Key Differences Between Specific Sliding And Sliding Factor in Gear Meshing Geometry

1. Differences in Definition and Physical Meaning

1.1 Specific Sliding

• Definition: Specific sliding is the ratio of the relative sliding velocity (along the tangential direction of the tooth profile) at the contact point of two gear tooth surfaces to the tangential velocity of one of the gears at that contact point. It quantifies the degree of local relative sliding. The formulas are as follows:(varsigma_1 = 1 - frac{rho_{y2}}{rho_{y1}}), (varsigma_2 = 1 - frac{rho_{y1}}{rho_{y2}})Where:

• (v_g) = Relative sliding velocity of the tooth surfaces;

• (v_1) = Tangential velocity of the pinion (small gear) at the contact point;

• (v_2) = Tangential velocity of the gear wheel (large gear) at the contact point;

• (rho_{y1}) = Radius of curvature of the pinion at the contact point;

• (rho_{y2}) = Radius of curvature of the gear wheel at the contact point;

• u = Ratio of the number of teeth of the gear wheel to the pinion, i.e., (u = Z_2/Z_1).

• Physical Meaning: It directly characterizes the impact of local relative sliding on tooth surface wear. For example, in involute gears, specific sliding is related to the radius of curvature of the tooth profile and the transmission ratio—the greater the difference in radii of curvature, the higher the specific sliding. For a pair of gear pairs, the specific sliding reaches its maximum values at the start and end of meshing (corresponding to the root sliding rates of the pinion and gear wheel, respectively).

1.2 Sliding Factor

• Definition: Sliding factor is the ratio of the sliding velocity to the pitch circle linear velocity, and it is typically used to evaluate the overall sliding characteristics of a gear pair. The formula is:(K_g = frac{v_g}{v_t} = frac{2g_{alpha y}}{d_{w1}}left(1 + frac{1}{u}right))With (g_{alpha y} = |rho_{c1} - rho_{y1}| = |rho_{c2} - rho_{y2}|)Where:

• (v_t) = Pitch circle linear velocity;

• (g_{alpha y}) = Distance between the contact point Y and the pitch point C;

• (d_{w1}) = Pitch circle diameter of the pinion.

• Physical Meaning: It reflects the overall sliding energy loss of the gear pair and is commonly used in the analysis of transmission efficiency. For instance, an increase in the pressure angle leads to a decrease in the sliding factor and an improvement in transmission efficiency.

2. Differences in Design Considerations

2.1 Design Focus for Specific Sliding

• Wear Control: Specific sliding directly affects the rate of tooth surface wear. For example, the distribution of specific sliding in internal meshing gears differs from that in external meshing gears. To reduce local high-sliding areas, the position of the meshing point must be adjusted using modification coefficients.

• Scuffing Risk: The difference in specific sliding (e.g., the specific sliding gap between the driving gear and the driven gear) is a key factor in scuffing failure. During design, modified gears should be used to balance the specific sliding of both gears, preventing excessive specific sliding on one side. Generally, the design requires controlling the specific sliding within 2.0.

• Pressure Angle Selection: An increase in the pressure angle can reduce specific sliding but will sacrifice the contact ratio (e.g., increasing vibration and noise). For example, heavy-duty gears often use a 25° pressure angle to reduce specific sliding, while low-noise gears prefer a pressure angle of less than 20°.

2.2 Design Focus for Sliding Factor

• Transmission Efficiency Optimization: Sliding factor is directly related to energy loss. For example, in external meshing gears, the sliding factor approaches zero near the pitch point but rises sharply when far from the pitch point. To reduce sliding under high-speed operating conditions, tooth profile modification or a reduction in the addendum coefficient can be adopted.

• Material and Heat Treatment: Areas with high sliding factors are prone to scuffing. Therefore, the design must consider the scuffing resistance of materials (e.g., carburized and quenched gears) and lubrication conditions. Generally, the design requires controlling the sliding factor within 0.5.