DE4407696C2 - Helical gearbox with parameters of the gear geometry corrected for the operating temperature - Google Patents

Description

The invention relates to a spur gear after The preamble of claim 1.

In a known spur gear (G. Niemann H. Winter "Machine Elements" Volume II, second, completely revised edition, Correct reprint, Springer-Verlag Berlin Heidelberg New York Tokyo 1985, Sn. 84, 85) is the influence of heating on the operating backlash in determining the Zahndickenabmaße considered. Is used in this spur gear to Achieving a lower weight of a transmission housing Aluminum or magnesium cast used, are the opposite Steel or cast iron higher thermal expansions and their effect to pay attention to the bearings (p. 296).

From Dubbel "Taschenbuch für die Maschinenbau", 17th edition edition, 1990, Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona, Sn. G115 to G121 the gearing geometry in particular also the involute gearing for which a test area Lα by the "Operating instructions CNC-controlled gear measuring center PNC 40 - Fully automatic CNC controlled gear measuring center  PNC 40 VA "from KLINGELNBERG; Klingelnberg Söhne Remscheid Werk Hückeswagen 88.02 Sheet "Calculation of rolling path and rolling angle" is defined.

In spur gearboxes of the type mentioned flan occur kenschäden, which are a consequence of the "flash temperature". In DIN 3990, to avoid this flank damage, a Flank correction proposed in the form of a head cancellation. It However, it has been shown that this measure is not sufficient is.

The object underlying the invention is therein, in a spur gear of the aforementioned Type to avoid the occurrence of flank damage more effectively.

The explained problem is in an advantageous manner with the kenn characterizing features of claim 1.

In the spur gear according to the invention results in Normal temperature a head drop involute, d. h., the flank lines Angular deviation fHα of the involute has a negative Value - and this is also the state of manufacture. In order to be slightly disturbed engagement conditions at normal temperature accepted. By heating the transmission to the operating temperature the involute changes so that under these conditions a rolling without interference interference is present.

By the invention, the life of the Stirnrädergetriebes increased, so that warranty and goodwill costs are reduced.

Details of the invention will become apparent from the following Description in connection with the drawing. In the drawing mean

Fig. 1 is a schematic representation of the invention, relevant parameters of the tooth geometry of a gear pair with involute teeth of a spur gear train at room temperature,

FIG. 2 shows the toothing geometry of FIG. 1 at operating temperature, and FIG

Fig. 3 is a schematic comparison of the edge engagement at room temperature on the one hand and operating temperature on the other hand, the tooth geometry of Fig. 1 on an enlarged scale.

Under the influence of temperature many physical changes Sizes such. B. the dimensions of the body.

Solid bodies expand proportionally with increasing temperature out. The extent depends on the type of substance and from the temperature increase d. H. Temperature difference.

From the thermodynamics is for the linear expansion of a body the following dependency is known:

δ 1 = α _* l1 _* Δt

in which:

δ t = t1-t2 temperature difference
l1 = length of the body at temperature t1,
l2 = length of the body at temperature t2,
δ 1 = l1-l2 change in length,
α = substance-dependent expansion coefficient.

The expansion with increasing temperature must be where larger Temperature fluctuations occur, be taken into account.

When using different materials you have to do it yourself pay attention to the different coefficients of expansion.

The known gearbox calculations refer to the space temperature. The influence of the operating temperature is at these theoretically neglected. Measurements on used gearboxes  gave operating temperatures of 130 ° C to 160 ° C, d. H. a considerable Temperature difference of about 110 ° C compared to room temperature.

The drawing quality of the gears and housing yields in the gearbox used an optimal rolling of the gear pairs. The dimensional changes under temperature influence but not considered.

Under drawing quality, the theoretically determined or Calculated quality class of the teeth of wheels and shafts understood, with respect to the housing, the axial distance a Relevant feature for the intervention conditions of a or more pairs of wheels.  

If the bends, Zahnschränkungen etc. neglected and only the changes in the transmission under temperature fluctuation analyzed, it follows:

• - the change of the base circle diameter  
• - the change of the axial distance by two factors:
  • a) linear change of the housing center distance
  • b) dimensional change of the distance between the mounted axles.

The change of the bearing distance is then important, if for Gears and housing different materials with under different coefficients of expansion are used, such. B. Steel and aluminum and in addition, if in storage the Shafts tapered roller bearings are used. The difference between Aluminum housing and steel shaft leads to an axial play of the shaft in the case.

If the axle bearings with tapered roller bearings, then it works Axial clearance due to the taper angle of tapered roller bearings in Ratio 1: 4 or 1: 3 in the radial play.

The comparison of the operating angle of a pair of wheels at different temperatures leads considering all dimensional changes to changes in this Wälz-Parame ters.

Thus, a change in the engagement conditions under Tem peratureinfluß be observed (graphical representation of the edge engagement F1 / F2 at room temperature and the edge engagement F'1 / F'2 at operating temperature in Fig. 3).

In particular, it should be noted that the two we Significant influencing factors, base circle and Achsabstandsverände partially offset, d. H. they do not always work negative on the meshing conditions of the pair of wheels.

As already mentioned, the center distance of the gear changes with an aluminum housing by two influencing factors namely:

1. Linear axle distance change under temperature influence

δ 1 = α _*

l1 _*

δ t

δ t = 110 ° C (temperature difference between room and operating temperature)
α = 23.9 _* 10 ^-6 l / ° C (coefficient of expansion for aluminum)
l1 = 152 mm (center distance in housing)

The axial distance thus changes mathematically / theoretically by:

w l = 0.399 mm

2. Achsabstandsveränderung by the axial play or radial play

In an axial play α la, due to the difference in length of the Thermal expansion of the housing and the shaft in the axial direction, results in a radial play δ r of:

δ r = δ la _* tan τ

τ = cone angle of tapered roller bearings

Practically this means that from an axial play normally with the factor about 1: 3 a radial play results. When using From an aluminum housing, other tapered roller bearings built-in and this results in a factor of about 1: 4.

Practical procedure:

δ la = δ Ig - δ lw

δ la - axial play
δ lG - Length of the housing
δ lw - linear expansion of the shaft

δ lG = αa _* lG δ t

αa = 23.9 _* 10 ^-6 l / ° C (coefficient of expansion for aluminum)
LG = 498 mm

δ lw = αw _* lw _* δ t
αw = 11.5 _* 10 ^-6 l / ° C (coefficient of expansion for steel)
lw = 509 mm

δ la = 1.309 - 0.644 = 0.665 mm

δ r1 = ¼ _* δ la

δ r1 - radial clearance in the bearing

δ r1 = 0.166 mm

The effective radial clearance corresponds to the length ratios zwi the position of the gearing and the bearing distance, d. H.:

δ r = 0.109 mm

3. Total axle distance change

If the axial play or radial play of both the main and considered the countershaft, then you get the following ge total center distance change:

δ a = δ l + 2 _* δ r
δ a = 0.617 mm

The change of the basic circle of the wheel pair is a linear Län range and is calculated using the formula:

δ db = α _* db _* δ t

in which:

α = 11.5 _* 10 ^-6 l / ° C (coefficient of expansion for steel).

The wheel pair examined in the gearbox has the characteristics:

- for helical gear I db1 = 133.726 mm Z1 = 24 - for helical gear II db2 = 139.298 mm z2 = z25 - helix angle β = 22 °

At a temperature difference δ t = 110 ° C, the following reason Circular changes calculated:

δ db1 = 0.169 mm
δ db2 = 0.176 mm

Following are parameters from the gearing calculation listed, in fact:

1. operating engagement angle αwt

db1, 2 - basic circuits
a - Center distance

2nd prong engagement angle αt

α - pressure angle
β - helix angle
βb - helix angle in the base circle

3. Pressure angle deviation fα

fHα - profile angle deviation
Lα - profile testing area

4. base circle deviation fb

For the analysis of the meshing conditions of the pair of wheels two groups of parameters formed namely:

The following relationships exist between the parameters of both groups relationships:

d'b1 = db1 + δdb1
d'b2 = db2 + δdb2
a2 = a1 + δ a

The operating angle at room and operating temperature is thus:

In the equation of the operating engagement angle at Be operating temperature replaced the characteristics d'b1, d'b2 and a2, then this leads to the following relation:

Simplified written:

Under the influence of the temperature fluctuation thus finds a Change in the engagement of the wheel pair instead. Consistent operating angle and hereby also identical rolling ratios are in the investigated case, i. H. aluminum Housing and steel wheels only theoretically possible, especially handy a complete compensation of the two influencing factors not can be done.

The change in the operational engagement angle may be due to the Value of the factor k.

It follows that the base circle for optimum design Operating temperature is less than that on the basis of a room temperature calculated theoretical base circle.

In this case, the design diameter is larger than the calculated on the basis of a room temperature theoretical base circle.

The calculations do not necessarily have to change the Basic circle lead. The same effect can be with a new be calculated pressure angle can be achieved.

C. If the value of the coefficient k = 1, then it changes the operating engagement angle is not under the influence of Be operating temperature, d. H. the rolling of the gears is optimal.

It is estimated that the vehicle transmission works 90% of its value Service life at operating temperature. Taking into account the dimensional Changes in the gearing characteristics, so festge provides that the pairs of wheels in known transmissions only at Room temperature, d. H. optimally circulate approx. 10% of the service life.

So that the pairs of wheels at operating temperature with the calculated ten engagement conditions with respect to load transfer and Ge deceleration, a gearbox design at Be operating temperature according to the teaching of claim proposed.

Example of the gearbox design at operating temperature

The example relates to a pair of wheels with an aluminum gear housing with tapered roller bearings. The operating temperature is 130 ° C and the room temperature is 20 ° C.

The center distance at 20 ° C is

a₁ = 152 mm

and at operating temperature

a₂ = 152.617 mm.

The helix angle in the pitch circle is β = 22 ° for the wheel pair (wheel and pinion). The following parameters are available for the pair of wheels:

module m = 5.55 Wheel: @ Base diameter d _b1 = 133.726 mm number of teeth Z₁ = 24 Pinion: @ Base diameter d _b2 = 139.298 mm number of teeth Z₂ = 25

At operating temperature, the wheels expand and become the base circuits the following values are determined.

At the wheel:

d ' _b1 = d _b1 + δd _b1 = d _b1 + (α × d _b1 × δ _t )

in which

α = 11.5 × 10 ^-6 1 / ° C
δ _t = 110 ° C
d ' _b1 = 133.726 + 0.169 = 133.895 mm

When pinion:

d ' _b2 = d _b2 + δd _b2 = d _b2 + (α × d _b2 × δ₁)

in which

α = 11.5 × 10 ^-6 1 / ° C
δ₁ = 110 ° C
d ' _b2 = 139.298 + 0.176 = 139.474 mm

The operating angle is given by the formula

calculated.

This results in:

• - at room temperature
• - At operating temperature, the then applicable values for basic circle and center distance are used.

The factor k is calculated using the formula:

If k ≠ 1, there are disturbed engagement conditions. To an undisturbed rolling behavior of the pair of wheels to reach the operating temperature, must wheel and Pinion corrected or retained.  

The difference in the operating angle of engagement at the different temperatures is thus:

δα _w1 = 26.414 - 26.089 = 0.325 °

The operating engagement angle characterizes a pair of wheels and its rolling behavior. In order to make the engagement conditions optimal, δα _{wt is assigned to them} in the ratio of the basic circle of wheel and pinion.

In the example ≈ 1 and therefore δα for the optimization of the wheel _wt / 2 and associated with the optimization of the pinion also δα _wt / 2.

The prewarning angle at operating temperature becomes the formula

and at room temperature with the formula

calculated.

The following values are determined:

• - at room temperature
• - at operating temperature

The pressure angle is determined from the formula: tanα = tanα cosβ × _t calculated.

The values are:

• at room temperature tanα₁ = tan α _t1 = cosβ = tan 21.433 x cos 22 °
  = 0.39256028 × 0.92718355
  = 0.363975554
  α₁ = 20 °
• - at operating temperature tanα₃ = tanα _t3 × cosβ
  = tan 21,635 × cos 22 °
  = 0.396634804 × 0.927183855
  = 0.367753386
  α₃ = 20.191 °

If the variant or solution sought with a modified pressure angle is, then the provision of the tooth profile should be done with this pressure angle or the tools for wheel and pinion must be designed with this pressure angle become.

But if you want to work with standardized tools (pressure angle = 20 °), then the profile correction takes place via the base circle. The optimization effect for the rolling behavior is the same. For this purpose, the pressure _angle deviation f _α with the formula

f _α = α _is - α _soll

determined. In the present case this means:

f _α = 20.191 - 20 = 0.191 °
or
f _α = 3.333 mrad

From the formula

the profile angle deviation f _{H α is} determined (see page 8).

The profile test area for the wheel is determined from the following known formula:

From the formula

the base circle deviation is calculated. For the wheel this gives the following value:

If there is a negative value for f _{H a} , this means that the base circle diameter for finishing the tooth flanks must be smaller than the predetermined value.

d _{b (k-soll)} = d _b - f _b = 133.726 to 0.177 = 133.549 mm

The finishing of the wheel (eg tooth flank grinding) is carried out with the base circle diameter of d _{b (k-soll)} = 133.549 mm

If δα _{wt is} not assigned to one-half of the wheel and pinion, then the calculation of the correction of the pinion must begin with the determination of the frontal meshing angle. In the present example, however, δα _wt / 2 has been assigned to each toothing, and consequently the calculation of the tooth flank modification for the pinion starts with the determination of the test range L _α .

The pinion is for the profile angle deviation

_H f _α = -3.333 × × tan 17.1717 21.635 °
= -22.7 μm

The base circle deviation of the pinion is:

Thus, the base circle diameter for producing the modified tooth flank of the pinion:

d _b (k-soll) = 139.298 to 0.184 = 139.114 mm

Claims (1)

Spurrädergetriebe in which the determined based on a room temperature theoretical design value (setpoint) at least one parameter of the tooth geometry of the involute toothing of a gear pair is replaced by a calculated taking into account the thermal expansion coefficient and on the basis of an operating temperature corrected design value (k setpoint), characterized in that as parameters with a corrected design value, the pressure angles (α) or the two base circle diameters (db1 and db2) are provided under the condition that k ≷ 1, where in that the corrected design value (α _(k-soll) ) of the pressure angle (α) is calculated from the operating pressure angle (α t3) determined on the basis of the operating temperature (t3), where and that the corrected design values (db1 _(k-soll) ) and (db2 _(k-soll) ) of the base circle diameter (db1 and db2) from the pressure angle deviation (fα) on the profile angle deviation (fHα) and from the resulting base circle Deviation (fb) are calculated, where because the tip diameter,
db1, db2 the base circle diameter at room temperature,
db1 + δdb1, db2 + δdb2 the base circle diameter at operating temperature,
df the root diameter,
a1 the center distance at room temperature,
a1 + δa the center distance at operating temperature
αwt1 the operating angle at room temperature
awt3 the operating angle at operating temperature
specify.