Measurement of the length of the common normal
Common normal length is a crucial parameter in gear transmission. It refers to the length of the common normal line between two opposite tooth profiles spanning a number of teeth on a gear. Measuring this line indirectly reflects the accuracy of parameters such as tooth thickness, pitch, and tooth profile, making it a crucial tool for gear quality inspection. Common normal length measurement offers advantages such as ease of operation, high accuracy, and independence from the accuracy of the gear center hole. It is widely used in gear manufacturing and inspection. Understanding the measurement principles, tools, methods, and data processing of common normal length is crucial for ensuring gear meshing performance and transmission quality.
The measurement principle of the normal length is based on the principle of gear meshing. For standard gears, the normal length Wk can be calculated using the formula: Wk = m [2.9521 (k-0.5) + 0.014z], where m is the module, k is the tooth span, and z is the number of gear teeth. The tooth span k is selected so that the normal length measurement line passes through the gear pitch circle as much as possible. For standard spur gears, the tooth span k can be calculated using the formula k = 0.111z + 0.5, rounding the result to an integer. For example, for a standard spur gear with a module m = 2 mm and 30 teeth z = 30, the tooth span k = 0.111 × 30 + 0.5 ≈ 3.83. Taking k = 4, the normal length W4 = 2 [2.9521 × (4 – 0.5) + 0.014 × 30] = 2 [2.9521 × 3.5 + 0.42] = 2 [10.33235 + 0.42] = 2 × 10.75235 ≈ 21.5047 mm. The tooth thickness of the gear can be determined by measuring the deviation between the actual normal length and the theoretical value. The normal length deviation ΔW = Wactual – WTheoretical. If ΔW is within the allowable range, the tooth thickness is acceptable.
The main tools for measuring normal length include the normal micrometer and the normal indicator. The normal micrometer is the most commonly used measuring tool. It consists of a scale frame, a fixed anvil, a movable anvil, and a differential cylinder. It has a measurement accuracy of up to 0.01mm and is suitable for measuring gears with high precision requirements. The anvils of the normal micrometer are two parallel planes. During measurement, the two anvils contact the tooth profile on opposite sides of the gear, and the normal length is obtained by reading the differential cylinder. The normal indicator has even higher measurement accuracy, up to 0.001mm, and is suitable for measuring high-precision gears. It consists of a scale frame, a stylus, and a dial indicator. The deviation in normal length is read by the movement of the dial indicator’s pointer. In addition, for gears with large modules and large diameters, a dedicated normal measuring instrument can be used to improve measurement efficiency and accuracy. When selecting a measuring tool, the appropriate tool should be selected based on the gear’s precision grade and size to ensure that the required measurement accuracy is met.
The steps for measuring the normal length are as follows: First, calculate the number of teeth spanned (k) and the theoretical normal length (Wk) based on the gear’s module and number of teeth. Then, select an appropriate normal micrometer and perform zero calibration to ensure the accuracy of the measuring tool. Next, secure the gear on a measuring table with the gear axis perpendicular to the measuring plane. Place the two anvils of the normal micrometer in contact with the tooth profiles on opposite sides of k teeth on the gear. Gently oscillate the micrometer until the minimum reading is found. This reading is the normal length. To eliminate gear installation and tooth profile errors, measurements should be taken at different positions on the gear (at least three evenly distributed positions), and the average value is taken as the actual normal length. Care should be taken when measuring the force. Excessive force may cause deformation of the gear or anvil, affecting measurement accuracy. Excessive force may result in loose contact between the anvil and the tooth profile, resulting in inaccurate readings. For gears with addendum chamfers or root fillets, ensure that the anvil contacts the active working section of the tooth profile during measurement, avoiding contact with the chamfer or fillet. This can lead to measurement errors.
Error analysis and data processing for normal line length measurement are crucial for ensuring the reliability of measurement results. Common measurement errors include instrument error, method error, and environmental error. Instrument error is primarily caused by manufacturing precision and calibration errors in measuring tools, such as indication error in normal line micrometers and anvil parallelism errors. These errors can be reduced by regularly calibrating the measuring tool. Method error is primarily caused by improper selection of the tooth span number and inaccurate measurement position. For example, an inappropriate selection of the tooth span number k can cause the measuring line to deviate from the pitch circle, leading to measurement deviation. Therefore, the tooth span number should be calculated strictly according to the formula. Environmental error is primarily caused by temperature fluctuations, which can cause thermal deformation of the gear and measuring tool, affecting measurement accuracy. Therefore, measurements should be performed in a constant temperature environment (generally 20 ± 2°C). Before measurement, the gear and measuring tool should be placed in this environment for a sufficient period of time to achieve temperature uniformity. When processing measurement data, the deviation between the actual normal line length and the theoretical value should be calculated to determine whether it is within the allowable range. For gears that fail the test, the cause should be analyzed and appropriate rework measures should be implemented.
Measuring the normal length has important applications in gear manufacturing. It not only verifies the accuracy of gear tooth thickness but also indirectly reflects the cumulative pitch error and tooth profile error. During gear machining, measuring the normal length can promptly identify machining errors, adjust machining parameters, and avoid batch scrap. For example, during gear hobbing, if the normal length is too large, it indicates excessive tooth thickness, which can be reduced by adjusting the axial or radial feed of the hob. If the normal length is too small, it indicates excessive tooth thickness, and appropriate adjustments can be taken. Before gear assembly, measuring the normal length ensures that the tooth backlash of meshing gears is within a reasonable range. Excessive backlash can lead to heat generation and increased wear during gear meshing; excessive backlash can cause unstable transmission, shock, and noise. Therefore, measuring the normal length is a key method for ensuring gear quality and transmission performance, and is crucial for improving the quality and reliability of mechanical products.
