GB/Z 6413.2-2003 Calculation method for the scuffing load capacity of cylindrical gears, bevel gears and hypoid gears Part 2: Integral temperature method
Some standard content:
ICS21.200
National Standard of the People's Republic of China
GB/Z6413.2—2003/IS0/TR13989-2:2000 replaces GB/T 6413—1986, GB/T11367-—1989Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears-Part 2 : Integral temperature method(ISO/TR 13989-2:2000, IDT)
2003-11-25 Issued
General Administration of Quality Supervision, Inspection and Quarantine of the People's Republic of China
2004-06-01 Implementation
GB/Z6413.2—2003/IS0/TR13989-2:2000GB/Z6413-2003 "Calculation method for the gluing load capacity of cylindrical, bevel and hypoid gears" is divided into two parts: Part 1: Flash temperature method;
Part 2: Integral temperature method.
This part is the second part of GB/Z6413-2003, corresponding to ISO/TR13989:2000 "Calculation method for the gluing load capacity of cylindrical, bevel and hypoid gears Part 2: Integral temperature method" (English version). This part is equivalent to ISO/TR13989-2:2000. For ease of use, this part has made the following editorial changes: - Modify some layout formats according to Chinese habits; - Use decimal point ', instead of comma ", " as decimal point; Delete the foreword and introduction of ISO/TR13989-2. GB/Z6413-2003 is divided into two parts. The following lists the ISO/TR corresponding to these two parts and the national standards to be replaced: Part 1: Flash temperature method (corresponding to ISO/TR13989 Part 1); Part 2: Integral temperature method (corresponding to ISO/TR13989 Part 2, replacing: GB/T6413-1986, GB/T 11367-1989).
Appendix A and Appendix B of this part are informative appendices. This part is under the jurisdiction of the National Technical Committee for Gear Standardization. Drafting unit of this part: Zhengzhou Machinery Research Institute. The main drafters of this part are Yang Xingyuan, Zhang Yuanguo, Wang Changlu, Wang Qi and Chen Aimin. The previous versions of the standards replaced by this part are: -GB/T6413—1986;
-GB/T 11367—1989.
G/Z6413.2—2003/S0/TR13989-2:2000 Introduction
For many years, there have been two calculation methods for the calculation of the gluing load capacity of cylindrical gears, bevel gears and quasi-double-purpose gears, namely the flash temperature method and the integral temperature method.
In 2000, IS0 released the two calculation methods in the form of IS0/TR (IS0/1R13989-1, 2). The flash temperature method is based on the change of contact temperature along the meshing line, and the integral temperature method is based on the weighted average of the contact temperature along the meshing line. This part of GB/Z6413 (integral temperature method) and GB/z6413.1 (flash temperature method) give roughly the same evaluation results on the risk of gear scuffing. Compared with the two methods, the integral temperature method is less sensitive to the presence of local temperature peaks. In gear devices, local temperature peaks usually exist in cases where the overlap is small or in contact near the base circle or other sensitive geometric parameters. 1 Scope
GB/Z6413.2—2003/IS0/TR13989-2:2000 Method for calculating the scuffing load capacity of cylindrical, bevel and hypoid gears
Part 2: Integral temperature method
This part of GB/Z6413 specifies the integral temperature method for calculating the scuffing load capacity of cylindrical, bevel and hypoid gears. 2 Normative references
The clauses in the following documents constitute the clauses of this part through reference to this part of GB/Z6413. For dated referenced documents, all subsequent amendments (excluding errata) 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, the latest versions are applicable to this part. GB/T1356-2001 Standard basic rack gears for general and heavy machinery (idt ISO53: 1998) GB/T 3374--1992 Basic terminology for gears (neq ISO/R 1122-1: 1983) GB/T3480-1997 Calculation method for load-bearing capacity of involute cylindrical gears (eqv ISO6336-1--6336-3: 1996) GB/T10062.1--2003 Calculation method for load-bearing capacity of sprocket gears Part 1: Overview and general influence factors (1SO10300-1.2001.IDT)
GB/T 10095, 1--2001
Precision of involute cylindrical gears Part 1: Definition and allowable values of tooth surface deviation on the same side of the gear teeth (idt ISO 1328-1:1997)
3 Terms, definitions, codes and units
3.1 Terms and definitions
According to the purpose of this part of GB/Z6413, the terms and definitions given in GB/T3374 are used. 3.2 Codes and units
Table 1 gives the codes used in this part of GB/Z6413. Table 1 Code and unit
Center distance
Equivalent center distance of equivalent cylindrical gear
Tooth width, take the smaller value of small wheel or large wheel
Effective tooth width of bonding
Specific heat capacity per unit volume
Single pair of teeth stiffness
Bond stiffness
Pitch circle diameter
Effective round circle diameter
Round circle diameter
Base diameter
N/(mm2?K)
N/(marn*μm)
N/(m-μm)
GB/T 10062. 1
Formula (46)
GB/T3480
GB/T3480
Formula (69)
Formula (70)
GB/Z 6413.2---2003/ISO/TR 13989-2 :2000
Ch.Ca,Cah
Tooth width midpoint diameter
Pitch circle diameter of equivalent staggered helical gearPitch circle diameter of equivalent cylindrical gear
Pre-circle diameter of equivalent cylindrical gear
Base circle diameter of equivalent cylindrical gear
Meshing part of meshing line between small wheel and large wheel
Meshing part of meshing line between small wheel and large wheel
Slip coefficient
Tooth addendum module at midpoint of tooth width of male hyperboloid gear
Normal module at midpoint of tooth width of male hyperboloid gearNormal module of equivalent staggered helical gear
Number of phase gears
Normal base circle pitch
Tooth ratio
Tooth ratio of equivalent cylindrical gear| |tt||Pitch circle linear speed
Tangential speed of small wheel and large wheel of hypoid gearMaximum sliding speed of small wheel tooth
Node sliding speed
Sliding speed
Sliding speed
Sliding speed
Table 1 (continued)
Tangential speed of bevel gear tooth width at midpoint on pitch coneSum of node tangential speeds
Tangential speed
Tangential speed
Unit gear tooth load, glued
Number of teeth of equivalent cylindrical gear
Heat erosion coefficient
Weighting coefficient
Nominal tooth tip relief
Effective tooth tip relief
Elastic modulus (Young's modulus)
N/(mm + S? + K)
Formula ((68)
GB/T 10062. 1
GB/T 10062. 1
GB/T 10062.1
武(90)(91)
武(90), Style(91)
武(62)
武(73)
武(7 4)
GB/T10062.1
contains (77), formula (78)
武(83)
武(82)
武(84),Formula (85)
Formula (87)
Formula (2) (47) Formula (81)
武(79)
武(80)
武(4)
GB/T 10062. 1
Formula (12)
Formula (37), Formula (38), Formula (49)
Table 1 (continued)
Nominal tangential load on the pitch cone at the midpoint of the tooth widthNormal gear tooth load
Nominal tangential load on the pitch circle
Service factor
Dynamic load factor
Tooth load distribution factor for calculation of glued load capacityTooth load distribution factor for calculation of glued load capacityHelix load distribution factor for calculation of glued load capacitySupport factor
Tooth load distribution factor for calculation of contact strengthTooth load distribution factor for calculation of contact strengthSupport factor
Contact parameters
Arithmetic mean roughness
Glue Safety factor for calculation of combined load-bearing capacity
Minimum safety factor for calculation of glued load-bearing capacityTorque of small wheel
Gluing torque of test small wheel
Geometry coefficient of small wheel tooth tip
Running-in coefficient
Tooth tip relief coefficient
Geometric coefficient of hypoid gear
Lubricant coefficient
Heat flash coefficient
Meshing coefficient
Roughness coefficient
Lubrication method coefficient
Welding coefficient of actual gear material
Welding coefficient of test gear
Relative welding coefficient
Meshing coefficient
Pressure angle coefficient
Contact coefficient
GB/Z 6413.22003/IS0/TR 13989-2:2000 unit
Formula (51)
GB/T 3480,GB/T 10062. 1
GB/T 3480,GB/T 10062. 1
6. 2. 4,GB/T 3480,
GB/T 10062. 1
GB/T 3480:
GB/T 10062. 1,6. 2. 4
Formula (52), Formula (53)
Formula (5),6.2.4,6.3.5
GB/T 3480,GB/T 10062. 1
GB/T 3480,GB/T 10062. 1
GB/T10062.1
Formula (55)
Formula (6)
Formula (14)
Formula (96)
Formula (22)
Formula (8)
Formula (32)
Formula (54) || tt | 6413.2—2003/IS0/TR 13989-2:2000 generation
Pratne
Pressure angle
Normal pressure angle at midpoint of tooth width of hypoid gearNormal pressure angle
Normal pressure angle of staggered helical gear
Face pressure angle of staggered helical gear
Face pressure angle
Face meshing angle
Face pressure angle of equivalent cylindrical gear||tt| |Any angle
Helix angle
Base circle helix angle
Table 1 (continued)
Helix angle of the midpoint of the tooth width of the hyperbolic gear on the pitching coneEquivalent helical angle of the staggered axis helical gear
Pitching cone angle
Meshing overlap
Meshing overlap
Equivalent overlapping in the normal section of the staggered axis helical gearSmall gear tooth height contact
Large gear Tooth tip height overlap
Overlap
End face overlap of equivalent cylindrical gear
Tooth tip overlap of equivalent cylindrical small wheel
Tooth tip overlap of equivalent cylindrical large wheel
Hertz auxiliary coefficient
Average friction factor
Dynamic viscosity at oil temperature
Thermal conductivity
Poisson's ratio
Kinematic viscosity of oil at 40℃
Radius of curvature at the tooth of small wheel and large wheel
Relative radius of curvature at the node in the normal section
Radius of curvature at the node in the normal section
Relative radius of curvature at the node
Hertz auxiliary Cai number
N/(sK)
mm\/s;cSt
Formula (63)
Formula (66)
GB/T 10062. 1
Formula (67), Formula (71)
Formula (63)
武 (86)
Formula (28), Wu (29)
Formula (28 ), formula (29)
formula (92), formula (93)
formula (30)
formula (31)
formula (45)
GB/T 10062. 1
GB/T 10062. 1
GB/T 10062. 1
Figure 7, Formula (57), Formula (59)
Formula (1), Formula (1a)
Formula (23), Formula (24)
Formula (76)
Formula (75)
Formula (3)
Figure 7, Formula (58), Formula (60)
@ainth
Subscript:
Hertz auxiliary angle
Flash temperature of pinion tooth top when load distribution is ignored
Average flash temperature of hyperbolic gear
Integral overflow
Allowable integral temperature
Bond integral temperature (allowable integral temperature )Average flash temperature of test gear
Oil pool or oil injection temperature
Body temperature
Test body temperature
Equivalent staggered axis helical gear axis angle
Equivalent staggered axis helical gear staggered angle
Run-in level
Parameters on the meshing line
Small wheel;
2---Large wheel
Equivalent gear item circle diameter:
b-Base circle of equivalent gear;
Midpoint of the width of bevel gear or hypoid gear: normal section;
Equivalent staggered axis helical gear;
?Tangent direction:
-Test gear.
Application range
Table 1 (continued)
GB/Z6413.2--2003/1SO/TR13989-2:2000Unit
Formula (56) to (60)
Formula (19)
Formula (18)
Formula (50)
Formula (17)
Formula (16)
Formula (94)
Formula (96)Formula (99)Formula (1 01)
Formula (20)
Formula (95), Formula (98), Formula (100)Formula (72)
Formula (65)
Formula (65)
Formula (10)
This calculation method is based on the bench test results of gears running at a pitch line speed of less than 80m/s. These formulas can be used for gears running at higher speeds, but the uncertainty increases with the increase in speed. The uncertainty is greater when the speed exceeds the range of test conditions. 4.1 Scuffing Damage
Once scuffing damage occurs, it will lead to serious damage to the gear tooth surface with the increase of power loss, dynamic load, noise and wear. If the severity of the operating conditions is not improved, it will also cause the gear teeth to break. In the scuffing caused by instantaneous overload, as the load is quickly reduced, that is, the load is redistributed, the tooth surface can be self-repaired to a certain extent. Even so, the residual damage will continue to be a cause of increased power loss, dynamic load and noise. In most cases, the use of lubricants with enhanced EP (extreme pressure) properties can improve the anti-scuffing ability of gears. However, it is important to be aware of some of the disadvantages of using EP oil: copper corrosion, embrittlement of elastic materials, and lack of global compatibility. When selecting the best lubricant, these unfavorable factors should be taken into account, and the amount of additives should be as small as possible while meeting the minimum addition amount. 5
GB/Z 6413.2--2003/ISO/TR 13989-2:2000 Due to the constantly changing parameters, the complexity of the chemical properties and the thermo-hydro-elastic effects in the transient contact zone, some discreteness must be expected when evaluating the probability of galling. In contrast to the relatively long time it takes for fatigue damage to develop, a single transient overload can produce severe galling damage, rendering the gear unusable. This should be carefully considered when selecting the appropriate safety factor for the gear, especially for gears required to operate at high peripheral speeds.
4.2 Integral temperature criterion
The present method for evaluating the probability of galling is based on the assumption that galling may occur when the mean value of the contact temperature along the meshing line equals or exceeds a corresponding "critical value". In the method given here, the integral temperature is the sum of the weighted average of the bulk temperature and the integrated value of the flash temperature along the meshing line. The bulk temperature is calculated in accordance with 6.1.5, and the mean value of the flash temperature is approximately replaced by the friction factor and the dynamic load along the meshing line. The weighting factor is quoted to take into account the possible different effects of the actual bulk temperature and the mathematically integrated average flash temperature on the galling phenomenon. The probability of scuffing is evaluated by comparing the integrated temperature with the corresponding critical value obtained from gear tests of lubricants for anti-scuffing (e.g., various FZG test methods, IAE gear test and Ryder gear test) or from scuffed gears in operation. 5 Influencing factors
5.1 Average friction factor mce
The actual friction factor between the tooth surfaces is an instantaneous and local value, which depends on the properties of the oil, the roughness of the tooth surface, such as the position of unevenness left by machining, the characteristics of the tooth surface material, the tangential speed, the forces on the tooth surface and the geometric dimensions. The evaluation of the group friction factor is more difficult because there is currently no effective determination method. The average friction factor m along the meshing line can be obtained by measurement [1 and estimated by formula (1). Although the local friction factor is close to zero at the node C, when formula (1) is introduced, its average value can be roughly obtained by the parameters of the node and the viscosity of the oil. (WBr KBr ) 0. 2
tine = 0.045
. noil-0.05 . Xr. Xi
IUscPredc
The friction factor of the integral temperature method takes into account the size of the gear in a different way than the friction factor of the flash temperature method. Formula (1) for calculating the friction factor is only valid in the following ranges, e.g. for the friction factor for thermal power. 1 m/s≤w50 m/s
For pitch circle speeds below 1 m/s, the friction factor is higher. For pitch circle speeds above 50 m/s, the limit value Ux at u=50 m/s must be used in formula (1). WBt≥150 N/mm2
For unit normal tooth load zezt150 N/m, the limit value gt=150 N/mm must be used in formula (1). Ux -- 2 - w+ tana' - cosa.
Padc = {+u?·a. cosp.
1) This formula for the friction factor is derived from gear tests with a center distance a of 100 mm. [Fh/b 70.2
me = 0. 048
. Dou-0. 05 . Rao0.25 - Xi
V, Predc
Where:
For poly(z)glycol: X, 0.75
For mineral oil: XL=1.0:
For polyalphaolefin: Xt-0.8
For traction fluid: X=1.5
For phosphate ester: XL=1,3;
9** (3)
(la)
Formula (1a) shows the test results in the range of a=91.5~~200mm. When applying this formula, Figures 9, 10 and 11 regarding bonding temperature @ints must be adjusted accordingly.
GB/Z6413.2—2003/IS0/TR13989-2.2000TWBt = KA-Ky- KB·KBa \
KB is the helix load factor, and the bonding takes into account the increased friction due to the increase in total overlap (see Figure 1). Ky
US. US
For 2;
For 23.5:
For ≥3. 5:
Helical load factor KY
KBy 1
KBy= 1 +0.2. Ve,2) .(5e,)
Ra = 0. 5. (Rat+- Ra)
Total roughness E
（5）
Ra1 and Raz are the tooth surface roughness values measured on the machined new tooth surfaces of the small wheel and the large wheel (for example, the Ra value of the standard test gear is ~0.35μm).
XR — 2.2
Wherein: bZxz.net
For mineral oil: Xi=1.0;
For polyolefins: X.=0.8,
For non-water-soluble poly(ethylene) glycol: X0.7For water-soluble poly(ethylene) glycol: X,0.6; For traction fluid: X=1.5;
For phosphate esters: X,=1.3.
5.2Run-in coefficient XE
The existing calculation method assumes that the gear has been well run-in. In fact, bonding damage often occurs within a few hours at the beginning of operation, for example: when the gearbox is tested under full load during inspection or when a pair of new gears are installed in production equipment, the gears are operated under full load conditions before proper running-in. Research [1] shows that the load capacity of a newly processed tooth surface is 1/4 to 1/3 of that of a properly run-in tooth surface, which is considered by a run-in coefficient Xe = 1+(1-).30.Ra
Where:
d=1, fully run-in (for carburized, braided and ground gears, if Rarunin=0.6Ranew, it can be confirmed to be fully run-in); GB/Z6413.2-2003/IS0/TR13989-2:2000e-0, newly processed.
5.3 Thermal flash coefficient XM
The thermal flash coefficient XM takes into account the influence of the material properties of the small wheel and the large wheel on the flash temperature. Calculation of the thermal flash coefficient at any point (symbol y) on the meshing line (see Figure 2): O
Top circle 1;
Top circle 2.
Parameters on the meshing line in Figure 2 r
VI+r)+
BM - V(1+F)+Bm2
If the material of the small wheel and the large wheel is the same, formula (9) can be simplified to: F0.25
Xm = (1 --A)0.25 . BM
In the above formula, the thermal meshing coefficient Bm is:
Bm = (Am C))
For case-hardened steel, it has the following typical characteristic values: ^m=50 N/(s · K),C,-3.8 N/(mm2 . K),E=206 000 N/mm2 and v=0.3 then
Xms -50.0 K·N- 0.75 s0.5 ·m-0.5.mm
For the characteristic values of other materials, see [7]. 5.4 Pressure angle coefficient X
Pressure angle coefficient X. It is used to consider the conversion of load and tangential speed on the pitch circle to the coefficient on the pitch circle. Method A: Coefficient Xaβ-A
Xxp A=1. 22 . (sino2αi :.coso 28α.: coso*25 )(coso.5α, coso.5 αt)
（10）
（11）
（12）
（13）
Table 2 shows the pressure angle coefficient values of standard racks with a pressure angle of αn=20°, the standard meshing angle α, and the commonly used 8
range of the helix angle β.
GB/Z6413.2—2003/ISO/TR13989-2:2000 Table 2 Method: Coefficient X-8
For gears with a normal pressure angle of α-20°, as an approximate consideration, the pressure angle coefficient can be approximated as: Xa 1
6 Calculation
6.1 Column gears
β-30°
This part of GB/Z6413 contains formulae for assessing the "probability of scuffing" (thermal scuffing) of oil-lubricated involute spur and helical gears.
It is assumed that the entire tangential load is equally distributed between the two helical lines of the double helical gear. This is not the case when there are forces such as external axial forces, the effects of which must be taken into account separately. The two helical lines should be treated as parallel single helical gears. A quantitative assessment can be made of the various factors affecting the probability of scuffing. These formulae are applicable to gears with external or internal teeth meshing with the basic rack specified in GB/T1356. For internally meshing gears, negative values must be introduced when determining the geometrical factor X given in 6.1.10. They may also be considered applicable to similar gears conforming to other basic racks with an end contact ratio of E ≤ 2.5. 6.1.1 Safety factor Su for the calculation of the gluing load capacity When uncertainties and inaccuracies in the assumptions cannot be excluded, it is necessary to introduce a safety factor Sms. It must be pointed out that the safety factor for the calculation of the gluing load capacity is temperature-dependent and not a factor that is multiplied by the gear torque so that the integral temperature m and the gluing integral temperature ?ms reach the same value. Recommendations for the selection of
Ssmn:
Ssnin<1 High risk of gluing.
Bnts ≥ Ssmin
.(14)
1≤Ssmin=2, critical range with medium risk of gluing, affected by the actual gear working conditions. Influencing factors include, for example, tooth surface roughness, running-in effect, accurate understanding of the load factor, load-bearing capacity of the lubricant, etc. Ssmin>2, low risk of gluing.
To give the relationship between the actual load and the integral temperature number, the corresponding load safety factor Ss can be approximately obtained by the following formula: Ss
6.1.2 Allowable integral temperature
@ins Oo
@in - @oil
++++++++++
(15）
( 16 )
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