Contact, Stops, Clearance & Backlash

What Is It?

Contact, stops, clearance and backlash are the non-linear, intermittent features of real mechanical connections that transform smooth mechanism loading into transient, impact-like loading. A hard stop arrests motion at a travel limit, generating a short-duration, high-magnitude load. Joint clearance — the gap between a pin and bore or a ball and race — allows free relative motion before contact, during which momentum develops that is converted to impact on contact. Backlash — the lost motion in a gear train or linkage — similarly allows free motion before engagement. Intermittent contact — a follower that lifts off a cam, a pawl that engages a ratchet — alternates between load transmission and free motion. Each of these features introduces a non-linearity that can produce transient loads far exceeding the steady-state reactions.

Why It Matters

These features are routinely small compared to the overall mechanism travel, which creates the temptation to ignore them. A bearing clearance of 0.1 mm in a mechanism with 50 mm of travel seems negligible. But the dynamic effect of clearance is not proportional to its size — it is proportional to the momentum that develops during the free-motion phase and the stiffness at contact. A small clearance allows a heavy component to build velocity before slamming into the bearing surface, producing an impact load that can exceed the steady-state reaction by a large margin. Ignoring clearance because it is small compared to the overall travel misses transient impact loads that may govern the structural design.

SMALL CLEARANCE CAN HAVE A LARGE DYNAMIC EFFECT WHEN IT ALLOWS MOMENTUM TO DEVELOP BEFORE CONTACT OCCURS.

Hard Stops

A hard stop is a rigid or near-rigid contact surface that arrests mechanism motion at a travel limit. When the mechanism reaches the stop, the kinetic energy of the moving mass must be dissipated in a very short distance, producing a high deceleration and therefore a high contact force. The peak contact force depends on the velocity at impact and the stop stiffness: a faster mechanism hitting a stiffer stop produces a higher force. The contact duration is very short — typically milliseconds — and the force profile is a sharp spike. Hard stops are common in mechanisms with defined travel limits: a door hinge hitting its open stop, a control surface reaching its mechanical deflection limit, a landing gear reaching its down-lock position.

Soft Stops

A soft stop uses a compliant element — an elastomeric bumper, a spring, a deformable buffer — to decelerate the mechanism over a longer distance, reducing the peak contact force. The energy is the same (kinetic energy of the moving mass), but it is absorbed over a longer stroke, so the force is lower and the duration is longer. Soft stops are used where the impact load from a hard stop would be structurally unacceptable. In a multibody model, a soft stop is represented as a non-linear spring that engages at the stop position with a stiffness matching the bumper or buffer characteristic. The stiffness may be progressive — increasing as the stop compresses — which further shapes the deceleration profile.

Joint Clearance

Joint clearance is the gap between mating surfaces in a joint — the difference between the bore diameter and the pin diameter, or between the ball and race in a spherical bearing. Within the clearance range, the joint allows free relative motion without transmitting load. When the relative motion exhausts the clearance, contact occurs and load is transmitted. The dynamic effect is profound: during the free-motion phase, the supported mass accelerates under whatever forces act on it (gravity, actuator, inertia), building velocity. When contact occurs, this velocity must be arrested by the contact stiffness, producing an impact load. The load is not a smooth transmission of the applied force — it is an impact superimposed on the steady-state load. The peak impact force can far exceed the steady-state reaction, and it occurs at a different time in the cycle than the peak steady-state load.

JOINT WITH CLEARANCE — PROGRESSION FROM FREE MOTION TO IMPACT:

  Phase 1: Free motion (within clearance)
    Pin ●         ○ Bore wall     →  no contact, no load transmitted
         ↕ clearance gap
         Mass accelerates freely → momentum builds

  Phase 2: Contact (clearance exhausted)
    Pin ●━━━━━━━━━● Bore wall     →  impact! Contact stiffness arrests momentum
         ↑ contact force spike

  Phase 3: Load transmission (post-impact)
    Pin ●━━━━━━━━━● Bore wall     →  steady-state load + oscillation from impact

  The impact force at contact can FAR EXCEED the steady-state reaction.

Backlash

Backlash is the lost motion in a gear train, linkage or threaded connection — the amount of relative rotation or translation that can occur before the mating teeth or surfaces engage and transmit load. Like clearance, backlash allows free motion during which momentum can develop, followed by impact when engagement occurs. Backlash is particularly important in reversing mechanisms: when the direction of motion reverses, the teeth disengage, the mechanism moves through the backlash arc, and then the teeth re-engage with an impact. In a multibody model, backlash is represented as a dead zone in the force–displacement relationship: zero force within the backlash range, then contact stiffness beyond. The impact load depends on the velocity at engagement and the tooth stiffness.

Contact and Non-Linearity Types

The table below summarises the types of contact and non-linearity in mechanical connections, their physical character, what they introduce into the loading, how they change the loading and when they matter. The "how it is modelled" column gives the typical multibody representation.

Intermittent Contact

Intermittent contact occurs when two bodies alternately touch and separate during the mechanism cycle. A cam follower that lifts off the cam at high speed, a pawl that engages and disengages a ratchet, a clutch that opens and closes — each involves periods of load transmission alternating with periods of free motion. Each re-engagement is an impact event: the contacting surfaces meet with relative velocity, and the contact stiffness produces a transient force. The structural implication is that the load on the support is not continuous — it has gaps and spikes. The fatigue assessment must account for the intermittent nature: fewer load cycles than a continuous load, but each cycle is an impact with higher peak stress.

Penalty and Contact Stiffness

In multibody codes, contact is typically modelled using a penalty method: when two bodies penetrate (or a clearance is exhausted), a contact force is applied proportional to the penetration depth, with a stiffness representing the contact stiffness of the mating surfaces. The penalty stiffness is a numerical parameter that must be high enough to prevent excessive penetration but not so high that it destabilises the solver. The physical contact stiffness depends on the material properties, geometry and surface condition of the contacting bodies — Hertzian contact theory provides estimates for simple geometries. The penalty stiffness should be based on the physical contact stiffness, not on an arbitrary value that makes the model run. Too low a stiffness allows excessive penetration and underestimates the impact force; too high a stiffness can cause numerical instability and overestimate the force.

• Penalty method: contact force proportional to penetration depth beyond the clearance or stop position
• Penalty stiffness represents the physical contact stiffness of the mating surfaces
• Too low: excessive penetration, underestimated impact force
• Too high: numerical instability, overestimated force, small time step required
• Physical contact stiffness can be estimated from Hertzian contact theory for simple geometries
• The penalty stiffness should be based on physical properties, not on a value chosen for convenience

Impact and Coefficient of Restitution

When two bodies meet with relative velocity, the impact has two phases: compression, during which the relative velocity is arrested, and restitution, during which the bodies may separate. The coefficient of restitution relates the rebound velocity to the approach velocity: e = v_rebound / v_approach. For a perfectly elastic impact, e = 1; for a perfectly plastic impact, e = 0. Real impacts have e between 0 and 1, with the value depending on material properties, geometry and velocity. The coefficient of restitution affects the energy dissipated in the impact and the subsequent rebound motion. In multibody models, the coefficient of restitution is a parameter of the contact model that should be chosen based on the physical materials and impact velocity.

Coefficient of restitution:

  e  =  − v_rebound / v_approach

where:
e            =  coefficient of restitution (0 ≤ e ≤ 1)
v_approach   =  relative velocity before impact
v_rebound    =  relative velocity after impact

Energy dissipated in impact:

  ΔE  =  ½ · m_red · v²_approach · (1 − e²)

where m_red is the reduced mass of the contacting pair.

How Clearance Turns Smooth Loading into Transient Loading

Consider a bearing supporting a shaft that oscillates sinusoidally. Without clearance, the bearing transmits the load smoothly — the reaction force follows the shaft motion continuously. With clearance, the shaft lifts off one side of the bore during the reversal, moves freely across the clearance gap, and impacts the other side of the bore. The reaction force is zero during the free motion, then spikes at impact, then oscillates as the shaft and bore vibrate at their contact stiffness. The smooth sinusoidal load has been replaced by a series of impact spikes with periods of zero load in between. The peak impact force can be many times the peak of the smooth load without clearance. This is the fundamental effect of clearance: it converts continuous loading into intermittent, impact-dominated loading.

IGNORING CLEARANCE IN A JOINT BECAUSE IT IS SMALL COMPARED TO THE OVERALL MECHANISM TRAVEL CAN MISS TRANSIENT IMPACT LOADS THAT EXCEED THE STEADY-STATE REACTIONS BY A LARGE MARGIN. Small clearance does not mean small dynamic effect.

When to Model Clearance, Backlash and Stops

The decision to model clearance, backlash or stops should be based on whether the feature materially affects the interface loads of interest. The relevant factors are: the velocity that can develop during the free-motion phase, the mass that is moving, the contact stiffness at engagement, and whether the mechanism reverses or reaches travel limits under the analysed conditions. If the free-motion velocity is low, the mass is small and the contact stiffness is moderate, the impact load may be negligible. If any of these factors is significant, the feature should be modelled. A sensitivity study — running the analysis with and without clearance — can quantify the effect and justify the modelling decision.

Verification

Contact, clearance and stop models should be verified for correct physical representation and for solver stability. The following checks apply to non-linear contact features in a multibody model.

• Verify that stop positions match the physical design limits — Incorrect stop position changes the impact condition
• Verify that clearance values match the physical joint tolerances — Use actual pin-bore or ball-race clearance from drawings
• Check that contact stiffness (penalty stiffness) is based on physical properties — Use Hertzian contact theory or material data, not arbitrary values
• Verify the coefficient of restitution is appropriate for the materials and velocity — Metal-on-metal e ≈ 0.5–0.8; elastomeric e is lower
• Check the solver time step is small enough to capture the contact event — Contact events are brief — a coarse time step may miss the peak
• Plot the contact force as a function of time and confirm the impact character — A smooth force curve suggests the contact is not engaging; a spike confirms impact
• Run a sensitivity study with and without the non-linear feature — Quantifies the effect and justifies the modelling decision

Key Takeaways

• Clearance, backlash and stops introduce non-linearities that convert smooth loading into transient impact loading
• Small clearance can have a large dynamic effect because it allows momentum to develop before contact
• Hard stops produce short-duration, high-magnitude forces; soft stops reduce the peak but extend the duration
• Backlash causes impact on re-engagement during direction reversal
• Contact stiffness (penalty stiffness) should be based on physical properties, not solver convenience
• The decision to model these features should be based on whether they materially affect the interface loads