# Effect of Gear Modification Coefficient on Gear Slip Rate

To analyze the influence of gear displacement coefficient, it should be divided into equal displacement, unequal positive displacement and unequal negative displacement. Root cutting will occur when the negative displacement coefficient is too large.When the pressure angle (a=20 degrees) and the crest height coefficient (ha*=1) are kept constant, the minimum displacement coefficient should satisfy the following limitations at first:

Therefore, in order to better analyze the influence of the deflection coefficient, the gear teeth Z1=31, Z2=32 and module m=6 are obtained.

#### 1. Influence of Gear Modification Coefficient on Sliding Rate in Equal Modification

Figure 1 shows the variation trend of slip rate when other parameters of gear remain unchanged and the displacement coefficients are x1/x2=-0.2/0.2, x1/x2=-0/0 and x1/x2=0.2/-0.2 respectively in isostatic transmission.

When other parameters of gear pair remain unchanged, the transmission ratio and theoretical engagement line length will not change with the variation of displacement coefficient, but the actual engagement line length will change. The selection of displacement coefficient has no influence on the bending shape of relative slip rate curve, but only on the slip rate at the starting position.When the gear is positively shifted, the relative slide at the top of the tooth increases while the relative slide at the root of the tooth decreases; when the gear is negatively shifted, the opposite occurs.Negative displacement of small wheel easily causes steep increase of relative sliding of tooth root, even approaching infinity, which easily reduces its anti-wear and gluing ability.

#### 2. Influence of Gear Modification Coefficient on Sliding Rate in Unequal Shift Positive Drive

Figure 2 shows the variation trend of slip rate when other parameters of gear remain unchanged and unequal displacement positive drive (y=0.6) has displacement coefficients of x1/x2=0.2/0.4407; x1/x2=0.32035/0.32035; x1/x2=0.4407/0.2 respectively.

It can be seen from Figure 2 that when the shift coefficient y=0.6 of the center distance remains unchanged, the distribution of the shift coefficient does not affect the length of the theoretical engagement line, only the starting position of the engagement line changes, but has no effect on the bending shape of the sliding rate curve.As the displacement coefficient of one gear increases, the sliding rate curve moves towards the top direction as a whole, the sliding rate at the root of the gear decreases and the sliding rate at the top increases; the corresponding sliding curve of the other gear moves towards the root direction as a whole, the sliding rate at the root of the gear increases and the sliding rate at the top of the gear decreases.

#### 3. Influence of Gear Modification Coefficient on Sliding Rate in Unequal Shift Negative Drive

Figure 3 shows the variation trend of slip rate when other parameters of gear remain unchanged and the coefficient of displacement is x1/x2=-0.15/-0.4032, x1/x2=-0.2766/-0.2766 and x1/x2=-0.4032/-0.15 respectively for unequal displacement negative drive (y=-0.6). 