GB/Z 6413.1-2003 Calculation method for the scuffing load capacity of cylindrical gears, bevel gears and hypoid gears Part 1: Flash temperature method
Some standard content:
GB/Z6413.1-2003/IS0/1R13989-1:2000 GB/Z6413-20034 cylindrical gear. Calculation method of the gluing load capacity of bevel gears and hypoid gears" is divided into two parts: Part 1: Flash temperature method:
Part 2: Integral temperature method.
This part is the first part of GB/Z6413, corresponding to IS0/TR13989:2000 "Calculation method of the gluing load capacity of cylindrical gears, bevel gears and hypoid gears Part 1: Internal temperature method (English version). This part is equivalent to 1S/TR13989-1:2000. For the convenience of use, this part has been edited as follows: some formatting formats have been modified according to Chinese habits: - the decimal point "*" has been used instead of the "" as a decimal point, and the foreword and introduction of ISC/TR13989-1 have been deleted. GB/Z6413 is divided into two parts. The corresponding ISO/TR of these two parts and the national standards to be replaced are listed on the following page: Part 1: Flash temperature method (corresponding to ISO/TR13989-1): - Part 2: Integral temperature method (corresponding to ISO/TR13989-2, replacing: GR/T6413-1986, GB/T11367-1989)
Appendix A and Appendix B of this part are informative appendices. This part was proposed by the China Machinery Industry Federation and was issued by the National Technical Committee for Gear Standardization. The drafting unit of this part: Zhengzhou Machinery Research Institute. This part is drafted by Wang Qi, Zhang Yuanguo, Chen Aimin, Yang Xingyuan, GB/Z6413.1-2003/S0/TR13989-1:2000 Introduction
For many years, there have been two calculation methods for the calculation of the scuffing load capacity of cylindrical gears, bevel gears and hypoid gears, namely the flash temperature method and the integral temperature method.
In 2000, ISO published the two calculation methods in the form of ISO/TR (ISO/TR13989-12). The flash temperature method is based on the contact temperature variation along the meshing line, and the integral temperature method is based on the mean of the contact temperature along the meshing line. The evaluation results of the scuffing risk of gears in this part of GB/Z6413 (flash temperature method) and GR/26113.2 (integral temperature method) are roughly the same. Compared with the two methods, the integral temperature method is less sensitive to the situation where there is a peripheral temperature peak. In gear assemblies, local temperature peaks usually occur in cases where the overlap is small or where the contact is close to the base circle and where other sensitive geometric parameters exist. 1 Scope
GB/Z 6413.1—2003/ISO/TR 13989-1:2000 Methods for calculating the scuffing load capacity of cylindrical, bevel and hypoid gears
Part 1: Flash temperature method
GB/Z.6413 This part specifies methods and formulas for evaluating the risk of scuffing based on the concept of the Brook contact temperature. Brook's basic concept applies to all machine parts with moving contact areas. The internal temperature formula is valid for operating conditions characterized by banded or nearly banded Hertzian contact areas and sufficiently high Peclet numbers. 2 Normative references
The clauses in the following documents become clauses of this part through reference in this part of GB/Z 6413. For any dated referenced documents, their subsequent amendments or revisions are not applicable to this part. However, parties to agreements based on this part are encouraged to study whether the latest versions of these documents can be used. For undated referenced documents, their latest versions are applicable to the date or part. GB/T 3374—1992 Basic terminology of gears (neg ISO/R 1122-1:1983) GB/3480--1997 Calculation method for the load-bearing capacity of involute cylindrical gears (eqTSO6336-1--6336-3:1996) GB/T3481-1997 Gear tooth wear and damage terminology (idt ISO10825:1995) GB/T10062.1-2003 Calculation method for the load-bearing capacity of bevel gears Part 1: Overview and general influence factors (ISO10300-1:2001, DT)
3 Terms, definitions, codes and units
3.1 Terms and definitions
The terms and definitions given in GB/T3374 and GB/T3481 apply to this part. 3.2 Codes and units
The codes used in this standard are shown in Table 1. According to the usual number method, length units are used in meters, meters and micrometers. For the coordination of the system, the units of BM, and X are suitable for the mixed use of meters and millimeters or millimeters and micrometers. Table 1 Codes and units
Center distance
Tooth width, the smaller of the large and small wheels
Effective tooth width
Hertz contact area width - half
Thermal contact coefficient
Thermal contact coefficient of small wheels
Thermal contact coefficient of large wheels
Tooth tip margin of small wheels
Tooth tip margin of large wheels
N/(mn2 - nih - t*-K)
N/(mmnl+m+8+ K)
. staK)
Formula (Figure) Number
Formula (11)
Formula (12)
Formula (A.1a)
Formula (3)
Formula (3)
Formula (48)
Formula (46)
GB/Z 6413.1—2003/IS0/TR 13989-1:2000 Code
Optimum tooth trim
Appropriate tooth tip trim of small wheel
Appropriate tooth tip trim of large wheel
Tooth root trim of small wheel
Tooth root trim of large wheel
Specific heat per unit mass of small wheel
Specific heat per unit mass of large wheel
Meshing stiffness
Pitch circle diameter of small wheel
Pitch diameter of large wheel
Gear circumference diameter of small wheel
Gear circumference diameter of large wheel
Elastic modulus of small wheel
Elastic modulus of large wheel
Equivalent elastic modulus
External axial load
Normal load in grinding test
Nominal load Force
Auxiliary parameters
Auxiliary parameters
Height of tooth top at midpoint of tooth width of pinion
Top quotient of concave top at midpoint of tooth width of gear
Service coefficient
Tooth load distribution coefficient for calculation of bonding load capacityBite ratioTooth load distribution coefficient for calculation of load capacityTooth load distribution coefficient for calculation of contact strengthTooth load distribution coefficient for calculation of contact strengthBranch coefficient
Dynamic load coefficient
Normal module
Speed of pinion
Number of meshing branches
Minor cleat number of small wheel material
Ammonium cleat number of large wheel material
Wall quality grade
Table 1 (continued)
J/(kg·K>
J/(kg - K)
N/(mm*μm)
T/anint
Formula (Figure) No.
Formula (15. 2)
Formula (9)
Formula (10)
武(H. 1)
Formula (34)
Formula (35)
Formula (34)
Formula (35)
FormulaNumber of points
Li number of point T on the meshing line
Parameters of point DE on the meshing line
Parameters of point E on the meshing line
EF on the meshing line Parameters of point
Parameters of point EU on meshing line
Parameters of point M on meshing line
Parameters of any point on meshing line
Square angle of tangential velocity of small wheel
Direction angle of tangential velocity of large wheel
Cone angle of small wheel pitch
Large wheel pitch
End surface weight content
Longitudinal overlap
Absolute (dynamic) viscosity of lubricating oil at upper frying temperatureContact temperature
Maximum contact humidity
Table 1 (continued)
Public military (figure) number
Equation (30)
Equation (30)
Equation (34)
Equation (7)| |tt||Formula (29)
武 (18)
武 (49)
Formula (50)
Formula (21)||tt ||Formula (68)
Formula (66)
Formula (49)
Formula (a)
Formula (70)
Formula (3 2)
Formula (72)
Formula (67)
Play (24)
Formula (49)
Formula (85)|| tt||Formula (7)
Formula (37)
Formula (39)
Formula (76)
武(52)
Formula (27)
Wu (3)
Formula (1)
Physical temperature
Maximum flash humidity
Maximum flash disk overflow during the test
Body temperature
Body temperature of the contact surface
Oil humidity before meshing
Body temperature of the large wheel teeth
Body temperature during the test
Oil humidity before meshing
Adhesive temperature
Adhesive temperature for a long contact time
Thermal conductivity coefficient of the small wheel
Thermal conductivity coefficient of the large wheel
Relative factor of the ring test
Average friction coefficient
Poisson's law of the material of the small wheel Ratio
Poisson's ratio of large wheel material
Mount of small wheel material
Density of large wheel material
Relative radius of curvature at node
Curvature radius at any point of small wheel
Curvature radius at any point of large wheel
Sum of relative radius of curvature at any point
Axle intersection angle
Torsion angle of hollow sleeve shaft of gear
Glazing and wear
4.1 Generation of gluing and wear
Table 2 (continued)
CB/6413.1-—2003/1S0/TR13989-1.2000
N/(s+K)
N/(s· K>
Formula [Figure] No.
Formula ((22)
武(2)
Formula (94)
Formula 22)
Formula (1)
Formula (20)
Formula (20)
Formula (94)
Formula (22)bZxz.net
Formula (94)
Formula (97)
Formula (9)
Formula (10)||t t||Equation (3)
Wu (A.10)
Equation (A.10)
Or (9)
Equation (10)
Equation (25)
Equation (5)
Equation (A.15)
Equation (17)
When the gear teeth are completely separated by the lubricating oil film, there is no contact between the convex and concave surfaces of the two tooth surfaces, and there is usually no bonding and wear. At this time, the friction coefficient and are small. When the oil film is thicker; due to the sudden thermal instability [19], this special case of bonding damage is not discussed here.
When the elastic flow accompanied by the dynamic oil film is thin, the convex and concave surfaces of the tooth surface occasionally come into direct contact. As the thickness of the oil film decreases, the number of direct contacts increases accordingly, which may cause abrasive wear, adhesive wear or bonding. Abrasive wear is caused by the rolling action of the gear teeth or the presence of abrasive particles in the lubricating oil. Adhesive wear is caused by the initial partial bonding and subsequent separation, resulting in the transfer of material particles on one or two meshing gear teeth. If the abrasive wear or adhesive wear is slight and alleviated over time, it will cause damage to the gear technology as a normal running-in process. GB/Z 6413.1-2003/IS0/TR 13989-1:2000 is different from slight wear. Adhesion is a serious form of adhesive wear that can cause extended damage to gear teeth. Unlike pitting and fatigue fracture, which have obvious development periods, transient overloads can cause long-term adhesion. Excessive air intake or contamination in the lubricating oil, such as suspended metal particles or water, can also increase the risk of adhesion. After high-speed gears are bonded, they cause greater dynamic loads due to vibration. Vibration transmission can cause advanced adhesion, pitting, and broken tooth damage. In most cases, the use of lubricants with enhanced anti-seizing additives can improve the anti-seizing capacity of gears. However, it is important to be aware of some of the disadvantages of using anti-seizing additives: copper corrosion, embrittlement of elastic materials, and lack of global compatibility. This method is not suitable for evaluating cold seizing, which usually occurs on low-speed (pitch speed less than 4/), poor quality quenched and tempered heavy-duty gears. 4.2 Conversion The lubrication condition of more severe steel sliding contacts under operating conditions lubricated with liquid lubricants can be described by a conversion diagram [20, 21] [22] 23]. The conversion diagram shown in Figure 1 is applicable to contacts operating at a constant oil bath temperature. When the normal force F and the relative sliding speed are both below the AIS line, that is, in zone I of Figure 1, the lubrication condition can be characterized by a friction coefficient of approximately 0.1 and a unit loss rate (i.e., volume loss per unit normal force per unit moving distance) of 10-210-mm/(·m).
When the value of point S is not reached and the load increases into zone II, the transition into the second lubrication condition is achieved. The characteristics of this light wear lubrication condition can be expressed by a friction coefficient of about 0.3~-0.4 and a unit wear rate of 1-~5 ml/(V·m). 42
Light wear structure
=0. 25 -.. 0, 35
No cell loss or very slight foot
Gluing—\ or hatching data,
Relative sliding degree t/(m/s)
Figure 1 Reverse shape transition diagram with an example of calculating contact temperature If the load increases further, the transition into the second lubrication condition is achieved, which is called the blood zone with A2-S as the boundary line. The characteristics of this zone or can be expressed by a friction coefficient equal to 0.4-0.5. However, compared with the I and II zones, the wear rate is quite high from [00 to 1000m7 (N·m). The wear surface shows severe wear in the form of bonding. When the relative sliding speed exceeds the S point, if the load increases, it will directly switch from the I zone to the mountainous area. There is sufficient evidence to prove that the position of the A]SA3 line depends on the viscosity of the lubricating oil _21] and the contact pressure of [.207.2] 1. When F. and F. fall below this line at the same time, it is considered that a thin lubricating oil film is separated from the tooth surface, but this film is penetrated by the rough convex part. This situation is called "transboundary elastohydrodynamic lubrication" [21]. 1) When it is not explicitly stated that extreme pressure (EP>) oil is used, anti-adhesion lubrication is used. 6
CB/2.6413.1--2003/1S0/TR 13989-1:2000 In zone III, the oil film on the body completely loses its function. This area is the "initial adhesion" area [25]. There is evidence that the transition that occurs with the A2.S line as the boundary is related to the contact temperature reaching a critical value. This is the basic concept of Brooke. The given transition diagram is suitable for new components (contact with unoxidized steel), such as gears, wheels and driven parts. This transition network conforms to the results of the four-ball test and the column-and-beam test. The temperature range along the AI-5-A3 line (starting from the oil pool temperature, followed by the entire body temperature and the contact surface wood temperature) is: 28℃ at = 0.001m/s to 498℃ at % = 10m/s. This temperature behavior strongly indicates that at a constant contact or bulk temperature of the contact surface, the (boundary) elastohydrodynamic lubrication is not impaired, for example due to softening of the chemically adsorbent material. On the contrary: the significant reduction in load-carrying capacity with increasing sliding speed is attributed to a decrease in lubricity [L24].2627[2829] In contrast to the above, the calculated contact temperature of the curve A2-S-A3 tends to a constant value, i.e. about 500°C for (Cr15 steel, see Figure 1. This indicates that the transition from zone II to zone III is related to the different steel types, from slight adhesion to severe adhesion, which causes a change in the surface wear mechanism, possibly also including the thermoelastic instability mechanism [30]31]. Therefore, the results show that adhesion is related to the critical value of the contact temperature. For steel: when lubricated with mineral oil, the critical value is about 500°C. It is not dependent on the load. , speed and geometric parameters: 4.3 Friction at initial bonding
In the conversion diagram shown in Figure 1, during bonding, the friction factor is 0.25 or 0.5 = The corresponding contact temperature is about 500°C. This contact temperature is the sum of the measured body temperature of the contact surface 28 and the calculated flash temperature 470°C. The friction coefficient used in calculating the flash temperature is the friction factor before conversion, that is, 0.35. If this method is not used for column and ring experiments but also for gear transmission (in the design stage), when calculating the contact temperature The selection of critical values of the degree and the friction coefficient should be agreed upon.
The gear load capacity can be estimated as follows:
When using a friction coefficient of 0.5 - on the safe side - depending on the lubricant: When using a friction coefficient of μ=0.25 to μ=1.35, it is more accurate: ... Based on previous experience, under stable working conditions, the friction coefficient used is lower, and the limited contact temperature is correspondingly lower.
According to experience, for mineral oils without and with a small amount of additives, the contact temperature of each oil and rolling material is A combination has a critical bonding temperature. Usually, this temperature is fixed and is independent of the operating conditions, load, speed and geometric parameters. For example, for mineral oils with rat additives and some types of compound oils, the critical bonding temperature changes with the operating conditions of the device. Therefore, the critical temperature at this time must be determined by experiments simulating the operating conditions of the gear device. 5 Basic principles
5.1 Contact temperature
As stated in the introduction, the contact temperature is the sum of the bulk temperature of the contact surface @see 5.4 and the flash temperature @ (see .2). - @ +@
The variation of flash temperature along the contact trajectory is shown in Figure 2. The maximum contact temperature is:
where:
rm is the maximum, it is either on the meshing trajectory or on the meshing trajectory. +++-( 2)
The possibility of glueing can be predicted by comparing the calculated maximum contact temperature with its critical value. The critical value of the contact temperature can be determined by gear glueing experiments or by using on-site investigations. 7
GB/Z 6413.1—2003/1S0/TR 13989-1:2000 Positions on the meshing surface
Figure 2 Contact temperature along the contact path
For the practicable assessment of the risk of galling, it is important to use the exact value of the gear body temperature in the analysis. 5.2 Flash temperature formula
For (approximately) banded contact areas and tangential velocities in different directions (e.g. hypoid gears), the Bullock flash temperature formula [12-14[167[32] is the most commonly used expression, see Appendix A, namely: 9m = 1.11 a + Xr - X, · teumI Ve We
(u - sinY) +Lmg + V(rge+ sinr) For cylindrical and bevel gears with banded contact areas and parallel tangential velocities, the most commonly used expression is see Appendix A, namely: On - 1.11 Em - Xr . X. - reima.[ \1 — 2
Or use the equivalent expression:
Bm+(r:)+Bue+ V(u)
① = 2. 52m *
Average friction factor (see Chapter 6)1
[() . I Ven -Ven / u I
Veyrel
Thermoelastic coefficient (see Appendix A), for commonly used steels, X-50K·N-/1-s1/2.m.mn
Engagement coefficient (see Chapter 8):
Load sharing coefficient (see Chapter 9)
End unit load (see 5.3), in Newton per millimeter (V/mm); Pinion speed, in revolutions per minute (r/tnin): Local relative radius of curvature, in millimeters (mm); Pytel
Local radius of curvature of pinion tooth profile, in millimeters (mm) For cylindrical gears:
Local radius of curvature of large wheel tooth profile, in millimeters (mm): For cylindrical gears:
For bevel gears., and see equations 37) and (38). 8
I,.a.sinaw
（3）
.（5)
（6）
For more suitable expressions, see Appendix A,
GB/7. 6413.12003/1SO/TR 13989-1,2000The two Peclet numbers must be high enough to satisfy almost all possible bonding situations. When the Peclet number is low, heat flows from the contact zone to the entire gear tooth, causing different temperature distributions. At this time, equations (3) and (6) are particularly effective. P 5
Am siny,
bn eme ce 5
Where:
The density of the small wheel material is in grams per cubic k/; The density of the large wheel material is in grams per cubic meter (kg/m); The specific heat per unit mass of the small wheel is in joules per gram Kelvin/(kg·K); The specific heat per unit mass of the large wheel is in joules per kilogram Kelvin/kg·K; The conductivity of the small wheel is in Newtons per second Kelvin [N (s·K); The thermal conductivity of the large wheel is in Newtons per second Kelvin [N/(s·K)] For cylindrical gears and bevel gears sin=sin1. 5.3 Unit load on end face
Unit load on the end face of cylindrical gear:
WBi = KA· Ky· Ki· KzaK.upUnit load on the end face of bevel gear:
i Ka·Ky-Kw-Ko.Kup
Wherein:
F: - nominal stroke force on the pitch circle, in Newton); b
tooth width, in millimeters (mm);
bm—0.856
KA——application factor (for round support gears, see GB/T 3480, for dimensional gears, see GR/T 10062.J) K-dynamic load coefficient (for cylindrical gears, see (GB/T3480, for lower bevel gears, see GB/T10062.1) Kna
Tooth load distribution coefficient for calculation of bonding load capacity: K=Khe
Kea for round bar gears and hungry gears, see GB/T3480 and GB/T10062.1 respectively K
Tooth load distribution coefficient for calculation of bonding load capacity: Ka—Kuu
KH for cylindrical gears and bevel gears, see GB/T3480 and (B/I10062.1 respectively: Km branch coefficient.
--{ 11 }
(12）
（13)
（14)
-（15）
The branch coefficient K is the coefficient of uneven load distribution on each branch when considering multi-branch transmission. If no reliable analytical data is available, it can be determined by the following method:
For a pressure gear transmission with n. n3) planetary gears: Kn
1 +0.25 /m:3
.For a double gear with a hollow shaft torsion angle of worm (\) under full load: Km: = 1+(0.2/@)
For a double helical gear with an external auxiliary force of F: F
-1+F. tanp
.{[6 )
-( 17 )
GB/7 6413.1——2003/IS0/TR 13989-1:2000 For other cases:
5.4 Distribution of body temperature
The most important friction loss in gear transmission is the friction loss in the gear tooth meshing area. The main form of loss is heat loss caused by the friction of the gear teeth. The mechanical energy consumed by the excess oil supply side discharge cannot be ignored sometimes. The loss caused by the shaft series (rolling shaft or sliding bearing) is another unavoidable friction loss. For high-speed gear transmission, the heat generated by the sliding bearing may be much greater than the heat generated by the gear meshing. Other heat sources are the friction of the stirring oil and the oil seal. All the heat sources have the following common characteristics: For each heat source, the friction of the fluid depends on the viscosity of the lubricating oil under the respective operating conditions. The heat of all sources is related, through the transmission elements to the heat sink,Such as the surrounding air or cooling system. The heat sub-relationship can be calculated by the following methods: finite element method of discrete components:
diffusion diagram method,
thermal network analogy method "18.
The body temperature of the contact surface can be appropriately taken as the average value of the overall body temperature @ and M of the two connected gear teeth. The following formula is a more accurate approximate formula (when the Peclet number is high): Om Bu.-yuet +Ou: +Bu.+ WonOwBm. - Vugl + Bm. + Vog
When the ratio of Bw.Ve\ is within a wide range, it can be approximated by a simple mathematical average formula: BM2 - Vug?
(+@m）
When the flash temperature exceeds 150℃ for a long time, it may have an adverse effect on tooth surface fatigue. 5.5 Approximate approximation of body temperature
(20)
For a rough study of body temperature, the oil temperature (including some factors of heat transfer caused by oil injection lubrication) plus the part that determines the flash temperature is estimated by taking the maximum value. Sm = @a +0. 47x, Xn -rm
Where:
For oil injection lubrication: X. —1. 2;
For bath lubrication; X,=1:
For meshing with additional oil injection cooling: X,=1. ;For when the gear is immersed in oil to provide sufficient cooling: X. 02. For a small wheel meshing with a large wheel:
The average flash temperature along the contact path, in degrees Celsius (T): @dr.
+( 22 )
(23)
However, in order to reliably evaluate the danger of engagement, it is important to replace the rough approximation with the exact value of the gear body temperature in the analysis:
6 Friction factor
In a meshing cycle: Some factors that affect the friction between gear teeth change. There is relative motion between the two meshing concave surfaces, and the acceleration is uniform on the tooth surface, while the deceleration is uniform on the other tooth surface. Pure rolling is only at the node position, and at any other position 10
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