arctan？ 1 。 Different from the horizontal plane, only the minimum stress condition of the object is guaranteed to be different. When an object is balanced by an oblique upward force, the self-locking condition may not be satisfied, but if the object is balanced by an oblique downward force, the self-locking condition may be satisfied first. But in production and life, more self-locking occurs in the vertical direction. For objects on rough slopes, self-locking will also occur when applying force at an appropriate angle. This situation is between the horizontal plane and the vertical plane, so I won't go into details here. 3. Two cases of self-locking machinery and its principle application 1. As shown in fig. 5, the diameter of the two wheels of the rolling mill is d = 50cm. When the roller rotates in the opposite direction, the distance between rollers is a=0.5cm. If the dynamic friction coefficient between roller and hot steel plate is μ=0. 1. Try to find the thickness b of the steel plate before it enters the roll. According to the meaning of the question, it can be understood that the rolled hot steel plate will move to the right and pass through the roller under the friction of the roller, so that the thick steel plate will become a thin plate after rolling. It is not difficult to solve this problem. Once the steel plate can be squeezed between the two wheels from the starting position, it can keep the steel plate moving to the right. The starting position is determined by the original thickness b of the plate, the distance a between the two wheels and the friction coefficient * * *. Solution: Let the right side be the X direction, and other quantities are shown in Figure 6, which must satisfy NxxFf? , that is, sincosNNFF, tan ① (the smaller α, that is, the smaller B, the easier it is to satisfy)
By the mathematical relationship 2211tan11cos?
)cos 1(2 2Ra b，75.0？ Bcm, the maximum thickness of the steel plate should not exceed 0.75cm. From the perspective of self-locking principle, it can be considered that the non-slip between the roller and the steel plate is a self-locking phenomenon. In the figure, f is the resultant force of wheel-to-plate action, and the corresponding friction angle is α0, which conforms to? 0tan, so use formula (1).
F 1 α α F2 Figure 3
Figure 5
7 G F F 1 F2 FN Ff (c)
θ
(a)(b)b A F FN fα0α Figure 6 fx FNx
30 Tantan? This can be understood as only when f is vertically downward to the right, that is, 0
GFFN2 3 sin2？ . The "self-locking mechanism" in this example is a practical mechanical tool. From the analysis, it can be seen that when the hook lifts a heavy object, θ tends to increase if there is no relative sliding. The greater the θ, the greater the FN, that is, the tighter it is squeezed, so the greater the maximum static friction that can be provided, the less likely it is for the heavy objects to slide down. Theoretically, as long as the angle θ between the ejector pin and the vertical direction and the friction angle between the short rod and the contact surface meet) 90(0? There will be self-locking and the hook will not slip. 4. Find the breakthrough point of connecting with life practice, and cultivate and improve students' creative thinking consciousness. The new curriculum standard emphasizes the cultivation of students' creative thinking, questions or answers some natural phenomena, applies what they have learned to life, and tries to carry out some small invention research. Self-locking principle is widely used in daily life and production, which is undoubtedly a good development platform. In the teaching of Example 2 above, open questions can be designed in time to further discuss the characteristics of this institution. If this mechanism is used, the length of the ejector pin (short rod in the title) must match the inner diameter of the cylindrical weight, so it is only suitable for lifting the weight with fixed shape, which is the shortcoming of this mechanism. Students can also be given a creative design: how to design a machine that can lift cylindrical (solid) objects. That is, the external clamping (grasping) machine lifts the heavy objects by grasping and hanging, and the structural principle as shown in Figure 8 is discussed. Although the design is a little more complicated, the basic principle remains the same. Students can be given an open homework topic to investigate which aspects and occasions in production and life involve self-locking phenomenon.