A torque proportioning differential (10, 60, or 120) is modified to exhibit a bias ratio that varies with torque transmitted by the differential. Thrust forces (34 and 36, 88 and 90, or 144 and 146) generated within the differential are opposed by at least one pair of surfaces (38 and 40, 96, 98 and 104, 106, or 152, 154 and 156, 158) having different frictional characteristics. One of the surfaces (38, 96 and 98, or 152 and 154) opposes a portion of the thrust forces, and the other surface (40, 104 and 106, or 156 and 158) opposes a remaining portion of the thrust forces. A control member (54, 100 and 102, or 152) responsive to the transmitted torque limits the respective portions of the thrust forces opposed by each of the two surfaces.

FIELD OF INVENTION 
The invention relates to the field of differentials used in automotive 
drive lines to divide engine power between two drive shafts and, in 
particular, to such differentials that also develop resistance to relative 
rotation between the two shafts as a function of torque transmitted to 
them by the differential. 
BACKGROUND 
Torque proportioning differentials develop a frictional resistance to 
differentiation between two interconnected drive shafts substantially 
proportional to a sum of torques transmitted to the drive shafts. During 
periods of differentiation, the resistance is apparent as a torque 
difference between the relatively rotating drive shafts. The torque 
difference varies linearly with the sum of the torques of the two drive 
shafts defining a substantially constant ratio that can be represented by 
a symbol "k" as follows: 
##EQU1## 
where "T.sub.d " is the torque difference between the drive shafts, and 
"T.sub.s " is the torque sum of the two shafts. The symbol k is also a 
coefficient that represents a proportion of the torque sum T.sub.s that 
can be developed as a torque difference T.sub.d. Thus, a linear equation 
for the torque difference T.sub.d can be written as follows: 
EQU T.sub.d =k T.sub.s. 
However, this proportioning characteristic is more commonly expressed as 
another ratio, referred to as "bias ratio", which is a ratio of respective 
amounts of torque in the two drive shafts. More particularly, bias ratio 
represents a quotient of the amount of torque in one of the two relatively 
rotating drive shafts having more torque divided by the amount of torque 
in the other relatively rotating drive shaft having less torque. However, 
bias ratio can also be expressed in terms of the torque difference T.sub.d 
and torque sum T.sub.s of the drive shafts as follows: 
##EQU2## 
Accordingly, bias ratio "B" is also related to the ratio "k" of the torque 
difference to torque sum as follows: 
##EQU3## 
Although most torque proportioning differentials exhibit approximately 
constant bias ratios over normal ranges of torque transmissions to the 
drive shafts, some differentials exhibit a bias ratio that decreases with 
the amount of torque transmitted by the differential. One such example 
supplements the torque proportioning characteristic with a constant 
frictional resistance to differentiation, known as "preload", that is 
independent of the total amount of torque transmitted to the drive shafts. 
The differential includes a planetary bevel gear arrangement carried 
within a housing for interconnecting the drive shafts and a pair of 
friction clutches that are preloaded to provide a constant amount of 
frictional torque for opposing relative rotation between either drive 
shaft and the housing. 
Torque is also transmitted between the differential housing and drive 
shafts by a pair of camming members. A shaft that mounts a pair of 
"spider" gears within the housing includes mating camming surfaces that 
separate the camming members as a function of the torque transmitted by 
the differential. The separating movement of the camming members further 
loads the friction clutches for opposing differential rotation of the 
drive shafts. Accordingly, the amount of frictional torque developed in 
opposition to differentiation is also a function of the torque transmitted 
by the differential. 
Accounting for the preload as a constant frictional torque "C.sub.O ", the 
torque difference T.sub.d that is available to oppose differential 
rotation between drive shafts is expressed as the following linear 
equation: 
EQU T.sub.d =C.sub.0 +k.sub.0 T.sub.s 
where coefficient "k.sub.0 " is a proportion of the torque sum T.sub.s that 
is developed as frictional torque for resisting differentiation. 
The bias ratio of this differential example is a function B(T.sub.s) of the 
torque sum transmitted to the drive shafts and is expressed in equation 
form as follows: 
##EQU4## 
The calculated bias ratio B(T.sub.s) is most affected by the preload 
torque C.sub.0 at torque sums T.sub.s that are less than the preload 
torque. In fact, the bias ratio approaches infinity at very low torque 
sums. However, the effect of the preload becomes negligible at high 
amounts of torque transmitted by the differential. 
Although it is desirable in certain differential applications to provide an 
initially high bias ratio that decreases with increasing amounts of torque 
transmitted by the differential, frictional resistance to differentiation 
exceeding the amount of transmitted torque (i.e., T.sub.d &gt;T.sub.s) is 
generally undesirable. The excessive frictional resistance at small 
amounts of transmitted torque acts as a brake that consumes power, 
produces unnecessary heat and wear within the differential, and can 
interfere with anti-lock braking systems. 
Another way of varying bias ratio with torque transmitted to a pair of 
drive shafts is disclosed in U.S. Pat. No. 3,264,900 (HARTUPEE). Torque is 
transmitted between a differential housing and a conventional bevel 
gearing arrangement interconnecting the drive shafts by a pair of camming 
members that are carried within the housing. The camming members have 
specially contoured surfaces that engage mating spherical surfaces of a 
spider shaft at angles of friction that increase with increasing amounts 
of torque transmitted through the camming members. Engagements between the 
spider shaft and camming members produce separating forces against 
respective friction clutch assemblies that resist relative rotation 
between the drive shafts. Although the resistance to differentiation 
increases with the amount of torque transmitted by the camming members, 
the resistance decreases as a proportion of the transmitted torque in 
accordance with the increasing angles of friction on the camming members. 
Thus, the proportion of the torque sum T.sub.s that is developed as a 
torque difference T.sub.d is a function k(T.sub.s) of the torque sum, 
yielding a torque difference T.sub.d that is expressed most generally by 
the following nonlinear equation: 
EQU T.sub.d =k(T.sub.s)T.sub.s 
and by appropriate substitution, the bias ratio can also be written in 
terms of the function k(T.sub.s) as follows: 
##EQU5## 
Actually, the general function k(T.sub.s) is much broader than that 
required to support the more limited objective of reducing bias ratio with 
increasing total torque. Also, the torque proportioning effect of the 
camming surfaces is very sensitive to amounts of separation between the 
camming members required to engage the friction clutches. Small amounts of 
wear in the friction clutches or even ordinary tolerancing variations in 
the clutches could significantly affect amounts of torque difference 
supported between the drive shafts at particular amounts of total torque 
transmitted by the differential. 
SUMMARY OF INVENTION 
Our invention provides for varying bias ratio as a function of torque 
transmitted by a differential to a pair of drive shafts, while developing 
a torque resistance to differentiation that is no greater than a sum of 
the torques to both drive shafts. In other words, the variation of bias 
ratio with the torque sum can be accomplished without a preload or any 
other constant force acting to help resist differentiation. The variation 
in bias ratio with the torque transmitted to the output shafts is 
relatively insensitive to wear of differential components, and the 
variation can be controlled so that bias ratio either increases or 
decreases with increasing amounts of torque transmitted by the 
differential. 
Our differential includes a housing rotatable about a pair of drive shafts 
and an operative connection between the drive shafts for permitting the 
drive shafts to rotate in opposite directions with respect to the housing. 
A component of the operative connection between the drive shafts imparts a 
thrust force that varies in magnitude with variations in torque 
transmitted between the housing and the drive shafts. A first frictional 
surface opposes at least a portion of the magnitude of the thrust force, 
and a second frictional surface opposes a remaining portion of the thrust 
force magnitude. A control member responsive to the transmitted torques 
limits engagement of the second frictional surface to opposing the 
remaining portion of the thrust force magnitude. The two frictional 
surfaces develop frictional resistances to relative rotation between the 
drive shafts in different proportions to their opposed portions of the 
thrust force magnitude. 
Preferably, the thrust forces are produced by a conventional gearing 
arrangement interconnecting the drive shafts. The two frictional surfaces 
are gear-mounting surfaces that oppose the thrust force imparted by one or 
more of the gears in the arrangement. One of the two mounting surfaces is 
supported by a spring in a position that is offset in a direction for 
opposing the thrust force. The spring functions as the control member by 
preventing the other mounting surface from opposing the thrust force until 
the thrust force opposed by the one mounting surface is of sufficient 
magnitude to compress the spring through the offset distance. One of the 
two mounting surfaces has a higher coefficient of friction than the other, 
and the surface with the higher coefficient of friction is preferably 
effective for generating frictional torque at a larger radius than the 
lower coefficient of friction surface. 
The result is a multi-stage torque proportioning differential that exhibits 
a first bias ratio up to a predetermined amount of torque transmitted to 
the drive shafts; and for transmitted torques over the predetermined 
amount, the differential exhibits a progressively varying bias ratio that 
approaches a second bias ratio at much larger amounts of transmitted 
torque. The second bias ratio may be greater than or less than the first 
bias ratio.

BEST MODES FOR CARRYING OUT THE INVENTION 
A first example (10) of our multi-stage torque proportioning differential 
is depicted in FIG. 1 as an improvement over a conventional worm gear 
differential. Carried within a housing 12 is a planetary worm gearing 
arrangement 14 interconnecting drive shafts 16 and 18 for opposite 
directions of rotation with respect to the housing 12. The gearing 
arrangement 14 includes a pair of side gears 20 and 22 coupled to 
respective drive shafts 16 and 18 and one or more pairs of element gears 
24 and 26 that include respective portions for meshing with one of the 
side gears and for meshing with each other. 
The side gears 20 and 22 have respective teeth 28 and 30 that are inclined 
in the same direction to their common axis of rotation 32 through the same 
"hand" helix angle (i.e., right hand or left hand). Respective thrust 
forces 34 and 36 are imparted by the side gears 20 and 22 in response to 
transmissions of torque from the differential housing 12 to the drive 
shafts 16 and 18. Magnitudes of the thrust forces are determined in part 
by the helix angles as proportions of the torque transmitted by the side 
gears. However, in contrast to conventional worm gear differentials that 
provide a single frictional mounting surface at one end of a housing for 
opposing side gear thrust forces, the modified differential 10 includes 
two different frictional mounting surfaces 38 and 40 for opposing 
different portions of a combined magnitude of the thrust forces 34 and 36. 
The frictional surface 38 is formed by a bearing 42 that is mounted within 
a bore 44 at one end of the housing 14. The other frictional surface 40 is 
formed as a countersunk bore 46 surrounding the bore 44. The side gear 20 
is coupled to a frusto-conical shaped washer 48 having an end surface 50 
for engaging the bearing 42 and a peripheral surface 52 for engaging the 
countersunk bore 46. The bearing 42 is supported in the bore 44 by a disc 
spring 54 acting through a conventional washer 56. 
The disc spring 54 urges the bearing 42 toward the conical washer 48 so 
that, with respect to movement of the conical washer 48 along the axis 32, 
the bearing 42 is positioned closer to the conical washer 48 than the 
countersunk bore 46. Accordingly, thrust forces 34 and 36, which are 
imparted by the respective side gears 20 and 22, are initially opposed by 
the bearing 42. However, the disc spring 54 supporting the bearing 42 
compresses in proportion to the magnitude of the combined thrust forces 
exerted by the end face 50 of conical washer 48 until the peripheral 
surface 52 of the washer 48 contacts the countersunk bore 46. 
The disc spring 54 is dimensioned so that the peripheral surface 52 of 
conical washer 48 contacts the countersunk bore 46 at a combined thrust 
force from the side gears corresponding to a predetermined amount of 
torque transmitted from the housing 12 to the drive shafts 16 and 18. The 
friction surface 38 formed by bearing 42 opposes a portion of the combined 
magnitude of the two thrust forces up to the predetermined amount while 
developing very little frictional torque opposing relative rotation 
between the conical washer 48 and housing 12. However, a remaining portion 
of the combined magnitude of the thrust forces exceeding the predetermined 
amount is opposed by the friction surface 40 formed by the countersunk 
bore 46. The friction surface 40 has a higher coefficient of friction than 
friction surface 38; acts at a larger radius than friction surface 38; 
and, in further contrast to the friction surface 38, is inclined to the 
thrust forces. Thus, the friction surface 40 develops a significant amount 
of additional frictional torque opposing relative rotation between the 
conical washer 48 and housing 12 in response to thrust forces having a 
combined magnitude that exceeds the predetermined amount. 
FIG. 2 plots a torque difference T.sub.d between relatively rotating drive 
shafts 16 and 18 as a function of a torque sum T.sub.s of both drive 
shafts in accordance with the expected performance of the just-described 
worm gear differential 10. The torque difference T.sub.d corresponds to 
the amount of frictional torque that is developed by all frictional 
surfaces within the differential in opposition to the relative rotation 
between drive shafts. The torque sum T.sub.s corresponds to the amount of 
torque transmitted from the differential housing 12 to the drive shafts 16 
and 18. 
The plot of torque difference T.sub.d is discontinuous at a value of the 
torque sum T.sub.s indicated along the abscissa at "T.sub.1 ". The value 
represented by T.sub.1 corresponds to the predetermined amount of torque 
transmitted from the housing to the drive axles at which the combined 
thrust forces 34 and 36 exerted by the respective side gears 20 and 22 
overcome the disc spring 54 and engage the peripheral surface 52 of washer 
48 with the countersunk bore 46. From "0" to T.sub.1 along the abscissa, 
the torque difference is a linear function of the torque sum defined by a 
first slope "k.sub.1 ". A second slope "k.sub.2 " in part defines a 
different linear function from T.sub.1 to "T.sub.m " (i.e., a very large 
torque sum). The two linear functions can be written as follows: 
EQU T.sub.d1 =k.sub.1 T.sub.s ; for T.sub.s .ltoreq.T.sub.1 and 
EQU T.sub.d2 k.sub.2 T.sub.s -(k.sub.2 -k.sub.1)T.sub.1 ; for T.sub.s &gt;T.sub.1. 
FIG. 3 plots bias ratio against the same ranges of torque sums. Values of 
the bias ratio are found from two different equations covering the same 
ranges as the two just-above linear functions for torque difference as 
follows: 
##EQU6## 
where "C.sub.1 " is a constant representing the expression "(k.sub.1 
-k.sub.2) T.sub.1 " in the second linear function for torque difference. 
Bias ratio remains at a constant first value "B.sub.1 " throughout a first 
range of torque sums less than the predetermined amount T.sub.1. However, 
bias ratio varies considerably throughout a second range of torque sums 
exceeding the predetermined amount T.sub.1 and approaches a second value 
"B.sub.2 " at much larger torque sums included within the second range. 
The values B.sub.1 and B.sub.2 are separately related to the respective 
proportions k.sub.1 and k.sub.2 in the manner shown below, which is the 
same manner as conventional bias ratios are calculated: 
##EQU7## 
The increase in bias ratio from the first value B.sub.1 to the second 
value B.sub.2 can be attributed to an increase in frictional torque 
generated by the frictional surface 40 formed by the countersunk bore 46 
over the frictional torque generated by the frictional surface 38 formed 
by bearing 42. 
FIG. 4 shows a second example of our multi-stage torque proportioning 
differential as an improvement over a conventional helical gear 
differential (sometimes referred to as a "spur gear differential"). The 
differential 60 includes a housing 62 rotatable about a pair of drive 
shafts 64 and 66. A planetary helical gear arrangement 68 carried within 
the housing 62 interconnects the drive shafts 64 and 66 for opposite 
directions of rotation with respect to the housing. Side gears 70 and 72 
are coupled to the respective drive shafts 64 and 66 for rotation about a 
common axis 74. Pairs of element gears 76 and 78, which are mounted for 
rotation about respective axes 80 and 82 that are parallel to the common 
axis 74, mesh with the respective side gears 70 and 72 and with each other 
for operatively interconnecting the side gears. 
In further contrast to the preceding example, the side gears 70 and 72 have 
respective teeth 84 and 86 that are inclined in opposite directions to the 
common axis 74. That is, the side gear teeth 84 and 86 have opposite hand 
helix angles. The opposite hand helix angles of the gear teeth 84 and 86 
direct respective thrust forces 88 and 90 of the side gears 70 and 72 
toward opposite ends of the housing 62 in response to transmissions of 
forward drive torque from the housing 62 to the drive shafts 64 and 66. 
Similar arrangements of frictional surfaces are made at outer ends of the 
two side gears 70 and 72. For example, the outer ends of the two side 
gears are formed with respective journals 92 and 94 that support 
respective friction washers 96 and 98 for rotation with the side gears. 
Disc springs 101 and 102 urge the respective washers 96 and 98 apart from 
the side gears. The friction washers 96 and 98 are treated to exhibit a 
relatively high coefficient of friction. However, ends 104 and 106 of the 
respective journals 92 and 94 are treated to exhibit a relatively low 
coefficient of friction. For example, the friction surfaces of the washers 
96 and 98 may be made from a bonded material of a type commonly used in 
clutches and brakes. The journal ends 104 and 106 may be coated with a 
friction-reducing material. 
The disc springs 100 and 102 urge the friction washers 96 and 98 toward 
respective ends 108 and 110 of the housing 62, so that the friction 
washers 96 and 98 are positioned closer to the respective housing ends 108 
and 110 than the journal ends 104 and 106. Accordingly, predetermined 
portions of the respective magnitudes of the oppositely directed thrust 
forces 88 and 90, which are imparted by the respective side gears 70 and 
72, are opposed by the friction washers 96 and 98 bearing against the 
respective housing ends 108 and 110. However, the disc springs 100 and 102 
supporting the respective friction washers 96 and 98 compress in 
proportion to the respective magnitudes of the thrust forces 88 and 90 
opposed between the friction washers 96 and 98 and the housing ends 108 
and 110. At predetermined magnitudes of the thrust forces, the ends 104 
and 106 of the journals also contact the housing ends 108 and 110 for 
opposing further increases in the magnitudes of the thrust forces. 
Preferably, both of the disc springs 100 and 102 are dimensioned so that 
the journal ends 104 and 106 contact the respective housing ends 108 and 
110 at thrust forces having respective magnitudes corresponding to a 
predetermined amount of torque transmitted from the housing 62 to the 
drive shafts 64 and 66. The friction washers 96 and 98 develop a 
considerable amount of frictional torque for opposing relative rotation 
between the side gears throughout a first range of the transmitted torques 
up to the predetermined amount. However, the journal ends 104 and 106 
develop a much smaller amount of additional frictional torque throughout a 
second range of transmitted torques above the predetermined amount. 
FIGS. 5 and 6 show respective performances of the differential 60 in 
measures of both torque difference T.sub.d and bias ratio B(T.sub.s) 
plotted against torque sum T.sub.s. Similar to the graph of FIG. 2, the 
plot of torque difference T.sub.d in FIG. 5 is discontinuous at the value 
T.sub.1, which is the predetermined amount of torque that distinguishes 
the two ranges of transmitted torques. However, the slope of torque 
difference within the first range between 0 and T.sub.1 is greater than 
the slope of the torque difference within the second range of transmitted 
torques exceeding the value of T.sub.1. Although the torque difference 
T.sub.d and bias ratio B(T.sub.s) can be described by the same equations 
used to describe torque difference and bias ratio in the preceding 
example, the values of the proportions (i.e., coefficients) k.sub.1 and 
k.sub.2 are different. 
The multi-stage torque proportioning differential 60 is particularly 
suitable for replacing known differentials that are preloaded for 
developing a high initial bias ratio that decreases with increasing torque 
sums to a predetermined lower bias ratio. FIG. 6 shows that the 
differential 60 also exhibits a high bias ratio throughout the first range 
of transmitted torques. However, the corresponding torque difference shown 
in FIG. 5 does not exceed the torque sum. In other words, the differential 
60 does not develop a braking torque to oppose differential rotation 
between drive shafts independently of the torque transmitted to them 
(i.e., the torque sum). However, throughout the second range of 
transmitted torques, bias ratios of both the known preloaded differential 
and the improved differential 60 approach a limited minimum value 
designated at B.sub.2 . 
A third example of our multi-stage torque proportioning differential is 
shown in FIG. 7. The differential 120 is another example of an improved 
helical gear differential having a housing 122 and a planetary helical 
gear arrangement 124 carried within the housing for interconnecting a pair 
of drive shafts 126 and 128. Side gears 130 and 132 are coupled to the 
respective drive shafts 126 and 128 for rotation about a common axis 134. 
Pairs of element gears 136 and 138 operatively interconnect the side gears 
for opposite directions of rotation with respect to the housing 122. 
The side gears 130 and 132 also have respective teeth 138 and 140 that are 
oriented in opposite directions to the common axis 134. However, in 
contrast to the differential 60, the opposite hand helix angles of the 
side gear teeth 138 and 140 develop, in response to the transmission of 
forward drive torque, respective thrust forces 144 and 148 that urge the 
two side gears together. 
Inner ends of the two side gears 130 and 132 are fitted with respective 
bushings 148 and 150. The bushing 148 carries a disc spring 152, and the 
bushing 150 carries a bearing 154 that is aligned with the disc spring 152 
along the common axis 134. The bushings also include respective annular 
rims 156 and 158 that exhibit in contact with each other a much higher 
coefficient of friction than the disc spring 152 in contact with the 
bearing 154. 
In response to the thrust forces 144 and 146 urging the respective side 
gears 130 and 132 together, contact is made between the disc spring 152 
and bearing 154 before any contact is possible between the annular rims 
156 and 158. However, the disc spring can be sufficiently compressed by a 
predetermined amount of drive torque to permit the annular rims 156 and 
158 to make contact. The disc spring 152 and bearing 154 generate little 
frictional torque opposing differential rotation of the side gears 
throughout a first range of drive torques less than the predetermined 
amount. However, the annular rims 156 and 158 generate frictional torque 
as a significant portion of the additional drive torque throughout a 
second such range over the predetermined amount. The expected differential 
performance is similar to that illustrated by FIGS. 2 and 3. 
However, in place of the disc spring 152 and bearing 154 of the embodiment 
shown in FIG. 7, it would be possible to mount a spherical bearing between 
separate disc springs that rotate with the respective side gears 130 and 
132. The disc springs would engage the bearing from opposite directions 
about respective openings that would be sized smaller than a diameter of 
the bearing. 
Although our invention has been described as a multi-stage differential 
exhibiting bias ratios that vary with torque transmissions between two 
values, it would also be possible to practice our invention with similar 
bias ratio variations between more than two values. For example, this 
could be accomplished by using two different strength disc springs in 
helical gear differential 60. It would also be possible to avoid abrupt 
transitions in bias ratio caused by the engagement of a second frictional 
surface by also supporting the second frictional surface with a spring. In 
addition, the thrust forces opposed by the different frictional surfaces 
could be generated by any one or more of the gears within the 
differential, as well as by other thrust generating components such as 
cams and couplings.