Basic tooth profile of cylindrical worm
The basic tooth profile of a cylindrical worm refers to the basic outline of the worm’s tooth shape in the axial cross-section. It is the foundation of worm design and CNC machining, and directly determines the meshing performance, transmission efficiency, and load-bearing capacity of the worm and worm wheel. The national standard (GB/T 10087-1988) specifies the basic tooth profile parameters of cylindrical worms, including tooth angle, tooth addendum height, tooth root height, top clearance, addendum radius, and root radius. The standardization of these parameters ensures interchangeability and fit accuracy between worms and worm wheels. Understanding and mastering the basic tooth profile of cylindrical worms is crucial for the correct design of worm drives, selection of CNC machining tools, and worm quality inspection.
The key parameters and definitions of the basic tooth profile of a cylindrical worm gear must be clearly defined; these parameters form the basis of tooth profile design. The tooth profile angle (α) refers to the angle between the worm tooth flank and the dividing line of the pitch cylinder in the axial cross-section. The standard setting is 20°. For power transmission worms, 25° can be used to increase load capacity; for worms requiring self-locking, 15° can be used to increase the helix angle. The addendum height (ha) is the radial distance from the pitch circle to the addendum circle. The standard addendum height is 1m (m is the module); the short tooth has an addendum height of 0.8m. This short tooth structure reduces addendum interference and is suitable for worms with larger modules or larger helix angles. The root height (hf) is the radial distance from the pitch circle to the root circle. The standard addendum height is 1.2m, and the short tooth has an addendum height of 1m. The root height must ensure sufficient root strength to prevent tooth breakage during use. Top clearance (c) refers to the radial clearance between the root circle of the worm gear and the top circle of the worm gear. The standard top clearance c=0.2m, and the short tooth top clearance c=0.25m. The function of the top clearance is to store lubricating oil and compensate for manufacturing errors.
The basic tooth profile of a cylindrical worm varies depending on the worm type. Common types include the Archimedean worm (ZA), involute worm (ZI), normal straight-flank worm (ZN), and conical envelope worm (ZK). The Archimedean worm has a straight axial tooth profile, making it easy to machine. It can be machined on a standard lathe with a straight-edge turning tool. It is suitable for low- and medium-power transmissions. However, the angle between the tooth contact line and the relative sliding direction is small, resulting in poor lubrication and low transmission efficiency (typically 70%-80%). The tooth profile of an involute worm is an involute on the end face and can be machined with a hob on specialized machine tools. It offers good tooth contact, high load capacity, and high transmission efficiency (85%-95%), making it suitable for high-speed and heavy-load transmissions. The normal tooth profile of a normal straight-flank worm is straight, making the helical surface formation more complex and requiring specialized tooling. It is suitable for worms with larger helix angles. The conical surface enveloping worm is made of a conical grinding wheel. It has a large tooth contact area, good meshing performance, high load capacity and efficiency, and is suitable for high-precision and heavy-load transmission occasions.
The size calculation of the basic tooth profile of a cylindrical worm needs to be carried out according to the module and tooth profile type. Taking the standard Archimedean worm as an example, the main size calculation formulas are as follows: pitch circle diameter d₁=mq ( q is the diameter coefficient, q=d₁/m ); addendum circle diameter da₁=d₁+2ha=d₁+2m ; root circle diameter df₁=d₁-2hf=d₁-2.4m ; addendum width sa=0.843m ; root width fa=0.697m ; tooth height h=ha+hf=2.2m . For example, for an Archimedean worm with a module m = 4mm and a diameter coefficient q = 10 , the pitch circle diameter d₁ = 4 × 10 = 40mm ; the addendum diameter da₁ = 40 + 2 × 4 = 48mm ; the root diameter df₁ = 40 – 2.4 × 4 = 40 – 9.6 = 30.4mm; the addendum width sa = 0.843 × 4 = 3.372mm; the root width fa = 0.697 × 4 = 2.788mm; and the tooth height h = 2.2 × 4 = 8.8mm. These dimensions must be clearly marked on the design drawing as a basis for processing and inspection.
The accuracy requirements for the basic tooth profile of a cylindrical worm gear must be determined based on transmission performance, primarily including tooth form error, pitch error, and surface roughness. Tooth form error refers to the deviation between the actual tooth profile and the theoretical tooth profile. For a grade 7 precision worm, the tooth form error is ≤0.012mm; for a grade 8 precision worm, it is ≤0.02mm; and for a grade 9 precision worm, it is ≤0.032mm. Excessive tooth form error can lead to poor contact between the worm and the worm wheel during meshing, causing localized stress concentration. Pitch error includes pitch deviation and cumulative pitch error. For a grade 7 precision worm, the pitch deviation is ≤±0.012mm, with a cumulative pitch error of ≤0.03mm/100mm. For a grade 8 precision worm, the pitch deviation is ≤±0.02mm, with a cumulative pitch error of ≤0.05mm/100mm. Excessive pitch error can affect transmission smoothness and generate vibration and noise. In terms of surface roughness, the Ra value of the worm tooth surface needs to be ≤1.6μm, and the Ra value of the worm tooth surface with precision above level 7 needs to be ≤0.8μm. Excessive roughness will increase the friction coefficient, reduce transmission efficiency, and aggravate tooth surface wear.
The inspection method for the basic tooth profile of a cylindrical worm gear should be selected based on the accuracy level. Commonly used methods include template comparison, tool microscope measurement, and three-dimensional coordinate measurement. The template comparison method is suitable for low-precision worm gears. A tooth template is fitted to the worm gear profile and the clearance is observed. A clearance of ≤0.02mm is considered acceptable. The tool microscope measurement method is suitable for medium-precision worm gears and can measure parameters such as tooth profile angle, addendum width, and root width with an accuracy of up to 0.001mm. The three-dimensional coordinate measurement method is suitable for high-precision worm gears. By scanning the tooth profile surface and comparing it with the theoretical tooth profile, it can comprehensively assess tooth profile error and pitch error, with an accuracy of up to 0.0001mm. During inspection, the measurement environment temperature (20±2°C) must be maintained to avoid measurement errors caused by temperature fluctuations. The worm gear must be placed in a constant temperature environment for at least 2 hours to align with the ambient temperature before measurement. Through rigorous inspection, the accuracy of the basic tooth profile of the cylindrical worm gear can be guaranteed, ensuring the performance and life of the worm gear transmission.
