Cylindrical worms and worm wheels
Cylindrical worms and worm wheels are the core components of worm drives, used to transmit motion and power between intersecting axes, typically at a 90° angle. They feature high transmission ratios, compact construction, and smooth transmission, making them widely used in machine tools, lifting machinery, metallurgical equipment, and other fields. Cylindrical worms can be categorized by tooth profile as Archimedean worms, involute worms, and normal straight flank worms. Archimedean worms are simple to machine and are the most widely used. Worm wheels are the gears that mesh with the worm, with arc-shaped teeth to accommodate the worm’s helical profile. Understanding the structural characteristics, parameter relationships, and machining requirements of cylindrical worms and worm wheels is crucial to ensuring the performance of worm drives.
The main parameters of cylindrical worms include module, pressure angle, lead angle, number of starts, and pitch circle diameter. Module (m) is a fundamental parameter of worm gearing and is equivalent to the module of the worm wheel. The standard module series is determined based on the worm diameter and transmission requirements and serves as the basis for calculating the geometric dimensions of the worm and worm wheel. The pressure angle (α) is the angle between the tooth profile curve and the tangent to the pitch circle in the worm’s axial plane. The standard pressure angle is 20°. The pressure angle affects the worm’s tooth strength and transmission efficiency. The lead angle (γ) is the angle between the helix on the worm’s pitch cylinder and the axis. It is calculated as tanγ = z1P / (πd1) (z1 is the number of starts, P is the pitch, and d1 is the pitch circle diameter). A larger lead angle improves transmission efficiency but reduces worm strength. Typical lead angles range from 3° to 30°. The number of heads (z1) refers to the number of helical teeth on the worm, which can be single-head, double-head, triple-head or quad-head. The more heads there are, the higher the transmission efficiency, but the greater the processing difficulty. Single-head worm has a large transmission ratio and is suitable for reduction transmission. Multi-head worm is suitable for occasions requiring higher speed.
The parameters of the worm wheel must match those of the worm to ensure proper meshing. The module (m) of the worm wheel must be equal to that of the worm, and the pressure angle must be the same as that of the worm. The number of teeth (z2) of the worm wheel is determined by the transmission ratio: i = z2 / z1, so z2 = i × z1. To ensure smooth transmission, the number of teeth in the worm wheel is typically 28 to 80. Too few teeth will result in a low overlap coefficient, making the transmission unstable; too many teeth will increase the worm wheel diameter, making the structure less compact. The formula for calculating the pitch circle diameter (d2) of the worm wheel is d2 = m × z2. The formula for calculating the outer diameter (da2) is da2 = d2 + 2m, and the formula for calculating the inner diameter (df2) is df2 = d2 – 2.4m. These dimensions must be determined based on the size of the worm and the installation space. In addition, the tooth width (b2) of the worm wheel should be determined according to the length of the worm, generally taking b2 = 0.75d1 (d1 is the pitch circle diameter of the worm) to ensure that the spiral teeth of the worm can fully engage with the teeth of the worm wheel.
The machining methods for cylindrical worms and worm wheels differ depending on their structural characteristics. Worms are typically machined on a lathe, using a similar method to machining trapezoidal threads. A forming turning tool is used, with the toolholder angle adjusted according to the lead angle, to create the worm’s helical tooth profile. Worms requiring higher precision require finishing processes such as milling and grinding to improve tooth surface roughness and dimensional accuracy. The tooth profile of an Archimedean worm is a straight line in the axial plane. During machining, the rake face of the turning tool should be parallel to the worm axis to ensure accurate tooth profile. Worm wheels, on the other hand, require hobbing using a hob with the same parameters as the worm. The hob’s module, pressure angle, and number of turns must be consistent with those of the worm. During hobbing, the hob’s axis should form a lead angle γ with the worm wheel’s axis to simulate the meshing state of the worm and worm wheel, ensuring proper tooth meshing. Worm wheels requiring higher precision require shaving or honing after hobbing to further improve tooth surface quality.
The transmission performance of cylindrical worms and worm wheels is significantly affected by material selection, lubrication conditions, and installation accuracy. Worms are typically made of high-strength alloy steel (such as 40Cr) and quenched to improve surface hardness and wear resistance, with tooth surface hardness generally ranging from 45 to 55 HRC. Worm wheels are often made of bronze (such as ZCuSn10Pb1) or cast iron. Bronze worm wheels offer excellent friction reduction and wear resistance, making them suitable for high-speed, heavy-load transmissions, while cast iron worm wheels are suitable for low-speed, light-load applications. Regarding lubrication, the high sliding speeds of worm drives easily generate frictional heat, necessitating the use of a high-viscosity gear oil and ensuring adequate lubrication to reduce tooth wear and heat generation and prevent bonding failure. During installation, the axes of the worm and worm wheel must intersect at a 90° angle, and the midplane of the worm must be tangent to the pitch circle of the worm wheel. Excessive installation deviations can lead to poor tooth contact, increased wear, and reduced transmission efficiency and service life. By rationally selecting parameters, optimizing processing technology and ensuring installation accuracy, cylindrical worm and worm gear transmission can achieve stable and efficient power transmission to meet the transmission needs of various mechanical equipment.
