Worm gear transmission is a special form of gear transmission, consisting of a worm and a worm wheel, used for the transmission of two intersecting shafts (usually 90°). Its main characteristics are:
Large transmission ratio (single - stage i = 5~100, or even higher)
Stable transmission with low noise
Self - locking property (the worm can be self - locking under certain conditions to prevent the worm wheel from being driven in reverse)
Low efficiency (usually 30%~90%, depending on lubrication and helix angle)
Due to its unique working principle, worm gear transmission is widely used in reduction mechanisms, lifting equipment, machine tool indexing devices and other fields.
The Working Principle of Worm Gears
2.1 Basic Transmission Principle
Worm gear transmission is similar to helical gear transmission, but the worm is similar to a screw, and the worm wheel is similar to a helical gear. Their meshing mode is as follows: when the worm rotates, its helical teeth push the teeth of the worm wheel to make circular motion. Because the helix angle of the worm is large and the number of teeth of the worm wheel is large, a large reduction ratio can be achieved.
2.2 Transmission Characteristics
Motion relationship: The ratio of the rotational speed of the worm (n₁) to the rotational speed of the worm wheel (n₂) is the transmission ratio: i = n₁/n₂ = z₂/z₁, where z₁ is the number of worm heads (usually 1~4) and z₂ is the number of worm wheel teeth. For a single - head worm (z₁ = 1), the transmission ratio is the largest, but the efficiency is low; for a multi - head worm (z₁ = 2~4), the efficiency can be improved, but the reduction ratio is reduced.
Direction of rotation of the worm:
Right - handed worm: Use the right - hand rule. Hold the worm with the right hand, and point the four fingers in the direction of the worm's rotation. Then the thumb points to the linear velocity direction of the worm wheel at the meshing point.
Left - handed worm: Use the left - hand rule. Hold the worm with the left hand, and point the four fingers in the direction of the worm's rotation. Then the thumb points to the linear velocity direction of the worm wheel at the meshing point.
Self - locking property: When the helix angle (γ) of the worm is smaller than the equivalent friction angle (φ), the transmission has self - locking property, that is, the worm wheel cannot drive the worm in reverse. The self - locking property is often used in lifting mechanisms, lifting platforms and other occasions that need to prevent reverse rotation.
Efficiency: The efficiency of worm gear transmission is low, mainly due to sliding friction loss: η = tan(γ + ϕ) / tanγ, where γ is the lead angle of the worm and φ is the friction angle.
The Design of Worm Gears
3.1 Main Parameters
Module (m): A series of standardized modules (such as 1, 1.25, 1.5, 2, 2.5, 3...).
Number of worm heads (z₁): Single - head worm (z₁ = 1) is used for large reduction ratio, and multi - head worm (z₁ = 2~4) is used for high - efficiency transmission.
Number of worm wheel teeth (z₂): Usually z₂ = 30~80. Too few teeth are easy to cause undercutting, and too many teeth will lead to too large volume.
Center distance (a): It affects the transmission size. The calculation formula is: a = m (z₂ + q)/2, where q is the worm diameter coefficient (q = d₁/m).
Helix angle (γ): It affects the transmission efficiency, generally γ = 3°~25°.
| Module | Index circle diameter | Worm diameter coefficient |
|---|---|---|
| m | d₁ | q |
| 1.25 | 20 | 16 |
| 22.4 | 17.92 | - |
| 1.6 | 20 | 12.5 |
| 28 | 17.5 | - |
| 2 | 22.4 | 11.2 |
| 35.5 | 17.75 | - |
| 2.5 | 28 | 11.2 |
| 45 | 18 | - |
| 3.15 | 35.5 | 11.27 |
| 56 | 17.778 | - |
| 4 | 40 | 10 |
| 71 | 17.75 | - |
| 5 | 50 | 10 |
| 90 | 18 | - |
| 6.3 | 63 | 10 |
| 112 | 17.778 | - |
| 8 | 80 | 10 |
| 140 | 17.5 | - |
| 10 | 90 | - |
| 160 | - | - |
3.2 Geometric Calculation
The basic geometric dimension calculation formulas for cylindrical worm transmission are as follows:
| Calculation item | Symbol | Formula | Calculation result | Remarks | |
|---|---|---|---|---|---|
| Center distance | A | A = 0.5M(Zz + q + 2) | 175.00 | - | |
| Module | Mdu | Mdu = 2A/(22 + q + 2) | 3.15 | - | |
| Axial section pressure angle | a | a = 20° | 20.00 | - | |
| Transmission ratio | i | i = Z2/Z1 = n1/n2 | 97.00 | - | |
| Modification coefficient | S | = (A/Mdu) - 0.5(q + z2) | 2.06 | - | |
| Radial clearance | C | C = 0.25Mdu | 0.79 | - | |
| - | Number of heads | Z1 | Z1 = 1, 2, 4 | 1.00 | - |
| - | Characteristic coefficient | q | q = Dfe1/Mdu | 10.00 | - |
| - | Addendum height | hdi | hdi = Mdu | 3.15 | - |
| - | Dedendum height | hg | hg = 1.25Mdu | 3.94 | - |
| Worm | Index circle diameter | Dte1 | Dfel = qMdu | 31.50 | - |
| - | Pitch circle diameter | Dje1 | Dje1 = Dfel + 2Mdu 5 = Mdu(q + 25) | 44.45 | - |
| - | Tip circle diameter | Ddi1 | Ddi1 = Mdu(q + 2) | 37.80 | - |
| Root circle diameter | Dg1 | Dg1 = Mdu(q - 2.5) | 23.63 | - | |
| Index circle helix lead angle | 入 | 入 = arctgZ1/q | 0.10 | - | |
| Normal module | mf | mf = Mducos 入 | 3.13 | - | |
| Helix length | L☆ | L = (12 + 0.1z2)Mdu | 68.36 | Z1 = 1, 2 | |
| - | - | L = (13 + 0.1z2)Mdu | 71.51 | Z1 = 4 | |
| Axial section pitch | P | P = πMdu | 9.90 | - | |
| Helix lead | Pz | PZ = πMduZ1 | 9.90 | - | |
| Axial tooth thickness on the index cylinder of the thread | Sz1 | Sz1 = 0.45Mdu | 97.00 | - | |
| Normal tooth thickness on the index cylinder of the thread | Sf1 | Sfl = Szlcos 入 | 96.52 | - | |
| Tooth thickness measurement height | h~ | h~ = Mdu | 3.15 | - | |
| Number of teeth | Z2 | Z2 = iZ1 | 97.00 | - | |
| Worm wheel | Index circle diameter | Die2 | Dfe2 = MduZ2 | 305.55 | - |
| - | Pitch circle diameter | Dje2 | Dje2 = Dfe2 = MduZ2 | 305.55 | - |
| - | Root circle diameter | Dg2 | Dg2 = 2(A - 0.5Ddi1 - 0.25Mdu) | 310.63 | - |
| - | Tip circle diameter | Ddi2 | Ddi2 = 2(A - 0.5Dfel + Mdu) | 324.80 | - |
| - | Maximum outer circle diameter | Dw2 | Dw2 = Ddi2 + Mdu | 327.95 | - |
| - | Rim width | b | b = 0.65Ddi1 | 24.57 | - |
| - | Addendum arc radius | R1 | R1 = 0.5Dfel - Mdu | 12.60 | - |
| - | Dedendum arc radius | R2 | R1 = 0.5Ddi1 + 0.25Mdu | 19.69 | - |
3.3 Strength Calculation
Worm wheel tooth surface contact fatigue strength (to prevent pitting): σH = ZEVY KAT2 ≤ [σH], where (ZE) is the material elastic coefficient, (KA) is the working condition coefficient (1.0~1.5), and (T2) is the worm wheel torque.
Worm wheel tooth root bending fatigue strength (to prevent fracture): σβ = 1 / (did2m) × 1.53KAT2 YFa2 Yβ ≤ [σF], where (YFa2) is the tooth profile coefficient and (Yβ) is the helix angle coefficient.
Heat balance calculation (to prevent overheating): Ploss = P₁(1 - η) ≤ kAΔt, where (P1) is the input power, (k) is the heat dissipation coefficient, (A) is the heat dissipation area, and (Δt) is the allowable temperature rise (usually ≤60℃).
The Processing of Worm Gears
4.1 Worm Processing
Turning: Suitable for small - batch production.
Milling: Suitable for multi - head worms.
Grinding: Used for high - precision worms (such as CNC worm grinders).
4.2 Worm Wheel Processing
Hobbing: Processed with worm - like hobs.
Fly - cutter cutting: Suitable for large - module worm wheels.
Honing / lapping: To improve the tooth surface finish.
4.3 Material Selection
| Part | Common materials | Heat treatment |
|---|---|---|
| Worm | 45 steel, 40Cr, 20CrMnTi | Quenching and tempering, carburizing and quenching |
| Worm wheel | Tin bronze (ZCuSn10P1), aluminum bronze (ZCuAl10Fe3) | Casting |
The Application of Worm Gears
5.1 Lifting Machinery
Winches, cranes (using self - locking property to prevent heavy objects from sliding down).
5.2 Industrial Reducers
Worm reducers (such as RV reducers).
5.3 Machine Tool Indexing Devices
Dividing heads, rotary tables (precision angle control).
5.4 Automobile Steering Mechanisms
Some mechanical steering systems adopt worm gear transmission, including steering gear, steering wheel, steering transmission shaft, steering shaft, steering arm, steering tie rod, universal joint, left steering knuckle, steering knuckle arm, right steering knuckle, steering trapezoid arm, etc.
5.5 Other Fields
Packaging machinery, conveying equipment, valve drives, etc.
5.6 Advantages and Disadvantages of Worm Gear Transmission
5.6.1 Advantages
Large transmission ratio and compact structure.
Stable operation and low noise.
Self - locking property (under specific conditions).
Suitable for occasions with limited space.
5.6.2 Disadvantages
Low efficiency (especially for single - head worms).
Severe heat generation, requiring good lubrication.
High manufacturing cost (the worm wheel needs wear - resistant materials).
Summary
Worm gear transmission plays an irreplaceable role in reduction mechanisms, lifting equipment and other fields due to its large reduction ratio, self - locking property and compact structure. Although its efficiency is low, its performance and service life can be significantly improved through optimized design, selection of appropriate materials and lubrication methods. In the future, worm gear transmission will continue to develop in the direction of high efficiency, precision and intelligence.
