Measurement of pitch circle chordal tooth thickness
The pitch circle chordal tooth thickness refers to the chord length between the tooth flanks on either side of the gear’s pitch circle. It is a key indicator of gear precision testing and directly affects gear meshing performance and transmission accuracy. Measuring pitch circle chordal tooth thickness is a key step in gear manufacturing quality control. By measuring the deviation between the actual chordal tooth thickness and the theoretical chordal tooth thickness, it is possible to determine whether the gear manufacturing accuracy meets the required standards. For standard gears, the pitch circle chordal tooth thickness can be calculated based on the gear’s module, number of teeth, and pressure angle. For example, for a standard spur gear with a module m = 2 mm, a number of teeth z = 20, and a pressure angle α = 20°, the theoretical pitch circle chordal tooth thickness is s = πm/2 × cos²(α/2) ≈ 3.14 × 2/2 × cos²10° ≈ 3.14 × 0.9698 ≈ 3.04 mm. When measuring pitch circle chordal tooth thickness, the pitch circle chordal tooth height (the radial distance from the tooth tip to the pitch circle chord) must also be measured to ensure accurate measurement position.
The main tools for measuring pitch-chord tooth thickness include tooth thickness vernier calipers, normal micrometers, and optical gear gauges. Different measuring tools are suitable for gears of different precision and specifications. The tooth thickness vernier caliper is the most commonly used measuring tool. It consists of a horizontal vernier scale for measuring pitch-chord tooth thickness and a vertical vernier scale for measuring pitch-chord tooth height. To use it, first calculate the theoretical pitch-chord tooth height based on the gear module and number of teeth, adjust the vertical vernier scale to this value, then extend the caliper’s two measuring jaws into the tooth groove, contacting both sides of the tooth profile. The reading on the horizontal vernier scale is the actual pitch-chord tooth thickness. The tooth thickness vernier caliper generally has a measurement accuracy of 0.02mm and is suitable for measuring medium-precision gears. The normal micrometer indirectly calculates the pitch-chord tooth thickness by measuring the normal length spanning k teeth on the gear. With a measurement accuracy of up to 0.01mm, it is suitable for gears with higher precision requirements. The optical gear measuring instrument uses optical principles to perform non-contact measurement with a measurement accuracy of up to 0.001mm. It is suitable for measuring high-precision gears and large gears.
The method for measuring pitch circle chordal tooth thickness depends on the gear type and accuracy requirements. The measurement methods for spur gears, helical gears, and bevel gears vary. Measuring the pitch circle chordal tooth thickness of spur gears is relatively simple and can be performed directly using a tooth thickness vernier caliper. During measurement, the caliper jaws should contact the tooth profile at the pitch circle to avoid measurement errors caused by skewed jaws. Measuring the pitch circle chordal tooth thickness of helical gears requires considering the influence of the helix angle. Measurements are typically performed within the normal section, using a normal tooth thickness vernier caliper or converting the normal tooth thickness to the end face tooth thickness for measurement. Measuring the pitch circle chordal tooth thickness of bevel gears is more complex. Because the tooth thickness of bevel gears gradually changes along the tooth width, measurements must be taken at the midpoint of the tooth width. A dedicated bevel gear tooth thickness caliper should be used to ensure accurate measurement positioning.
Numerous factors influence the accuracy of pitch circle chordal tooth thickness measurements, primarily including the accuracy of the measuring tool, the accuracy of the measurement position, gear installation errors, and ambient temperature. Measuring tool accuracy is essential for ensuring accurate measurement results. Before use, tools such as tooth thickness vernier calipers and normal micrometers must be calibrated to ensure their zero error and indication error are within the allowable range. Accurate measurement position is crucial. If the contact point between the measuring jaws and the tooth profile deviates from the pitch circle during measurement, the measurement result will be either too high or too low. Therefore, the vertical vernier scale must be precisely adjusted to the theoretical pitch circle chordal tooth height. Gear installation errors, such as a misalignment between the gear axis and the measuring tool’s reference plane, can also lead to measurement errors. During measurement, the gear must be mounted on a dedicated measuring bracket, ensuring that its axis is perpendicular to the measuring plane. Temperature fluctuations can cause thermal expansion and contraction in the gear and measuring tool, affecting measurement accuracy. Therefore, precision measurements should be performed under constant temperature conditions (20±2°C). The gear and measuring tool must be allowed to sit in this environment for a sufficient period of time to achieve temperature uniformity before measurement.
Data processing and error analysis of pitch circle chord tooth thickness measurements are crucial for assessing gear machining quality. The difference between the measured actual pitch circle chord tooth thickness and the theoretical value is the tooth thickness deviation. This deviation should be kept within the specified design range. For example, the upper deviation for a grade 7 gear is -0.016mm, and the lower deviation is -0.056mm. Excessive tooth thickness deviation can result in excessive or insufficient backlash during gear meshing. Excessive backlash affects transmission stability, generating vibration and noise; insufficient backlash can cause gear seizure due to thermal expansion. For gears with out-of-tolerance measurement results, the causes of the error—such as tool wear, machine tool transmission errors, and workpiece clamping errors—should be analyzed, and appropriate correction measures should be implemented, such as resharpening the tool, calibrating the machine tool, or improving the clamping method. Through rigorous pitch circle chord tooth thickness measurement and error analysis, gear machining quality can be effectively controlled, ensuring meshing performance and service life.
