Basic dimensions of trapezoidal threads
Trapezoidal threads, a primary type of transmission thread, are widely used in equipment such as machine tool lead screws, jacks, and presses. Standardization of their basic dimensions is essential for ensuring transmission accuracy and interchangeability. The national standard GB/T 5796.1-2005 specifies the basic thread profile, diameter, pitch, thread height, and tooth width of trapezoidal threads. Trapezoidal threads are categorized by thread direction as left-hand or right-hand (right-hand is the default), and by thread angle as 30° (Chinese and German standards) or 29° (American standard). The 30° trapezoidal thread is the most widely used in Chinese machinery manufacturing.
The basic tooth profile of the trapezoidal thread is the benchmark for determining various dimensions. It consists of the tooth top, tooth bottom and working surfaces on both sides. The tooth profile angle α=30°. This angle design can not only ensure the transmission efficiency of the thread, but also withstand large axial loads. The main parameters of the basic tooth profile include: crest clearance ac, which is used to store lubricant and compensate for manufacturing errors. When the pitch P ≤ 4mm, ac = 0.25mm; when 4mm < P ≤ 12mm, ac = 0.5mm; when P > 12mm, ac = 1mm; tooth height h, which refers to the radial distance from the top to the bottom of the thread, is calculated as h = 0.5P + ac. For example, for a trapezoidal thread with a pitch of P = 6mm, h = 0.5 × 6 + 0.5 = 3.5mm; crest width f, which is the axial width of the thread crest, f = 0.366P. For a thread with a pitch of P = 6mm, f = 0.366 × 6 ≈ 2.196mm; and groove bottom width w, which is the axial width of the thread groove bottom, w = 0.366P – 0.536ac. Taking P = 6mm as an example, w = 2.196 – 0.536 × 0.5 ≈ 1.928mm. Precise control of these parameters is the key to ensuring the meshing performance of trapezoidal threads.
The diameter range for trapezoidal threads includes the major diameter d (external thread crest diameter / internal thread root diameter), the minor diameter d₁ (external thread root diameter / internal thread crest diameter), and the pitch diameter d₂ (the diameter of the imaginary cylinder where the thread thickness and the groove width are equal). The major diameter is the nominal diameter of the thread and is directly indicated in the thread designation (e.g., Tr40×7 represents a trapezoidal thread with a major diameter of 40mm and a pitch of 7mm ). The values of the major and minor diameters are related to the pitch. For external threads, the major diameter d is equal to the nominal diameter; for internal threads, the major diameter D =d+2ac ; the minor diameter d₁=d-2h for external threads and D₁=d₁ for internal threads ; and the pitch diameter d₂=D₂=d-0.5P (for external threads) or D₂=d-0.5P (for internal threads). The pitch diameter is a key parameter for controlling thread clearance and directly affects transmission smoothness. For example, the external thread of Tr40×7 , d=40mm , h=0.5×7+0.5=4mm , d₁=40-2×4=32mm , d₂=40-0.5×7=36.5mm ; the internal thread D=40+2×0.5=41mm , D₁=32mm , D₂=36.5mm .
The pitch series is a key component of trapezoidal thread size standardization. National standards specify preferred pitches, common pitches, and third-series pitches to accommodate various transmission requirements. Preferred pitches include 1.5mm, 2mm, 3mm, 4mm, 6mm, 8mm, 12mm, 16mm, 20mm, 24mm, and 32mm, such as the Tr30×6 (preferred pitch of 6mm). Common pitches include 2.5mm, 5mm, 7mm, 9mm, and 10mm, suitable for medium-load transmission. Third-series pitches (such as 1.25mm and 18mm) are used in specialized applications. Pitch selection depends on transmission speed and load. Small pitches (≤4mm) are suitable for high-speed, light-load transmission, while large pitches (≥12mm) are suitable for low-speed, heavy-load transmission. For example, machine tool feed screws often use preferred pitches of 6mm and 8mm, while jack screws often use large pitches of 16mm and 20mm.
Trapezoidal thread dimensional tolerances are categorized as medium precision (Grades 4, 5, and 6) and high precision (Grades 7, 8, and 9) based on application requirements. The higher the tolerance grade, the smaller the permissible dimensional deviation. The pitch diameter tolerance is the core of trapezoidal thread tolerances. The pitch diameter tolerance es for external threads is a negative value (upper deviation), while the pitch diameter tolerance Ei for internal threads is a positive value (lower deviation). For example, a Tr40×7-7e external thread has a basic pitch diameter of 36.5mm. The upper deviation es for tolerance zone 7e is -0.18mm, and the lower deviation ei is -0.18-0.32 = -0.50mm. Therefore, the actual pitch diameter must be within the range of 36.00-36.32mm. The tolerances for the major and minor diameters are relatively loose. The major diameter tolerance for external threads is controlled between -0.3mm and -0.8mm (depending on the diameter and pitch), while the minor diameter tolerance for internal threads is controlled between +0.3mm and +1.0mm. In actual production, it is necessary to select corresponding processing equipment and measuring tools according to the accuracy level of the thread. Medium-precision threads can be processed by ordinary lathes, while high-precision threads need to be processed by CNC lathes or screw grinders, and accurately detected using thread micrometers, three-needle measurement methods, etc.
