About Silicone Hot Water Bag:
Do you have a hot water bag for winter?Are you prepare it?Silicone Hot Water Bag is one of our silicone products.It's made fda silicone,it's heat resistant,and you don't worry it will hurt you.It have many styles in shape or design,you can give it to your friends as a gift.It's very suitable for girls and we can use if in winter.It's a amazing gift in winter.If you are interested in our Silicone Hot Water Bag,you can visit these fashionable design hot water bag such as Silicone Hot Water Bag,Hot Water Bag,Mini Hot Water Bag,Hot Bag Water,Water Hot Bag,Hot Water Bag Silicon.
Product introduction:
1.Product name:Silicone Hot Water Bag,Hot Water Bag,Mini Hot Water Bag,Hot Bag Water,Water Hot Bag,Hot Water Bag Silicon
2.Place of origin:Guangdong China
3.Color:any pantone color
4.Effect:Any effect according to customer's requirement
5.MOQ:500pcs.
6.Package:1 pcs/opp,customized design is available.
7.Design:Customized/stock
8.Certification:FDA,LFGB,SGS,ROHS,etc.
9.Usage:Use for keep warm
10.Silicone Hot Water Bag photos for reference.
Silicone Hot Water Bag,Hot Water Bag,Mini Hot Water Bag,Hot Bag Water,Water Hot Bag Dongguan OK Silicone Gift Co., Ltd. , https://www.dgsiliconebabyproducts.com
1 Introduction The clock gear is a small modulus gear. The tooth profile rarely uses an involute. Instead, it uses a tooth profile consisting of a circular arc and a straight line. This tooth profile is derived from the correction of the cycloid profile. In the processing of gears, but the process of this gear transmission is different from the traditional gear.
In the field of mechanical watches and clocks, the driving force for driving watches and clocks is derived from the elastic potential energy of the spring stock, and the power is transmitted to the speed governing mechanism through the speed increasing transmission, thereby controlling the precise travel time of the watch. In this transmission process, since the energy stored in the energy source is not large, high transmission efficiency is required. Therefore, it is of great significance to improve the transmission efficiency of the clock gear transmission.
2 The basic parameters of the gear tooth profile In the design process of the clock gear, the original parameters are: transmission ratio i21, center moment A and gear modulus m. From these original parameters, the number of teeth Z1 of the engaged wheel and the wheel can be determined. Z2, according to the relationship between the tooth shape parameters, the range of variation of the main parameters can be obtained.
For a pair of meshed timepiece gears, the main parameters refer to the four parameters that determine the tooth shape: the tooth tip arc radius Ï1 of the gear, the tooth tip arc radius Ï2 of the wheel, and the tooth tip circle center circle of the gear Radius rc1, the center circle radius rc2 of the tooth top circle of the 龆 wheel. For the timepiece gear, the center circle radius rc1 of the tooth top circle of the gear is smaller than the radius RD1 of the index circle, and the radius rc2 of the center circle circle of the tooth top circle of the 龆 wheel Slightly less than or equal to the radius of the index circle r2, the radius Ï1 and Ï2 of the tooth tips of the gear and the wheel are respectively smaller than the rc1 and rc2 of the center circle of the tooth top circle, and all four parameters are greater than 0, otherwise The structure is not shaped.
Efficiency of 3 timepiece gear transmission 3.1 Influence factors of gear transmission efficiency of a pair of clocks The transmission efficiency of a pair of clock gears mainly depends on two main factors: friction loss between gears, friction loss in the driven shaft and driven shaft support. When analyzing the transmission characteristics of the clock gear transmission, it is often only considered the friction loss between the teeth, but does not consider the friction loss in the shaft support, but in fact, for the engagement of a pair of teeth, the effect of these two frictions on the efficiency It cannot be ignored.
The above two factors are actually directly related to the tooth shape parameters. Therefore, selecting the appropriate tooth shape parameters can improve the theoretical transmission efficiency of the clock gear. Of course, in practice, gear transmission efficiency is also related to machining accuracy, tooth surface quality, center moment error and other factors, but in the end, these manufacturing errors can be fully converted to tooth shape changes.
3.2 Analysis of average transmission efficiency In general, the meshing section of the clock gear can be divided into two meshing sections (this is the most common meshing condition) regardless of the tooth tip participating in the meshing: the gear arc segment and the wheel arc Segment engagement; the gear arc segment meshes with the linear portion of the wheel. Due to the different directions of the frictional force, the gear arc segment and the 圆弧 wheel arc segment are usually meshed into the front line meshing and the center line rear meshing. Similar to the involute gear, different instantaneous transmission efficiency analytical formulas can be obtained according to different mechanism models.
Let the instantaneous transmission efficiency be η, the instantaneous work of the main and driven wheels be dW1, dW2, the main and driven wheel torques are M1 and M2, respectively, and the angular velocities of the main and driven wheels are ω1 and ω2, respectively.
η=dW1dW2=M2×ω2×dtM1×ω1×dt=M2M1×ω2ω1=ij21?
I21 (1) Therefore, as long as the instantaneous gear ratio i21 and the instantaneous torque ratio ij21 of different meshing stages are obtained, the instantaneous transmission efficiency analytical formula of each meshing section can be obtained.
Regardless of the friction loss in the journal support, let p1, m1, p2, m2, p3, and m3 be intermediate variables, and f be the friction coefficient between the teeth, as defined in the reference: The radius line of the center of the arc serves as a reference line indicating the meshing position, and the angle between the line and the center line is set to be the angle of engagement when the meshing is started, and the angle between the line and the center line is defined as the angle of engagement when the meshing is terminated.
Ψ1 and ψ2 respectively indicate the angle between the radius line of the center of the arc of the toothed tooth of the overbiting wheel and the center line when the tooth is engaged at the center line.
Ψj, ψc, ψ1, ψ2 then use the dichotomy programming to solve the transcendental equation to calculate the values. By substituting each value into the average efficiency calculation formula, an analytical formula of the average efficiency can be obtained.
However, according to the above analytical formula, the tooth shape parameter can not be solved at all, and there is no application value in practice. In this regard, this paper proposes a computer numerical calculation method, and selects the ideal close to the theoretical result within the effective range through computer programming and screening. Tooth shape.
3.3 Numerical calculation of maximum average transmission efficiency and tooth shape parameter optimization method Under the condition that there is no self-locking phenomenon during meshing, it is very important to study the average transmission efficiency. The best theoretical tooth profile can be obtained with the goal of maximizing the average transmission efficiency.
As mentioned above, when the original parameters i21, A and m of the clock gear transmission are determined, the basic tooth shape parameters Ï1, Ï2, rc1, rc2 of the timepiece gear have a certain range of variation, and these parameters can be varied within the range of their changes. A variety of different tooth shapes, using these tooth shape parameters to solve the intrusion angle, the exit angle and the various conversion angles, and then in the three intervals [ψj,ψ1], [ψ1,ψ2], [ψ2,ψc] respectively Taking a certain step size, the average efficiency of each segment is obtained by using the instantaneous efficiency of each segment, and then the average efficiency of the three segments is averaged to obtain the total average efficiency.
However, in the course of the engagement of the clock gear, there is a common situation that the entire meshing section ends before the gear has not reached the gear arc segment and the spur straight segment, that is, the meshing process has only two segments: the gear The arc segment and the circular arc segment mesh in front of the center line and mesh behind the center line. There is no mesh segment of the gear and the straight segment of the wheel. Therefore, it is necessary to judge whether the conversion angle ψ2 exists or not. The former method calculates the average efficiency, otherwise it is necessary to recalculate the entry angle and the exit angle according to another formula, and then simply calculate the total average in the above two ways [ψj,ψ1] and [ψ1,ψc]. effectiveness. Starting from this idea, within a certain range of calculation accuracy, a comprehensive scan of each tooth profile parameter can finally find a tooth profile parameter, which can meet the goal of maximum average efficiency. However, it is not enough to judge by the maximum average efficiency. Especially when the average efficiency is ideal, there may be a case where the instantaneous transmission efficiency is low or “zero†at a certain point during the whole meshing process. At this time, the entire transmission mechanism It is entirely possible to "self-lock" at this point and cannot drive. From a practical point of view, these self-locking points are usually located at the beginning of the meshing. In order to prevent this problem from occurring, in the numerical calculation of the average efficiency, it is necessary to avoid the points and intervals where the instantaneous efficiency is too low, and first exclude it. The whole process is to use the computer "sea selection" to get the appropriate tooth shape parameters, using C language programming.
4 fast approximation algorithm using the above calculation method to obtain the tooth shape that meets the engineering requirements, requires a lot of calculations, commonly used microcomputers may take dozens of hours of calculation, in order to speed up the calculation, this paper proposes a simple numerical calculation method, which guarantees In the case of calculation accuracy, the amount of calculation can be greatly reduced.
The guiding idea of ​​this calculation method is that the scanning step size of each parameter is set to the length of the interval of 1/10, and the average efficiency is calculated to obtain a set of data at the maximum efficiency. In the vicinity of the set of data, there is obviously the most efficient tooth profile. Use this set of data as the center point of each parameter reduction parameter, take the ±1/10 interval as the new parameter change interval, and use the 1/10 length of the new interval as the step size to scan the new interval to get the second time. Approximate data, after many similar approximation operations, the calculation accuracy can be close to 1/100 or even smaller of the parameter transformation interval, and the calculation time can be reduced by more than half, which is enough to meet the requirements of engineering calculation. The tooth shape parameter values ​​of the strip wheel and the two gears, the two wheel and the three toothed shaft, the three wheel and the second pinion, the second wheel and the escapement pinion are calculated by the optimization calculation method proposed in this paper. The tooth profile parameters and their average efficiency values, as well as the tooth profile parameters and average efficiency before and after optimization are listed in Table 1. Using the method proposed in this paper, the tooth profile parameters with higher transmission efficiency can be obtained more quickly (f take 0.2, f1, f2). Take 0.15).
6 Conclusion The optimization calculation method of basic tooth shape parameters of computer-based clock gears proposed in this paper is obtained by programming on the basis of the transmission efficiency analysis of the clock gear meshing transmission, and the teeth obtained by the optimization method are verified by examples. The gears formed by the shape parameters have higher transmission efficiency than the tooth shapes obtained by the conventional calculation method. This method is suitable for the optimization of various gears, and is not limited to the clock gears.
