter = Worm Outside Diameter - 2 × Module
6. Worm Lead = π × Module × Number of Threads
7. Helix Angle (Lead Angle) tgB = (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 Worm Threads: Single-thread worm (only one helical line on the worm, meaning the worm rotates one revolution, and the worm gear rotates one tooth); Double-thread worm (two helical lines on the worm, meaning the worm rotates one revolution, and the worm gear rotates two teeth).
The module refers to the size of the helical line on the screw; the larger the module, the larger the helical line on the screw.
The diameter coefficient refers to the thickness of the screw.
Module: The pitch circle of a gear is the basis for designing and calculating the dimensions of various parts of the gear. The circumference of the gear pitch circle = πd = z p, so the pitch circle diameter is
d = z p/π
Since π is an irrational number in the above formula, it is inconvenient to use it as a reference for positioning the pitch circle. To facilitate calculation, manufacturing, and inspection, the ratio p/π is artificially defined as some simple values, and this ratio is called the module, represented by m.
05Types of Worm Gear Drives
According to the shape of the worm, worm gear drives 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 mostly machined on a lathe using a cutting tool with a straight 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), and conical enveloping cylindrical worm gear (ZK).
Involute worm gear (ZI type) – The cutting edge plane is tangent to the worm gear base cylinder, and the end face teeth are involute, suitable for higher speeds and larger power.
Archimedean worm gear (ZA type) – The tooth profile in the plane perpendicular to the axis is an Archimedean spiral, and the tooth profile in the plane passing through the axis is a straight line. It is easy to manufacture but has lower accuracy (axial straight-profile worm gear).
Normal straight-profile worm gear (ZN) – Can be ground with a modified grinding wheel, making processing relatively simple. It is often used for multi-start worm gears, and the transmission efficiency can reach 0.9.
Conical enveloping cylindrical worm gear (ZK) – This is a non-linear helical surface worm gear. It cannot be machined on a lathe and can only be milled on a milling machine and ground on a grinding machine. This type of worm gear is easy to grind, resulting in higher accuracy, and its application is becoming increasingly widespread.
06Processing Technology of Metal Worm Gears
1. Determining the Material of the Blank
⑴ Excellent machinability, resulting in good surface finish and small residual internal stress, with less wear on the cutting tools.
⑵ Tensile strength generally not less than 588 MPa.
⑶ Good heat treatment properties, good hardenability, not prone to quenching cracks, uniform structure, small heat treatment deformation, and able to obtain high hardness, thus ensuring the wear resistance and dimensional stability of the worm gear.
⑷ Uniform material hardness and metallographic structure meeting the standards. Commonly used materials include: T10A, T12A, 45, 9Mn2V, CrMn, etc. Among them, 9Mn2V has better processability and stability, but poor hardenability; its advantage is small deformation after heat treatment, suitable for manufacturing high-precision parts, but it is prone to cracking, and has poor grinding properties. The higher the hardness of the worm gear, the more wear-resistant it is, but it is more difficult to grind during manufacturing. 2. Selection of Machining Datum Surfaces
Worm gear datum surfaces: Structurally, worm gears come in two forms: assembled worm gears and integral worm gears. Assembled worm gears use the inner bore as the machining datum surface. Therefore, the inner bore should be precision machined first, and then the outer diameter and support journals are machined using the inner bore as the datum surface. The thread machining also uses the inner bore as the datum surface, thus requiring a mandrel. Generally, the inner bore accuracy of precision indexing worm gears is very high, and some require grinding to ensure accuracy.
The inner bore of general-precision indexing worm gears should have an accuracy of at least grade 1, a surface roughness of at least 0.12, and an end face runout of no less than 0.005 mm. When machining the worm gear on a mandrel, the radial runout of the two end shoulders should first be checked to ensure it is within the specified tolerance. This should be checked at each subsequent process. During worm gear assembly, the radial runout of the two end shoulders should also be checked. The mandrel accuracy must be equal to or higher than the accuracy of the shaft that mates with the assembled worm gear.
Integral worm gears use the center hole as the machining datum surface. The requirements for the center hole are very high; it should have a taper to ensure smoothness and contact area. The center hole should be checked and corrected before each process. The support journals should ensure coaxiality with the center hole and their own geometric accuracy. Before semi-finishing and finishing processes, the radial runout and axial runout of the support journals should be checked to ensure they are within tolerance.
When selecting the rough datum, the main consideration is how to ensure that each machined surface has sufficient machining allowance, so that the dimensions and positions between the unmachined datum surface and the machined surface meet the drawing requirements.
The selection of the rough datum should meet the following requirements:
(1) The rough datum should be selected from the machined surface. This is to ensure the accuracy of the relative positional relationship between the machined surface and the unmachined surface. If there are several surfaces on the workpiece that do not require machining, the surface with the highest requirement for relative positional accuracy with the machined surface should be selected as the rough datum. This is to ensure uniform wall thickness, symmetrical shape, and fewer clamping operations.
(2) Select the important surface with uniform machining allowance requirements as the rough datum.
(3) The surface with the smallest machining allowance should be selected as the rough datum. This ensures that the surface has sufficient machining allowance. (4) As much as possible, a flat, smooth surface with a sufficiently large area should be selected as the rough datum to ensure accurate positioning and reliable clamping. Surfaces with gates, risers, flash, or burrs should not be selected as rough datums; if necessary, preliminary machining is required.
(5) The rough datum should be avoided from being used repeatedly, because most of the surfaces of the rough datum are rough and irregular, and repeated use makes it difficult to guarantee the positional accuracy between the outer surfaces.
According to the principle of rough datum selection, clamping the outer circle and machining most of the surface in one clamping operation can ensure 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
(1) Non-hardened assembled worm gear
Material preparation-Normalizing-Rough turning-(Tempering)-Semi-finish turning of outer diameter, rough turning of helical surface-Artificial aging-Finish turning (finish grinding) of inner hole and end face-Keyway cutting-Semi-finish turning of helical surface-Filing (trimming incomplete teeth)-Semi-finish grinding of outer diameter-Finish grinding of helical surface-Low-temperature aging-Lapping of center hole-Finish grinding of outer diameter-Finish grinding of helical surface
(2) Carburized and hardened integral worm gear
Forging-Annealing-Rough turning-Normalizing-Semi-finish turning of outer diameter and helical surface-Filing (trimming incomplete teeth)-Carburizing-Finish turning of outer diameter (removing parts that do not need carburizing)-Quenching and tempering-Lapping of center hole-Turning of fastening threads-Milling of grooves-Semi-finish grinding of outer diameter-Semi-finish grinding of helical surface-Low-temperature aging-Lapping of center hole-Finish grinding of outer ring and end face-Finish grinding of helical surface
Blanking: According to the regulations, the blank must be forged to obtain a good metal fibrous structure.
Rough turning: Ensure coaxiality and leave an appropriate amount for finishing.
Heat treatment and tempering treatment HRC28-32, semi-finish turning, each part leaves 0.5mm for finish turning, the worm gear part and the two ends of the relief groove are turned to the required specifications, worm gear cutting, rough cutting, whether using layered method or cutting method, etc. are all acceptable.
Measure the allowance at the middle diameter, the semi-finish cutting allowance provides a good basis for finish machining. Low-speed finishing is required on all three surfaces, and the cutting tool must be sharp with a good edge roughness. Each surface must be finished individually. Precision turning of all parts is required to ensure concentricity.
Ordinary cylindrical worm gears, when machined on a lathe using a straight cutting edge, can be classified into Archimedean worm gears (ZA), involute worm gears (ZI), and normal straight-profile worm gears (ZN), depending on the cutting tool's mounting position. ZA Archimedean worm gears: The cutting tool's plane passes through the worm gear's axis, and the worm gear cut with a cutting edge angle of 2α=40° has a straight tooth profile in the axial plane, and the normal section tooth profile is a convex curve. The tooth profile curve on the end face is an Archimedean spiral, hence the name Archimedean worm gear. This type of worm gear is relatively easy to machine and measure, so it is widely used.
However, machining is difficult when the lead angle γ is too large. It is difficult to grind an accurate tooth profile with a grinding wheel, so the transmission accuracy and efficiency are low. ZI involute worm gears: The cutting edge plane of the cutting tool is tangent to the base cylinder of the worm gear. The resulting worm gear has a convex profile curve in the axial plane, and the tooth profile on the end face perpendicular to the axis is an involute curve, hence the name involute worm gear. This type of worm gear can be ground, so it has higher transmission accuracy and efficiency, and is suitable for mass production and high-power, high-speed precision transmission.
ZN normal straight-profile worm gears: When the worm gear lead angle γ is large, in order to obtain a reasonable rake angle and relief angle for the cutting tool, the cutting tool's plane is placed on the normal plane of the worm gear's helix during machining. The resulting worm gear has a straight tooth profile in the normal section, hence the name normal straight-profile worm gear. The tooth profile curve on the end face perpendicular to the axis is an extended involute curve, hence it is also called an extended involute worm gear. This type of worm gear has better cutting performance, is conducive to machining multi-start worm gears, and can be ground with a grinding wheel. It is often used in multi-start precision worm gear transmissions in machine tools. With the advancement of technology and product requirements, the need for further increased cutting speed arose, and the turning method encountered a bottleneck, leading to the development of whirlwind milling. This method uses 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 methods for worm gear whirling: internal whirling and external whirling.
Internal whirling: The workpiece circumference is tangent to the cutting tool circumference internally (the worm gear is inside the cutter head). Accuracy can reach DIN7 Ra0.8.
External whirling: The workpiece circumference is tangent to the cutting tool circumference externally (the worm gear is outside the cutter head). Accuracy can reach DIN6 Ra0.4.
