Diameter and pitch of trapezoidal threads
The diameter and pitch of a trapezoidal thread are the core parameters that determine its transmission performance and structural dimensions, and directly affect the thread’s load-bearing capacity, fit accuracy, and interchangeability. In mechanical design, the diameter of a trapezoidal thread usually refers to the nominal diameter (i.e., major diameter), while the pitch is the axial distance between the corresponding points of two adjacent teeth on the mid-diameter line. The two must be standardized and matched in accordance with national standards to ensure that threaded parts produced by different manufacturers can accurately fit together. For example, the accuracy of the diameter and pitch of key transmission components such as machine tool lead screws and jack screws must be controlled within ±0.02mm, otherwise it will cause transmission jamming or excessive clearance. Therefore, a deep understanding of the definition, series specifications, and design principles of trapezoidal thread diameter and pitch is crucial to ensuring the stability of mechanical transmission systems.
The diameter series of trapezoidal threads includes major diameter, pitch diameter, and minor diameter, with strict dimensional relationships between them. The major diameter ( d or D ) is the nominal diameter of the thread. For external threads, the major diameter is the crest diameter, while for internal threads, it is the root diameter. It is the primary identifier of the thread specification (for example, Tr40×7 indicates a trapezoidal thread with a major diameter of 40mm and a pitch of 7mm ). The pitch diameter ( d₂ or D₂ ) is a key parameter of thread fit. Its dimension is the major diameter minus twice the crest height (crest height h₁ = 0.5P ), that is, d₂ = d-2 × 0.5P = dP . For example, the pitch diameter of a Tr40×7 is 40-7 = 33mm . The minor diameter ( d₁ or D₁ ) is the minimum diameter of a thread. For external threads, the minor diameter is the root diameter, while for internal threads, it is the crest diameter. The formula for calculating d₁ is d-2 × (0.5P + ac) ( ac is the clearance, typically 0.5mm ). Therefore, the minor diameter of a 40×7 thread is 40-2 × (3.5 + 0.5) = 40-8 = 32mm . These dimensional relationships must strictly adhere to the GB/T 5796.1-2005 standard to ensure that the thread engagement depth and load-bearing area meet design requirements.
The choice of pitch series should be determined based on the transmission requirements and the structural space. National standards categorize trapezoidal thread pitch into coarse and fine series. Coarse pitch (e.g., P4mm, P6mm, P8mm, P10mm) is suitable for transmitting power or bearing heavy loads, and features a robust thread profile and high strength. Fine pitch (e.g., P2mm, P3mm) is suitable for precision adjustment or thin-walled parts, and features a shallower thread profile, which reduces the impact on the workpiece’s strength. The pitch value must match the major diameter. For example, for a 30mm major diameter thread, common pitches are 3mm, 6mm, and 10mm, with larger pitches corresponding to larger diameters to ensure the thread’s load-bearing capacity is proportional to the diameter. The cumulative pitch error must also be considered during design. For long lead screws (length > 1m), the cumulative pitch error must be ≤0.1mm per 1000mm; otherwise, transmission accuracy will decrease. When designing a CNC lathe lead screw, a machine tool factory improved the transmission efficiency by 15% by optimizing the pitch series (selecting Tr50×6) while reducing the processing difficulty.
The accuracy of the diameter and pitch directly impacts the fit of the thread. National standards categorize trapezoidal thread accuracy into grades 3, 4, 5, 6, 7, 8, and 9, with grade 3 being the highest and grade 9 the lowest. Commonly used accuracy levels are grade 7 (medium accuracy) and grade 8 (general accuracy). The tolerances of the major and minor diameters primarily affect the thread’s assembly clearance, while the pitch diameter tolerance determines the tightness of the fit. For example , the pitch diameter tolerance of a grade 7 external thread is 0.2mm, while that of an internal thread is 0.3mm. After mating, the clearance can be controlled within 0.1mm. Pitch accuracy requires control of both single pitch error (≤0.02mm) and cumulative pitch error (≤0.05mm/300mm). Higher accuracy grades require higher requirements for processing equipment and measuring tools. A precision instrument factory uses a grade 6 trapezoidal thread (Tr32×4) to reduce the positioning error of the fine-tuning mechanism from 0.05mm to 0.01mm, meeting the needs of high-precision measurement.
The design principles for diameter and pitch must balance performance and process feasibility. In power transmission, the required thread diameter must be calculated based on the transmitted torque (torque T = 0.2 × F × d₂ , where F is the axial force). For example, to transmit 1000 N · m of torque, a thread with a pitch diameter ≥ 50 mm should be selected . The choice of pitch also considers transmission speed (lead S = n × P , where n is the number of threads). For fast transmission, a multi-start, high-pitch thread (such as a double-start Tr60×12 with a lead of 24 mm ) is preferred, while a single-start, low-pitch thread (such as a single-start Tr20×2 with a lead of 2 mm ) is preferred for precision transmission. Furthermore, the capabilities of the processing equipment must be considered. Large-diameter, high-pitch threads (such as Tr100×16 ) require heavy-duty lathes, while small-diameter, fine-pitch threads (such as Tr12 ×2) can be produced on standard lathes. A heavy machinery factory, by rationally matching the diameter and pitch (Tr80×10), not only met the 300kN axial force load requirement, but also ensured a processing qualification rate of over 98%.
