CN104632997A - Safety structure for automobile dual-mass flywheels - Google Patents

Abstract

The invention discloses a safety structure for automobile dual-mass flywheels. The safety structure comprises the primary flywheel, the secondary flywheel and a connecting cover, the outer wall of the circumferential face, with the largest diameter, of the connecting cover is an ellipse-like form line, and the ellipse-like form line is obtained by conducting Y-axis mirroring on a curve obtained by conducting X-axis mirroring on an isogonal spiral line in a first quadrant; two bosses are symmetrically distributed on an inner ring of the secondary flywheel, each boss arc is a symmetric arc with the radius of R and the opening angle of beta 0, the minor axis of the ellipse-like form line is smaller than the distance from the highest point of each boss to the circle center, and the long axis of the ellipse-like form line is smaller than the radius of the inner ring of the secondary flywheel. After the dual-mass flywheels are damaged internally (for example a spring failure), the safety structure can still transmit power of an engine to ensure normal traveling of an automobile, and traveling accidents due to sudden power outage are avoided.

Description

Automobile dual-mass flywheel safeguard construction

Technical field

The present invention relates to automobile dual-mass flywheel, specifically refer to a kind of automobile dual-mass flywheel safeguard construction, this structure after double mass flywheel internal sabotage, still can be transmitted engine power, belong to automobile technical field.

Background technique

Along with the raising required life safety when the universal gradually of automobile and driving, safety traffic is subject to more and more becoming many concerns.Double mass flywheel is the important composition parts of automotive transmission, is also the key affecting automotive safety.In the course of the work, the shock-absorbing spring of double mass flywheel inside can occur to stretch frequently, and generation is clashed into by spring seat and secondary flywheel frequently, makes the vibration damper life-span be subject to great impact.And double mass flywheel is hermetically sealed parts, namely scrap after taking apart, timing maintenance cannot be implemented as motor is the same with gearbox, also cannot predict damping element when to destroy, therefore for improving the working life of double mass flywheel, reduce spring wear, improve the vibration damper life-span to reduce contained spring and spring seat by situations such as conquassation, lubricating oil filling fat in spring housing usually, to reduce spring housing's internal heat generation and spring seat weares and teares; Some increases stop pin at spring end, when spring works is shielded to during ultimate angle by stop pin, increases spring bluff piece to protect spring simultaneously; Some employing rubber springs replace helical spring; Have by changing between flywheel sidewall and spring assembly to avoid spring wear.

But said method is only to improve the component lifes such as spring; safety protection effect can not be played after spring or spring seat lose efficacy; after spring or spring seat lost efficacy; engine power can not be delivered to clutch; occur that power is prominent disconnected; if there is this situation during driving, probably there is traffic accident.

Summary of the invention

For prior art above shortcomings, the object of the present invention is to provide a kind of automobile dual-mass flywheel safeguard construction based on self-lock mechanism, this structure can after double mass flywheel internal sabotage (as spring failure), still engine power can be transmitted, ensure automobile normal running, avoid power to dash forward and break and the driving accident of appearance.

Technological scheme of the present invention is achieved in that

Automobile dual-mass flywheel safeguard construction, comprise elementary flywheel, secondary flywheel and connection lid, startup gear ring is provided with at elementary flywheel outer peripheral surface, some flanges are evenly provided with at elementary flywheel inner peripheral surface, between adjacent two flanges, be respectively equipped with vibration damper, each vibration damper is made up of two spring seats and the spring between two spring seats; What connection lid was formed for double step has the outer peripheral surface structure that three road surface diameters increase successively, connects lid first order step and elementary flywheel is bolted to connection; It is characterized in that: the outer wall of described connection lid maximum diameter circumferential surface is the oval molded line of class, and such oval molded line carries out Y-axis mirror image by the equiangular helical spiral of first quartile again about X-axis mirror image curve obtained and obtains; Described secondary flywheel inner ring is symmetrically distributed with two boss, and boss camber line is radius be R subtended angle is β ₀and the circular arc of symmetry, the minor axis of the oval molded line of described class is less than the distance of boss peak to the center of circle, and the major axis of the oval molded line of class is less than the radius of secondary flywheel inner ring;

Described connection lid can relatively rotate with secondary flywheel, and when double mass flywheel normally works, the oval molded line of class that boss and the connection of secondary flywheel are covered does not contact; When after defective shock absorber, the boss of secondary flywheel with connect class ellipse molded line cover and wedge self-locking, make elementary flywheel, secondary flywheel be not separated, continue engine power to be delivered to clutch.

Further, the oval major axis b of molded line of described connection lid class and the ratio of minor axis a to ensure that the oval molded line of class any normal of meaning of taking up an official post to be similar to direction, footpath, pole and to overlap.

Further, the subtended angle β of described boss ₀be greater than maximum wedging angle θ ' _max; And meet following condition,

R-a＜1.5mm；R-R ₁＝10～13mm；R ₂-R＝70～80mm；R ₃-b＜3mm；ψ ₀＝ψ’+(5°-10°)；

Wherein, R is boss radius of curvature; R ₁for connection lid inner radii, R ₂for secondary flywheel exradius, R ₃for secondary flywheel inner circle radius; A and b is respectively minor axis and the long axis length of connection cap-type line; ψ ₀for initial relative torsional angle; ψ ' is the relative torsional angle between primary and secondary flywheel when spring reaches maximum compressibility.

Compared to existing technology, the present invention has following beneficial effect:

1, the present invention is after double mass flywheel internal failure; realize self-locking with connection lid external form linear contact lay after boss is wedged, being combined as a whole by primary and secondary flywheel becomes single mass flywheel, plays good safety protection effect; avoiding occurring that when driving a vehicle power is prominent disconnected, causing danger.Only fundamentally can not eliminate danger by changing vibration damper, after spring or spring seat reach the life-span, driving still can be caused dangerous, the generation that this structure can fundamentally eliminate danger.

2, the present invention select equiangular helical spiral to ensure the normal of molded line any place and initial point are definite value to the angle of this line, self-locking conditions satisfied before and after contact can be guaranteed, and calculate simple.

3, structure of the present invention and processing simply, do not increase mechanism or part, and be convenient to realize, cost is lower, only increase by two symmetrical boss at secondary flywheel inner ring and change to connect the outer molded line of lid, just can realize self-locking.

4, self-locking contact of the present invention, can ensure only resiliently deformable to occur when reaching vehicle Maximum Torque, by boss or the conquassation of connection lid, can not ensure reliability of structure.Before the little available crush of elastic deformation amount, parameter of curve carries out the calculating of transmitting torque simultaneously, simplifies calculating, reduces amount of calculation.

Accompanying drawing explanation

Fig. 1 be automobile dual-mass flywheel of the present invention partly cut open front schematic view.

Fig. 2 is automobile dual-mass flywheel complete section side schematic view of the present invention.

Fig. 3 is the I quadrantal diagram of equiangular helical spiral.

Fig. 4 is the outer molded lines of connection lid.

Fig. 5 is connection lid schematic diagram.

Fig. 6 is connection lid sectional drawing.

Fig. 7 is point of contact power analysis chart.

Fig. 8 is self locking type line analysis figure.

Fig. 9 is safety apparatus structure Parameter Map.

Figure 10 is connection lid force analysis figure.

Figure 11 connects the amount of deformation plotted curve of lid and boss.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in more detail.

Fig. 1 and Fig. 2 is the schematic diagram of the double mass flywheel that safeguard construction is housed, mainly comprise elementary flywheel 1, secondary flywheel 5 and connection lid 6, startup gear ring is provided with at elementary flywheel 1 outer peripheral surface, some flanges are evenly provided with at elementary flywheel inner peripheral surface, between adjacent two flanges, be respectively equipped with vibration damper, each vibration damper is made up of two spring seats and the spring between two spring seats.Connection lid has for double step formation the outer peripheral surface structure that three road surface diameters increase successively, from the back side, the depression that middle formation is edge with molded line 9, depression corresponds to the first order step that connection lid front is formed, uniform 6 attachment holes 10 of recess, corresponding with 6 holes of elementary flywheel 1 and be connected by bolt, the hole 12 be arranged symmetrically with is positioning hole, Fig. 5 is the front elevation of connection lid, and Fig. 6 is its sectional drawing.

The outer wall of described connection lid 6 maximum diameter circumferential surface is the oval molded line 7 of class, such oval molded line 7 carries out Y-axis mirror image by the equiangular helical spiral of first quartile again about X-axis mirror image curve obtained and obtains, as shown in Figure 3, the oval molded line 7 of class as shown in Figure 4 for the equiangular helical spiral of first quartile.Described secondary flywheel 5 inner ring is symmetrically distributed with two boss 8, and boss camber line is radius be R subtended angle is β ₀and the circular arc of symmetry, the minor axis of the oval molded line 7 of described class is less than the radius R of boss 8, and the major axis of the oval molded line 7 of class is less than the radius of secondary flywheel inner ring 11.Described connection lid 6 can relatively rotate with secondary flywheel 5, when double mass flywheel normally works, engine power is delivered to spring seat 2 extrusion spring 3 through elementary flywheel 1 and promotes spring seat 4, drives secondary flywheel 5 to rotate, and now the boss 8 of secondary flywheel does not contact with the oval molded line 7 of class that connection is covered.When after defective shock absorber, the boss of secondary flywheel 8 with connect the class ellipse molded line 7 cover and wedge self-locking, make elementary flywheel 1, secondary flywheel 5 be not separated, continue engine power to be delivered to clutch.

For meeting above-mentioned requirements, each size of Fig. 9 need meet certain requirements: the oval major axis of molded line of connection lid class and the ratio of minor axis are to ensure that the oval molded line of class any normal of meaning of taking up an official post to be similar to direction, footpath, pole and to overlap.For the surface of contact wedged under guarantee peak torque condition is large as far as possible, to reduce contact stress, and make boss subtended angle β ₀be greater than the angle θ ' of maximum wedging _max=θ _max-θ ₀.

The restriction relation of the radial geometric parameter of each circular arc of Fig. 9 need meet:

R-a＜1.5mm，R-R ₁＝10～13mm

R ₂-R＝70～80mm，R ₃-b＜3mm

Connection lid just contacted after shock-absorbing spring loses efficacy with secondary flywheel boss, therefore initial relative torsional angle ψ ₀relative torsional angle ψ ' between primary and secondary flywheel when should reach maximum compressibility than spring is larger, therefore gets

ψ ₀＝ψ’+(5°-10°)

Wherein, R is boss radius of curvature; R ₁for connection lid inner radii, R ₂for secondary flywheel exradius, R ₃for secondary flywheel inner circle radius; A and b is respectively the footpath, the shortest and the longest pole of connection cap-type line; ψ ₀for initial relative torsional angle; ψ ' is the relative torsional angle between primary and secondary flywheel when spring reaches maximum compressibility;

Its principle is as follows: as shown in Figure 7, and-ω to get loose direction for connection lid 6 and secondary flywheel, and making a concerted effort of positive pressure N and frictional force F suffered by certain point of contact of connection lid G is F _r, n-n is the normal of connection lid G point.If make a concerted effort F _rdirection all the time on the right side of footpath, pole OG, then the direction that gets loose will be contrary with resultant moment of force direction all the time, realize self-locking.

for friction angle, α is the angle of contact point pole footpath and normal, is called for short method angle, pole.All satisfied with the resultant direction of the arbitrary point of contact of secondary flywheel inner ring convex platform after the wedging of connection lid namely make a concerted effort F _rcontrary with the direction that gets loose to the moment direction of an O, then can ensure that wedging rear self-locking does not get loose.

The method forming the outer molded line of connection lid can adopt as involute, elliptic curve and helix, but must ensure that before and after being out of shape, the method angle, pole of outer molded line is less than friction angle, in order to reduce the complexity of later stage calculating, here equiangular helical spiral is selected, because the method angle, pole of any point does not become definite value on this line, friction angle is also definite value, and before and after being out of shape, method angle, pole changes hardly, as long as the method angle, pole ensureing not to be out of shape molded line is less than the self-locking that friction angle just can realize being out of shape rear molded line.

Put G as shown in Figure 8 for any point on connection cap-type line, its footpath, pole is ρ, G ' is for this molded line being put a point of proximity of G, polar angle increment is Δ θ, and footpath, pole increment is Δ ρ, when Δ θ goes to zero, G ' is the tangent direction of a G, ∠ OGE levels off to right angle, and ∠ G ' GE=α, obtained by right-angled triangle Δ G ' GE:

$\tan \mathrm{\α}=\frac{G^{\′}E}{\mathrm{EG}}=\frac{\mathrm{\Δ\ρ}}{\mathrm{\ρ\Δ\θ}}=\frac{\mathrm{d\ρ}}{\mathrm{\ρd\θ}}$

If λ=tan is α, have

$\frac{\mathrm{d\ρ}}{\mathrm{\ρ}}=\mathrm{\λd\θ}---\left(1\right)$

To above formula integration, obtaining curved dies is

ρ＝ae ^λθ(2)

For meeting aforementioned claim, only need make λ < μ (friction factor), can self-locking be ensured.The I quadrant of ρ and θ relation curve in formula (2) is first carried out X-axis mirror image, and gained molded line carries out Y-axis mirror image again, forms the outer molded line of connection lid.

The Elastic Contact mechanics model of automobile dual-mass flywheel safety installations and Torque Performance Analysis:

Safety protection device is reduced to two-dimension plane structure analysis, and as shown in Figure 9, system of coordinates Oxy is based upon on connection lid 6, and secondary flywheel 5 turns over initial relative torsional angle ψ ₀time, the oval molded line of connection lid class and boss camber line come in contact and meet at a G ₀, boss camber line is radius be R subtended angle is β ₀and about the circular arc of line m-m symmetry, secondary flywheel exradius is R ₂, inner circle radius is R ₃.Minor axis and the major axis of connection cap-type line are respectively a and b.

Two boss are arranged symmetrically with, and contact situation is identical, only analyzes single contact.When time, ρ=b, substitutes into formula (2) and obtains

$\mathrm{\&lambda;}=\frac{2}{\mathrm{\&pi;}}\ln \frac{b}{a}---\left(3\right)$

Because of λ=tan α, therefore

$\mathrm{\&alpha;}=\arctan \left(\frac{2}{\mathrm{\&pi;}}\ln \frac{b}{a}\right)---\left(4\right)$

Formula (3) is brought into the curved dies that formula (2) obtains class oval molded line I quadrant

$\mathrm{\&rho;}=a{e}^{\left(\frac{2}{\mathrm{\&pi;}}\ln \frac{b}{a}\right)\mathrm{\&theta;}}---\left(5\right)$

When boss starts to contact with connection lid, the footpath, pole of connection lid is equal with boss radius, has θ ₀for point of contact G ₀corresponding polar angle, has according to geometrical relationship

${\mathrm{\&psi;}}_0=\frac{\mathrm{\&pi;}}{2}\ln \frac{R}{a}{\left(\ln \frac{b}{a}\right)}^{-1}-\frac{{\mathrm{\&beta;}}_0}{2}---\left(6\right)$

When relative torsional angle ψ increases gradually, boss is continued wedging, and connection lid comes in contact distortion with secondary flywheel boss.As shown in Figure 10, to connect lid for analytic target, G for before the distortion of connection lid on restricted type line η a bit, G ₁for point corresponding after G distortion.Because elastic deformation amount is less, suppose the rear curve η of distortion ₁normal constant along η Normal direction, then G ₁suffered positive pressure N and the G of point ₁g conllinear, frictional force F is perpendicular to N, F _rfor making a concerted effort of positive pressure N and frictional force F.α is the method angle, pole of curve η, α ₁for positive pressure N and G ₁the angle in point pole footpath.

Consider connection lid and the resiliently deformable of secondary flywheel contact action, use Winkler model to calculate elastic contact deformation.Contact interface is considered as a series of separate spring by Winkler model, and the pressure suffered by every bit is directly proportional to its normal deformation amount, G ₁the contact stress of point is

$\mathrm{\&sigma;}=E_1\frac{{\mathrm{\&xi;}}_1}{l_1}=E_2\frac{{\mathrm{\&xi;}}_2}{l_2}---\left(7\right)$

E in formula ₁and E ₂be respectively the Young's modulus of connection lid and boss, ξ ₁for connection lid amount of deformation, ξ ₂for the amount of deformation at secondary flywheel boss place.L ₁, l ₂be respectively connection lid and boss at point of contact G ₁normal thickness.

The PRACTICE OF DESIGN done shows, a and b difference is very little the oval molded line of class is similar to circle, and normal direction straight line overlaps with footpath, pole is approximate, and normal thickness can substitute with direction, footpath, pole thickness, so, had by Fig. 9 geometrical relationship

$\left\{\begin{array}{c}{l}_1=\mathrm{\&rho;}-R_1\\ l_2=R_2-R\end{array}\right.---\left(8\right)$

Connection lid is magnitude of interference ρ-R with the juxtaposition metamorphose amount sum of boss, namely

ξ ₁+ξ ₂＝ρ-R (9)

Simultaneous formula (7) and formula (9), solve

${\mathrm{\&xi;}}_1=\frac{(\mathrm{\&rho;}-R)E_2{l}_1}{E_1{l}_2+E_2{l}_1}---\left(10\right)$

Formula (8) and formula (10) are substituted into formula (7) and can contact stress be tried to achieve

$\mathrm{\&sigma;}=\frac{(\mathrm{\&rho;}-R)E_1{E}_2}{E_1(R_2-R)+E_2(\mathrm{\&rho;}-R_1)}---\left(11\right)$

At triangle △ GG ₁in O, have according to the cosine law

${\mathrm{\&rho;}}_1=\sqrt{{\mathrm{\&rho;}}^2+{{\mathrm{\&xi;}}_1}^2-2\mathrm{\&rho;}{\mathrm{\&xi;}}_1\cos \mathrm{\&alpha;}}---\left(12\right)$

In formula: ρ ₁for G ₁point pole footpath.

Can in the hope of the method angle, pole after distortion by sine

${\mathrm{\&alpha;}}_1=\arcsin \left(\frac{\mathrm{\&rho;}\sin \mathrm{\&alpha;}}{{\mathrm{\&rho;}}_1}\right)---\left(13\right)$

At triangle △ GG ₁in O, OG and OG ₁the difference at folded method angle, pole is

δ＝α ₁-α (14)

The computational methods of the torque transmitted are:

Suppose that connection lid axial thickness is h, as shown in Figure 6, surface of contact is divided into infinitesimal rectangular area sum, the positive pressure on unit dimension dA is

N＝σdA＝σhρ ₁dθ (15)

Positive pressure N and the F that makes a concerted effort _rfolded friction angle is infinitesimal face make a concerted effort be

According to Figure 10 geometrical relationship must get loose trend time to make a concerted effort F _rto the arm of force of O point be

If connection lid is wedged with boss, then put G ₁suffered frictional force is contrary with the F equal and opposite in direction direction of Fig. 6, now makes a concerted effort and F _rsymmetrical about pressure N place straight line, to the arm of force of O point be with joint efforts

G ₁the point infinitesimal torque of transmitting be with joint efforts with the product of the arm of force

dT ₁＝F _RL ₁(19)

dT ₂＝F _RL ₂(20)

DT in formula ₁, dT ₂be respectively self-locking torque when infinitesimal gets loose and wedging torque.

When boss continues wedging, and when relative torsional angle is ψ, boss is (θ with the scope of connection lid contact angle θ ₀, θ), wherein wedging angle θ '=θ-θ ₀, due to symmetry properties, respectively to dT ₁, dT ₂integration is also multiplied by 2 and tries to achieve self-locking torque T when getting loose ₁with wedging torque T ₂

Because amount of deformation is little, deformation curve almost overlaps with non-deformation curve, the α therefore in formula (21) and formula (22) ₁available α substitutes, ρ ₁available ρ substitutes, and little to Influence on test result after replacement, error can be ignored in practical engineering calculation, but accelerates the computational process of design after simplifying, and improves design efficiency.Torsiometer formula after simplification is

Embodiment 1

2.0L sedan car Double-quality flywheel safety installations as shown in Figure 1 and Figure 2.

Motor maximum output torque T _max=192Nm, when shock-absorbing spring is compressed to maximum flow, the relative torsional angle of primary and secondary flywheel is ψ '=21 °, and connection cover material is 45 steel, and Young's modulus is E ₁=2.1 × 10 ⁵mPa, yield strength is σ _s1=500MPa.Secondary flywheel material is spheroidal graphite cast iron, E ₂=1.5 × 10 ⁵mPa, yield strength is σ _s2=480MPa.Surface of contact friction factor μ=0.17, surface of contact thickness is h=8.5mm.The each dimensional parameters of Fig. 9 is R ₁=50mm, R ₂=137.05mm, a=60mm, b=62.5mm, R=60.9mm, R ₃=64.5mm, β ₀=12 °.By calculating following parameter alpha=1.49 °, ψ ₀=26.83 °, θ ₀=32.83 °, friction angle during wedging angle θ '=6 °, amount of deformation ξ ₁, ξ ₂with the relation curve of torsion angle as shown in figure 11; Known by Figure 11, compared with physical dimension, amount of deformation is very little, and connection lid amount of deformation ξ ₁much smaller than the amount of deformation ξ at secondary flywheel boss place ₂.Therefore, before and after above supposed connection lid distortion, Normal direction is constant is set up.The difference at method angle, maximum pole is 3.805 × 10 ^-4°, numerical value is minimum, and therefore before and after distortion, method angle, pole is substantially constant, meets the rear α of distortion ₁still friction angle can be less than self-locking requirement.

Stress σ increases with θ and increases, when wedging angle θ '=6 ° are θ _maxwhen=38.83 °, wedging moment of torsion reaches maximum engine torque 192Nm, and now theoretical maximum calculates contact stress σ is 296.2MPa.The yield limit σ of connection lid and boss _sbe respectively 1.69 and 1.62 with the ratio of theoretical maximum contact stress and safety coefficient, meet the demands.Before and after simplifying, torque difference is 0.029Nm to the maximum, and maximum relative error is 0.02%, and this error can be ignored in engineering practice.

Finally it should be noted that, above embodiment is only in order to illustrate technological scheme of the present invention and unrestricted, although claimant's reference preferred embodiment is to invention has been detailed description, those of ordinary skill in the art is to be understood that, technological scheme of the present invention is modified or equivalent replacement, and do not depart from aim and the scope of the technical program, all should be encompassed in the middle of right of the present invention.

Claims (3)

1. automobile dual-mass flywheel safeguard construction, comprise elementary flywheel (1), secondary flywheel (5) and connection lid (6), startup gear ring is provided with at elementary flywheel outer peripheral surface, some flanges are evenly provided with at elementary flywheel inner peripheral surface, between adjacent two flanges, be respectively equipped with vibration damper, each vibration damper is made up of two spring seats and the spring between two spring seats; What connection lid was formed for double step has the outer peripheral surface structure that three road surface diameters increase successively, connects lid first order step and elementary flywheel is bolted to connection; It is characterized in that: the outer wall of described connection lid (6) maximum diameter circumferential surface is the oval molded line (7) of class, and such oval molded line (7) carries out Y-axis mirror image by the equiangular helical spiral of first quartile again about X-axis mirror image curve obtained and obtains; Described secondary flywheel (5) inner ring is symmetrically distributed with two boss (8), and boss camber line is radius be R subtended angle is β ₀and the circular arc of symmetry, the minor axis of the oval molded line (7) of described class is less than the distance of boss (8) peak to the center of circle, and the major axis of the oval molded line (7) of class is less than the radius of secondary flywheel inner ring (11);

Described connection lid (6) can relatively rotate with secondary flywheel (5), and when double mass flywheel normally works, the oval molded line of class that boss and the connection of secondary flywheel are covered does not contact; When after defective shock absorber, the boss of secondary flywheel with connect class ellipse molded line cover and wedge self-locking, make elementary flywheel, secondary flywheel be not separated, continue engine power to be delivered to clutch.

2. automobile dual-mass flywheel safeguard construction according to claim 1, is characterized in that, the oval major axis b of molded line of described connection lid class and the ratio of minor axis a to ensure that the oval molded line of class any normal of meaning of taking up an official post to be similar to direction, footpath, pole and to overlap.

3. automobile dual-mass flywheel safeguard construction according to claim 1, is characterized in that, the subtended angle β of described boss ₀be greater than maximum wedging angle θ ' _max; And meet following condition,

R-a＜1.5mm；R-R ₁＝10～13mm；R ₂-R＝70～80mm；R ₃-b＜3mm；ψ ₀＝ψ’+(5°-10°)；

Wherein, R is boss radius of curvature; R ₁for connection lid inner radii, R ₂for secondary flywheel exradius, R ₃for secondary flywheel inner circle radius; A and b is respectively minor axis and the long axis length of connection cap-type line; ψ ₀for initial relative torsional angle; ψ ' is the relative torsional angle between primary and secondary flywheel when spring reaches maximum compressibility.