Worm gear reducer transmission principle detailed explanation

Worm gear reducer transmission principle detailed explanation

Worm drive:

Worm drive is a kind of transmission that transfers motion and power between two axes in a space staggered way. The included angle between two axes can be any value, and the commonly used one is 90 °. Worm drive is used to transmit motion and power between staggered shafts.

1. Introduction

Worm drive is composed of worm and worm gear. Generally, the worm is the driving part. Worm and thread can be divided into right-hand and left-hand worm drives, which are called right-hand worm and left-hand worm respectively. If there is only one helix on the worm, it is called a single headed worm. That is, if the worm rotates once, the worm rotates over one tooth. If there are two helix on the worm, it is called a double headed worm. That is, if the worm rotates once, the worm rotates over two teeth.

2. Features

(1) Large transmission ratio and compact structure. The number of worm heads is represented by Z1 (generally Z1=1~4), and the number of worm gear teeth is represented by Z2. From the transmission ratio formula I=Z2/Z1, it can be seen that when Z1=1, that is, the worm is a single head, the worm must turn Z2 to turn the worm gear, so a large transmission ratio can be obtained. Generally, in power transmission, the transmission ratio I=10-80 is taken; In the indexing mechanism, I can reach 1000. Such a large transmission, such as gear transmission, requires multi-level transmission, so the worm transmission is compact in structure, small in size and light in weight.

(2) The transmission is stable without noise. Because the worm gear is a continuous spiral gear, it is continuous when it is engaged with the worm gear. The worm gear does not enter or exit the engagement process, so it works stably and has little impact, vibration and noise.

(3) It is self-locking. When the helix angle of the worm is very small, the worm can only drive the worm gear, but the worm gear cannot drive the worm to rotate.

(4) The efficiency of worm transmission is low, and it is generally believed that the efficiency of worm transmission is lower than that of gear transmission. In particular, the efficiency of the self-locking worm drive is below 0.5, and the general efficiency is only 0.7~0.9.

(5) The heat is large, the tooth surface is easy to wear, and the cost is high.

3. Cylindrical worm

Cylindrical worm drive is a worm drive with cylindrical indexing surface.

The commonly used worm drives are Archimedes cylindrical worm drive and circular arc tooth cylindrical worm drive. ① The tooth profile of the end face of Archimedes worm is Archimedes helix, and the tooth profile of its axial surface is a straight line. Archimedes worm can be machined with trapezoidal turning tool on the lathe, so it is simple to manufacture, but difficult to grind, so the accuracy is not high. In Archimedes cylindrical worm drive, the included angle between the contact line of worm and worm gear tooth surface and the relative sliding speed is very small, so it is not easy to form a lubricating oil film, so the bearing capacity is low. ② The spiral tooth cylindrical worm drive is a worm drive in which the axial (or normal) tooth profile of the worm is concave arc and the tooth profile of the worm gear is convex arc. In this transmission, the included angle between the contact line and the relative sliding speed is large, so it is easy to form a lubricating oil film, and the convex and concave tooth profiles mesh. The equivalent curvature radius of the tooth profile on the contact line is large, and the contact stress is low, so its bearing capacity and efficiency are higher than other cylindrical worm transmissions.

4. Main parameters

The parameters and geometric dimensions of various cylindrical worm drives are basically the same. It is the main parameter of Archimedes cylindrical worm drive. The plane passing through the worm axis and perpendicular to the worm gear axis is called the mid plane. On the middle plane, the tooth profile of the worm [1] is a straight line, the tooth profile of the worm gear is an involute, and the engagement of the worm and the worm gear is equivalent to the engagement of the rack and the involute gear. Therefore, the calculation of parameters and geometric dimensions of worm drive is roughly the same as that of gear drive, and the parameters and dimensions on the middle plane are taken as the benchmark in design and manufacturing.

5. Worm drive

The axial pitch pX of the worm shall be equal to the circumferential pitch pt on the end face of the worm gear, so the axial modulus of the worm shall be equal to the end face modulus of the worm gear, expressed in m, and m shall be taken as the standard value. The axial pressure angle of the worm shall be equal to the end face pressure angle of the worm gear α Means, usually standard pressure angle α= 20°。

Worm is equivalent to a helix, and its helix is also divided into left-handed and right-handed, single headed and multi headed. Generally, the number of worm heads Z1=1~4, the more the number of worm heads, the higher the efficiency; However, if there are too many heads, such as Z1>4, the indexing error will increase and it is not easy to process. The number of teeth of the worm gear Z2=iZ1, i is the transmission ratio of the worm gear, i=n1/n2=Z2/Z1. For the worm drive with general power transmission, Z2=27~80. When Z2<27, the worm gear teeth are prone to undercutting; When Z2 is too large, the bending strength of worm gear teeth may be insufficient. Use d1 to represent the diameter of the worm indexing circle, then the spiral rise angle on the worm indexing cylinder λ It can be calculated by the following formula that q=Z1/tg is introduced into the above formula λ， Then the diameter of the dividing circle of the worm can be obtained as d1=qm. Where q is called worm characteristic coefficient. In order to limit the number of hobs, the standard specifies the q value matched with each module. Generally, q=6~17. Diameter of worm gear indexing circle d2=Z2m.

6. Failure form

In worm drive, the failure forms of worm gear teeth include pitting, wear, gluing and tooth bending and breaking. However, the worm transmission efficiency is generally low, the sliding speed is high, and it is easy to heat up, so the scuffing and wear damage are more common.

In order to avoid scuffing and slow down wear of worm drive, the materials of worm drive must have the properties of antifriction, wear resistance and scuffing resistance. Generally, the worm is made of carbon steel or alloy steel. The spiral surface should be heat treated (such as quenching and carburizing) to achieve high hardness (HRC45-63), and then ground or honed to improve the bearing capacity of the transmission. Worm gears are mostly made of bronze, and sometimes brass or cast iron is used for transmission that is not important for low speed. In order to prevent scuffing and slow down wear, a good lubrication method should be selected, and lubricating oil containing anti scuffing additives should be selected. For the scuffing and wear of worm drive, there is no mature calculation method. The contact stress of the tooth surface is an important factor that causes the scuffing and wear of the tooth surface, so the calculation of the contact strength of the tooth surface is still the basic calculation of the worm drive. In addition, sometimes the bending strength of gear teeth should also be checked. Generally, the worm gear is not easy to be damaged, so it is not necessary to calculate the strength of the gear, but check the strength and stiffness of the worm shaft when necessary. Heat balance calculation shall also be carried out for closed transmission. If the heat balance calculation cannot meet the requirements, heat sink or forced cooling device shall be installed outside the box.

7. Structure introduction

Generally, the worm and the shaft are made into a whole, which is called the worm shaft. The structure of the worm gear can be divided into three types: worm drive. ① Integral type: used for cast iron and bronze worm gear with small diameter. ② Gear ring press fit type: the hub is cast iron or cast steel, and the rim is bronze. ③ Bolt connection type: the flange and hub are connected by reamed holes and bolts. This structure is easy to assemble and disassemble.

8. Transmission application

Worm drive is often used in situations where two shafts are staggered, transmission ratio is large, transmission power is not too large or intermittent work.

When worm drive is required to transmit large power, Z1 is usually taken as 2~4 to improve transmission efficiency. In addition, due to the fact that when γ 1 The smaller transmission is self-locking, so it is often used in hoisting machinery such as winches for safety protection. It is also widely used in machine tools, automobiles, instruments, metallurgical machinery and other machines or equipment. The reason is that the use of axle motion can reduce the consumption of force, so it is vigorously promoted.