The modification coefficient of gears.
- Definition
The gear modification coefficient is the displacement distance (in terms of the module) of the cutting tool relative to the standard position during gear processing. It is represented by the letter X. When the cutting tool moves away from the center of the gear blank, the modification coefficient is positive (positive modification); when the cutting tool moves closer to the center of the gear blank, the modification coefficient is negative (negative modification).
- Impact on gear dimensions
Tooth thickness on the reference circle: When positively modified, the tooth thickness on the reference circle increases. Compared with a standard gear (X = 0), the tooth thickness is increased. Conversely, for negative modification, the tooth thickness decreases.
Root diameter: Positive modification will increase the root diameter, which means that the root strength of the gear is strengthened to a certain extent; negative modification will decrease the root diameter.
Tip diameter: Positive modification will increase the tip diameter, which may change parameters such as the actual center distance of gear transmission; negative modification will decrease the tip diameter.
- Impact on gear meshing performance
Contact ratio: The modification coefficient affects the contact ratio of gear transmission. Appropriate selection of the modification coefficient can increase the contact ratio, enabling more gear teeth to be in mesh simultaneously during transmission, thereby improving the smoothness of transmission. For example, in some high - speed and heavy - load gear transmissions, reasonably selecting the modification coefficient to increase the contact ratio can reduce vibration and noise.
Avoidance of undercutting: When the number of teeth is small, positive modification can avoid undercutting. Undercutting will weaken the root strength of the gear teeth and affect the transmission quality of the gear. For example, for a gear with 14 teeth, appropriate positive modification (selecting a suitable modification coefficient) can effectively prevent undercutting.
Improvement of tooth surface contact strength and root bending strength: Reasonable selection of the modification coefficient can make the distribution of contact stress on the tooth surface more uniform, thereby improving the tooth surface contact strength. At the same time, it can also adjust the bending stress at the root to improve the root bending strength. For example, in a pair of gear transmissions, by using positive modification for the pinion and negative modification for the gear, and ensuring that the total modification coefficient is an appropriate value, the matching of tooth surface contact and root bending strength can be optimized.
- Selection principles of modification coefficients
Selection according to transmission requirements: If the gear transmission is required to have high load - carrying capacity and transmission efficiency, the modification coefficient needs to be selected by comprehensively considering the tooth surface contact strength and root bending strength. For example, for heavy - load and low - speed gear transmissions, more emphasis may be placed on improving root bending strength; for high - speed and light - load transmissions, more attention may be paid to tooth surface contact strength and contact ratio.
Satisfaction of non - backlash meshing conditions: When designing modified gear transmissions, it is necessary to ensure that a pair of gears have no backlash during meshing. This requires calculating appropriate modification coefficients based on parameters such as center distance, module, and number of teeth.
Consideration of gear processing manufacturability: When selecting modification coefficients, the processing technology of the gear also needs to be considered. If the modification coefficient is too large, it may lead to difficulties in gear processing and increased processing costs. For example, in hobbing, an excessively large modification coefficient may deteriorate the cutting - in and cutting - out conditions of the hob, affecting processing accuracy.
