The tangential frictional force Ft can be decomposed as the product of a frictional factor f times the normal force N. Since friction is not fully developed f ≤µ where µ is the coefficient of friction. With reference to Fig. 7, equilibrium require that 

    If the computed factor f exceeds the coefficient of friction,the particle will slide.In the crusher model,  the pressure is computed according to the  pressure response model presented by Evertsson and Lindqvist.  The  pressure  response  model  relates  compression ratio (i.e. the compressive engineering strain of the particle bed: deformation/original thickness), and variational coefficient of the particle size distribution to crushing pressure. A seconddegree polynomial in two variables (compression and variational coefficient of size distribution) was fitted to test results. The total pressure  is computed using the pressure response model  So the shear–stress   and normal pressure    at the surface is hence computed according to Eqs. (6) and (7).

 where   is the total pressure computed from the  pressure，response model. The proposed wear model hence looks as：

 Here K is a new model parameter that scales the effect of the shear force when there is no slip. Sliding wear in a jaw crusher has been found to be three to six times faster than squeezing-only  wear, at the same crushing load [10]. 

2.2.  Wear measurements

 A measurement rig that was previously developed for measuring the worn geometry  of  cone  crushers  was  used.  The method resembles the one used by Rosario (2004). The crusher is stopped and a probe detects the location of the surfaces of the mantle and concave. The device is made of a frame that is attached to the main shaft of the crusher (see Fig. 9). A step motor moves a carrier by turning a threaded rod. Small stepping motors send out probes. The number of pulses sent to the step motor corresponds to a certain position relatively to the measuring frame. When a probe contacts the liner the controller stops the motor and the number of pulses is registered. The number  of pulses is then converted into geometric coordinates.  The measurements were carried out at the NCC quarry  located  approximately  70 km:s  east  from  Goteborg,  Sweden.  The crusher was a secondary SANDVIK H6800 crusher, with   a coarse crushing chamber. The material fed to the crusher was 32–250 mm granite that had previously been crushed in a primary jaw crusher. 

 3.  Results 

 3.1.  Measurements

    Where     is  the  total  pressure  computed  from  the  pressure 

response model. The proposed wear model hence looks as: 

shows the measured worn geometry, compared to a cross section of the nominal CAD-geometry.

3.2 Simulation versus measurement of wear

The  worn  liner  profiles  were  computed  using  the  crusher model. Fig. 11  shows worn mantle profiles at different times,using the two different wear models. The left profile shows the worn geometry obtained using the previous wear model that is independent of shear forces. The right profile shows the worn geometry from the new shear-dependent wear model. There is an obvious difference between the two models in prediction of wear in the upper part of the chamber. The effect of non-sliding shear force is scaled so that simulations fit measured data. The wear model parameter K in Eq. (8) was selected so that the wear  was correctly predicted at two points on the liner: where the maximum wear occurs, near the bottom of the mantle, and on one point located near the top of the liner, one-third of the chamber height from the top. K = 50 gives the best agreement. A shear wear factor of 50 may seem high, but the shear force