In this article, we will explore the cloning design and calculation of modified helical cylindrical gears. The design and calculation of modified gears are crucial, especially when the width of the modified gear is narrow, and it is necessary to determine all the parameters of the modified helical cylindrical gear based on its modulus, number of teeth, center distance, and diameter of the addendum circle. This process involves complex considerations and precise calculations to ensure the gears can function properly without issues such as excessive meshing clearance, high noise during transmission, unstable rotation, root cutting at the tooth root, and poor tooth strength.
1. Introduction to the Structure and Working Principle of the Electric Vehicle Glass Lifter
The structure and working principle of the electric vehicle glass lifter are as follows (see Figure 1). When the DC motor 10 is activated, it drives the worm shaft 3 connected to it to rotate. The lower end of the worm shaft is fixed with a DC motor, the middle is sleeved with a copper bearing 9, and the upper end is made with two sections of worm teeth in the left and right directions. When the worm shaft 3 rotates forward (clockwise), the teeth of the right worm mesh with the worm gear teeth of the right worm gear 双联 4 for power transmission, while there is a gap between the teeth of the left worm and the worm gear teeth of the left worm gear 双联 7, so power cannot be transmitted. When the worm shaft rotates in reverse (counterclockwise), it is the teeth of the left worm that mesh with the worm gear teeth of the left worm gear 双联 for power transmission. And there is also a gap between the teeth of the right worm and the worm gear teeth of the right worm gear 双联，so power cannot be transmitted either. The electric lifter operates based on this transmission principle. In other words, as long as the forward and reverse rotations of the worm shaft can be controlled, the rotation directions of the left and right worm gear 双联 worm gears can be controlled, and thereby the rising and falling of the car window glass can be controlled. There will be no confusion in the switching of the rotation directions of the left and right worm gears or the occurrence of motion interference. The right worm gear is integrated with the right gear and is called the right worm gear 双联，while the left worm gear is integrated with the left gear and is called the left worm gear 双联. Both the left and right gears mesh with the large gear 5, and they are all helical cylindrical gears. Their helical teeth gradually engage and disengage during rotation, making the meshing transmission more stable. The forward rotation of the worm shaft causes the right worm gear 双联，the large gear, the spline shaft 6, and the grooved wheel to rotate. The rope 11 wound in the groove of the grooved wheel has its two ends respectively connected to the upper and lower ends of the glass. When the grooved wheel rotates forward, one end of the steel rope is wound in the groove, causing the glass to rise along the guide groove of the car window. And the steel rope connected to the lower end of the glass is released. Conversely, the glass will descend. In this way, as long as the forward and reverse rotations of the motor can be controlled by pressing the switch, the rising and falling of the glass can be controlled. If it can be improved to control the forward and reverse rotations of the remote control motor, it can achieve the remote control of the glass lift, which will bring greater convenience to the driver. When the glass rises and falls to the limit position, due to the increased resistance, the steel rope will slip in the groove of the grooved wheel, thereby protecting the electric lifter from being damaged.
2. Observation and Measurement of the Transmission Components of the Electric Lifter
The transmission components of the electric lifter include the worm shaft, the right worm gear 双联，the left worm gear 双联，and the large gear; the spline shaft, the grooved wheel, the steel wire, etc. Our main research objects are the left and right gears and the large gear.
2.1 Observation of the Left and Right Gears
Both the left and right gears are helical cylindrical gears, and the number of teeth of each is 8. In gear processing, there are certain restrictions on the minimum number of teeth of the gear (Zmin). Otherwise, the phenomenon of root cutting will occur during tooth cutting, resulting in weakened tooth strength and reduced gear transmission quality. For gears with root cutting, on the one hand, the strength of the tooth root part that bears the maximum bending moment will be weakened; on the other hand, because the involute tooth profile outside the base circle is easily cut off, the meshing coefficient will be reduced when it meshes with another gear. To avoid root cutting, it is necessary to know the minimum number of teeth that does not produce root cutting (Zmin). The minimum number of teeth of a spur gear is:
, where .
It can be seen that Zmin is related to the transmission ratio i during tooth cutting, the tooth profile angle , and the tooth height coefficient f. When using a rack cutter for tooth cutting, when , that is, . However, in actual situations, a small amount of root cutting is allowed, and the actual allowed minimum number of teeth . For example, when , , , and , the minimum number of teeth of the external meshing spur gear is 17. When , , , and , the minimum number of teeth of the cylindrical gear without root cutting is 14, and the actual minimum number of teeth can be 12. It can be seen that when the number of teeth of the left and right gears is 8, root cutting is bound to occur during tooth cutting, so modified gears must be used to avoid root cutting.
2.2 Detection of the Left Gear, Right Gear, and Large Gear of the Sample and the Gear Box
For the measurement of the left gear, right gear, and large gear, it is only necessary to measure their diameters of the addendum circle: D, and the center distance A between the worm and worm gear, the left and right gears, and the large gear shaft in the gear box. Then, by comparison, it can be clearly distinguished whether these sample transmission components are of the non-modified or modified nature. Theoretically, there is also a method of modification for helical cylindrical gears, but generally, the method of changing the helix angle can be used to avoid root cutting, so the method of modification is actually rarely used. Therefore, it can be judged that the left, right gears, and large gear are all helical cylindrical gears, and there is a method of modification for helical cylindrical gears to avoid the phenomenon of root cutting. Therefore, the left, right gears, and large gear are set as helical cylindrical gears rather than helical gears. The comparison table of the measured values of the left, right gears, and large gear and the calculated non-modified theoretical values of the left, right worm, and left, right worm gear is shown in Table 1.
| Value | Parameter | Measured Value (Sample) | Theoretical Value (Non-Modified) |
|---|---|---|---|
| Diameter of the addendum circle of the right gear Dw, left | Diameter of the addendum circle of the large gear Dw | Center distance between the left and right gears and the large gear 4 | Center distance between the worm and the worm gear 4 |
| 111.86 | 147.44 | 27.80 | 15.20 |
| 10.88 | 147.55 | 26.96 | 14.90 |
It can be clearly seen from Table 1 that the actual size of the diameter of the addendum circle of the left and right gears is Φ11.86 mm, which is 0.98 mm larger than the non-modified theoretical value of Φ10.88 mm, which is very obvious. And the actual size of the diameter of the addendum circle of the large gear is Φ47.44 mm, which is 0.11 mm smaller than the non-modified theoretical value of Φ47.55 mm. In addition, the actual center distance between the left and right gears and the large gear is 27.8 mm, which is also 0.84 mm larger than the non-modified center distance between the left and right gears and the large gear of 26.96 mm. This also fully shows that the left, right gears, and large gear have also adopted the method of modification.
3. Selection of the Types of Modification Methods for the Transmission Components of the Automobile Lifter
There are various types of modified helical cylindrical gear transmission, and it is very important to correctly select the modification method, otherwise, the purpose of modification cannot be achieved, and the purpose of cloning the electric vehicle glass lifter cannot be achieved either.
3.1 Selection of the Types of Modified Meshing of Helical Cylindrical Gears
For the types of modified meshing of helical cylindrical gears, there are two types: height modification and angle modification. When the center distance A of the height meshing is equal to the center distance of the non-modified meshing, that is, , the modification coefficient , that is, . At this time, the gear with is positive modification, and the other gear with is negative modification. The center distance A of the car lifter is 27.8 mm, and the center distance of the non-modified meshing is 26.96 mm, , which obviously does not belong to this type of modification method. Angle modification can be divided into two methods: positive angle modification and negative angle modification. And each method can be divided into three cases, which can be distinguished according to the values of the modification coefficients of the two meshing gears.
3.1.1 Positive Angle Modification Meshing
(1) Both and are positive values.
(2) is positive, and is zero.
(3) is positive, is negative, and .
3.1.2 Negative Angle Modification Meshing
(1) Both and are negative values.
(2) is zero, and is negative.
(3) is positive, is negative, and .
However, for height modification meshing, the center distance A of their meshing is the same as the center distance of the non-modified meshing, that is, . And the center distance A of the angle modification meshing is different from the center distance of the non-modified meshing. When , it is positive angle modification; when , it is negative angle modification. The types of modification meshing are shown in Table 2. It can be judged based on the values in Table 1 and the content in Table 2. That is, when , , and , the purpose is to avoid the angle modification meshing of root cutting, and .
| Right Gear’s Tooth Number Z1 | Tooth Number Sum of the Gear Pair Z1 + Z2 | Center Distance A | Modification Coefficient | Modification Method | Main Purpose |
|---|---|---|---|---|---|
| Z1 < 17 | Z1 + Z2 ≥ 34 | A = m/2(Z1 + Z2) | Height Modification | Avoid Root Cutting | |
| A ≠ m/2(Z1 + Z2) | Angle Modification | Avoid Root Cutting | |||
| Z1 + Z2 < 34 | A > m/2(Z1 + Z2) | Angle Modification | Avoid Root Cutting | ||
| Z1 > 17 | Z1 + Z2 > 34 | A = m/2(Z1 + Z2) | Height Modification | Improve Meshing Performance or Adjust Center Distance | |
| A ≠ m/2(Z1 + Z2) | Angle Modification | Improve Meshing Performance or Adjust Center Distance |
